The Fundamental Difference in Interpretations of Quantum Mechanics
A topic that continually comes up in discussions of quantum mechanics is the existence of many different interpretations. Not only are there different interpretations, but people often get quite emphatic about the one they favor so that discussions of quantum mechanics can easily turn into long arguments. Sometimes this even reaches the point where proponents of a particular interpretation claim that anyone who doesn’t believe it is “idiotic”, or some other extreme term. This seems a bit odd given that all of the interpretations use the same theoretical machinery of quantum mechanics to make predictions, and therefore whatever differences there are between them are not experimentally testable.
In this article, I want to present what I see as a fundamental difference in interpretation that I think is at the heart of many of these disagreements and arguments.
I take no position on whether either of the interpretations I will describe is “right” or “wrong”; my purpose here is not to argue for either one but to try to explain the fundamental beliefs underlying each one to people who hold the other. If people are going to disagree about interpretations of quantum mechanics, which is likely to continue until someone figures out a way of extending quantum mechanics so that the differences in interpretations become experimentally testable, it would be nice if they could at least understand what they are disagreeing about instead of calling each other idiots. This article is an attempt to make some small contribution towards that goal.
The fundamental difference that I see is how to interpret the mathematical object that describes a quantum system. This object has various names: quantum state, state vector, wave function, etc. I will call it the “state” both for brevity and to avoid adopting any specific mathematical framework since they’re all equivalent anyway. The question is, what does the state represent? The two fundamentally different interpretations give two very different answers to this question:
- (1) The state is only a tool that we use to predict the probabilities of different results for measurements we might choose to make of the system. Changes in the state represent changes in the predicted probabilities; for example, when we make a measurement and obtain a particular result, we update the state to reflect that observed result, so that our predictions of probabilities of future measurements change.
- (2) The state describes the physically real state of the individual quantum system; the state allows us to predict the probabilities of different results for measurements because it describes something physically real, and measurements do physically real things to it. Changes in the state represent physically real changes in the system; for example, when we make a measurement, the state of the measured system becomes entangled with the state of the measuring device, which is a physically real change in both of them.
(Some people might want to add a third answer: the state describes an ensemble of a large number of similar systems, rather than a single system. For purposes of this discussion, I am considering this to be equivalent to answer #1, because the state does not describe the physically real state of a single system, and the role of the ensemble is simply to enable a frequentist interpretation of the predicted probabilities.)
(Note: Originally, answer #1 above talked about the state as describing our knowledge of the system. However, the word “knowledge” is itself open to various interpretations, and I did not intend to limit answer #1 to just “knowledge interpretations” of quantum mechanics; I intended it to cover all interpretations that do not view the state as directly describing the physically real state of the system.)
The reason there is a fundamental problem with the interpretation of quantum mechanics is that each of the above answers, while it contains parts that seem true, leads us, if we take it to its logical conclusion, to a place that doesn’t make sense. No choice gives us just a set of comfortable, reasonable statements that we can easily accept as true. Picking an interpretation requires you to decide which of the true things seems more compelling which ones you are willing to give up, and/or which of the places that don’t make sense is less unpalatable to you.
- For #1, the true part is that we can never directly observe the state, and we can never make deterministic predictions about the results of quantum experiments. That makes it seem obvious that the state can’t be the physically real state of the system; if it were, we ought to be able to pin it down and not have to settle for merely probabilistic descriptions. But if we take that idea to its logical conclusion, it implies that quantum mechanics must be an incomplete theory; there ought to be some more complete description of the system that fills in the gaps and allows us to do better than merely probabilistic predictions. And yet nobody has ever found such a more complete description, and all indications from experiments (at least so far) are that no such description exists; the probabilistic predictions that quantum mechanics gives us are the best we can do.
- For #2, the true part is that interpreting the state as physically real makes quantum mechanics work just like all the other physical theories we’ve discovered, instead of being a unique special case. The theoretical model assigns the system a state that reflects, as best we can in the model, the real physical state of the real system. But if we take this to its logical conclusion, it implies that the real world is nothing like the world that we perceive. We perceive a single classical world, but the state that QM assigns is a quantum superposition of many worlds. We perceive a single definite result for measurements, but the state that QM assigns is a quantum superposition of all possible results, entangled with all possible states of the measuring device, and of our brains, perceiving all the different possible results.
Again, my purpose here is not to pick either one of these and try to argue for it. It is simply to observe that, as I said above, no matter which one you pick, #1 or #2, there are obvious drawbacks to the choice, which might reasonably lead other people to pick the other one instead. Neither choice is “right” or “wrong”; both are just best guesses, based on, as I said above, which particular tradeoff one chooses to make between the true parts and the unpalatable parts. We have no way of resolving any of this by experiment, so we simply have to accept that both viewpoints can reasonably coexist at the present state of our knowledge.
I realize that pointing all this out is not going to stop all arguments about interpretations of quantum mechanics. I would simply suggest that, if you find yourself in such an argument, you take a moment to step back and reflect on the above and realize that the argument has no “right” or “wrong” outcome and that the best we can do at this point is to accept that reasonable people can disagree on quantum mechanics interpretations and leave it at that.
- Completed Educational Background: MIT Master’s
- Favorite Area of Science: Relativity
What we directly observe in a measurement device are only macroscopic (what I called ''classical'') observables, namely the expectation values of certain field operators. These form a vast minority of all conceivalbe observables in the conventional QM sense. For example, hydromechanics is derived in this way from quantum field theory. Everyone knows that hydromechanics is highly chaotic in spite of the underlying linearity of the Schroedinger equation defining (nonrelativistic) quantum field theory from which hydromechanics is derived. Thus linearity in a very vast Hilbert space is not incompatible with chaos in a much smaller accessible manifold of measurable observables.I think that's a very interesting subject–the reconciliation of the linearity of Schrodinger's equation with the chaotic nonlinearity of macroscopic phenomena. But I really don't think that chaos in the macroscopic world can explain the indeterminism of QM. In Bell's impossibility proof, he didn't make any assumptions about the complexity of the hidden variable [itex]lambda[/itex], or the difficulty of computing measurement outcomes from [itex]lambda[/itex], or the sensitivity of the outcomes to [itex]lambda[/itex].
