What is a Pure State and Mixed State?

[vanesch]

There's no evident reason why the underlying physical measure should be a probability measure -- why isn't it possible, for example, for

P(particle in (0, 2))

to be bigger than

P(particle in (0, 1)) + P(particle in (1, 2))

I like it This is this famous "non-contextuality" requirement!

 

[CarlB]

I don’t deny that thinking of the electromagnetic field as a tensor sitting at every spacetime point is a powerful visual aid to solving problems in classical electrodynamics. If you only want to use the physics, this is OK. But not if you want to understand it. There just isn’t any way in which one and the same thing can be both a computational tool and a physical entity in its own right. The "classical" habit of transmogrifying computational devices into physical entities is one of the chief reasons why we fail to make sense of the quantum formalism, for in quantum physics the same sleight of hand only produces pseudo-problems and gratuitous solutions.

You also get pseudo-problems in the classical context. Instead of thinking of the electromagnetic field as a tool for calculating the interactions between charges, you think of charges as interacting with the electromagnetic field. How does this interaction work? We have a tool for calculating the interactions between charges, but no tool for calculating the interactions between charges and the electromagnetic field. With the notable exception of Roger Boscovich, a Croatian physicist and philosopher of the 18th Century, nobody seems to have noticed that local action is as unintelligible as the ability of material objects to act where they are not. Why do we stop worrying once we have transmuted the mystery of action at a distance into the mystery of local action?

and later

According to d'Espagnat, the elision of the subject is not possible within unadulterated, standard quantum mechanics. I maintain that it is possible. I want a conception of the quantum world to which the conscious subject is as irrelevant as it was to the classical view of the world. It's rather like a game I like to play: let's go find a strongly objective conception of the quantum world that owes nothing to subjects or conscious observations. It is precisely for this reason that I reject the naïve quantum realism that identifies reality with symbols of the mathematical formalism.

I wish I had been taught this way back in 1977 when I took my first QM class and was blown away by the lack of explanation for the meaning of the theory.

This seems related to Mach's program and the foundations of relativity. Instead of interpreting the Lorentz and Poincare calculations as indications of how calculations depend on frame of reference, the inclination is to suppose that these formulas are spacetime itself. Poincare's version of relativity still supposed an ether, but made it unobservable. And now, for most physicists, the absence of the necessity of a preferred frame of reference in Einstein's theory is considered as proof that no such thing can exist.

Carl

 

[koantum]

probabilities have achieved a fundamental status in QM because it was doing a good job predicting the outcomes of our frequency-counting experiments... not because there was some theoretical or intuitive reason to do so.

As a rule, a lucky guess comes first; the reason why it was lucky is found later.

In MWI, though, there is at least the possibility of deriving probabilities as emergent phenomena, by considering a limit of the resulting states of frequency-counting experiments of increasing length.

No, there isn’t. Even vanesch agreed with that https://www.physicsforums.com/showpost.php?p=948676&postcount=16".

 

[koantum]

I must have completely misunderstood you then.

If I talk to quantum-state realists, they think I belong to the shut-up-and-calculate (SUC) sect. If I talk to members of this sect, they take me for a quantum-state realist. As far as I am concerned, they are both wrong.
The SUCers assert that the quantum world cannot be described; its features are forever beyond our ken. All we can usefully talk about is statistical correlations between measurement outcomes. Indeed, nothing of relevance can be said without reference to measurements, but this does not mean that the features of the quantum world are beyond our ken. A great deal can be learned by analyzing the quantum-mechanical probability assignments in various experimental contexts, as I do http://thisquantumworld.com" .
The quantum-state realists aspire to describe the objective features of the quantum world. So do I. But they insist on describing these features without reference to measurements, and this doesn’t work.

I thought you wanted to show the *naturalness* of the quantum-mechanical formalism, in the sense that you start by stating that we had it wrong all the way, that physical theories do not describe anything ontological, but are algorithms to compute probabilities of measurements, and that that single assumption is sufficient to arrive at the quantum-mechanical formalism.

Gosh, I wish I could do that. But on second thoughts, to what avail?

I don't think you have made any _clearer_ quantum mechanics. I think that an introduction to quantum theory should NOT talk about these issues, and should limit itself to a statement that there ARE issues, but that these issues can only reasonably discussed once one understands the formalism. I think that anyone FORCING upon the novice a particular view is not doing any service to the novice.

I have given you just a glimpse of the way I teach quantum mechanics. You are not in a position to judge on that basis. I certainly show the students how quantum physics is taught elsewhere. There you are confronted with a set of axioms like the following:

1. There are quantum systems.
2. The states of system S are the unit vectors of a Hilbert space.
3. Between measurements, states evolve unitarily, as dictated by a Schrödinger equation involving a Hermitean operator called Hamiltonian.
4. Every observable O is associated with a Hermitean operator O.
5. The possible outcomes of a measurement of O are the eigenvalues of O.
6. Immediately after a measurement yields a particular eigenvalues, the system is in the eigenstate corresponding to that eigenvalue.
7. If the system is in state |u>, then a measurement of O yields the value v with probability |<v|u>|².
8. Composite quantum systems are described by the tensor product of the Hilbert spaces of their component systems.

Next you are told that this is the way it is. Admittedly, there are problems with this set of axioms, but you won't be able to understand them. So for now, shut up and calculate. If you want to know, for example, why energy is a Hermitean operator, you have to figure it out for yourself. You are not even told that the concept of energy in quantum mechanics is totally different from the corresponding classical concept. Since you had the misfortune of learning classical physics first, you come to quantum physics with a heavy load of inadequate concepts, and nobody tells you this. Then you try to make sense of it all. Poor chap. Small wonder that generation after generation of physics students is told:

Do not keep saying to yourself, if you can possibly avoid it, "But how can it be like that?" because you will go "down the drain" into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that. (Feynman, The Character of Physical Law, 1967)​

If those poor students were told that the quantum formalism is nothing but an algorithm for assigning probabilities to possible measurement outcomes on the basis of actual outcomes, all of the above axioms would at once make sense to them. The difference between the quantal and the classical probability algorithm is readily understood as a consequence of Nature's fuzziness, and the latter is readily understood as Nature's means to "fluff out" matter: to create stable objects that occupy space out of finite numbers of particles that don’t.
The first-year students of my class thankfully have very little prior exposure to any physics. We start with quantum physics (experiments and the rules by which we calculate the probabilities of the possible outcomes) and only later come to classical physics, by learning how quantum physics degenerates into classical physics and under which conditions classical physics provides useful approximations. I emphasize at this point that such terms as mass, energy, momentum, etc. acquire new and entirely different meanings in the transition from quantum to classical, and that care should be taken to keep them apart.

the simplest set of laws, to me, would be an overall probability distribution (hidden variable approach). THAT is intuitively understandable, this is what Einstein taught should be done, and this is, for instance, what Bohmians insist upon. This is the simplest, and most intuitive approach to the introduction of "ordinary" objects, no ?

You know well enough that the contextuality of the more general situations I mentioned rules out such a probability distribution. In Bohmian mechanics every observable except position is contextual. The relevant Einstein quote here is: "Everything should be made as simple as possible, but not simpler."

I wanted to indicate that if you have postulated an ontological concept from which you DERIVE observations, that this is more helpful than to stick to the observations themselves, and that such an ontology makes certain aspects, such as the relationship between different kinds of observations, more obvious.

If Alice and Bob perceive a teapot on the table between them, it is useful to assume that the reason this is so is that there is a teapot on the table between them. I agree. But quantum mechanics has many experimentally confirmed consequences that are totally inconsistent with the conception of a world of self-existent objects with self-existent properties (which could then be considered as the causes of our perceptions). Moreover, it has nothing to do with perceptions. It has everything to do with measuring devices (recall my definition) and their relation to the rest of the world.

in a classical context, your approach of claiming that we should only look at an algorithm that relates outcomes of measurement, and not think of anything ontological behind it, is counter productive.

I am not concerned with classical contexts. I want to understand the quantum world.

You have difficulties imagining there is an Euclidean space in classical physics ?

Of course not in classical physics. But the classical world is a fiction. I want to understand the real world which is quantum. (Sounds familiar, eh?)

But you seemed to imply that there was also a kind of "existence" to POTENTIAL outcomes of measurement in the quantum case: it was a "fuzzy" variable, but as I understood, it DID exist, somehow. I had the impression you said that there WAS a position, even unmeasured, but that it was not a real number, but a "fuzzy variable".

What I'm saying is that if you want to describe the unmeasured quantum world, the only way to do it is in terms of the probabilities of the possible outcomes of unperformed measurements. How do you describe, say, a hydrogen atom in a stationary state? This stationary state is a probability algorithm, which is based on the outcomes of three measurements: energy, total angular momentum, and one angular momentum component. It assigns probabilities to the possible outcomes of every possible measurement. Now if you want this algorithm to be a description of the hydrogen atom, then it’s a description in terms of the possible outcomes of unperformed measurements, right? And what is the salient feature of the atom thus described? Unschärfe or fuzziness!

I take on the position that… there REALLY is a wave function.

That's why I won't be able even to make you see (let alone accept) my point of view. As said, to me it simply makes no sense to think of a probability algorithm as something that REALLY exists, and if the wave function is not really a probability algorithm, I haven’t the faintest notion what it could be, nor can you tell me.

It is the idea that "your measurement apparatus can be in a superposition but you only see one term of it"

No, it's the idea that a probability algorithm REALLY exists, or the fact that you can't tell me what the wave function is if it's not a probability algorithm.

So you have one "branch" or "world" or whatever, where you observe that D1 clicked and D2 didn't, and you have another one where D1 didn't click and D2 did…. No bafflement.

??!?

Well, Einstein's elements of reality are simply the wavefunction,

Good Lord!

and everything becomes clear, no ?

Not to me.

To me, the fundamental dogma of physics is the assumption that all of nature IS a mathematical structure (or, if you want to, that maps perfectly on a mathematical structure). Up to us to discover that structure. It's a Platonic view of things.

You are right to call it a dogma, as in religion.

I don't follow what you're talking about ? We have no tool for calculating the interactions between charges and the EM field ?

Sorry. According to you, Maxwell's equations allow us to calculate the effects of charges on the electromagnetic field (as well as the effect of the electromagnetic field on itself), and the Lorentz force law allows us to calculate the effects of the electromagnetic field on charges. According to me, who has never seen an electromagnetic field but only interacting charges, the electromagnetic field is a tool for calculating the action of charges on charges. I'm not quite on my own here.

The electromagnetic field is, after all, a mental construct introduced for the purpose of discussing interactions between charges. (E.H. Wichmann, Berkeley Physics Course Vol. 4, 1967; original emphasis.)​

 

[koantum]

I don't see how you are constructing a conception of the quantum world which is strongly objective, if you START by saying that we only have an algorithm, and no description!

Maybe I should explain this in a new thread. Maybe I will!

Well, you consider quantum theory then solidly PROVEN beyond doubt, and by pure reasoning ?? And what if one day, quantum theory is falsified ? Do familiar objects disappear in a puff of logic then ?

Not by pure reasoning alone. I assume that those "ordinary" objects (which "occupy" space and neither collapse nor explode the moment they are created) are composed of a (large but) finite number of objects that do not "occupy" space, either because they are pointlike or because they have no form at all. Like many physicists these days, particularly quantum field theorist, quantum theory in general and the standard model in particular are here to stay as effective theories. In this sense Wilczek (Nobel 2004) refers to the standard model simply as "the theory of matter" (Wilczek, "Future summary", International Journal of Modern Physics A 16, 1653-78, 2001).

