Quantum myth 4: The only reality is the measured reality

[Hurkyl]

Easy to say, but what is the physical mechanism for the split?

I don't understand the question -- AFAIK, unitary evolution is fundamental in the usual formulations of quantum mechanics, so it doesn't make sense to ask for the physical mechanism behind it. (Make sure you don't fall into the trap of infinite regress! Nor into the trap of letting aesthetics dictate the physics)

Where does the energy come from that causes the split?

Why would splitting need energy?

 

[Demystifier]

Demystifier. Ok, I'll be listening, because I really want to know what you think. As I struggle to repair the state of mechanics as it lays today, how might I apply Ocaam's Razor?

Can you rephrase your question? I have no idea what exactly do you ask me.

 

[Phycho]

Hurkyl, you've turned over to MWI proponent?

I'd say if theu niverse made copies of it self each split it would need infinite energy, yes, defendable position ? hell no

 

[Hurkyl]

I'd say if theu niverse made copies of it self each split it would need infinite energy

When you say 'copies itself', do you mean it sort of like passing the universe through a copy machine to produce a Star Trek-like parallel universe? If so, then there's no problem, because that has nothing to do with MWI.

 

[peter0302]

Every time you add a new degree of freedom, you need more energy. It's basic thermodynamics.

 

[Phrak]

Hurkyl- If I may paraphrase, what you are saying is that in the MWI, there is no physical splitting. Instead, for any system of particles, the wave equation of the system evolves unitarily. Is this correct? Though I suppose there may be more than one MWI interpretation.

-Demystifier. Sorry, it was a poor question on my part.

 

[Phycho]

When you say 'copies itself', do you mean it sort of like passing the universe through a copy machine to produce a Star Trek-like parallel universe? If so, then there's no problem, because that has nothing to do with MWI.

Hehe, I mean more, if a particle splits, it copies itself if this is true on a macroscopic scale.
Every second there are copies of you splitting off to other universes.
Is this the MWInterpretation you support?

 

[peter0302]

What other MWInterpretation is there?

Perhaps the argument is over semantics (it usually is with people here). Each possible state of a particle has a particular probability amplitude - you might think of this as its "thickness." If there are two equal possibilities, both states are 50% as thick as the state from which the possibilities originated. And so forth. They split ad inifnitum.

So it's not as though "copies" are being made, so much as you're taking a hologram and dividing it in two (as you may or may not know, when you cut a hologram in half you get two copies of the same image, though you can view less of it in each one).

I think Hurkyl's argument is that since you're splitting - not copying - there's no energy problem. But that doesn't solve the basic thermodynamics issue that every time you add a new degree of freedom you need more energy, and there's no question that every quantum possibility is a new degree of freedom - and they quickly accumulate at gigantic rates - and so, it would seem, would the energy requirements.

 

[Hans de Vries]

and they quickly accumulate at gigantic rates -

If the universe would split each 3.10^-25 second (say, the lifetime of the Z-boson) in
two, then we would have something like 10^(10²⁴) parallel universes after 1 second.

Written out in decimal (with 500 digits/meter) this is a number with a length of
circa 60,000 light years. Each further second the length of this written number,
giving the total amount of parallel universes, becomes longer by 60,000 light years.

That is, the length of the written number describing the count of different parallel
universes would grow with a speed of 2000 billion times the speed of light... Regards, Hans

 

[Hurkyl]

Hurkyl- If I may paraphrase, what you are saying is that in the MWI, there is no physical splitting. Instead, for any system of particles, the wave equation of the system evolves unitarily. Is this correct?

Yes. When MWI uses the term "splitting", it is describing a behavior that a unitarily evolving system can demonstrate. The same is true of terms like "parallel universes".

I think a good example would be based on the famous experiment with a photon and half-silvered mirrors. After striking the first half-silvered mirror, there is one "world" with a photon in a superposition of being reflected and transmitted. This photon can self-interfere, and we find that the photon is guaranteed to reach detector 2.

Now, if the photon somehow interacted thermodynamically with the environment between the first and last mirror (thus destroying its coherence), it will have "split", and we now have two "parallel worlds", one where the photon was reflected, and one where the photon was transmitted. The photon can no longer self-interfere, so when it strikes the second mirror, it will go to either detector with equal probability.

(We could force a thermodynamic interaction by, for example, putting a device along one path that measures whether or not the photon took that path)

Hehe, I mean more, if a particle splits, it copies itself if this is true on a macroscopic scale.
Every second there are copies of you splitting off to other universes.
Is this the MWInterpretation you support?

If you mean "copy" like a copy machine in which you started with one particle and now have two particles, then I'm not aware of that being any flavor of the many-worlds interpretation.

I think Hurkyl's argument is that since you're splitting - not copying - there's no energy problem. But that doesn't solve the basic thermodynamics issue that every time you add a new degree of freedom you need more energy, and there's no question that every quantum possibility is a new degree of freedom - and they quickly accumulate at gigantic rates - and so, it would seem, would the energy requirements.