I think this discussion has many components, not sure which post rubis post related to.
For the record My core issue is not the principle of information update as such, i agree is the most natural component. My issues are different and more subtle.
My previous point of emergence did not refer to the collapse, it rather referred to to the rule of evolution in between updates.
The real quation about quantum theory is: Why does it make sense to have non-commuting observables in the first place?The way i see it (inference interpretation), is because it allows the the observer to maximise its predictive power, when computing the expectation from the state of information. And this stabilises the observer from the destabilising environment.
It can be understood as datacompression of the abduced rules of expectation.
I think this can be described mathematically as well. But it requires a different foundation and framework pf physics, which is not yet in place. But developing that goes hand in hand with understanding and vague insight.
/Fredrik
I'm not too keen about Heisenberg.His philosophy (what you called ''wild speculations'') in 1925 lead him to the discovery of the canonical commutation relations.
So whatever is keeping us from making deterministic predictions about the results of quantum experiments, it isn't chaos due to nonlinear dynamics of the quantum state.
However, it is chaos in the (classical) part of the quantum state that is accessible to measurement devices.
Can you elaborate?What we directly observe in a measurement device are only macroscopic (what I called ''classical'') observables, namely the expectation values of certain field operators. These form a vast minority of all conceivalbe observables in the conventional QM sense. For example, hydromechanics is derived in this way from quantum field theory. Everyone knows that hydromechanics is highly chaotic in spite of the underlying linearity of the Schroedinger equation defining (nonrelativistic) quantum field theory from which hydromechanics is derived. Thus linearity in a very vast Hilbert space is not incompatible with chaos in a much smaller accessible manifold of measurable observables.
. . . and the whole Copenhagen Interpretation had to be clarified by Henry Stapp:
http://www.informationphilosopher.com/introduction/physics/Stapp_Copenhagen_Interpretation.pdf
Philosophy need not be speculation. Neither Bohr's nor Einstein's nor Heisenberg's nor Feynman's philosophy was wild speculation.Well, Einstein was at least understandable in his very clear criticism against QT. As is clear since Bell's work and the confirmation of the violation of the Bell inequality he was wrong, and QT came out right. Bohr has his merits in clearly stating the idea of complementarity and that QT is about what can be prepared and measured in a atomistic world. Unfortunately he was not very clear in his own writings but had to be translated by others into understandable statements. I'm not too keen about Heisenberg. E.g., he didn't get his own finding of the uncertainty principle right and was corrected by Bohr. Also his version of QT, matrix mechanics, had to be clarified in the "Dreimännerarbeit" by him, Bohr, and Jordan.
Projection of which probability distribution upon what?When you have a distribution ##rho(x)## at time ##t##, then if you have gotten to know that ##xin A##, you multiply ##rho(x)## by the characteristic function ##chi_A(x)##. The projection is ##rho(x)rightarrow chi_A(x)rho(x)##. It's the same thing that happens to the quantum state ##psi(x)## if you have learned the result of a measurement of the position operator ##hat x##. In quantum theory you have the additional complication that observables might not commute. If you have an observable in a different basis, you have to perform this multiplication in that basis, so for instance a measurement of the momentum ##hat p## results in a multiplication of the fourier transformed state ##tilde psi(p)## by the characteristic function ##chi_A(p)##. Every projector ##hat P## in quantum theory is a multiplication operator by some characteristic function in the eigenbasis of the corresponding observable, so for the special case of commuting observables, the mathematics of projections is exactly the same as in classical probability theory.
I can imagine that as a topic in special relativity.I probabily don't have time for a long discussion about this, but this seems to be a good overview article: https://arxiv.org/abs/0812.1996
No, I really mean the rigorous measure theoretical formulation of probability theory and collapse is just the projection of the probability distribution.Projection of which probability distribution upon what?
For example, you could study the Brownian motion of relativistic particles instead of Newtonian particles.I can imagine that as a topic in special relativity.
These two options are generally called “psi-epistemic” and “psi-ontic,” respectively, in the foundations community. Psi-epistemic interpretations do not necessarily entail that QM is incomplete, see http://www.ijqf.org/wps/wp-content/uploads/2015/06/IJQF2015v1n3p2.pdf for example. I didn’t have time to read all 8 pp of this thread, so my apologies if something along these lines was already posted.
I make the mild objection that "collapse" in the sense of a "realization" of some event in a probability space is not a topic treated by probability theory. It is a topic arising in interpretations of probability theory when it is applied to specific situations. What you are calling "classical probablity theory" is, more precisely, "the classical interpretations used when applying probability theory".No, I really mean the rigorous measure theoretical formulation of probability theory and collapse is just the projection of the probability distribution. Of course, nobody in probability theory calls it "collapse". I don't like the word either, because it suggests that it is a physical process, but I just used it in order to stick with the terminology of the thread. Mathematically, it refers to the insertion of the projectors in the construction of probability measures on the space of paths of a stochastic process, i.e. the fact that these probability distributions have the form ##UPUPUP rho_0##, when evaluated on cylindrical sets. (##U## denotes time evolution, ##P## denotes projection.)
I agree that applications of probability theory to model macroscopic events like coin tosses involves the somewhat mysterious assumption that an event can have a probability of 1/2 of being "possible" and then not happen. (If it didn't happen, why can we assert it was possible?).I don't really understand how that relates to my post.