So you seem to claim that, from the pure observation of the existence of ordinary objects, the ONE AND ONLY POSSIBLE PHYSICAL THEORY that makes logical sense is quantum theory ? No need for any empirical input then ? If only we would have been thinking harder, it would have been OBVIOUS that quantum theory is the ultimate correct theory ?

Not the ONE AND ONLY POSSIBLE PHYSICAL THEORY that makes logical sense, but an effective theory that will survive whatever underlying theory might one day be unearthed. (My own intuition tells me that all there is is effective theories. The ultimate mathematical theory is a myth invented by the Pythagoreans.)

I'd bet that… 500 or 1000 years from now, quantum theory is an old and forgotten theory (except maybe for simplified calculations, as is classical physics today).

My bet is that not only quantum theory but the entire Pythagorean mind set, which thinks of reality in terms of mathematical structures, will be dead and gone. (Which is one of the reason why I'm looking beyond the quantum formalism for the relation between it and a non-mathematical reality.

Quantum theory being the current paradigm, it is only waiting to be falsified, no ?

The mathematical formalism stands. The claptrap about evolving real wave functions won't survive.

But that doesn't mean that in the mean time, we should not build up an ontological picture of what we have, now, today, in order to make sense of it. With a formalism comes an ontology.

Wish it would. The quantum formalism has come of age. Its ontology is as yet nowhere in sight, thanks to the Pythagorean bias of most physicists.

But trying to force upon a certain formalism, the ontology of another one, and you have troubles. Trying to force upon quantum theory, the ontology of classical physics, and you create a whole lot of pseudoproblems.

But this is exactly what I'm saying. Quantum physics, taken seriously as a probability algorithm, implies a spacetime ontology that is inconsistent with that of classical physics. Yet this classical spacetime ontology is taken for granted by virtually every physicist. This is another reason why we find it so hard to beat sense into quantum mechanics.

The so-called Pythagoreans, who were the first to take up mathematics, not only advanced this subject, but saturated with it, they fancied that the principles of mathematics were the principles of all things. (Aristotle, Metaphysics 1-5)​

 

[vanesch]

No, there isn’t. Even vanesch agreed with that https://www.physicsforums.com/showpost.php?p=948676&postcount=16".

Indeed, but my statement should not be misunderstood. I claim that unitary quantum theory, as such, does not make any probabilistic statements, given that it is a deterministic theory: we have a state vector evolve in a hilbert space according to a unitary flow. No deterministic theory ever gives intrinsically rise to a probabilistic statement what so ever: this needs to be AN EXTRA POSTULATE in one way or another.
Also - this is what I tried to outline several times already - no deterministic or other theory without an interpretation which links the formal elements to (subjective?) experience/observation can be tested in the lab either. As such, unitary quantum theory doesn't say anything about observation - this is in the same situation as classical physics, btw.

So, to turn a formalism into a "physical theory related to empirical observation" one NEEDS TO STATE, in any case, how both are related ; this is called a physical interpretation of the formalism.

Nor unitary quantum theory, with its unitary flow through hilbert space (= unitary time evolution), nor classical physics with its hamiltonian flow through phase space, are "ready to be confronted with experiment". You STILL need to say how this formal element maps upon observation. IN THIS MAPPING, one can, eventually, MAKE USE OF PROBABILISTIC CONCEPTS or not. This is then the "interpretative postulate" that LINKS the formal theory to the empirical (subjective?) observation.

What I prefer to do then, is to call the formal elements in the theory "the ontology of the theory" and picture that these things are "out there", and the interpretative postulate as the "link between subjective experience and the ontology". No more, no less.

Now, I have the "luck", in quantum theory, to find SEVERAL possible probabilistic "interpretative postulates" which don't introduce inconsistencies ; that means, for me then, that there is no hope to DERIVE IT from the formal framework. I like to compare that to the 5th postulate of Euclidean geometry, which cannot be derived from the 4 others: this was established by showing that hyperbolic geometry was consistent. When you find two different, compatible schemes with a certain axiomatic system, then for sure you cannot derive one (or the other) from the axiomatic system.

That said, there can be more "natural" probabilistic interpretations than others. Most MWI proponents (not I) seem to have a preference for an "equi-probable" measure over orthogonal states in one way or another.
It has to be said that there is some "naturalness" to this choice. However, if you do this strictly, you then run into some problems to derive the Born rule, but can try to get around that by POSTULATING extra requirements. A nice such approach is partly worked out by Robin Hanson, with his "mangled worlds" concept, for instance. It's not clear yet whether it will turn out to be viable, but the main idea is that terms with small hilbert norm are NOT stable under decoherence interactions (while terms with big hilbert norms are): they continuously merge, re-split etc. If you postulate that you cannot observe such an instable "world", and you place a lower cutoff on the considered relative hilbert norms, something close to the Born rule emerges (or at least, there are indications that this happens).

Nevertheless, all these considerations require extra postulates of "perceptive interpretation", in one way or another. These postulates will introduce the probabilistic aspects if the theory is to be seen that way.

 

[vanesch]

If I talk to quantum-state realists, they think I belong to the shut-up-and-calculate (SUC) sect. If I talk to members of this sect, they take me for a quantum-state realist. As far as I am concerned, they are both wrong.

Maybe you're simply in a superposition of both situations ? Or maybe your belonging to either is a fuzzy variable ?

The quantum-state realists aspire to describe the objective features of the quantum world. So do I. But they insist on describing these features without reference to measurements, and this doesn’t work.

I don't know why you say that it doesn't work. MWI works. You may not like it, but I surely don't see why you say that it doesn't work. And there IS an explanation which contains a reference to "measurements" which are features of subjective experience in this view. Again, you may not like it, but that doesn't mean that it is not possible.

Next you are told that this is the way it is. Admittedly, there are problems with this set of axioms, but you won't be able to understand them. So for now, shut up and calculate. If you want to know, for example, why energy is a Hermitean operator, you have to figure it out for yourself. You are not even told that the concept of energy in quantum mechanics is totally different from the corresponding classical concept.

I don't understand this. The hamiltonian is the generator of the postulated unitary time translation one-parameter group. We call it "energy" but that doesn't mean anything. We could have called it "smurkadosh".

If those poor students were told that the quantum formalism is nothing but an algorithm for assigning probabilities to possible measurement outcomes on the basis of actual outcomes, all of the above axioms would at once make sense to them.

Well, I don't know what ELSE they are told, with the above axioms ! OF COURSE that the axioms you wrote down are "an algorithm to calculate probabilities of outcomes"! That's pretty evident, no ? Ok, I prefer "formalism" and not "algorithm" because it is not directly runnable on a Turing machine. It's a mathematically written down formalism. A machinery. As is the formalism of hamiltonian or lagrangian classical mechanics.

And next, you have to use your common sense, intuition and all that to fill in the interpretational issues, such as: "given an apparatus, what measurement operator goes with it and why ?" but which is usually not an issue because people (salesmen, the problem statement, habits in the field) TELL you to what it is supposed to correspond. So when you talk about the "position measurement" of a particle, then you use X, for instance. But this is usually made so evident that you even don't think about it.

So with some common sense, "cultural habits", and "because they told me so", you arrive at knowing what apparatus goes with what hermitean operator, and the formalism can be used.

What we are discussing about, however, is: can we assign some REALITY to this formalism ? Does the formalism indicate us an ontology ? And *this* metaphysical question should not be directly addressed: I think that it is good to say that you should first understand the formalism, as a way to calculate outcomes of measurements. And many people stop short of it, and for them it is just fine to have this mixture of "common sense" assignments of formal elements to "things in the lab", and to crank the handle of the formalism, without a deeper interpretational scheme. This is the "shut up and calculate" crowd. I respect that attitude. The problem only comes about when these people are then suddenly confronted with issues like Bell's theorem and so on, and have an INCONSISTENT picture.

The difference between the quantal and the classical probability algorithm is readily understood as a consequence of Nature's fuzziness, and the latter is readily understood as Nature's means to "fluff out" matter: to create stable objects that occupy space out of finite numbers of particles that don’t.

Well, everybody his opinion of course, but personally, if one would have told me THIS as a student, it would not have been very enlightening - I would even have taken my professor for someone chatting out of the back of his head. "nature's fuzziness that is meant to stabilize ordinary objects taking up a finite amount of space". Come on ! Nature has no "aim to produce stabilized ordinary objects" does it ?

I fail to see what such a statement brings about beyond the "hey, use your common sense, tradition, what they tell you..." to associate lab stuff to formal elements of the quantum formalism, and turn the handle of the formalism to find outcomes of measurement probabilities.

If Alice and Bob perceive a teapot on the table between them, it is useful to assume that the reason this is so is that there is a teapot on the table between them. I agree. But quantum mechanics has many experimentally confirmed consequences that are totally inconsistent with the conception of a world of self-existent objects with self-existent properties (which could then be considered as the causes of our perceptions). Moreover, it has nothing to do with perceptions. It has everything to do with measuring devices (recall my definition) and their relation to the rest of the world.

Well, an MWI-er such as I does NOT have "many experimentally confirmed consequences that are totally inconsistent with the conception of a world of self-existent objects with self-existent properties", you know.
Only, the properties are not the directly perceived ones (= outcomes of measurement), but rather the state of the wavefunction, from which the perceptions can be DERIVED (contextually).

Of course not in classical physics. But the classical world is a fiction. I want to understand the real world which is quantum. (Sounds familiar, eh?)

I think that this is a mistake. If you do classical physics, then the classical world is "real". If you do quantum physics, then the quantum world is "real". And the day that quantum physics will be falsified, yet another theory will be "real".

What I'm saying is that if you want to describe the unmeasured quantum world, the only way to do it is in terms of the probabilities of the possible outcomes of unperformed measurements.

I think that this is NOT the right vision. This is clinging too much onto naive realism, in that "measurement-observation-perception = reality". It is the basic tenet of the classical world view: the state of a system is given by what I could possibly measure of it: all potential measurement outcomes "are" there. In other words, the total refusal of contextuality: that a "measurement" is the result of an interaction of an observer and a system, and that, without this interaction, the "measurement result" is not a property of the system. It is funny that you insist upon most people being too much loaded with classical concepts, and then you fall for this classical idea!

How do you describe, say, a hydrogen atom in a stationary state? This stationary state is a probability algorithm, which is based on the outcomes of three measurements: energy, total angular momentum, and one angular momentum component. It assigns probabilities to the possible outcomes of every possible measurement. Now if you want this algorithm to be a description of the hydrogen atom, then it’s a description in terms of the possible outcomes of unperformed measurements, right? And what is the salient feature of the atom thus described? Unschärfe or fuzziness!

Yes, you're forced into this corner because you insist upon the existence of "measurement results" as "existing" for the system. You cannot imagine, apparently, that a "measurement result" is just the perceived outcome of an interaction, but it must be "already in the system". This is an extremely classical view. Measurements = "showing things that exist of the system" and not "perceived results of interactions between two systems, one which we call "measurement apparatus" and the other which we call "system".

That's why I won't be able even to make you see (let alone accept) my point of view. As said, to me it simply makes no sense to think of a probability algorithm as something that REALLY exists, and if the wave function is not really a probability algorithm, I haven’t the faintest notion what it could be, nor can you tell me.

The wave function is a mathematical object that maps upon the ontology of quantum theory, and to me, the ONLY thing that you can use to describe an ontology, is a mathematical object. Your reaction to this is:

You are right to call it a dogma, as in religion.

But I wonder, what ELSE but a mathematical object could possibly satisfy "a description of an ontology" ? How could you precisely say what something is, and NOT use a mathematical object to do so ?