I know that splitting is closely related to quantum thermodynamics (one buzzword: decoherence); splitting is supposed to be an irreversible process, which is only possible in the thermodynamic sense. (because unitary evolution is always theoretically reversible, even if not practical) Unfortunately, that statement nearly exhausts my hard knowledge about quantum thermodynamics.

 

[Phrak]

Yes. When MWI uses the term "splitting", it is describing a behavior that a unitarily evolving system can demonstrate. The same is true of terms like "parallel universes".

I think a good example would be based on the famous experiment with a photon and half-silvered mirrors. After striking the first half-silvered mirror, there is one "world" with a photon in a superposition of being reflected and transmitted. This photon can self-interfere, and we find that the photon is guaranteed to reach detector 2.

Now, if the photon somehow interacted thermodynamically with the environment between the first and last mirror (thus destroying its coherence), it will have "split", and we now have two "parallel worlds", one where the photon was reflected, and one where the photon was transmitted. The photon can no longer self-interfere, so when it strikes the second mirror, it will go to either detector with equal probability.

Thanks Hurkyl. But the truth is, now I'm really confused. MWI seems to recognize two distinct processes. The first, unitary evolution, or what might be called causal evolution, if I'm not abusing terminology. Secondly, splitting, a result of decoherence. What I'm getting at, here, is that decoherence is not recognized as causal evolution of the larger system consisting of particle plus environment, right?

 

[Hurkyl]

What I'm getting at, here, is that decoherence is not recognized as causal evolution of the larger system consisting of particle plus environment, right?

Actually, that's the neat part: decoherence is the result of ordinary unitary evolution of the particle + environment system!

 

[reilly]

Yes. When MWI uses the term "splitting", it is describing a behavior that a unitarily evolving system can demonstrate. The same is true of terms like "parallel universes".

I think a good example would be based on the famous experiment with a photon and half-silvered mirrors. After striking the first half-silvered mirror, there is one "world" with a photon in a superposition of being reflected and transmitted. This photon can self-interfere, and we find that the photon is guaranteed to reach detector 2.

Now, if the photon somehow interacted thermodynamically with the environment between the first and last mirror (thus destroying its coherence), it will have "split", and we now have two "parallel worlds", one where the photon was reflected, and one where the photon was transmitted. The photon can no longer self-interfere, so when it strikes the second mirror, it will go to either detector with equal probability.

You are describing a standard probability chain -- they have been used for many years without any ascription of reality to individual branches -- except in science fiction stories --. Why bother, when Hans has noted, conservatively, the description of the MWI universe defies physics, not to mention common sense. Where are these universes? In what sense are they real?

If, somehow, they are real, then what about inter-universe dynamics? Why not a subset of universes that conspire to create a superconducting super-universe? It all sounds to me like:if you can imagine it, it is real. But then, I could imagine that what I imagined is real isn't real. (Note that all this imagining is the direct result of physical processes, so clearly our individual rates of creating alternate universes go on unabated into mathematical territories , largely-yet- to- be -explored by humans. Think topological nightmares, non-separable subspaces, regions where the Axiom of Choice holds; regions where it does not. If I can think it, it's real, or is it?

And, by the way, is the one photon world you mention above, just one, or is it many worlds, all differing by slightly different molecular configurations of the silvered screen, differing by traffic patterns in New York City, differing by whether at cash register 12 in Store 18 in Rochester NY, Ralph asks for paper or plastic.

In fact, for the silvered screen and photon, there are huge numbers of possibilities. That is, we are effectively dealing with a scattering problem with, well more than 10^^23 target silver atoms. If we look just at the infrared portion of the emission spectrum of the silver atoms, we'll find that each atom has a probability to emit none to, say, 10^^(10^^10) or more low energy photons -- Poisson process and all that -- in any time interval you want. So, there are an arbitrarily large number of "universes" for the "one " universe; typical of Poisson processes of Poisson processes of ... Is it not the height of irony, that MWI can only be realistically described by statistical methods -- those pesky Poisson processes certainly mess things up.
Regards,
Reilly

 

[Hurkyl]

You are describing a standard probability chain -- they have been used for many years

I'm not familiar with the term "probability chain" in this context, but your comment is entirely unsurprising. The MWI invokes no new physics -- it merely uses a subset of existing physics -- it is only natural to expect its features to be familiar from other contexts.

without any ascription of reality to individual branches

I'm quite aware that there are many interpretations of quantum mechanics.

-- except in science fiction stories --. Why bother, when Hans has noted, conservatively, the description of the MWI universe defies physics, not to mention common sense. Where are these universes? In what sense are they real?

I thought we were talking about MWI. Why are you talking about science fiction?

If, somehow, they are real, then what about inter-universe dynamics?