What's an example of that?For example, you could study the Brownian motion of relativistic particles instead of Newtonian particles.
In classical probability theory, the collapse too isn't an emergent phenomenon that just needs to be derived from a better theory. Instead, it's an elementary ingredient in the theory of stochastic processes, which can't be removed from the theory.A measurement in classical probability theory has occured, when the experimenter somehow has learned the measurement result.I make the mild objection that "collapse" in the sense of a "realization" of some event in a probability space is not a topic treated by probability theory. It is a topic arising in interpretations of probability theory when it is applied to specific situations. What you are calling "classical probablity theory" is, more precisely, "the classical interpretations used when applying probability theory".
I agree that applications of probability theory to model macroscopic events like coin tosses involves the somewhat mysterious assumption that an event can have a probability of 1/2 of being "possible" and then not happen. (If it didn't happen, why can we assert it was possible?).
It would be interesting to hear opinions about whether there are problems in interpreting the "collapse" of the wave function that are distinct from the elementary metaphysical dilemma of applying probability theory to coin tosses.
One can also have classical probabilistic theories of classical relativistic systems and of course they too will include collapse.What's an example of that?
There is nothing contradictory about having two types of time evolution (unitary evolution, collapse). In fact, this happens in classical Newtonian physics as well and we fully understand it. Whenever we have a stochastic description of some perfectly classical system, we have a probability distribution at ##t=0##, which is then evolved by a probability conserving time evolution, then collapsed upon measurement, then evolved again, etc. The standard example is Brownian motion, which arises from completely classical equations like ##F=ma##. In fact, this scheme applies to all classical probabilistic theories with time evolution, so it would actually be more mysterious if time evolution didn't work analogously in quantum mechanics, which too is probabilistic after all. In classical probability theory, the collapse too isn't an emergent phenomenon that just needs to be derived from a better theory. Instead, it's an elementary ingredient in the theory of stochastic processes, which can't be removed from the theory. And since classical probability theory is a special case of quantum theory (when all observables commute), there must be something within quantum theory that reduces to classical collapse if only commuting observables are considered.
Moreover, the notion of measurement in quantum theory is no less well-defined than in classical probability theory. A measurement in classical probability theory has occured, when the experimenter somehow has learned the measurement result. It's up to the experimenter to decide when this happened. However, the mathematical formulation is perfectly rigorous and if the experimenter knows the time of measurement and the measurement precision very well, then the theory will produce numbers that match the measured data very well.
Also, collapse is not in conflict with relativity. One can also have classical probabilitic theories of classical relativistic systems and of course they too will include collapse.
The only misconception about collapse is that it is often considered to be a type of time evolution. In fact, it's not a type of time evolution. It's just a necessary mathematical ingredient if you want to compute the probability distribution on the space of paths of a stochastic process. So by analogy, it's unlikely a type of time evolution in quantum theory either, because again, in the case of commuting observables, quantum theory reduces to classical probabilty theory.
The real quation about quantum theory is: Why does it make sense to have non-commuting observables in the first place?
The issue I was talking about when I coined "soft contradiction" wasn't really inductive versus deductive. It was really about how we reason with huge numbers (or very tiny numbers). Let me give a toy example: Suppose I say that
…
I feel that the rules of thumb for using QM may be a similar type contradiction. That recipe consists of
They work very well. However, since measurement devices are themselves quantum systems (even if very complex) and measurements are just ordinary interactions between measurement devices and the systems being measured, these two rules may very well be contradictory. But a detailed analysis of the measuring process as a quantum interaction may infeasible, so actually deriving a contradiction (that everyone would agree was a contradiction) may never happen.So by "soft contradiction" you mean a contradiction that occur only during certain – possible, but improbable – conditions.
Thus the softly flawed inference is justified?
If so, i would still think that relates to the discussion of general inference. I see your case as a possible kind of rational inference of a deductive rule but in an subjectively probabilistic inductive way, and it´s also something that can be generalized.
A possible driving force for a rational agent to abduct an approximative deductive rule, to base expectations and thus action on, is that of limited resources.
A deductive rule that are right "most of the time", can increase the evolutionary advantage of the agent in competition. As the agent can not store all information, it has not choice but to choose, what to store and how, and what to discard.
This is perfectly rational, but it also brings deep doubts on the timeless and observer invariant character of physical law.
I have also considered that this might even be modelled as an evolving system of axioms, where evolution selects for the consistent systems. An agent is associated with its axioms or assumptions. And different systems of axioms can thus be selected among, in terms of effiency of keeping their host agent in business. Meaning, efficient coding structurs for producing expectations of their environment.
This is also a way to see how deductive systems are emergent, and there is then always an evolutionary argument for WHY these axioms etc. Ie. while axioms in principle are CHOICES, the choices are not coincidental. This would then assume a one-2-one mapping between the axioms in the abstraction, and the physical postualtes which are unavoidably part in the mud of reality. In this view, the axioms are thus simply things that "seem to be true so far" but arent be proved, and they serve the purposes of a efficient betting system, but they can be destroyed/deleted whenever inconsistent evidence arrives.
These ideas gives a new perspecive into the "effectiveness of mathematics". Like Smolin also stated in this papers and talks, the deductive systems are effective precisely because they are limited. But to really appreciate this, you must also understand how and why deductive systems are emergent.