Sorry. According to you, Maxwell's equations allow us to calculate the effects of charges on the electromagnetic field (as well as the effect of the electromagnetic field on itself), and the Lorentz force law allows us to calculate the effects of the electromagnetic field on charges. According to me, who has never seen an electromagnetic field but only interacting charges, the electromagnetic field is a tool for calculating the action of charges on charges. I'm not quite on my own here.

In fact, you've never SEEN anything ELSE but some electromagnetic radiation (which is called "light in your eyes").

The electromagnetic field is, after all, a mental construct introduced for the purpose of discussing interactions between charges. (E.H. Wichmann, Berkeley Physics Course Vol. 4, 1967; original emphasis.)​

I've, for my part, never SEEN a charge... so I could turn this around and say that charges are mental constructs introduced for the purpose of allowing field modes to interact... Some of which I've seen directly.

 

[koantum]

MWI works.

If a theory mistakes possibilities for actualities I don’t say it works. I say it's a silly category mistake.
If someone says the wave function is a probability algorithm on weekdays and Ultimate Reality on Sundays, I say: make up your mind.
Some MWI enthusiasts (Vaidman and Plaga come to mind) have claimed that it is an in principle testable interpretation. Imagine a test for the validity of MWI. There will then be worlds in which it is true as well as worlds in which it is false. Something for everyone.

The hamiltonian is the generator of the postulated unitary time translation one-parameter group. We call it "energy" but that doesn't mean anything. We could have called it "smurkadosh".

You would tell your students that energy doesn’t mean anything?

I prefer "formalism" and not "algorithm" because it is not directly runnable on a Turing machine.

The word "algorithm" was used centuries before Turing.

"given an apparatus, what measurement operator goes with it and why ?"

Rather, we first define our concepts and then we see how we measure them. Energy, for instance, is the quantity whose conservation is implied by the homogeneity of time. For position it's of course obvious how we define and measure it.

What we are discussing about, however, is: can we assign some REALITY to this formalism ? Does the formalism indicate us an ontology ? And *this* metaphysical question should not be directly addressed: I think that it is good to say that you should first understand the formalism, as a way to calculate outcomes of measurements.

I fully agree. Unfortunately the fact that we use this formalism to calculate the probabilities of measurement outcomes is usually mentioned almost as an afterthought. I'd be very happy if the first thing students are told is that the quantum formalism is a probability algorithm.
Perhaps I should tell you something about our students at the Sri Aurobindo International Centre of Education and my class. In the so-called "free-progress" section of our higher secondary and undergraduate levels, students are free to choose their subjects and their teachers (from a list of available teachers and subjects offered, of course). Everyone of my students has chosen to be in my class, which is offered (i) to physics students as a philosophical complement to their regular physics classes and (ii) to students more interested in philosophy than science per se.

"nature's fuzziness that is meant to stabilize ordinary objects taking up a finite amount of space". Come on ! Nature has no "aim to produce stabilized ordinary objects" does it ?

Asking what the laws of physics must be like if they are to allow the existence of "ordinary" objects (as defined by me) is one thing. Asking what Nature has in mind is quite another.

the state of the wave function, from which the perceptions can be DERIVED (contextually).

Really? You can take a wave function and derive sensory perceptions from it? Wishful thinking! Neuroscientists can't even derive sensations from the neurobiology.
It would make more sense to take sense perceptions as your starting point and then discover the correlations between sensory data we call measurement outcomes. This way you don’t have to (and of course can't) derive perceptions because the quantum formalism is embedded in and presupposes sensory perceptions. My approach differs from this in that it makes not sensory perceptions but measurements primary. Recall: any event or state of affairs from which the truth or the falsity of a statement about something can be inferred qualifies as a measurement outcome. You want to derive from the wave function the existence of events or states of affairs from which something can be inferred? IMO this is as impossible as explaining why there is anything rather than nothing at all.
What you do is to transmogrify the correlations among perceptions into What Exists, after which you are left with the pseudo-problem of deriving the perceptions from What Exists.

This is clinging too much onto naive realism, in that "measurement-observation-perception = reality". It is the basic tenet of the classical world view: the state of a system is given by what I could possibly measure of it: all potential measurement outcomes "are" there.

Where did I ever say this? I insist that no property or value is possessed (by a system or an observable) unless the possession is indicated by a measurement!

You cannot imagine, apparently, that a "measurement result" is just the perceived outcome of an interaction

A measurement outcome is the indicated outcome of a system apparatus interaction. I cannot imagine anything else.

The wave function is a mathematical object that maps upon the ontology of quantum theory, and to me, the ONLY thing that you can use to describe an ontology, is a mathematical object.

What IS the ontology of quantum theory? You are stating a tautology. What you are saying is as plausible as a baker's claim that the ONLY thing that you can use to describe an ontology is dough.

But I wonder, what ELSE but a mathematical object could possibly satisfy "a description of an ontology" ?

Lack of imagination, I'd say.

In fact, you've never SEEN anything ELSE but some electromagnetic radiation (which is called "light in your eyes").

Careful with that. Light (electromagnetic radiation) is instrumental in my seeing things. I don’t see the light by which I see. If I saw all that electromagnetic radiation that according to the classical story is crisscrossing the space between me and the objects I perceive, I couldn’t perceive these objects.

I've, for my part, never SEEN a charge

Comb your hair in dry air in front of a mirror and you'll see a charged object – yourself.

field modes ... Some of which I've seen directly.

No you haven’t, not directly. What you've see is material things from which you infer (rightly or wrongly) the presence of field modes.

 

[vanesch]

If a theory mistakes possibilities for actualities I don’t say it works.

And vice-versa. Just a matter of opinion.

If someone says the wave function is a probability algorithm on weekdays and Ultimate Reality on Sundays, I say: make up your mind.

They only say that it is ultimate reality ; they don't say it is a probability algorithm. Of course, with the "ultimate" comes the caveat: until we know better (the eternal ephemere nature of scientific knowledge, which is only there to be falsified).

Some MWI enthusiasts (Vaidman and Plaga come to mind) have claimed that it is an in principle testable interpretation. Imagine a test for the validity of MWI. There will then be worlds in which it is true as well as worlds in which it is false. Something for everyone.

You always make the same mistake: imagine that there is such a test (which is: to observe quantum interference between what's postulated to be a "measurement process"). Now the OBSERVED OUTCOME of the test is not necessarily the truth value of the test, because there is only a finite probability to observe that outcome. Unless the test is "sure" (100% probability), in which case, there are NO universes in which the outcome is false. Terms that are NOT present in the wavefunction are not "possible worlds".

You would tell your students that energy doesn’t mean anything?

Energy doesn't mean anything BEYOND its defining property, which is the generator of time translations. For instance, the fact that "energy is conserved" is ONLY the result of the fact that it is the generator of time translations. And energy doesn't have much other uses except for the fact that it is a conserved quantity over time.

The word "algorithm" was used centuries before Turing.

Yes, but Turing gave it its mathematical definition.

Rather, we first define our concepts and then we see how we measure them. Energy, for instance, is the quantity whose conservation is implied by the homogeneity of time. For position it's of course obvious how we define and measure it.

No, it isn't. That's the whole point I wanted to outline. The "obvious" comes simply from "habits, what they told you, how people used to do it...", and from the fact that we have rather good visual impressions which give us an impression of "seeing positions".
How do you determine, say, the width of 10^(-23) m ? Or of 10^17 m ?
"position" is simply a "common sense" (probably biologically evolved) mental concept, not more than "light or dark" or something of the kind.

I fully agree. Unfortunately the fact that we use this formalism to calculate the probabilities of measurement outcomes is usually mentioned almost as an afterthought. I'd be very happy if the first thing students are told is that the quantum formalism is a probability algorithm.

Funny, but that's what they told me, and how I understood most intro texts to the matter. Well, not a "probability algorithm", but a "formalism that allows you to calculate probabilities of outcomes of measurement". Which I think is the obvious, correct, and interpretation-neutral statement which allows people to set this issue asside until they know enough about the formalism.

(to be continued...)

 

[vanesch]

(continuation...)

Perhaps I should tell you something about our students at the Sri Aurobindo International Centre of Education and my class. In the so-called "free-progress" section of our higher secondary and undergraduate levels, students are free to choose their subjects and their teachers (from a list of available teachers and subjects offered, of course). Everyone of my students has chosen to be in my class, which is offered (i) to physics students as a philosophical complement to their regular physics classes and (ii) to students more interested in philosophy than science per se.

Well, there's not much philosophy in your approach, I'd say. If I understand you correctly, what you try to give as an ontological picture is that potential measurement outcomes cannot be precise values, but must have some "objective" fuzziness to them and that this somehow suggests the form the quantum formalism has. I even fail to see EXACTLY what your approach is about, except to vaguely say that one should NOT assign any reality to the wavefunction, but to the "fuzziness" of potential measurement outcomes.

Asking what the laws of physics must be like if they are to allow the existence of "ordinary" objects (as defined by me) is one thing. Asking what Nature has in mind is quite another.

That's postulating a strange ontology, which gives existence to "ordinary objects in your list" and not to anything else, without precisely specifying WHAT this ontology is about.

It would make more sense to take sense perceptions as your starting point and then discover the correlations between sensory data we call measurement outcomes. This way you don’t have to (and of course can't) derive perceptions because the quantum formalism is embedded in and presupposes sensory perceptions.

This is the OBVIOUS, minimalistic approach of a scientific theory, and it is entirely based upon a solipsist viewpoint: a scientific theory is an organizing scheme of subjective experiences, and all what exists are your subjective experiences.
All the rest is hypothesis. Everything which goes beyond solipsism is hypothesis. The "existence" of ordinary objects is hypothesis. So in ANY case you'll have to make a hypothesis about what is existing, because - a you point out yourself - the starting point of all knowledge are subjective experiences - perceptions. We've evolved biologically (well, that's also a hypothesis, that we even have a body!) probably in such a way, that we mentally organize our perceptions in such a way that we make the almost inconscious experience of assigning an ontological reality to what we perceive. It is "common sense" in a very litteral way: we're almost automatically organizing our subjective experiences in such a way to make the ontological hypothesis of the existence of "ordinary objects". You could call this a pre-build in "scientific theory" from which our brains "boot up". The internal perceptions make us also make the hypothesis that we have a physical body, included in the list of "ordinary objects".
But now, our physical theories may become more sophisticated, in such a way that they conflict with the "build in" common sense ontological hypotheses (the "existence of ordinary objects"). So one has then to make a choice, at least when one WANTS to make a hypothesis of ontology: should we stick to our "common sense" build in ontological hypotheses, or should we consider that these are what they are, namely just organizing principles of our daily subjective experiences, and can we accept that more sophisticated theories (which are of course not build into our brains) need more sophisticated ontologies ?
The ENTIRE interpretational difficulty of quantum theory resides in the refusal to let go our primary common sense ontological hypotheses ; the refusal to let go the idea that "ordinary objects are real".

My approach differs from this in that it makes not sensory perceptions but measurements primary. Recall: any event or state of affairs from which the truth or the falsity of a statement about something can be inferred qualifies as a measurement outcome.

There is no absolute way to infer the truth or falsity of something, apart from the truth or falsity of a subjective experience. This is the entire basis of the non-falsifiability of solipsism. So when you do the above, you are MAKING IN ANY CASE ontological assumptions. If, by doing so, you introduce problems, then that's of course more a problem of the assumptions than of the theory at hand.

You want to derive from the wave function the existence of events or states of affairs from which something can be inferred? IMO this is as impossible as explaining why there is anything rather than nothing at all.
What you do is to transmogrify the correlations among perceptions into What Exists, after which you are left with the pseudo-problem of deriving the perceptions from What Exists.