They interact exactly as specified by unitary evolution. Observable effects are incredibly rare for conceptually the exact same reason that you never observe a vacuum spontaneously appear in your kitchen because all of the air evacuated into the living room: it's just too unlikely.

Why not a subset of universes that conspire to create a superconducting super-universe?

I can make neither heads nor tails of this question.

It all sounds to me like:if you can imagine it, it is real.

Let me know when you're done talking about science fiction.

Is it not the height of irony, that MWI can only be realistically described by statistical methods

I'm confused; quantum thermodynamics is the very foundation of the MWI! The whole idea is that quantum decoherence (a statistical phenomenon) closely approximates the effects of wavefunction collapse, thus obviating the need for using collapse in quantum mechanics. I don't understand how it could possibly be ironic that 'MWI can only be realistically described by statistical methods'.

 

[peter0302]

Reilly, it's odd that you would have so much hostility toward MWI when you yourself believe that consciousness causes wavefunction collapse, which is no less outlandish than MWI.

In general it's funny to watch all the different people argue over their interpretations. The only sensible interpretation is that we don't know until we can find an experiment to disprove one or the other. That's what we should be arguing about. Not whether something sounds like science fiction or not.

 

[GiZeHy]

Hi folks,

i am happy to see people in this thread, who are engaged with quantum physics and ask themselves kind of philosophical questions, because i believe that this is the main drive for many of us to understand how the universe, and all within it, behaves.

To approach the main question of the thread we must combine the knowledge of all sciences. It really is quite naive to argue that there is no reality beside the measured one. In fact, if one is intensely thinking about it, there is no direct answer to this question. I can only deduce it from experiences in this so called reality.

The main conflict thinking about it is that physics is a science to explain incidents that are measurable. It is the same with quantum physics. But how do you know that something does not exist when you cannot measure it? If one is getting results concerning a certain experiment, it does not mean that there are no other influences. Imagine that gravity cannot be explained in detail. We only create formulas of what we experience. With a grand united theory these will be expanded and used in another way.
(Beside: What about different realities because of different outcomes of experiments? Think about the particle/wave conflict. I think it is blowing enough minds that beholding an experiment or not affects the result of it)

Actually one could equate the measurements with experiences of a conscious mind, because the measurements are only a tool to enhance the perception of the senses. Think of a child and its reality. Is is aware of quarks, atoms, molecules, their forces and interactions and so on? No...probably not ;) Does it exist? What if everything exists but we cannot measure it, what if it only exists because we built something that is able to measure it? We see that there are many aspects to consider concerning this kind of question.

 

[Hans de Vries]

I'm not familiar with the term "probability chain" in this context, but your comment is entirely unsurprising. The MWI invokes no new physics -- it merely uses a subset of existing physics -- it is only natural to expect its features to be familiar from other contexts.

I'm quite aware that there are many interpretations of quantum mechanics.

Isn't the idea of an interpretation of quantum mechanics to find the underlaying
physics which produces the effects we see? So it *should* be new physics...

I thought we were talking about MWI. Why are you talking about science fiction?

Ok, but when people are freely talking about other, parallel, universes in which supposedly
they can have other jobs, partners or children, you can expect such associations with
science fiction.
And all these stories are simply the logical consequence of the definition of MWI
you just gave two posts back, that is, all possible quantum outcomes continue to
exist in one of a countless number of parallel universes.If you are a specific mix of genes of both your parents, then all kind of other gene mixes
similar to you would live in other universes. All theoretically possible mutations during the
evolution of species on Earth would live somewhere, separated into countless universes.
There are human like creatures with wings somewhere, mermaids, centaurs, they would
all exist in their own universe, parallel to us in the same space time.

This all is just the direct consequence of the elementary definition of MWI which states
that all possible quantum outcomes continue to exist in one of a countless number
of parallel universes.

And all these universes live in the same space/time in superposition and are non-interacting.
They can interact until they decohere, but we are not in danger of being hit by an SUV
driven by an intelligent dinosaur in a universe where they didn't mass-extinct.

How does such a superposition work at all? There's nothing like that known or observed
in current physics. All fields in a specific universe must be "labeled" with a unique label
which tells fields belonging to another universe that they should not interfere.

What if something goes wrong here and two different universes end up with the same
"label", Fields of different universes will interfere and in such a case you can run into
an SUV driven by a dinosaur.Does this all sound strange? yes, of course it sounds strange, but it's just the logical
consequence of taking MWI serious... Regards, Hans.

 

[Phrak]

Reilly, it's odd that you would have so much hostility toward MWI when you yourself believe that consciousness causes wavefunction collapse, which is no less outlandish than MWI.

In general it's funny to watch all the different people argue over their interpretations. The only sensible interpretation is that we don't know until we can find an experiment to disprove one or the other. That's what we should be arguing about. Not whether something sounds like science fiction or not.