/Fredrik
… There's a lot of development and experiments on the ontic state vs epistemic one. But i can't ignore the universality of interactions which works best locally. What exactly means when we observed something in QM? ..Would there be any effect on observation like– how certain observations of local dynamics are affected interactively. Why can it be absolute observer-independent state of a system in QM? instead by the notion of information about a system, exchanged via physical interactions. Instead of objects just series of events. For what its worth. It can eliminate of some of the artifact like MWI. I remember the talk regarding time. The basic reason is that global time which is observer-independent. Instead of depending on a choice of observer, it depends on the process whose quantum state is known–parameter of change. That is, a vector in a boundary Hilbert space that contains information about past during and future. Like how a positive functional defined on the C* algebra of the process. Here "state" does not mean "state at a given instant of time". The state is a quantum description of what can be known about an entire process occurring in an enclosed spacetime region– GCQFT. Would it be possible that what we are observing a phenomenon of visual limitation constrained by the linearity of time approaching its limits like mirages?
it is chaos in the (classical) part of the quantum state that is accessible to measurement devices.Can you elaborate?
Come again – you better give the detail of that one.
All interpretations, every single one, has the formalism of QM so Bells follows.No, because all outcomes occur in MWI.
MWI does not meet the conditions for Bell's theorem. Bell's theorem cannot be used to say that MWI is incompatible with local realism.Come again – you better give the detail of that one.
All interpretations, every single one, has the formalism of QM so Bells follow.
Thanks
Bill
Just for reference the more convetional terminology for the various kinds of inferences here are, deductive vs inductive inference.
"hard contradictions" are typically what you get in deductive logic, as this deals with propositions that are true or false.
"soft contradictions" are more of the probabilistic kind, where you have various degrees of beliefs or support in certain propositions.The issue I was talking about when I coined "soft contradiction" wasn't really inductive versus deductive. It was really about how we reason with huge numbers (or very tiny numbers). Let me give a toy example: Suppose I say that
These two together might very well be contradictory. For some initial condition of a cat, maybe Newton's laws imply that the cat wouldn't land on its feet. But it might be completely infeasible to actually derive a contradiction. It certainly is not feasible to check every possible initial condition of a cat and apply Newton's laws to all the atoms making up the cat's body to find out if it would land on its back. Maybe there is some advanced mathematics that can be used to get the contradiction, using topology or whatever, but in the naive way that people might apply Newton's laws, chances are that a contradiction will never be derived.
Or imagine a mathematical statement [itex]S[/itex] such that the shortest proof (using standard mathematical axioms, anyway) takes [itex]10^{100}[/itex] steps. Then if I add [itex]neg S[/itex] to my axioms, then the resulting system is inconsistent. However, it's unlikely that any contradiction will ever be discovered.
I feel that the rules of thumb for using QM may be a similar type contradiction. That recipe consists of
They work very well. However, since measurement devices are themselves quantum systems (even if very complex) and measurements are just ordinary interactions between measurement devices and the systems being measured, these two rules may very well be contradictory. But a detailed analysis of the measuring process as a quantum interaction may infeasible, so actually deriving a contradiction (that everyone would agree was a contradiction) may never happen.
There is actually an approach to making systems of reasoning with soft contradictions of the type I'm worried about into consistent systems. That is, instead of thinking of the rules as axioms in a mathematical sense, you organize them this way:
I think that's ugly, but I think it's doable. I think it's something like the way that we deal with the world in our everyday life. If you're trying to figure out how to get your girlfriend to stop being mad at you, you don't try to deduce anything using quantum field theory, you stick to the "relationship domain". Of course, there could be some overlap with other domains, because maybe the problem is that she suffers from headaches that make her irritable, and they might be due to a medical condition. So maybe you need to bring in the "medical domain". And maybe that condition could be treated by some kind of nanotechnology, which might involve physics, after all.
That depends on what you mean by orthodox. If you mean the formalism then you have to explain MW. The answer of course is its principles, axioms, whatever you want to call it doesn't have it.Them you would say that Bell's theorem does not show that quantum mechanics is inconsistent with local realism.
Philosophy = discussing the possible meanings, definitions, delineations, etc. of concepts, and the arguments for the various uses.Maybe the misunderstanding about philosophy is that "The value of philosophy is, in fact, to be sought largely in its very uncertainty"
http://skepdic.com/russell.html
The value of philosophy is, in fact, to be sought largely in its very uncertainty. The man who has no tincture of philosophy goes through life imprisoned in the prejudices derived from common sense, from the habitual beliefs of his age or his nation, and from convictions which have grown up in his mind without the co-operation or consent of his deliberate reason. To such a man the world tends to become definite, finite, obvious; common objects rouse no questions, and unfamiliar possibilities are contemptuously rejected. As soon as we begin to philosophize, on the contrary, we find, as we saw in our opening chapters, that even the most everyday things lead to problems to which only very incomplete answers can be given. Philosophy, though unable to tell us with certainty what is the true answer to the doubts which it raises, is able to suggest many possibilities which enlarge our thoughts and free them from the tyranny of custom. Thus, while diminishing our feeling of certainty as to what things are, it greatly increases our knowledge as to what they may be; it removes the somewhat arrogant dogmatism of those who have never travelled into the region of liberating doubt, and it keeps alive our sense of wonder by showing familiar things in an unfamiliar aspect.Best regards
Patrick
there is a tendency to call something philosophical if it not quite clearPhilosophy = discussing the possible meanings, definitions, delineations, etc. of concepts, the arguments for or against the various uses, and associated fallacies.
This can be done (like anything else) with different degrees of clarity.
There is a big difference between not being clear (which is in philosophy never completely the case) and being wild speculation. Speculation has nothing to do with philosophy but is just unfounded reasoning.Good point – they are different. But I have to say there is a tenancy to call something philosophical BS if it not quite clear – I think I fall for that one often. You shouldn't – but I find it hard not to.