Ha, but that is EXACTLY the nature of the hypothesis of an ontology! You have the choice between that, and solipsism.

As I said before, you're not obliged to make the hypothesis of an ontology, and keep to solipsism, claiming that ALL there is, are your subjective experiences. BUT, BUT, it is not very helpful to do so. You can stick to the common sense ontology, and then you run into problems with quantum theory, unless you REMOVE some ontology for some things which are not on your list of common sense objects. It's where ALL the interpretation problems of quantum theory come from: quantum theory, as a universal theory, is NOT compatible with common sense ontology.

A measurement outcome is the indicated outcome of a system apparatus interaction. I cannot imagine anything else.

But there is no quantum-mechanical way to do that! You know as well as I that if you track down the physical interaction of the system and the apparatus, that both end up in an entangled state, not in a "definite outcome" state.

Careful with that. Light (electromagnetic radiation) is instrumental in my seeing things. I don’t see the light by which I see. If I saw all that electromagnetic radiation that according to the classical story is crisscrossing the space between me and the objects I perceive, I couldn’t perceive these objects.

Que ? You only see the light that enters your eyes, no ? From that, you INFER that there must be sources of them. But if I had a perfect hologram just in front of your eyes that sent exactly the same electromagnetic radiation in your eyes, you wouldn't be able to make the difference. That's why I claim that the only thing you've ever SEEN, was light impinging on your eyes.

Comb your hair in dry air in front of a mirror and you'll see a charged object – yourself.

I'll "see" an EM field penetrating my eyes, which has such a structure that it makes, according my build-in common sense ontological hypotheses, me postulate that there is an object in front of me, called mirror, and that this mirror projects light upon me that must come from what's in front of the mirror, namely my body.

No you haven’t, not directly. What you've see is material things from which you infer (rightly or wrongly) the presence of field modes.

I think you've already made some ontological hypotheses along the way, namely that the light you see "comes from material sources". It's normal. We're wired up that way to think so. It's responsible for the success of 3D virtual reality goggles.

 

[koantum]

They only say that it is ultimate reality ; they don't say it is a probability algorithm.

We went through this: you then need some extra postulate to get the only things (probabilities) that you can compare with experiments.

Unless the test is "sure" (100% probability), in which case, there are NO universes in which the outcome is false.

It could of course be the other way: there are NO universes in which the outcome is true.

Energy doesn't mean anything BEYOND its defining property, which is the generator of time translations. For instance, the fact that "energy is conserved" is ONLY the result of the fact that it is the generator of time translations. And energy doesn't have much other uses except for the fact that it is a conserved quantity over time.

I almost agree. Energy means a lot of things in the limit in which quantum mechanics degenerates into classical mechanics, and it's worth discussing (I'm not proposing to do that here!) how and why these classical significances arise from the defining property.
Besides, I like Feynman's image of rotating arrows moving along the alternative spacetime paths that are summed in his path-integral calculation of a particle propagator. Based on this intuition, I tend to think of the energy associated with a spacetime path as the rate at which the particle "ticks" (in cycles per second) as it travels along this path. This helps to understand, for instance, why there is such a thing as inertial time: an inertial time scale is one in which freely moving particles tick at constant rates. (Don’t protest: I know you favor visual aids that have heuristic value).

Yes, but Turing gave it its mathematical definition.

What? Before it didn’t have a mathematical meaning? But OK. What if I say that quantum states are "probability measures" instead of "probability algorithms". Is this more acceptable? A measure on the set of projectors? I'm afraid this term sounds too Boolean.

No, it isn't. That's the whole point I wanted to outline. The "obvious" comes simply from "habits, what they told you, how people used to do it...", and from the fact that we have rather good visual impressions which give us an impression of "seeing positions". How do you determine, say, the width of 10^(-23) m ? Or of 10^17 m ? "position" is simply a "common sense" (probably biologically evolved) mental concept, not more than "light or dark" or something of the kind.

I am with you most of the way. But this is another topic that is best treated separately. I'll get back to it.

Funny, but that's what they told me, and how I understood most intro texts to the matter.

Perhaps it was different in my time (the 70s) and my country (then Germany). People talked and wrote as if state vectors or wave functions represented systems somehow directly, not merely as tools for calculating the probabilities of measurement outcomes.
And even when the relation between wave functions and probabilities was discussed, it was biased and unbalanced. The fact that wave functions determine probabilities of measurement outcomes was emphasized, whereas the fact that measurement outcomes determine wave functions was blunted by an embarrassed "it seems so".

To be continued...​

 

[koantum]

(Continuation)

Well, there's not much philosophy in your approach, I'd say.

Please allow for the fact that we touched on only a small part of the philosophy so far.

I even fail to see EXACTLY what your approach is about, except to vaguely say that one should NOT assign any reality to the wave function, but to the "fuzziness" of potential measurement outcomes.

I purposely didn’t commit myself as to the ontological status of fuzzy observables. All I said is: if you want to describe a quantum system between measurements, the only way to do this is in terms of assignments of probabilities to the possible outcomes of unperformed measurements. All right, I characterized the resulting probability distributions as descriptive of an objective fuzziness in order to distinguish it from a merely subjective ignorance. Our ignorance of the electron's position doesn’t stabilize the hydrogen atom. Its objective fuzziness does.
But this fuzziness is just the beginning. It leads to the incomplete spatiotemporal differentiation of the world, which in turn allows one to define macroscopic objects rigorously, which in turn allows one to understand how a fundamental physical theory that is formally nothing but a probability algorithm (OK, a tool for calculating probabilities) can be complete: how it can encompass the measurement outcomes which it presupposes.

we're almost automatically organizing our subjective experiences in such a way to make the ontological hypothesis of the existence of "ordinary objects". You could call this a pre-build in "scientific theory" from which our brains "boot up". The internal perceptions make us also make the hypothesis that we have a physical body, included in the list of "ordinary objects".

You assume too much about yourself as creator of your world. You won't find your way in Paris using a map of London. There is a correspondence in the sense that Nature will knock you on the nose if you use the wrong theory. In this sense there is a correct theory.

But now, our physical theories may become more sophisticated, in such a way that they conflict with the "build in" common sense ontological hypotheses (the "existence of ordinary objects"). So one has then to make a choice, at least when one WANTS to make a hypothesis of ontology: should we stick to our "common sense" build in ontological hypotheses, or should we consider that these are what they are, namely just organizing principles of our daily subjective experiences

OK so far but, as said, there is agreement (up to a point) between these organizing principles and whatever they are working on. The assumption of a self-existent world with self-existent objects with self-existent properties works so well that it may well be MEANT to work that well. If you can hold on to that for a microsecond, then we can understand the quantum formalism very well as the necessary mechanism by which what is MEANT to be is manifested, brought into being, or realized. Enough ontology for the day?

The ENTIRE interpretational difficulty of quantum theory resides in the refusal to let go our primary common sense ontological hypotheses ; the refusal to let go the idea that "ordinary objects are real".

Not the ENTIRE. There are about as many solutions to the problem of interpretation as there are ways of formulating the problem. We've already noticed that the way one formulates the problem half predetermines the solution, and if the formulation produces a pseudo-problem, the solution is gratuitous.
I see no reason to let go the idea that ordinary objects are real. There is much more to them than commonsense has it but that doesn’t make them unreal. The problem is to understand the relation between the quantum formalism and ordinary objects. That you need the quantum formalism in order to have them is just one of them. Another is that the quantum formalism describes how ordinary objects are manifested, brought into being, made to exist, whatever. I mentioned elsewhere that it should be expected that the microworld doesn’t have the same features as the macroworld, for if it did, one could never understand how these features are realized, brought into being….

There is no absolute way to infer the truth or falsity of something, apart from the truth or falsity of a subjective experience.

You shouldn’t stop here. Only pre-linguistic experience can be trusted. The moment it is formulated, it is enmeshed in a system of questionable hypotheses.

you are MAKING IN ANY CASE ontological assumptions. If, by doing so, you introduce problems, then that's of course more a problem of the assumptions than of the theory at hand.

Apparently there is a mirror symmetry between what I say about your approach and what you say about mine.

Ha, but that [to transmogrify the correlations among perceptions into What Exists] is EXACTLY the nature of the hypothesis of an ontology! You have the choice between that, and solipsism.

Nonsense. There are plenty more choices. You are limited to these choices only because you confuse mathematics with ontology.

Me: A measurement outcome is the indicated outcome of a system apparatus interaction.
You: But there is no quantum-mechanical way to do that!

This just means we have different ideas about what a quantum-mechanical way is.

You know as well as I that if you track down the physical interaction of the system and the apparatus, that both end up in an entangled state, not in a "definite outcome" state.

Sorry, I know exactly the opposite (to the extent that you allow me to know anything).

You only see the light that enters your eyes, no ?

Sorry, haven’t seen light entering my eyes. Only see things with the help of the light entering my eyes.

I'll "see" an EM field penetrating my eyes, which has such a structure that it makes, according my build-in common sense ontological hypotheses, me postulate that there is an object in front of me, called mirror, and that this mirror projects light upon me that must come from what's in front of the mirror, namely my body.

The bottom line: everyone sees what they want to see.

 

[vanesch]

What? Before it didn’t have a mathematical meaning? But OK. What if I say that quantum states are "probability measures" instead of "probability algorithms". Is this more acceptable? A measure on the set of projectors? I'm afraid this term sounds too Boolean.

Well, you know that strictly speaking, quantum states are NOT probability measures over the potential measurement outcomes, at least not in the Kolmogorov sense - we've been through that already a few times.
And if you tell me now that quantum states are "mathematical entities that contain the simultaneous description of the (fuzzy) quantities which can be outcomes of measurements", yes of course. You can see the "ensemble of fuzzy quantities" which are possessed by the system as mathematically equivalent to the wavefunction. And then, in the way that you assign "reality" to this set of fuzzy quantities, you assign reality to that mathematically equivalent structure, which is the wavefunction.
I mean:
{set of fuzzy quantities} <==> wavefunction

If you trace through the entire chain, then, your body also possesses FUZZY QUANTITIES. After all, there's no distinction between a quantum system under study and your body, right ? Your eyes have seen, and have not seen, the bulb flash: this quantity "have seen bulb flash" is JUST AS WELL a fuzzy quantity. You happen to perceive *A* precise outcome, not a fuzzy one. Why ? You tell me.
What's the difference with the MWI viewpoint ?

Perhaps it was different in my time (the 70s) and my country (then Germany). People talked and wrote as if state vectors or wave functions represented systems somehow directly, not merely as tools for calculating the probabilities of measurement outcomes.
And even when the relation between wave functions and probabilities was discussed, it was biased and unbalanced. The fact that wave functions determine probabilities of measurement outcomes was emphasized, whereas the fact that measurement outcomes determine wave functions was blunted by an embarrassed "it seems so".

I think it is an equivalent viewpoint, once you assign the same "fuzzyness" to your body state quantities as you do to the "potential measurement outcomes".

 

[vanesch]

Not the ENTIRE. There are about as many solutions to the problem of interpretation as there are ways of formulating the problem. We've already noticed that the way one formulates the problem half predetermines the solution, and if the formulation produces a pseudo-problem, the solution is gratuitous.

I'm preferring MWI exactly because, apart from the mental step needed to let go the idea that "ordinary objects are real", there are no pseudoproblems left. The usual pseudoproblems being that there IS no fundamental microscopic ontology, or that there are two different processes in nature (measurements and interactions), or that there is "immediate action at a distance" (killing off special relativity).
In MWI, there IS a fundamental ontology, there is no distinction between "measurements" and "interactions" and locality is respected. You only need a very weird relationship between "ontological reality" and "subjective experience" but if you can mentally get over that idea, all the usual difficulties with QM are gone.