Additionally, it should not come as a surprise that, if the practice of scientific inquiry in physics is a sound means of discovering true things, it should lead to propositions that cannot be answered as either true or false.

In fact, I think it could be successfully argued, that if advances in physics do not lead to questions that cannot be formally answered, it should be in search of repair.

[ / waxing philosophical off]

 

[Hurkyl]

Isn't the idea of an interpretation of quantum mechanics to find the underlaying
physics which produces the effects we see? So it *should* be new physics...

The idea of an interpretation of quantum mechancs is no more and no less than a method to connect the mathematical theory with something else (usually the 'real world'). And the main point of MWI is that unitary evolution appears to be sufficient to produce all quantum effects we see. (in particular, there is no need to further postulate a wavefunction collapse)

And one point that people seem to be fond of overlooking -- even if one adopts a different metaphysical philosophy about quantum mechanics, MWI is still a useful description of unitary evolution during the events where it does happen uninterrupted.

Ok, but when people are freely talking about other, parallel, universes in which supposedly
they can have other jobs, partners or children, you can expect such associations with
science fiction.

Given any science, you can expect associations with science fiction. If you want to levy criticism on MWI, it's your job to make sure you know what you're talking about. (in particular, it's not other peoples' job to educate the rest of the world so they stop confusing you about what MWI really means)

And all these stories are simply the logical consequence of the definition of MWI
you just gave two posts back, that is, all possible quantum outcomes continue to
exist in one of a countless number of parallel universes.

Only in the sense that collapse (as postulated by CI) does not occur. MWI doesn't talk about anything that wasn't already present in the quantum state space.

There are human like
creatures with wings somewhere, mermaids, centaurs, they all exist in their own universe.

Assuming such things are actually physically possible, of course. (And assuming you don't mean 'their own universe' in a Star Trek sense)

How does such a superposition work at all? There's nothing like that known or observed
in current physics.

Yes there is -- it's right there in the Hilbert space.

All fields in a specific universe must be "labeled" with a unique label
which tells fields belonging to another universe that they should not interfere.

The "labels" on the components of a specific subsystem are how (and if) it is entangled with the environment.

What if something goes wrong here and two different universes end up with the same
"label", Fields of different universes will interfere and in such a case you can run into
an SUV driven by a dinosaur.

Does this all sound strange? yes, of course it sounds strange, but it's just the logical
consequence of taking MWI serious...

Please elaborate upon how that is a 'logical consequence of taking MWI serious[ly]'. I'm having great difficulty imagining how interference (as governed by the ordinary unitary evolution of quantum mechanics) could lead to such a 'merging' of 'universes' as you describe, and I'm having even greater difficulty imagining how it could lead to a 'universe' in which dinosaurs simultaneously went extinct and did not go extinct. Neither of these appear to be a possible outcome of a global-scale quantum erasure event.

 

[Phrak]

Actually, that's the neat part: decoherence is the result of ordinary unitary evolution of the particle + environment system!

This is different than I expected. The explanations of MWI I've previously encountered were significantly different, and usually invoked "splitting" as a single bifercation. All very suspicious from the beginning and carrying a bit more metaphysics. No mention was ever made of interference between 'worlds'. Thanks for the clarification.

In principle, then, decoherence is a reversible process; as much so as thermodymanic processes are reversible, if not feasibly reversible. I think, to further clarify things the observer should be evaluated as part of the measuring process.

To make things as simple as possible, I'd want to see how two different 'toy observers' record the result measuring spin. One observer would be a von neumann reversible logic element, and the other a thermodynamic logic element, such as in artificial neuro-networks, and computers where entropy necessarily increases with each change of state.

 

[Hans de Vries]

How does such a superposition work at all? There's nothing like that known or observed
in current physics. All fields in a specific universe must be "labeled" with a unique label
which tells fields belonging to another universe that they should not interfere.

Yes there is -- it's right there in the Hilbert space.

No real world physical Hilbert space will work here, There are way to many parallel
universes. Superposition requires distinguishing between different orthogonal states.
How do you distinguish between two photons if their wavelength differs less than
Planck's length?

Why doesn't Pauli's exclusion principle work anymore if two electron's are virtually
in the same state at the same place, but said to be in "different universes"?

Why don't two electrons at the same place repel each other anymore? Decoherence?
can't be. It has nothing to do with interaction terms. New physics is required to explain
this.

The "labels" on the components of a specific subsystem are how (and if) it is entangled with the environment.

Entanglement requires a common location in the past where the entanglement is
established. How can a photon which is split of (into another universe) go trough
the wall in our universe and hit the wall in its own universe. The particles in the
wall can not be entangled differently with the photon because of the definition
of entanglement.