Tanks
Bill
Einstein and Feynman IMHO are good – they are clear – that is the key – for Bohr that wasn't always the caseThere is a big difference between not being clear (which is in philosophy never completely the case) and being wild speculation. Speculation has nothing to do with philosophy but is just unfounded reasoning.
I will post my thoughts now you have clarified (at least to me) what you mean we can get to the heart of the issue.OK we have the principle of general invariance – the laws of physics should be expressed in coordinate free form.
This is an actual physical statement because it makes a statement about physical things – laws of physics.
We have the Principle of Least Action about the paths of actual particles – same as the above.
What I don't understand is why you don't think the same of the statement observations are the eigenvalues of an operator. That seems to be exactly the same as the above – it talks about something physical – an observation.
Thanks
Bill
Phisolsophy need not be speculation. Neither Bohr's nor Einstein's nor Heisenberg's nor Feyman's philosophy was wild speculation.Einstein and Feynman IMHO are good – they are clear – that is the key – for Bohr that wasn't always the case such as his explanation of EPR. Modern scholars, as I have posted elsewhere think his explanation, supposedly definitive, wasn't quite that. BTW Einstein, while clear was far from always right, not by a long shot. His math was particularly bad – his early papers required a lot of comments explaining the errors when collected and published – how they got through referees reports beats me – he wasn't famous then so it simply wasn't – well it's Einstein so who are we to criticize.
Thanks
Bill
So whatever is keeping us from making deterministic predictions about the results of quantum experiments, it isn't chaos due to nonlinear dynamics of the quantum state.However, it is chaos in the part of the quantum state that is accessible to measurement devices.
This is all solid scientific work and not wild "philosophical" speculation.Phisolsophy need not be speculation. Neither Bohr's nor Einstein's nor Heisenberg's nor Feyman's philosophy was wild speculation.
Orthodox QM does have collapse.That depends on what you mean by orthodox. If you mean the formalism then you have to explain MW. The answer of course is its principles, axioms, whatever you want to call it doesn't have it.
Thanks
Bill
I learned GR from MTW, since they use the term general covariance it was what stuck with me.Now you mention MTW then I understand – only some texts make the distinction. Its not important and I will post my thoughts now you have clarified (at least to me) what you mean we can get to the heart of the issue. Wald is sneaky – he uses the concept of diffeomorphism – but I think its really the same thing – however that is definitely something for the relativity forum.
Thanks
Bill
Looks like a variance in terminology, then. As @Auto-Didact mentions, MTW uses the term "general covariance" to mean what you are using the term "general invariance" to mean. (And since I also learned GR from MTW, I would use "general covariance" to mean that as well.) So you and he actually agree on the physics; you're just using different words.When he mentioned he learnt it from MTW I figured that. Ohanian makes a big deal out of it – MTW doesn't. Interestingly my personal favorite book – Wald – bypasses it by using the concept of diffeomorphism, although I have always though its just a more rigorous version of the same thing. Maybe someone actually knows the difference. I will start a thread on the relativity forum about it.
Thanks
Bill
So you are really talking about the informal motivation for Ballentine's axioms? I think by your ideas, even the orthodox axioms would be "wrong", but it would be better to say they are not well motivated. On the other hand, Hardy's axioms (equivalent to the orthodox axioms) are presumably better motivated.Yes. I believe that a mathematical axiomatization of physics can and should only be done once physics is actually complete (Gödel says hi).
Before that, all mathematical simplification of physical theory should have as motivation the discovery of more physics or other sciences; any prematurely undertaken axiomatization which inhibits reaching this goal by pretentiously giving some completed deductive viewpoint which then also actually ends up hampering further progress in physics is nothing but an inadequate nuisance, at risk of becoming dogma. Using your less vitriolic words might be a better way of communicating this though.
but it's not a good way to learn quantum theory since their writings tend to clutter the physics with superfluous philosophical balast which confuses the subject more than it helps to understand it.While i absolutely get your point, that to learn quantum theory, what the mature says, how to apply it etc, can probably be easiest done studying the cleaned up writings, where the historical context and the logic used to construct the theory is left out, as it unavoidable contains detoures and wrong turns.
But wether its wise to decouple the state of science from its historical inference is a question of wether you seek knowledge or understanding, just like Feynman said in the video in post#82 or Auto-Didact.
I have read both kind of books, i also love the rigour of pure mathematics books. It is a different world though, thinking always in terms of what can be deduced from the given axioms, or the more fuzzy problems of understanding our world. And one does not exclude the other. because solving fuzzy problems with deductive tools simply does not work, because you can not even define the problem, and are then led to the fallacious conclusion that they are not worthy thinking about.
/Fredrik
The difference is that in the case of the axioms for classical mechanics the content of every mathematical statement can be at least in principle connected to an observational statement, either through the principles involved, through the laws derived or through the postulates stated. On the other hand, Ballentine's mathematical statements upon closer inspection have only mathematical content.
As for your question, probably, but I'm no logician/mathematician, so in my doing of mathematics I tend to avoid anything axiomatic or Bourbaki-esque like the plague. Then again I do like the word bijective :pSo you are really talking about the informal motivation for Ballentine's axioms? I think by your ideas, even the orthodox axioms would be "wrong", but it would be better to say they are not well motivated. On the other hand, Hardy's axioms (equivalent to the orthodox axioms) are presumably better motivated.
I understand what you mean, but maybe that is too strong. After all, the standard axioms are also mathematical. The standard axioms of classical mechanics are also mathematical (the are all definitions in disguise).
Aren't all axioms definitions in disguise? I guess this goes into the tricky issue of the relationship between axioms and models (eg. standard and non-standard models of arithemetic). But I guess scientists use second order logic, so the model is unique.The difference is that in the case of the axioms for classical mechanics the content of every mathematical statement can be at least in principle connected to an observational statement, either through the principles involved, through the laws derived or through the postulates stated. On the other hand, Ballentine's mathematical statements upon closer inspection have only mathematical content.