Now, I can also accept the idea that people DON'T want to go into these considerations, and just think of quantum theory as some tricks to calculate outcomes of measurements.

I can again accept the idea (I'm even half convinced of it) that quantum theory as it stands, will, one day, find a completion/falsification/whatever, which will change the picture and formalism completely or partially and that all the speculation of quantum theory being universal in the form it has today is premature to say the least. (my only response to that is that, given that we don't know yet what will be the eventual modifications, as we don't have anything else, we'll have to do with what we have today, as a mental exercise).

However, I jump up and down, each time I read that one CANNOT GIVE an ontological description to the quantum-mechanical formalism without running severely in contradictions, because this is not true. You can do so and then there are no problems left (except for the counter-intuitive idea of letting go the ontological existence of ordinary objects).

I see no reason to let go the idea that ordinary objects are real. There is much more to them than commonsense has it but that doesn’t make them unreal.

Again, THIS is the fundamental EXTRA hypothesis which makes all "ontological" views on quantum theory run into havoc. And it is pretty obvious that you will arrive at troubles when you take ordinary objects for real: that is the very superposition principle of quantum theory, which cannot be applied to ordinary objects, if they are to be real.

The problem is to understand the relation between the quantum formalism and ordinary objects. That you need the quantum formalism in order to have them is just one of them. Another is that the quantum formalism describes how ordinary objects are manifested, brought into being, made to exist, whatever. I mentioned elsewhere that it should be expected that the microworld doesn’t have the same features as the macroworld, for if it did, one could never understand how these features are realized, brought into being….

Now, everybody has his/her own cherished "pre-postulates" of course. Mine is clear: it is the necessity to assign a 1-1 relationship between a mathematical object and the ontological world. Call it reductionism, or platonic realism or whatever. Yours is that the ordinary objects you see are the "fundamental ontological entities" in some sort of way. This colors one's picture of the world.

 

[koantum]

I jump up and down, each time I read that one CANNOT GIVE an ontological description to the quantum-mechanical formalism without running severely in contradictions, because this is not true.

I fully agree with you.

it is pretty obvious that you will arrive at troubles when you take ordinary objects for real: that is the very superposition principle of quantum theory, which cannot be applied to ordinary objects, if they are to be real.

You will get into trouble if you take wave functions for real, for then a cat can be both alive and dead, which is pure nonsense. You won't arrive at this nonsense of you understand that the quantum formalism does nothing but correlate measurement outcomes, whose existence it presupposes. To make your approach consistent with the existence of measurement outcomes, you need many worlds. I want to understand this one world. The plural of "world" is (for me) a contradiction in terms.

Call it reductionism, or platonic realism or whatever.

How about Pythagorean mysticism?

Yours is that the ordinary objects you see are the "fundamental ontological entities" in some sort of way.

Absolutely not. I haven’t yet told you what my fundamental ontological entities are. To be able to conceive of them, you need to accept the quantum formalism as being fundamentally a probability algorithm.

Well, you know that strictly speaking, quantum states are NOT probability measures over the potential measurement outcomes, at least not in the Kolmogorov sense

Apropos of Kolmogorov. There are two misconceptions about quantum-mechanical probabilities:

• that they are subjective rather than objective,
• that they are absolute rather than conditional. "Every probability is a conditional probability" - Hans Primas, "Time–Entanglement Between Mind and Matter" in Mind and Matter 1 , 81–119, 2003.

Why is the wave function commonly regarded as the primary object and the propagator as derivative? Partly because of the historical precedence of Schrödinger's "wave mechanics" over Feynman's propagator-based formulation of quantum mechanics, in which the propagator is the primary object from which the wave function is derived. But there is a more insidious reason, namely the primacy of absolute over conditional probabilities in Kolmogorov's mathematical foundation of probability theory. This too is a fortuitous case of historical precedence, for an alternative to Kolmogorov's axiomatic formulation of probability theory has been developed by A. Rényi, and every result of Kolmogorov's theory can be translated into Rényi's formulation, which is based entirely on conditional probabilities.
If you take the wave function (rather than the propagator) as the primary object, you will take the probabilities it defines in an absolute sense, as depending on nothing but the wave function. If you take the propagator as the primary object, then it is obvious that the wave function is only a tool for calculating conditional probabilities – probabilities that are determined by the outcomes of actual measurements and the time of the measurement to the possible outcomes of which they are assigned.
Besides, you know the enormous advantage of the propagator formalism over the wave function formalism – its explicit relativistic invariance. With the wave function formalism you schlep with you the useless burden of a preferred reference frame, which of course is as unobservable as your evolving wave function.

After all, there's no distinction between a quantum system under study and your body, right ?

Wrong. There is a crucial difference between macroscopic objects and all the rest. But (once again) to be able to understand it, you need to accept the quantum formalism as being fundamentally a probability algorithm.

You happen to perceive *A* precise outcome, not a fuzzy one. Why ? You tell me.

There happens to be a world. Why? You tell me?

 

[vanesch]

You will get into trouble if you take wave functions for real, for then a cat can be both alive and dead, which is pure nonsense.

I have no fundamental problems with saying that a cat is both alive and dead, if I also have the explanation of why I only see one of both. I mean: postulating something extra which is not observable is not "nonsense", it is neutral. If I tell you that at exactly the place where you are, there's a fire-spitting dragon, made of stuff which with you cannot interact, and which spits fire with which you cannot interact, then that is a totally neutral statement: it is not a priori true, or it is not a priori false. It should not be classified as "obviously not true" because you cannot know.
Now, if the only aim of the introduction of this dragon, is, well, to be able to say that there is such a dragon, then you can rightly object to this extraneous statement, which serves no other purpose than to talk about non-interacting dragons, because of Occam's razor. However, if the introduction of this dragon makes go away a lot of OTHER problems, then I don't see what's wrong with it. After all, you don't know, and there's no way to know, if there are not many of these dragons around ! There's no way for you to state that they are not there.

To come back to the cat: if I can resolve the "formal ontology", "locality" and "measurement/interaction dichotomy" problems, by saying that there is an unobserved dead cat when I see a live cat, then I find that a totally acceptable statement. This is the difference with the dragon: the dragon came "out of the blue". The cat was suggested by the formalism. In both cases, we're talking about something that is "real but unobservable". But the first one gets (rightly) cut away because of Occam's razor (the dragon doesn't serve any purpose) ; in the second case, it serves the purpose of simplifying the concept.

Again, if you don't like cats which are live and dead, be my guest. But it is not nonsensical to say so - especially if it can solve other issues.

You won't arrive at this nonsense of you understand that the quantum formalism does nothing but correlate measurement outcomes, whose existence it presupposes. To make your approach consistent with the existence of measurement outcomes, you need many worlds. I want to understand this one world. The plural of "world" is (for me) a contradiction in terms.

Because you know as well as I do that this is just a colloquial way of talking. The "worlds" are nothing else but the alternative subjective perceptions of the observer, which only experiences one.
There's not much difference with "time" in relativity: there, yesterday and tomorrow "exist" as much as "today" exists. But you have the impression that only "today" exists, while yesterday "doesn't exist anymore" and tomorrow "has not yet come into existence". Nevertheless, the whole 4-manifold "exists" and all time slices have equivalent ontology. Why do you only experience one slice ? Are these also "parallel worlds" ? Is a "copy of you" experiencing yesterday, while you are experiencing "today", and another copy of you is experiencing "tomorrow" ? It is not so different.

Absolutely not. I haven’t yet told you what my fundamental ontological entities are. To be able to conceive of them, you need to accept the quantum formalism as being fundamentally a probability algorithm.

I'd like to hear that. And I wonder how you are going to do this, without introducing them as a mathematical object!

Apropos of Kolmogorov. There are two misconceptions about quantum-mechanical probabilities:

• that they are subjective rather than objective,
• that they are absolute rather than conditional. "Every probability is a conditional probability" - Hans Primas, "Time–Entanglement Between Mind and Matter" in Mind and Matter 1 , 81–119, 2003.

What could it mean, "objective probabilities" except for the fact that the alternatives "exist", and not that "only one exists, but we don't know which one" ?
And of course all probabilities are conditional ! They are conditional on the initial state you care to specify.

If you take the wave function (rather than the propagator) as the primary object, you will take the probabilities it defines in an absolute sense, as depending on nothing but the wave function. If you take the propagator as the primary object, then it is obvious that the wave function is only a tool for calculating conditional probabilities – probabilities that are determined by the outcomes of actual measurements and the time of the measurement to the possible outcomes of which they are assigned.

Of course. I agree with what you write here: what is of course real is not the "wavefunction at a certain moment", but the entire unitary structure over time. You can even go to the Heisenberg picture if you want to, that doesn't change the idea. "taking the wavefunction seriously" does not mean that one should attach a specific meaning to psi(t) for a given value of t (especially in a relativistic setting). The wavefunction is nothing else but something like a "spacelike slice" of this unitary structure, in a similar way as space is a spacelike slice of minkowski space.
The propagators are another way to look upon this structure, this time more along the timelike axis. It is as if we were going to have a discussion to what's real: spacelike slices of Minkowski space, or world lines of particles. That's a hollow discussion. This is like arguing over the meaning of phase space, and how this meaning gets altered under canonical transformations. It's the entire structure of course, and not one specific "coordinate description" which is real.

Besides, you know the enormous advantage of the propagator formalism over the wave function formalism – its explicit relativistic invariance. With the wave function formalism you schlep with you the useless burden of a preferred reference frame, which of course is as unobservable as your evolving wave function.

I fully agree here. The two things go hand in hand, and are in fact different aspects of the unitary structure over hilbert space introduced by the time evolution operator.

Wrong. There is a crucial difference between macroscopic objects and all the rest. But (once again) to be able to understand it, you need to accept the quantum formalism as being fundamentally a probability algorithm.

Again, this is what I refuse to do: make any distinction between an electron and an apple, in principle. A universal theory must treat them in the same way. Sorry, it's my religion I'm convinced that from the moment you do this, you introduce too much intuitive naive realism into the theory.

 

[Steve Esser]

koantum and vanesch: Thank you for the valuable debate. (Don't stop!)

 

[CarlB]

Again, this is what I refuse to do: make any distinction between an electron and an apple, in principle. A universal theory must treat them in the same way. Sorry, it's my religion I'm convinced that from the moment you do this, you introduce too much intuitive naive realism into the theory.

This is another way of saying that you believe that quantum mechanics is correct and complete and you will therefore refuse to acknowledge any evidence to the contrary. You should realize that you are going against not only Einstein in this belief, but also against all those physicsists busily attempting to unite gravity and QM.

If the MWI interpretation were correct, then the quantum gravity problem should already have been solved, along with all the other mysteries of physics so well described by Smolin in "A Crisis in Fundamental Physics".

http://www.nyas.org/publications/Upd...sp?UpdateID=41

Instead, the situation after MWI is identical to the situation before MWI. It brought no new information to the table, no new predictions, nothing of any use. The same could be said of the various string theories, as well as the things that are dear to my own heart, Bohmian mechanics and David Hestenes' geometric algebra.

When Einstein discovered relativity, a flood of applications soon followed. When various people put QM together, again a flood of applications followed. By contrast, all the various modern attempts to refound QM and or relativity have been completely barren. That's another word for useless. All these theories have provided is badly justified new possibilities for religious devotion.

When a new foundation for QM and or relativity appears, you will know it by its utility.

Carl

 

[koantum]

Smolin,"A Crisis in Fundamental Physics".
http://www.nyas.org/publications/Upd...sp?UpdateID=41

That link didn't work for me. http://www.nyas.org/snc/update.asp?updateID=41&page=1#" did.