Please elaborate upon how that is a 'logical consequence of taking MWI serious[ly]'. I'm having great difficulty imagining how interference (as governed by the ordinary unitary evolution of quantum mechanics) could lead to such a 'merging' of 'universes' as you describe

That's not the problem. The problem is to imagine why parallel universes, which
exist simultaneously in the same space, don't interact or interfere at all. What is the
physical mechanism which allows them to differentiate between each other so that
all the laws of physics are overruled and nothing happens anymore.

Then, the pragmatic question is how this hypothetical mechanism can be so perfect
that it never goes wrong, even if the number of different parallel universes must be
something like 10^(10^(10^...)))

Each particle in our universe lives at the same space and time as 10^(10^(10^...)))
other particles but somehow it can distinguish between the ones with which it should
interact and the ones with which it should not interact, and all of this should never
go wrong...Regards, Hans

 

[Hurkyl]

To make things as simple as possible, I'd want to see how two different 'toy observers' record the result measuring spin. One observer would be a von neumann reversible logic element,

I've always thought a CNOT gate is the perfect example of this. A CNOT gate is a gate that operates upon a pair of qubits, enacting the following transformation (written in the 0-1 basis):

$$\text{CNOT} | x, y \rangle = | x, y \oplus x \rangle$$
(where $\oplus$ means addition modulo 2; i.e. $1 \oplus 1 = 0$)

If you have a CNOT that works with a photon spin as its first input, then you can perform a measurement as follows:

(1) Initialize a qubit to $| 0 \rangle$ and feed it into the second input
(2) Take your photon and feed it into the first input
(3) Pass them through the CNOT gate
(4) Let the photon continue on its way
(5) Your qubit now contains the spin of the photon

This does have the basic expected properties of a measurement: if we just look at the relative state of the photon (i.e. the partial trace of the joint state down to the photon's state), this procedure would cause it to transition from the state $\alpha | 0 \rangle + \beta |1 \rangle$ into a statistical mixture of $|0\rangle$ with probability $|\alpha|^2$ and $|1\rangle$ with probability $|\beta|^2$. And since it is in a mixture rather than a coherent superposition, the $|0 \rangle$ and $|1 \rangle$ states cannot self-interfere.

Computing this explicitly via density matrices, the input state is

$$\left( \begin{array}{cc}{ |\alpha|^2 & a b^* \\ a^* b & |\beta|^2 \end{array} \right) \otimes \left( \begin{array}{cc}{ 1 & 0 \\ 0 & 0 \end{array} \right) = \left( \begin{array}{cccc}{ |\alpha|^2 & 0 & a b^* & 0 \\ 0 & 0 & 0 & 0 \\ a^* b & 0 & |\beta|^2 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right)$$

After applying the CNOT gate, we get

$$\left( \begin{array}{cccc}{ |\alpha|^2 & 0 & 0 & a b^* \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0\\ a^* b & 0 & 0 & |\beta|^2 \end{array} \right)$$

Finally, taking the partial trace yields

$$\left( \begin{array}{cc}{ |\alpha|^2 & 0 \\ 0 & |\beta|^2 \end{array} \right)$$

But now, if we have good control over everything, we can cause our qubit to interact with the photon again in the same way via another CNOT gate. Since the composition of two CNOT gates is a no-operation, this would erase the measurement and restore the coherence of the superposition.

and the other a thermodynamic logic element, such as in artificial neuro-networks, and computers where entropy necessarily increases with each change of state.

Let's stick with this simple example; we can use our CNOT gate to build something like a classical XOR gate as follows:

(1) Tie the two input bits into the XOR gate.
(2) Pass the bits through the XOR gate.
(3) Radiate the first bit into the environment as heat

The remaining bit is now the XOR of the two input bits, and unless we have Maxwell demonesque powers to manipulate the environment, we are unable to reverse the operation.

 

[Hurkyl]

Hans de Vries: Look up the term 'mixed state'.

 

[reilly]

Reilly, it's odd that you would have so much hostility toward MWI when you yourself believe that consciousness causes wavefunction collapse, which is no less outlandish than MWI.

In general it's funny to watch all the different people argue over their interpretations. The only sensible interpretation is that we don't know until we can find an experiment to disprove one or the other. That's what we should be arguing about. Not whether something sounds like science fiction or not.

Peter -- I'm pressed for time, but as politicians are won't to say. let me be perfectly clear that I do not for a minute believe that consciousness causes wave-function collapse.

But, collapse does occur by means of well-known physical processes in the brain -- this is basic neuroscience. Further, there's a long history in many fields that use probability and statistics of precisely this notion of collapse, although the word "collapse" is not used. In fact, for example,this approach is commonplace in market research, applied economics if you will -- a field in which I worked for many years. Typically one says, "you don't know, then you know"; a physicist might well say that the probability, say to buy a Chevy SUV, collapses upon purchase of same.

Thats why I believe in practical Copenhagen, Schrodinger+Born; to me this implies standard probability theory, as used in many disciplines. Peierls discussed this knowledge interpretation many years ago, and it seems to me that his interpretation, to which I subscribe, is completely consistent with what neurosciance tells us about how we perceive and know.