As for your question, probably, but I'm no logician/mathematician, so in my doing of mathematics I tend to avoid anything axiomatic or Bourbaki-esque like the plague. Then again I do like the word bijective :p
Here is where my viewpoint not just diverges away from standard philosophy of science, but also from standard philosophy of mathematics: in my view not only is Pierce's abduction necessary to choose scientific hypotheses, abduction seems more or less at the basis of human reasoning itself. For example, if we observe a dark yellowish transparant liquid in a glass in a kitchen, one is easily tempted to conclude it is apple juice, while it actually may be any of a million other things, i.e. it is possibly any of a multitude of things. Yet our intuition based on our everyday experience will tell us that it probably is apple juice; if we for some reason doubt that, we would check it by smelling or tasting or some other means of checking and then updating our idea what it is accordingly. (NB: contrast probability theory and possibility theory).I was away yesterday, but in short. I agree with you on abduction. Indeed the human brain seems to be designed so that It encodes not a record to events, but it abduces the "best rule" and store that. This is what our memories are not always accurate, but are tweaked. Best rule, means the rule to best predict the future give the constraints of our limited capacity of storage and processing power. I dont dig up references now but this is supported by some neuroscientis working on understanding human brain.
After all this is perfectly natural and intuitive for anyone that understands evolution. The motivation for the brain to develop this behaviour is simply survival.
As inferences are general abstractions, there are analogies between inferences executed by the human brain, and the physical inferences executed by subatomic sys tems. But with that said, i am usually careful to mix the discussions as anyone who is not on the same page so to speak, are with highest possible certainly going to misunderstand things grossly, and think we are suggesting that the human brain of consciousness have a role to play in fundamental physics and measurement. This is not so.
/Fredrik
I'd put it much stronger, I'm sure Ballentine's derivation is incorrect, because it isn't a real physical derivation because it makes no direct statement whatsoever about observations or experimental facts in the world.
Ballentine's axioms are both semantically closed mathematical statements/propositions, which implies any deductions made from them can have no empirical content but only mathematical content, meaning whatever can be deduced solely on the basis of them can never legitimately be called a physical theory. To paraphrase Poincaré, those axioms are definitions in disguise.I understand what you mean, but maybe that is too strong. After all, the standard axioms are also mathematical. The standard axioms of classical mechanics are also mathematical (the are all definitions in disguise).
Aren't all axioms definitions in disguise? I guess this goes into the tricky issue of the relationship between axioms and models (eg. standard and non-standard models of arithemetic). But I guess scientists use second order logic, so the model is unique.
And actually that's why I am not sure Ballentine's axiomatization is correct. Ballentine has a huge rant against collapse. I consider Ballentine among the worst books on QM fundamentals, and not even worth discussing. In contrast, Hardy's "5 reasonable axioms" derivation and others following his footsteps like the "informational" derivation by Chiribella and colleagues does also derive collapse.I'd put it much stronger, I'm sure Ballentine's derivation is incorrect, because it isn't a real physical derivation because it makes no direct statement whatsoever about observations or experimental facts in the world.
Ballentine's axioms are both semantically closed mathematical statements/propositions, which implies any deductions made from them can have no empirical content but only mathematical content, meaning whatever can be deduced solely on the basis of them can never legitimately be called a physical theory. To paraphrase Poincaré, those axioms are definitions in disguise.
After having written that I was gonna edit and make the post more complete since I actually think so as well, I agree that state vector reduction is directly part of standard QM.
It however isn't part of what many physicists deem to be 'orthodox QM', namely a pure mathematical treatment of the Schrodinger equation.
Collapse theories with dynamics such as GRW or DP OR are theories competing with QM/beyond QM.And actually that's why I am not sure Ballentine's axiomatization is correct. Ballentine has a huge rant against collapse. I consider Ballentine among the worst books on QM fundamentals, and not even worth discussing. In contrast, Hardy's "5 reasonable axioms" derivation and others following his footsteps like the "informational" derivation by Chiribella and colleagues does also derive collapse.
Orthodox QM does have collapse.After having written that I was gonna edit and make the post more complete since I actually think so as well, I agree that state vector reduction is directly part of standard QM.
It however isn't part of what many physicists deem to be 'orthodox QM', namely a pure mathematical treatment of the Schrodinger equation.
Collapse theories with dynamics such as GRW or DP OR are theories competing with QM/beyond QM.
I agree with all of this except specifically that collapse is de facto not actually an interpretation of QM because orthodox QM has no collapse, orthodox QM being purely the Schrodinger equation and its mathematical properties. As I said above however QM as a whole is a mathematically inconsistent conjoining of the Schrodinger equation and the stochastic selection of the state from the ensemble which occurs empirically.
Collapse is therefore a prediction of a phenomenologic theory which directly competes with QM, but which has yet to be mathematically formulated. This theory should then contain QM as some particular low order limit, analogous to how Newtonian mechanics is a low order limit of SR.Orthodox QM does have collapse.
… and Newton didn't have differential geometry. This underlines my point of view as a matter of historical developments and doesn't contradict it. Newton wasn't the one and only, but rather one in a long row before and after him, many of them mathematicians by the way, who contributed to physics. It is as if you say before Euclid there wasn't geometry, or before Zermelo there wasn't sets. It is still a rough oversimplification. To distinguish heritage and history at this point is hair splitting. This might make sense in philosophy as you called Wittgenstein as your witness, but not here. Still, why shouldn't Kepler count? And this is only the easiest example I've found without digging too deep into years of date.