 

[koantum]

I have no fundamental problems with saying that a cat is both alive and dead, if I also have the explanation of why I only see one of both.

Unfortunately I don’t have that explanation. Fortunately I don’t need it. As far as I am concerned, the two cat states are possibilities. Whereas there is only one actual world, there can of course be many possible ones.

postulating something extra which is not observable is not "nonsense", it is neutral.

There I agree. I play the same game, but the extra I postulate is not an ontology isomorphic to a probability algorithm (that is, a mathematical tool for calculating probabilities of possible measurement outcomes on the basis of actual ones).

If I tell you that at exactly the place where you are, there's a fire-spitting dragon, made of stuff which with you cannot interact…

Then what about Popper's definition of a scientific theory? To be scientific, it has to be falsifiable.

However, if the introduction of this dragon makes go away a lot of OTHER problems, then I don't see what's wrong with it.

That's a BIG if. What if it creates a lot of OTHER problems?

The cat was suggested by the formalism.

Not by the formalism but by what I call the "evolutionary paradigm": the belief that physics is neatly divisible into kinematics (concerned with the description of systems at anyone time, their "states") and dynamics (concerned with the evolution of states from earlier to later times).
This hangover from classical times keeps alive the belief in the existence of evolving, instantaneous states that are descriptive of physical reality. And it leaves us with no alternative to seizing upon the wave function as that evolving, instantaneous ontological state. Hence the mother of all pseudo-problems: why two modes of evolution rather than one? It's a pseudo-problem because the real number of modes of evolution is zero.

The "worlds" are nothing else but the alternative subjective perceptions of the observer, which only experiences one.

So we had better call it the "many minds interpretation" (David Z. Albert, Quantum Mechanics and Experience, Harvard UP 1992). According to Albert, everyone schleps with them a non-denumerable infinity of minds. Schizophrenia with a vengeance!

There's not much difference with "time" in relativity: there, yesterday and tomorrow "exist" as much as "today" exists. But you have the impression that only "today" exists, while yesterday "doesn't exist anymore" and tomorrow "has not yet come into existence". Nevertheless, the whole 4-manifold "exists" and all time slices have equivalent ontology. Why do you only experience one slice ? Are these also "parallel worlds" ? Is a "copy of you" experiencing yesterday, while you are experiencing "today", and another copy of you is experiencing "tomorrow" ? It is not so different.

There is a significant difference. I'll discuss it in a separate post.

I'd like to hear that. And I wonder how you are going to do this, without introducing them as a mathematical object!

This deserves a separate thread.

What could it mean, "objective probabilities" except for the fact that the alternatives "exist", and not that "only one exists, but we don't know which one" ?

What it means is that the hydrogen atom (and everything made of atoms) is "fluffed out" by the objective fuzziness of relative positions and momenta (not excluding those between macroscopic objects) rather than by our ignorance of the exact values of these observables. We use objective probabilities to describe objective fuzziness and subjective probabilities to describe subjective ignorance.

And of course all probabilities are conditional ! They are conditional on the initial state you care to specify.

This illustrates the nefariousness of the evolutionary paradigm. There is no initial wave function. The wave function is only a tool that helps in the calculation of probabilities of later outcomes given earlier outcomes, just as the electromagnetic field is only a tool that helps calculating (later) effects on the behavior of charges caused by the (earlier) behavior of other charges.

what is of course real is not the "wave function at a certain moment", but the entire unitary structure over time.

That starts a completely new ballgame!

"taking the wave function seriously" does not mean that one should attach a specific meaning to psi(t) for a given value of t (especially in a relativistic setting). The wave function is nothing else but something like a "spacelike slice" of this unitary structure, in a similar way as space is a spacelike slice of minkowski space.

A spacelike slice? May I remind you of your post in which you agreed with me that the wave function evolves in the configuration space of the universe? (Pardon me, I meant to say: that the wave function exists in the configuration spacetime of the universe?)

the time evolution operator

What's that? If what exists is the spatiotemporal whole, how can anything evolve?

 

[koantum]

The "worlds" are nothing else but the alternative subjective perceptions of the observer, which only experiences one. There's not much difference with "time" in relativity: there, yesterday and tomorrow "exist" as much as "today" exists. But you have the impression that only "today" exists, while yesterday "doesn't exist anymore" and tomorrow "has not yet come into existence". Nevertheless, the whole 4-manifold "exists" and all time slices have equivalent ontology. Why do you only experience one slice ? Are these also "parallel worlds" ? Is a "copy of you" experiencing yesterday, while you are experiencing "today", and another copy of you is experiencing "tomorrow" ? It is not so different.

You are right in that the experiential now has no counterpart in the physical world. There simply is no objective way to characterize the present, and since the past and the future are defined relative to the present, they too cannot be defined in physical terms. The temporal modes past, present, and future can be characterized only by how they relate to us as conscious subjects: through memory, through the present-tense immediacy of qualia, or through anticipation. The proper view of physical reality therefore is not only what the philosopher http://philosophy.fas.nyu.edu/object/thomasnagel" has called "the view from nowhen" (the physical world does not contain a preferred time corresponding to the particular moment from which or at which I experience it).
To philosophers, the perplexities and absurdities entailed by the notion of an advancing objective present or a flowing objective time are well-known. To physicists, the unreality of a temporally unextended yet persistent and continually changing present was brought home by the discovery of the relativity of simultaneity. For any two events A,B there exist two reference frames F_A and F_B and a third event C such that C is simultaneous with A in F_A and simultaneous with B in F_B. This "simultaneity by proxy" compels us to conceive of all parts of the spatiotemporal whole as coexistent and as equally real.
It has been argued that quantum mechanics is just barely consistent with relativity. An inconsistency is perceived by wave function enthusiast who (unlike you) feel the need to reintroduce an absolute simultaneity. Here is what http://www.columbia.edu/cu/philosophy/Faculty/_facultypages/davidAlbert.html"'s "peaceful coexistence" of the two.
Case in point: If I assume that quantum mechanics is nothing but a tool for calculating the probabilities of possible outcomes given actual outcomes, then I can demonstrate that the spatiotemporal differentiation of reality doesn’t go "all the way down." Nothing in the world corresponds to a precise position or a sharp instant of time. We should therefore conceive of the world first and foremost as a whole. Our theoretical model of it should not be built on spacetime points or temporally unextended "nows" and spatial points, but instead should be built "from the top down," by a differentiation that Nature has not carried as far as conceivable.
Quantum mechanics thus agrees with special relativity in that it too is inconsistent with presentism: the view that only the continually changing present is real. Special relativity because of the relativity of simultaneity, and quantum mechanics because it implies that reality is not built up from infinitely thin successive presents but instead is an incompletely differentiated spatiotemporal whole.
Now comes the punch line: if the world is an incompletely differentiated spatiotemporal whole, then determinism is out of the window. Any theory postulating deterministic evolution presupposes the existence of a completely differentiated spacetime manifold. If that is a fiction, so is determinism.
I almost forgot to point out the difference between many worlds and many times. I am aware of the many times but not of the many worlds. Of course I am not simultaneously aware of the many times – that would be a contradiction in terms. But I have subjective evidence of the many times and no subjective evidence whatever of the many worlds. The problem of the apparent impossibility of objectifying the Technicolor reality of the experiential present (which deeply troubled Einstein) is therefore genuine. Your invocation of a multitude of coexistent worlds of which we are unaware, on the other hand, is a gratuitous solution of a pseudo-problem.

 

[antfm]

Hi Ulrich (koantum),
Thank you very much to you (and rest of debatants) for this beautiful discusion. Sorry for the interruption, but could you please expand a bit more the idea of the world as an "incompletely differentiated spatiotemporal whole"?
I think I grasp the idea, but doesn't it imply somehow a framework over which to establish the differentiation?
Am I missing something? Thanks again, and sorry if this is too elementary.
Antonio

 

[vanesch]

This is another way of saying that you believe that quantum mechanics is correct and complete and you will therefore refuse to acknowledge any evidence to the contrary.

On the contrary! The belief that the only sensible *hypothesis* (and, as I outlined several times, it will always remain a hypothesis because of the non-falsifiability of solipsism) of an ontology is a mathematical structure (because mathematical structures are the only things of which we can make sense, apart from our qualia) has nothing to do with "the belief that quantum mechanics is correct and complete". You are not allowed to use qualia as the defining properties of an ontology - almost by definition of an ontology ; so what remains are mathematical structures. Only, which one ? I'd say that you have to deal with the structures you have, at the moment, of the theories that are seen as "most fundamental" today. This can change, tomorrow.

What I'm saying is, that IF YOU WANT TO GIVE A SENSE to quantum theory, then you have to take (one of its) mathematical representations seriously. And if you want to give a sense to general relativity, then you have to take its mathematical representation seriously. And if you want to give a sense to classical physics, then you have to take its mathematical formalism seriously. In each case, you have a different *hypothesis* of ontology - simply because you have a different mathematical formalism.
If I do general relativity, then "what is out there" is a 4-dim manifold. And if I do quantum theory, then "what is out there" is the unitary structure of the theory (hilbert space + evolution operator). If I do classical physics, then "what is out there" is the phase space.

Now, it is of course rather disturbing to have to CHANGE ontology, according to with which theory you're working. But if you understand that a certain theory's mathematical formalism is an approximation of an underlying theory, then of course you can keep the underlying formalism - with its ontology - to interpret the approximative theory: the mathematical objets of the approximative theory correspond to approximations of the mathematical objects of the underlying theory. This is what happens, for instance, when going from general relativity to Newtonian physics: the 4-manifold (which is then taken to be "real") is to be viewed as sliced up according to a certain time coordinate, and this coordinate is then seen as "the time axis" of Newtonian physics, while the spacelike slices are seen as seen as "space" in Newtonian physics. We now see that what were considered two distinct ontological objects (time, and space), are in fact a specific slicing up of the "encompassing" ontological object (4-manifold).

As to MWI, I consider that it is the most evident interpretation of the *current mathematical formulation* of quantum theory as we know it - so as long as you think that this formalism "stands" I think that it is the clear ontology that goes with it, simply because it's what the mathematical structure says. And - I repeated this often - the day that this formalism needs a change, then this ontology will change also. After all, ontology is nothing but a hypothesis: there doesn't need to be a real world out there in the first place.
What is, in my eyes, an aberation, however, is to consider ontologies which GO AGAINST the mathematical structure of quantum theory. The projection postulate does such a thing. It violates unitarity, it violates Lorentz invariance, and it isn't even specified WHEN it should be applied - you're left to your intuition to do so.
But again, the day that one changes the formalism, one changes also the ontology - so I see no point of your claim that I believe quantum theory is ultimately correct. I even think that as long as the challenge with GR is open, that all bets are off. Which doesn't mean, that we know WHAT will give and what will remain. It might very well be that the superposition principle remains - in one form or another. It might be that in a future theory, we might understand what the projection postulate actually meant, because it is then naturally incorporated in the structure of the theory. Or not. But it doesn't make any sense to speculate over that if you don't know which way it will go, and if you don't have a reasonable mathematical formalism that does so.

You should realize that you are going against not only Einstein in this belief, but also against all those physicsists busily attempting to unite gravity and QM.

First of all, except for its historical value, I don't think it matters much what Einstein thought. After all, what I say probably also goes against what thought Saint Augustin. So what ?