The only sensible interpretation, in my opinion, is one that works in a consistent fashion. For example, we interpret electrical and magnetic forces as being caused by fields -- that's an interpretation that works quite nicely -- note that we don't know directly, for sure, what happens when two charges are very close. But our intepretation suggests that, classically at least, 1/r is the correct potential, and that we can in interpret delta functions as point charge distributions.

The issue, it seems to me, is there collapse in addition to neural collapse? Again, neural collapse occurs; there is absolutely no doubt about it.
Regards,
Reilly

PS -- Science fiction? To me, that's exactly what MWI is. Again, as Hans and I have pointed out, we do not have the mathematics nor the language to give a rigorous account of MWI.

Probability chains are simply a description of the branching due to conditional probabilities -- used in portfolio analysis, strategic planning -- business and military --quality control; decision theory in general, human factors work, ... MWI is precisely formulated as a probability chain.

 

[Hurkyl]

PS -- Science fiction? To me, that's exactly what MWI is.

Then please stop posting. If you prefer not to talk about MWI, but instead about cartoony sci-fi bastardizations of it, then do so elsewhere.

Again, as Hans and I have pointed out, we do not have the mathematics nor the language to give a rigorous account of MWI.

Please remind me how that went. I seem to recall you spent most of your effort recounting fanciful "everything you can imagine is true" science fiction fantasies and marveling over thermodynamics. You briefly asked about dynamics (which is precisely the familiar unitary evolution of quantum mechanics) so if that is the content of your accusation of lack of rigour, then it is rather disingenious to post as if it is MWI you are criticizing, which instead you are criticizing quantum mechanics as a whole.

As for Hans, all he seems to be doing is demonstrating a lack of knowledge of the dynamics of mixed states.

MWI is concerned only with the analysis of the unitary evolution of quantum states -- so that means if you really and truly have a criticism of 'lack of rigor' that is applicable only to MWI (and assuming you aren't making a strawman argument), then that means your criticisms specifically regard the analytical methods. However, all of your fanciful imaginings describe incredulity as to the dynamics -- which means you either have deep misgivings about quantum mechanics as a whole, or you simply don't know what you're talking about.

 

[reilly]

Then please stop posting. If you prefer not to talk about MWI, but instead about cartoony sci-fi bastardizations of it, then do so elsewhere.


Please remind me how that went. I seem to recall you spent most of your effort recounting fanciful "everything you can imagine is true" science fiction fantasies and marveling over thermodynamics. You briefly asked about dynamics (which is precisely the familiar unitary evolution of quantum mechanics) so if that is the content of your accusation of lack of rigour, then it is rather disingenious to post as if it is MWI you are criticizing, which instead you are criticizing quantum mechanics as a whole.

As for Hans, all he seems to be doing is demonstrating a lack of knowledge of the dynamics of mixed states.

MWI is concerned only with the analysis of the unitary evolution of quantum states -- so that means if you really and truly have a criticism of 'lack of rigor' that is applicable only to MWI (and assuming you aren't making a strawman argument), then that means your criticisms specifically regard the analytical methods. However, all of your fanciful imaginings describe incredulity as to the dynamics -- which means you either have deep misgivings about quantum mechanics as a whole, or you simply don't know what you're talking about.

hurkyl

With all due respect, your characterization of my two recent posts is misleading -- count the words dealing with "imagination and science fiction" -- they are less than 10%. You have not dealt with any of my or Han's questions, but rather have just accused us of not getting it.

What is it that we do not know?

I talked about the problematic role of Poisson processes in the MWI approach -- Poisson chains seem dangerously close to generating a non-separable Hilbert space. What's your understanding of this issue?

My concern, re rigor is, for example: in what space does this unitary evolution take place? Can you demonstrate that MWI works with a separable Hilbert space?

Let's suppose that I wish to do an electron scattering experiment.During the time in which the experiment is conducted, many universes will be created, as, for example, all of our perceptions involve some random elements -- which our perceptual systems average out. How do we know what universe to use when doing the analysis of the scattering data? How much history do we need to consider?
Regards,
Reilly

 

[Hurkyl]

What is it that we do not know?

That the state space analyzed by MWI is exactly the one ordinarily used in QM. That the relative state of a subsystem would be mixed or that mixed states do not interact under unitary evolution.

The brief history as I know it (and hopefully reasonably accurate) is that MWI started with the relative state interpretation: if you have a state for the entire system, you could restrict it to a particular subsystem (e.g. via partial trace). In this way, it was seen to be possible that subsystems could be in a mixed state, even if the entire state was pure. Then MWI got a huge boost from the discovery of decoherence, which indicated that the coupling of the subsystem with the environment naturally caused subsystem states to tend to statistical mixtures of a particular basis. Everything else in MWI has been efforts to analyze the behavior of these things.