Anyway, this is a discussion which a) belongs in a separate thread and b) in a different sub-forum. I'll therefore end my participation in it now, the more as I have the feeling you try to convince by repetition instead of argumentation.I agree, this discussion is somewhat fruitless. Both Kepler and Galileo used mathematics, and in that descriptive sense could be said to be doing 'mathematical physics'. The problem is that mathematical physics has historically always referred to calculus/analysis/differential equation type physics namely classical physics without modern physics i.e. what you and I learned in undergraduate physics along with most physicists post-Newton in history. The curriculum of course over the years has become supplemented with more and more subjects from mathematics, probably most strikingly linear algebra which almost no physicist knew before almost halfway past the 20th century. In any case, we are literally arguing semantics, so I'll stop as well.
From actual history, we know that Kepler did not yet have the full tools of Vieta's (elementary) algebra nor Descartes' analytic geometry …… and Newton didn't have differential geometry. This underlines my point of view as a matter of historical developments and doesn't contradict it. Newton wasn't the one and only, but rather one in a long row before and after him, many of them mathematicians by the way, who contributed to physics. It is as if you say before Euclid there wasn't geometry, or before Zermelo there wasn't sets. It is still a rough oversimplification. To distinguish heritage and history at this point is hair splitting. This might make sense in philosophy as you called Wittgenstein as your witness, but not here. Still, why shouldn't Kepler count? And this is only the easiest example I've found without digging too deep into years of date.
Anyway, this is a discussion which a) belongs in a separate thread and b) in a different sub-forum. I'll therefore end my participation in it now, the more as I have the feeling you try to convince by repetition instead of argumentation.
Why doesn't Kepler (1619) count? Because his laws certainly satisfy:
In my opinion it has been simply a matter of the time he lived in. Several parallel developments in mathematics and physics took place and developed in a mathematical handling of physical laws. To reduce this complex process to a single person or even book is which I find disrespectful towards all others who have been involved in it. It is an oversimplification and irregular reduction of history.Many modern mathematicians/scientists tend to mistake what is heritage for what is history. Coincidentally, Feynman also explained this difference: "What I have just outlined is what I call a ‘physicist’s history of physics’, which is never correct… a sort of conventionalized myth-story that the physicist tell to their students, and those students tell to their students, and it is not necessarily related to actual historical development, which I do not really know!". I quote Unguru “to read ancient mathematical texts with modern mathematics in mind is the safest method for misunderstanding the character of ancient mathematics".
From actual history, we know that Kepler did not yet have the full tools of Vieta's (elementary) algebra nor Descartes' analytic geometry, i.e. our conception of a formula was literally a foreign concept to his mind, while it is widely known that Newton directly self-studied Descartes which enabled him to invent calculus, i.e. those prerequisites were central to inventing mathematical physics and it was Newton and only Newton who did so; all other physical theories were subsequently modeled after Newton's paradigmatic way of doing mathematical physics using differential equations.
Addendum: In fact, it is known that Kepler even fudged his statistical analysis of the orbits to end up with his laws. His laws of course are not general enough to be called fundamental laws of physics, while Newton's clearly were; we still to this day say Newton's laws are limiting cases to GR. Still, you have a point that Keplers laws were stated using mathematics, just not in the mathematical physics way we state fundamental laws today. This is mostly because Kepler's laws are just a mathematical encoding of experimental phenomenology, i.e. they are principles, perhaps even fundamental ones. Much of the same can be said for Galileo's work.
Not according to OhanianLooks like a variance in terminology, then. As @Auto-Didact mentions, MTW uses the term "general covariance" to mean what you are using the term "general invariance" to mean. (And since I also learned GR from MTW, I would use "general covariance" to mean that as well.) So you and he actually agree on the physics; you're just using different words.
Before Newton there simply was no such approach to physics and therefore no true inkling of physical law; in this sense it can be said that Newton invented (mathematical) physics.Why doesn't Kepler (1619) count? Because his laws certainly satisfy:
Derivation from first principles of physics is the de facto physicist technique of discovering physical laws and theories from principles based on observation in the form of mathematical statements.In my opinion it has been simply a matter of the time he lived in. Several parallel developments in mathematics and physics took place and developed in a mathematical handling of physical laws. To reduce this complex process to a single person or even book is which I find disrespectful towards all others who have been involved in it. It is an oversimplification and irregular reduction of history.
You know the principle of general covarience is wrong don't you (or rather is totally vacuous as first pointed out by Kretchmann to Einstein – and Einstein agreed – but thought it still had heuristic value)? But that is best suited to the relativity forum.
Its modern version is the principle of general invariance: All laws of physics must be invariant under general coordinate transformations.
Is that what you mean?
Then yes I agree. My two examples of the modern version of classical mechanics would fit that as well.
But I am scratching my head about why the principles I gave from Ballentine would not fit that criteria?
Thanks
BillI learned GR from MTW, since they use the term general covariance it was what stuck with me.
Ballentines "derivation" is very much an axiomatic formalisation/deduction similar to using the Kolmogorov axioms to formalise probability theory. His "derivation" feels nothing at all like say deriving Maxwell's equations from experimental observations, like deriving Einstein's field equations from Gaussian gravity, or even like deriving the covariant formulation of electrodynamics from respecting the Minkowski metric. The key takeaway here is that Ballentine's 'principles' contain no actual observational content whatsoever, making them (mathematical) axioms not (physical) principles.
This of course is not to say that there aren't any first principles in QM, there definitely are, for example most famously Heisenberg's uncertainty principle, which is an experimental observation; a proper physics derivation of QM from first principles should contain a first principle like this, not some semantically (NB: I forgot the correct term) closed statement like the Born rule.