On the other hand, I think you're mistaking when you think that I go against what people are doing on the GR-QM front, on the contrary. Many of these schemes SIMPLY DON'T MAKE SENSE if you consider projection. Most, if not all, "official" approaches stick to strict unitarity. Even Hawking admitted that probably, the evaporation of a black hole is a strictly unitary process. The entire issue of conservation of information (read: unitarity, which is OPPOSITE to projection) in a quantum process such as the formation and evaporation of a black hole only makes sense if you leave out projection (and HENCE place yourself in an MWI context).
So the entire question is: will it be possible to conserve the superposition principle, and unitary dynamics, while unifying with gravity, or does one need a fundamental change of this entire machinery. In fact, (Penrose style thinking) gravity is the last hope of killing off unitarity (and hence opening the possibility of introducing the projection postulate as a dynamical phenomenon). Even Penrose, who is certainly not in favor of the MWI view, thinks that the MWI view is the _only sensible interpretation_ if quantum theory turns out to remain strictly unitary in the presence of gravity. Hence his hope that gravity will introduce a deviation from unitarity.

 

[vanesch]

The temporal modes past, present, and future can be characterized only by how they relate to us as conscious subjects: through memory, through the present-tense immediacy of qualia, or through anticipation. The proper view of physical reality therefore is not only what the philosopher http://philosophy.fas.nyu.edu/object/thomasnagel" has called "the view from nowhen" (the physical world does not contain a preferred time corresponding to the particular moment from which or at which I experience it).

Exactly. Well said. So you agree with me that the notion of "present time" is only a construction of our subjective experience, as you state so well: "temporal modes past, present, and future can be characterized only by how they relate to us as conscious subjects". Couldn't agree more.

To physicists, the unreality of a temporally unextended yet persistent and continually changing present was brought home by the discovery of the relativity of simultaneity.

Very good. It's what I've been trying to say already quite a while.

For any two events A,B there exist two reference frames F_A and F_B and a third event C such that C is simultaneous with A in F_A and simultaneous with B in F_B. This "simultaneity by proxy" compels us to conceive of all parts of the spatiotemporal whole as coexistent and as equally real.

Case in point: If I assume that quantum mechanics is nothing but a tool for calculating the probabilities of possible outcomes given actual outcomes, then I can demonstrate that the spatiotemporal differentiation of reality doesn’t go "all the way down."

I agree with that. But I think that you can say more about it. Again, you don't HAVE to, but you can. Again, I don't mind seeing quantum theory as "just a tool to calculate probabilities of outcomes". I think it is the minimalistic version (the one that should adhered to when first being introduced to the theory). But I fail to see the refusal to try to make more sense of it.

Nothing in the world corresponds to a precise position or a sharp instant of time. We should therefore conceive of the world first and foremost as a whole. Our theoretical model of it should not be built on spacetime points or temporally unextended "nows" and spatial points, but instead should be built "from the top down," by a differentiation that Nature has not carried as far as conceivable.

Sure. That's what I call "the mathematical structure" that should correspond to the proposed ontology. I never said that it had to split into something that is "at an instant in time" or so.

Quantum mechanics thus agrees with special relativity in that it too is inconsistent with presentism: the view that only the continually changing present is real. Special relativity because of the relativity of simultaneity, and quantum mechanics because it implies that reality is not built up from infinitely thin successive presents but instead is an incompletely differentiated spatiotemporal whole.

Yes, I am with you here. That's why it is not simply the wavefunction, but the entire unitary structure which is that famous mathematical structure I like to refer to.

Now comes the punch line: if the world is an incompletely differentiated spatiotemporal whole, then determinism is out of the window.

I don't think so ; and, from the beginning, determinism has no issue here. By coincidence, the Schroedinger equation is deterministic, but that's no issue. I think you want to say that "dynamics" is out of the window. But I don't think that that is correct: after all, "dynamics" is nothing else but symmetries of the mathematical structure of nature "in the direction of what we experience as time", while what's usually called kinematics is more related to the symmetries of the mathematical structure "perpendicular" to what we call time.

Any theory postulating deterministic evolution presupposes the existence of a completely differentiated spacetime manifold. If that is a fiction, so is determinism.

I think you attach too much importance to the split between "state" and "evolution". It is a practical way of talking about the overall structure, just as "spacelike surface" and "world line" are practical ways of talking about spacetime.

I almost forgot to point out the difference between many worlds and many times. I am aware of the many times but not of the many worlds. Of course I am not simultaneously aware of the many times – that would be a contradiction in terms. But I have subjective evidence of the many times and no subjective evidence whatever of the many worlds. The problem of the apparent impossibility of objectifying the Technicolor reality of the experiential present (which deeply troubled Einstein) is therefore genuine. Your invocation of a multitude of coexistent worlds of which we are unaware, on the other hand, is a gratuitous solution of a pseudo-problem.

Well, I think you are seeing too much distinctions: I think that the "many times" and the "many worlds" are much more analogous concepts. But hey, I'm already very happy to talk with someone who SEES the issue of many times ; mostly I get the silly reaction that there are not many times, because t is the value of current time or something of the kind

I think both ideas are very similar in the following sense:
in the same way you can say that "you are only aware of "now" and other times simply don't exist ; history is simply an algorithm to calculate the present world, but the past doesn't exist", you can say that, of the many branches, only the one I live in, exists. But, in the same way as history has a clear influence on what is there today, you SOMETIMES have indications of the existence of the other branches. I gave in a parallel thread the example of the EPR style experiment: for me, this is the empirical verification that these branches exist. As I said there, if we wouldn't have had the entire discussion about local/non-local, and Einstein and Bell, I think that the EPR experiment would have been the best demonstration of the empirical evidence of parallel branches: namely of the quantum interference between two very macroscopic systems (namely Alice and Bob and their notebooks) which shows up in the EPR correlations.
Using locality and the spacelike separation, you allow for the phases of the two branches not to decohere, and when you bring them together again, you get an interference pattern ; in the same way as you get such a pattern when a lightbeam splits and comes together.

 

[CarlB]

As to MWI, I consider that it is the most evident interpretation of the *current mathematical formulation* of quantum theory as we know it ...

What is, in my eyes, an aberation, however, is to consider ontologies which GO AGAINST the mathematical structure of quantum theory. The projection postulate does such a thing. It violates unitarity, it violates Lorentz invariance, ...

Yes, these are true. Bohmian mechanics, an alternate ontology to the MWI that has been promoted by some damned smart guys, violates unitarity and, indeed, violates Lorentz invariance.

... and it isn't even specified WHEN it should be applied - you're left to your intuition to do so.

This is not at all true. This gets to the heart of the "many times" viewpoint, I think.

In the quantum ontology, wave functions apply to situations in an indefinite future. That is, they correspond to experiments that have not yet been performed. To collapse a wave function requires that one wait for the experiment to be done, which is a passage of time that is not modeled in either QM or relativity. I agree that the transition between the future and past (as opposed to the evolution of wave functions as the time coordinate in spacetime is changed either positively or negatively, or the evolution of particle positions evolves in a classical theory) is not modeled in any of these theories. But it is the existence of this gulf, the difference between the past and future, that makes relativity compatible with quantum mechanics. In short, they do not apply to the same region of OUR experience, as opposed to spacetime. If anything, the only indication the difference between these theories suggest is that the ontology of spacetime which is in the future of a given observer is different from the ontology of the spacetime which is in his past.

So the entire question is: will it be possible to conserve the superposition principle, and unitary dynamics, while unifying with gravity, or does one need a fundamental change of this entire machinery. In fact, (Penrose style thinking) gravity is the last hope of killing off unitarity (and hence opening the possibility of introducing the projection postulate as a dynamical phenomenon). Even Penrose, who is certainly not in favor of the MWI view, thinks that the MWI view is the _only sensible interpretation_ if quantum theory turns out to remain strictly unitary in the presence of gravity. Hence his hope that gravity will introduce a deviation from unitarity.

To unite the wave and particle of a given experiment in the sense of the mathematical ontology, one must put the particle description into a form which is the same. One does this by using a few simple tricks from Bohmian mechanics. These tricks allow one to write a version of Schroedinger's equation where the Heisenberg uncertainty principle is violated.

A student really should spend an hour or two trying to set up an initial condition for the Schroedinger wave equation that violates the HUP. One eventually discovers that the reason that it is impossible is because the amplitude and the phase are related. To separate them out, one must rewrite the Schroedinger equation in a way that splits the information that gives the probability density from the information that gives, in the Bohmian interpretation, the velocity field for the possible particle tracks. Having split these, one can add an extra parameter that changes the wave function from one that obeys the HUP to one that allows particles to be restricted to a Bohmian trajectory.

I think this is a lot more natural than the MWI, which requires great straining of intuition, and it preserves the (approximate) correctness of the ontology of QM and relativity.

By the way, I've just released my first great hope to get allowed onto Arxiv.org. It gives a prediction for the masses of the neutrinos from the Koide mass formula for the charged leptons:
http://brannenworks.com/MASSES.pdf

Carl

 

[koantum]

the notion of "present time" is only a construction of our subjective experience

I hesitate to use the word "construction". Like qualia, the experiential now defies objectification, true enough. But how, in what sense, does experience construct? I'd use the word for our theoretical activities; we construct theories with maths as our chief or only tool.

I don't mind seeing quantum theory as "just a tool to calculate probabilities of outcomes". I think it is the minimalistic version (the one that should adhered to when first being introduced to the theory). But I fail to see the refusal to try to make more sense of it.

I don’t refuse to do this. Quite the contrary. I'll return to this in a separate thread.
Next, I said if the world is an incompletely differentiated spatiotemporal whole, then determinism is out of the window, to which you replied

I don't think so ; and, from the beginning, determinism has no issue here. By coincidence, the Schroedinger equation is deterministic, but that's no issue.

Huh? Determinism is very much an issue. You believe in an ontology that evolves unitarily and therefore deterministically. I don't. Of course, omitting the term evolution and speaking of, say, a "unitarily structured spatiotemporal whole" leaves this issue untouched. Is this what you meant?
Next, I said that any theory postulating deterministic evolution presupposes the existence of a completely differentiated spacetime manifold. If the latter is an exploded myth, so is the former. Your response to this:

I think you attach too much importance to the split between "state" and "evolution". It is a practical way of talking about the overall structure

I agree, but this is beside the point. You can't have a deterministic evolution and a reality that is incompletely differentiated with respect to space and time. You can't have the cake and eat it too.

But hey, I'm already very happy to talk with someone who SEES the issue of many times ; mostly I get the silly reaction that there are not many times, because t is the value of current time or something of the kind

I know exactly what you mean.

you SOMETIMES have indications of the existence of the other branches.

If I am not mistaken, the world splitting of Everett's original MWI is as irreversible as the collapses of collapse theories (and therefore has the same measurement problem). If you allow re-interference, you aren’t really an Everettic; you are an existentialist à la Zurek, whose "existential interpretation" makes the consequences of "taking unitary evolution seriously" very clear. He arrives at a double relativity of "existence." One, existence is relative to branches: there is one for each branch. Two, the existence of a branch is relative rather than absolute: there can be more or less of it. The less a branch is capable of re-interference with other branches, the more it exists. This is the kind of "philosophy" that makes most physicists abhor philosophy.

"To tell you the truth, I think most of my colleagues are terrified of talking to philosophers - like being caught coming out of a pornographic cinema." (Max Tegmark, University of Pennsylvania)​

My assessment of Zurek's interpretation can be found at http://in.arxiv.org/abs/quant-ph/0401179" or in the International Journal of Quantum Information 2(2), 201-220, 2004.

mathematical structures are the only things of which we can make sense, apart from our qualia

Come on! You have never read a book, seen a movie, listened to a piece of music that made a lot of sense? If you did, then please show me how you reduce it to maths and qualia.

"Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover." - http://plato.stanford.edu/entries/russell/"​

As to MWI, I consider that it is the most evident interpretation of the *current mathematical formulation* of quantum theory

Rather, the most simple-minded interpretation.