I talked about the problematic role of Poisson processes in the MWI approach -- Poisson chains seem dangerously close to generating a non-separable Hilbert space. What's your understanding of this issue?

I can't see how. What state space you would ordinarily use to quantum mechanically study a mole of silver atoms? MWI would assign that very same state space to that system. Are you suggesting quantum mechanics is incapable of describing such systems with a separable Hilbert space?

My concern, re rigor is, for example: in what space does this unitary evolution take place? Can you demonstrate that MWI works with a separable Hilbert space?

MWI works in a separable Hilbert space if and only if that is what you would ordinarily use in quantum mechanics.

 

[Phrak]

Hurkyl- thanks for the clarification regarding toy observes. It goes a long way in clearing things up.

Other than coming to terms with the googleplex of unmeasurable "parallel" universes, there are a couple of things one would want out of a decent interpretation.

In the Copenhagen non-interpretation interpretation the energy-momentum that curves spacetime has no position until it is measured. But it's difficult to see if MWI disambiguates this problem. If one were in possession of the state of the universe, evolved from the beginning, that would be fine, perhaps. But supposedly, we still have a predictively correct accounting using general relativity, even when we don't have the entire description of state, but begin instead with some sort of subspace slice through Hilbert space. I'm wondering if this could be seen as some sort of gauge invariance, but that's as far as I get.

Sencondly, I've heard objections made (Wheeler, and others) that MWI, in the original form by Hughes Everett, fails to correctly predict probobility densities, or some such, without an additional postulate that adds a correction factor.

Thanks for any sort of clarification on these.

 

[Hurkyl]

In the Copenhagen non-interpretation interpretation the energy-momentum that curves spacetime has no position until it is measured.

Details of approaches to quantum gravity are well beyond my current understanding.

Sencondly, I've heard objections made (Wheeler, and others) that MWI, in the original form by Hughes Everett, fails to correctly predict probobility densities, or some such, without an additional postulate that adds a correction factor.

I know I have seen people suggest that the probability of an outcome should be proportional to the number of worlds containing that outcome (and I think this is what you're referring to). I don't know if this was ever a part of any form of MWI.

I know I have managed to derive the Born rule in a simple toy case, with a mild continuity assumption. I have since read that it has been proven (but I don't know the precise statement, nor the proof method) that the Born rule is the only possible statistical rule that can be observed in a 'world'.


A sketch of my derivation is as follows:
1. Suppose you have N identical, independent qubits, each in the state $\alpha |0\rangle + \beta |1\rangle$
2. Choose a positive number $\varepsilon$.
3. Construct an observable $X_{N,\beta,\epsilon}$ representing the following experiment:

Measure each of the qubits.
If the proportion of $|1\rangle$'s is within $\epsilon$ of $|\beta|^2$, output '1'
Otherwise, output '0'​

4. Compute $\lim_{N \rightarrow +\infty} E(X_{N, \beta, \epsilon}) = 1$

I interpret this final result as telling me that as we repeat the (independent) experiment of observing qubits in the state $\alpha | 0 \rangle + \beta 1 \rangle$, the proportion of $|1\rangle$'s converges to $|\beta|^2$ with probability 1 -- therefore, the Born rule satisfies the frequentist interpretation of probabilities.


In my opinion, the key conceptual point is 'internalization' -- the observation of frequencies was made into an experiment modeled by the formalism of QM.

 

[Hans de Vries]

As for Hans, all he seems to be doing is demonstrating a lack of knowledge of the dynamics of mixed states.

Hurkyl,

Nobody will find an answer to the questions, and the worries, we have about MWI by
just studying Decoherence theory.

Why we don't feel the gravitation of a star we are moving through in a parallel universe
is not explained by looking at manipulations with the non relativistic Schroedinger theory.
The same is true for many other interactions.

Of course you are not expected to provide the answers either. Nobody can.



Regards, Hans

 

[Phrak]

Details of approaches to quantum gravity are well beyond my current understanding.

All I know of quantum gravity are the two words stuck together (i.e.: nothing). But my point was that any interpetation that admits no objective realism, of one sort or another, to the wave equation is incompatible with the differentiable manifold of general relativity. This would apply equally well to a theory of quantum gravity that doesn't replace the differentiable manifold with something else.

If I understand you correctly, MWI does attach physical significance to the wave equation, so it has at least half a chance of being compatible with general relativity.

The hard part, is as Hans noted, describing how a mass in one decoherence has no effect in another decoherence where the mass is located elsewhere; one would want to account for how the shape of spacetime seamlessly transitions from one decoherence to another.

I know I have seen people suggest that the probability of an outcome should be proportional to the number of worlds containing that outcome (and I think this is what you're referring to). I don't know if this was ever a part of any form of MWI.