What is, in my eyes, an aberation, however, is to consider ontologies which GO AGAINST the mathematical structure of quantum theory. The projection postulate does such a thing.

There I agree. If quantum mechanics only correlates measurement outcomes, you don’t need collapsible wave functions.

if you leave out projection (and HENCE place yourself in an MWI context)

That's a non sequitur.

 

[koantum]

In quantum ontology, wave functions apply to situations in an indefinite future. That is, they correspond to experiments that have not yet been performed.

Careful! The Born rule is time-symmetric in that it allows us to assign posterior probabilities (probabilities of possible outcomes of earlier measurements on the basis of later outcomes) as well as prior probabilities (probabilities of possible outcomes of later measurements on the basis of earlier outcomes). Quantum mechanics even allows us to assign probabilities that are time-symmetric in the sense that they are assigned on the basis of later as well as earlier outcomes. For this you need to use the ABL rule (after Aharonov, Bergmann, and Lebowitz) instead of the Born rule. Take a look at my paper on the time-symmetry of quantum mechanics (http://in.arxiv.org/abs/quant-ph/0006116" , American Journal of Physics 69, 864-873, August 2001). This symmetry of the formalism is spoilt by every interpretation that gives more importance to quantum states evolving from past to future than to quantum states evolving from future to past.

 

[CarlB]

Careful! The Born rule is time-symmetric in that it allows us to assign posterior probabilities (probabilities of possible outcomes of earlier measurements on the basis of later outcomes) as well as prior probabilities (probabilities of possible outcomes of later measurements on the basis of earlier outcomes).

My point is that there is an obvious ontology for splitting the domain of relativity and quantum mechanics, one that is compatible with common sense and provides a natural arrow of time. I don't mean to suggest that this is the unique interpretation compatible with quantum mechanics. What I'm saying here is that if one restricts the domains of these two theories, the incompatibility between them disappears. I don't mean to say that either theory is particularly fond of having its domain restricted, just that the two theories are not, in themselves, incompatible with common sense.

Oh, there are issues when you try to split spacetime into two domains, past and future, this way because the split itself defines a preferred reference frame, but the assumption of no preferred reference frame is also in violation of common sense. Adding an (apparently) undetectable preferred reference frame to special relativity changes absolutely (pun) no predictions of the theory and therefore does the theory no great damage. except in the eyes of those who prefer purity in their physics to common sense. To me, relativity is a guide to indicate when a physical prediction is incompatible with known observations, not something that rules out a preferred reference frame. I think that Lorentz symmetry is an accidental symmetry, not a true part of nature, and I expect to live long enough to see it experimentally disproved.

By the way, I love your writing and point of view on QM, and have downloaded all 20 of your arxiv papers. I look forward with great joy to reading them at my leisure. If there is something I'm missing elsewhere, some articles that didn't make it to arxiv, please do point me.

Carl

 

[koantum]

Adding an (apparently) undetectable preferred reference frame to special relativity changes absolutely (pun) no predictions of the theory and therefore does the theory no great damage.

But what do you gain by this?

If there is something I'm missing elsewhere, some articles that didn't make it to arxiv, please do point me.

You find a complete list of my papers at http://thisquantumworld.com/papers.htm" . Those you don't find in the arxiv are rather more philosophical and less commonsensical, I'm afraid.

 

[koantum]

This is just to tell you that I have started https://www.physicsforums.com/showpost.php?p=956010&postcount=1".

 

[koantum]

could you please expand a bit more the idea of the world as an "incompletely differentiated spatiotemporal whole"?

I'll get to it in https://www.physicsforums.com/showpost.php?p=956010&postcount=1"what you're looking for.

 

[vanesch]

I hesitate to use the word "construction". Like qualia, the experiential now defies objectification, true enough. But how, in what sense, does experience construct? I'd use the word for our theoretical activities; we construct theories with maths as our chief or only tool.

I agree, the word "constructed" was poorly chosen ; sometimes I quickly type a response in between playing with the kid, making dinner and talking to my wife

Huh? Determinism is very much an issue. You believe in an ontology that evolves unitarily and therefore deterministically. I don't. Of course, omitting the term evolution and speaking of, say, a "unitarily structured spatiotemporal whole" leaves this issue untouched. Is this what you meant?

Yes. And for us, "temporaly oriented beings", it is convenient to split this in "state" and "evolution", but indeed, I mean the entire structure. As such, there's no difference between, say, the Heisenberg and the Schroedinger view.

I agree, but this is beside the point. You can't have a deterministic evolution and a reality that is incompletely differentiated with respect to space and time. You can't have the cake and eat it too.

I don't know. Imagine a sphere in 3 dimensions, and consider this sphere as an "incompletely differentiated object with respect to the xy and the z axis". I can write down a deterministic evolution equation that "evolves" each xy slice of the sphere in its next slice, along the z-axis, up to one ambiguity, which is, whether we're in the lower or the upper half of the sphere.

If I am not mistaken, the world splitting of Everett's original MWI is as irreversible as the collapses of collapse theories (and therefore has the same measurement problem). If you allow re-interference, you aren’t really an Everettic; you are an existentialist à la Zurek, whose "existential interpretation" makes the consequences of "taking unitary evolution seriously" very clear. He arrives at a double relativity of "existence." One, existence is relative to branches: there is one for each branch. Two, the existence of a branch is relative rather than absolute: there can be more or less of it. The less a branch is capable of re-interference with other branches, the more it exists. This is the kind of "philosophy" that makes most physicists abhor philosophy.

I put all these variants under the MWI denomination - I didn't even hear about this particular |school". For me, MWI is when you give some ontological status to the mathematics of the unitary part of quantum theory, and you refuse to introduce collapse as a physical phenomenon - which leads to the "existence of all possible outcomes" and then you need to fiddle around with conscious observation in one way or another to say that you only "experience one" of these outcomes. There's a multitude of variations on the concept, the differentiation of which I do not find very illuminating.

As to your original point of "irreversibility" of branching: I'd say that a priori, it is just as "reversible" (the fusion of two branches into one) as is the reversibility in classical physics:
If say,
|bob1>|u> evolves into |bob0>|w>
and
|bob2>|v> evolves into |bob0>|y>

then the two "bob" branches
a |bob1>|u> + b |bob2>|v>

evolve into
|bob0> (a |w> + b |y>)

Of course, now, bob0 doesn't remember from which branch "he came", so nothing unusual !

But, just as in the case of classical physics, it is not because this is in principle possible that we happen to live "that part of the evolution" as to witness it - in exactly the same way as irreversibility in classical physics".

"To tell you the truth, I think most of my colleagues are terrified of talking to philosophers - like being caught coming out of a pornographic cinema." (Max Tegmark, University of Pennsylvania)​

I think it has more to do with a kind of "macho" culture together with a lack of education of physicists. I've been there too, you know. Got straightened up by my wife, who's a classicist.

"Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover." - http://plato.stanford.edu/entries/russell/"​

Yes. That's about what I meant. We can only abstractly (once we do away with all intuition, qualia,...) talk about mathematical constructions. As an ontology is an abstract construction which we invent to explain our subjective experiences, I don't see what it can be outside of this.

cheers,
Patrick.

 

[CarlB]

But what do you gain by this?

As I mentioned, one needs some sort of split in order to distinguish between a region of spacetime over which QM has domain (i.e. the future), while still keeping the other to be covered by the usual intuition of point particles. One also gains the ability to consider theories that violate Lorentz symmetry.

Thanks for the extra articles, which I am sure I will enjoy as I did the Bhagavad Gita so many years ago.

Carl

 

[koantum]

Hi Patrick (aka vanesch),
I said: "You can't have a deterministic evolution and a reality that is incompletely differentiated with respect to space and time." Your response was "I don't know." Haven't thought of it, eh? Well, I intend to be more explicit in the "promises to keep" tread, where you'll get a second chance.

For me, MWI is when you give some ontological status to the mathematics of the unitary part of quantum theory, and you refuse to introduce collapse as a physical phenomenon - which leads to the "existence of all possible outcomes" and then you need to fiddle around with conscious observation in one way or another to say that you only "experience one" of these outcomes. There's a multitude of variations on the concept, the differentiation of which I do not find very illuminating.

In other words, you live in the faith that all problems arising from this conception will in the end be solved one way or the other. What you do not find very illuminating is attempts to solve these problems or to expose the absurdity of that conception by ferreting out its absurd consequences. I call this playing the ostrich.

As to your original point of "irreversibility" of branching: I'd say that a priori, it is just as "reversible" (the fusion of two branches into one) as is the reversibility in classical physics

This is what compels Zurek to deny that each branch exists in an absolute, unqualified sense.

Russell: Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.
You: Yes. That's about what I meant. We can only abstractly (once we do away with all intuition, qualia,...) talk about mathematical constructions.

Why do you want to do away with all intuition, qualia,…? If we admit only quantities then we can only talk about quantities. That's rather boring, I'd say. What does you wife think? Do you belong to the old school according to which qualities are nothing but quantities? I, for one, belong to a school to which quantities are nothing but means of manifesting or realizing qualities. I do not want to reduce everything to physics. I want to understand physics in the context of a whole that includes much more than physics.

an ontology is an abstract construction which we invent to explain our subjective experiences

This is a very narrow (and I'd say rather silly) definition of ontology. You need to explain happiness mathematically?

The very best,
Ulrich

 

[vanesch]

Why do you want to do away with all intuition, qualia,…?

I think you misunderstood me: there is, on one side, the world of qualia, of your subjective experiences. It's the one we know that exists. And then, on the other hand, we tend to set up a mental construction of which we postulate the existence, in order to organize our qualia: that's the ontology. So of course your qualia cannot be involved in the construction of your ontology ! Your ontology needs to be their *explanation*. As this is an abstract mental construction, I do not see what it can be else but a mathematical object, given that it must be an abstract mental construction. I don't know of any OTHER abstract mental constructions.

It is this dichotomy between constructed ontology and subjective experience which makes me reject your idea of "taking measurements as starting positions" if you do not identify "measurements" with "subjective experiences".

If we admit only quantities then we can only talk about quantities. That's rather boring, I'd say. What does you wife think? Do you belong to the old school according to which qualities are nothing but quantities? I, for one, belong to a school to which quantities are nothing but means of manifesting or realizing qualities. I do not want to reduce everything to physics. I want to understand physics in the context of a whole that includes much more than physics.

Ah, that's a fundamental difference then. I think that everything, except for our subjective experiences, is physics, and that even our subjective experiences are *derivable* from physics, although they cannot be part of it of course. That's why I'm a reductionist in heart and bones.
I know not everybody shares this idea with me, but I take it as the *definition* of physics.

This is a very narrow (and I'd say rather silly) definition of ontology. You need to explain happiness mathematically?

Well, I'd say that happiness is first of all a subjective experience, and hence does not belong to an ontological description ; but that we'd rather POSTULATE an ontology from which we can eventually derive our "experience of happiness", given an appropriate rule which will be outside of the ontology proper. So, there will be an ontological ORIGIN of my or your happiness, which will find its origin probably in some neurological state. The very fact that this neurological state will be related to the subjective experience of "happiness" will, IMO, always be something that remains outside of an ontological description itself: I don't think we will ever have a *theory* that will allow us to deduce which matter states are related to "an experience of happiness". But we might find out, by experiment, that specific matter states of the human brain lead to subjects who declare "being happy".

But in any case, to be able to tell exactly what these states are, you need to symbolise these brainstates abstractly, and I don't see how you can do this without making it into a mathematical object. That was the idea. Now, "happiness" is probably a very complicated concept. Let's start with "seeing a red light flash".