After a little internet searching, I see that Everett's 1957 MW interpetation has been understood in several different ways by various people, giving rise to at least 3 distinct interpretations; MWI being one of them.

This is what I was referring to, concerning total probability outcomes:

http://plato.stanford.edu/entries/qm-everett/"

Another problem with a splitting-worlds theory concerns the statistical predictions of the theory. The standard collapse theory predicts that J will get the result "spin up" with probability a-squared and "spin down" with probability b-squared in the above experiment. Insofar as there will be two copies of J in the future, J is guaranteed to get each of the two possible measurement results; so, in this sense, the probability of J getting the result "spin up", say, is one. But that is the wrong answer. A principle of indifference might lead one to assign probability ½ to each of the two possible measurement outcomes. But such a principle would be difficult to justify, and probability ½ is the wrong answer anyway. The moral is that it is impossible to get the right answer for probabilities without adding something to the theory.

In hindsight, I don't see that it matters that the total probability outcome should be greater than one, only that the experimenter should, in the least, subjectively deduce that the total probability outcome, as indicated from his results, imply that it is unity.

I know I have managed to derive the Born rule in a simple toy case, with a mild continuity assumption. I have since read that it has been proven (but I don't know the precise statement, nor the proof method) that the Born rule is the only possible statistical rule that can be observed in a 'world'.


A sketch of my derivation is as follows:
1. Suppose you have N identical, independent qubits, each in the state $\alpha |0\rangle + \beta |1\rangle$
2. Choose a positive number $\varepsilon$.
3. Construct an observable $X_{N,\beta,\epsilon}$ representing the following experiment:

Measure each of the qubits.
If the proportion of $|1\rangle$'s is within $\epsilon$ of $|\beta|^2$, output '1'
Otherwise, output '0'​

4. Compute $\lim_{N \rightarrow +\infty} E(X_{N, \beta, \epsilon}) = 1$

I interpret this final result as telling me that as we repeat the (independent) experiment of observing qubits in the state $\alpha | 0 \rangle + \beta 1 \rangle$, the proportion of $|1\rangle$'s converges to $|\beta|^2$ with probability 1 -- therefore, the Born rule satisfies the frequentist interpretation of probabilities.

In my opinion, the key conceptual point is 'internalization' -- the observation of frequencies was made into an experiment modeled by the formalism of QM.

Forgive me, but your posts have become a bit difficult to follow. Do you think your toy case addresses the objection concerning total probability in a manner favorably to MWI?

Edit: Rather than referring to "splitting", and "many worlds" or "parallel universe", that are conceptually misleading, I think the term "decoherence group", or simply a "decoherence" (used as a noun), should replace "parallel universe".

 

[Hurkyl]

All I know of quantum gravity are the two words stuck together (i.e.: nothing). But my point was that any interpetation that admits no objective realism, of one sort or another, to the wave equation is incompatible with the differentiable manifold of general relativity. This would apply equally well to a theory of quantum gravity that doesn't replace the differentiable manifold with something else.

If I understand you correctly, MWI does attach physical significance to the wave equation, so it has at least half a chance of being compatible with general relativity.

I should point out that some flavors of Copenhagen view quantum states as being objectively real -- they just undergo collapses now and then. I am under the (vague) impression that Bohmian mechanics also takes something functionally equivalent to the wavefunction as being objectively real. And then there are flavors of (what I understand as) the relational interpretation, in which it views quantum states as directly corresponding to something real -- it's just that many different quantum states can correspond to the same physical 'state'.

So MWI doesn't have a monopoly on treating quantum states as being real.

In hindsight, I don't see that it matters that the total probability outcome should be greater than one,

I'm sorry, I missed where that came from.

Edit: Rather than referring to "splitting", and "many worlds" or "parallel universe", that are conceptually misleading, I think the term "decoherence group", or simply a "decoherence" (used as a noun), should replace "parallel universe".

That might be reasonable; alas, history often saddles us with unfortunate terms (e.g. we're still saddled with 'imaginary numbers', despite Gauss's best efforts). I confess I generally prefer to think of the quantum state 'abstractly' -- so while I can see why some people like such terminology and others don't, I really don't have an informed opinion.

 

[Phycho]

Hurkyl, I'd just like to point out Bohm is 100% realistic objective interpretation.
It's nickname are "The realist interpretation".

I've never heard of any CInterpretation that treats reality as objective.

 

[Phrak]

Thanks for all that, Hyrkl. I've found a website on qbits, gates, computing and algorithms. I'll be studying the first half of it. It seems to be the way to go, to evaluate MWI, if not other interpretations.

It looks be well done, if not a bit verbose: http://beige.ucs.indiana.edu/M743-talk-2/node2.html"

 

[Count Iblis]

Hurkyl's proof amounts to replacing the Born rule by a weaker rule that says that if a system is in an eigenstate of an observable, then a measurement will yield that eigenstate with 100% probability.