Isn't that what "the principle of general covariance" means?Not according to Ohanian:
https://www.amazon.com/Gravitation-Spacetime-Second-Hans-Ohanian/dp/0393965015
There has been long debate of it:
http://www.pitt.edu/~jdnorton/papers/decades.pdf
Ohanian (1976, pp252-4) uses Anderson’s principle of general invariance to
respond to Kretschmann’s objection that general covariance is physically vacuous. He
does insist, however, that the principle is not a relativity principle and that the general
theory of relativity is no more relativistic than the special theory (~257). Anderson’s
ideas seem also to inform Buchdahl’s (1981, Lecture 6) notion of ‘absolute form
invariance’.
Its Anderson's principle of invarience which technically is – The requirement that the Einstein group is also an invariance group of all physical systems constitutes the principle of general invariance.
I will need to dig up my copy Ohanian to give his exact definition of the two – ie invarience and covarience. What I posted is his definition of invarience which I will need to contrast to his definition of covarience. That will take me a couple of minutes – but need to goto lunch now. I will see if I can do it now, otherwise it will need to wait until I get back.
Thanks
Bill
Its modern version is the principle of general invariance: All laws of physics must be invariant under general coordinate transformations.Isn't that what "the principle of general covariance" means?
the best example is the principle of general covariance.You know the principle of general covarience is wrong don't you (or rather is totally vacuous as first pointed out by Kretchmann to Einstein – and Einstein agreed – but thought it still had heuristic value)? But that is best suited to the relativity forum.
Its modern version is the principle of general invariance: All laws of physics must be invariant under general coordinate transformations.
Is that what you mean?
Then yes I agree. My two examples of the modern version of classical mechanics would fit that as well.
But I am scratching my head about why the principles I gave from Ballentine would not fit that criteria?
Thanks
Bill
And I could also say the same thing.
Didn't you get what was being inferred – we do not use the same methods as Newton because they do not work. We cant elucidate those 'first principles' you talk about, even for such a simple thing as what time is.
The modern definition of time is – its what a clock measures.
Wow what a great revelation – but as a first principle – well its not sating much is it beyond common sense – basically things called clocks exist and they measure this thing called time. It does however have some value – it stops people trying to do what Newton tried – and failed.
Want to know what the 'first principles' of modern classical mechanics is:
1. The principle of least action.
2. The principle of relativity.
Now, if what you say is true then you should be able to state those in your 'first principles' form. I would be very interested in seeing them. BTW 1. follows from QM – but that is just by the by – I even gave a non rigorous proof – see post 3:
https://www.physicsforums.com/threa…fication-of-principle-of-least-action.881155/
You will find it doesn't matter what you do, you at the end of the day end up with very vague, or even when looked at deeply enough, nonsensical statements. That's why it's expressed in mathematical form with some terms left to just common sense in how you apply it. In fact that's what Feynman was alluding to at the end of the second video you posted. Physics is not mathematics but is written in the language of math. How do you go from one to the other? Usually common-sense. But if you want to go deeper then you end up in a philosophical morass that we do not discuss here.
Thanks
BillI'm not sure that you understand that I am saying that our first principles are all literally mathematical statements – all our first principles are observational facts in the form of mathematical statements, the best example is the principle of general covariance.
This changes nothing of the fact that the physicist's method of doing mathematics and of deriving new laws looks almost nothing like the modern mathematician's axiomatic style of doing formal mathematics as is customary since Bourbaki; the gist of mathematics used in physics was maybe 'modern' in the 18th/19th century.
Derivation from first principles is the physicist technique of connecting physical laws and principles
tl;dr mathematicians and physicists tend to use mathematics in completely different ways due to different purposes, this is a good thing.
You somehow manage to twist and misunderstand everything I say. Nowhere did I imply that we still use the same first principles that Newton used, I said that physicists still use derivation from first principles as invented by Newton,And I could also say the same thing.
Didn't you get what was being inferred – we do not use the same methods as Newton because they do not work. We cant elucidate those 'first principles' you talk about, even for such a simple thing as what time is.
The modern definition of time is – its what a clock measures.
Wow what a great revelation – but as a first principle – well its not sating much is it beyond common sense – basically things called clocks exist and they measure this thing called time. It does however have some value – it stops people trying to do what Newton tried – and failed.
Want to know what the 'first principles' of modern classical mechanics is:
1. The principle of least action.
2. The principle of relativity.
Now, if what you say is true then you should be able to state those in your 'first principles' form. I would be very interested in seeing them. BTW 1. follows from QM – but that is just by the by – I even gave a non rigorous proof – see post 3:
https://www.physicsforums.com/threa…fication-of-principle-of-least-action.881155/
You will find it doesn't matter what you do, you at the end of the day end up with very vague, or even when looked at deeply enough, nonsensical statements. That's why it's expressed in mathematical form with some terms left to just common sense in how you apply it. In fact that's what Feynman was alluding to at the end of the second video you posted. Physics is not mathematics but is written in the language of math. How do you go from one to the other? Usually common-sense. But if you want to go deeper then you end up in a philosophical morass that we do not discuss here.
Thanks
Bill
Newton – first principles – well lets look at those shall we:
Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time …
What utter nonsense, and there is zero doubt Feynman would agree. I know those vireos you posted very well and they say nothing of the sort.
With all due respect to Newton of course who as Einstein said was really the only path a man of the highest intellect could take in his time.
But things have moved on.
Thanks
BillYou somehow manage to twist and misunderstand everything I say. Nowhere did I imply that we still use the same first principles that Newton used, I said that physicists still use derivation from first principles as invented by Newton, i.e. we still use the method, which Newton invented, of mathematically deriving physical laws from first principles. Before Newton there simply was no such approach to physics and therefore no true inkling of physical law; in this sense it can be said that Newton invented (mathematical) physics.
In the video Feynman makes crystal clear that the physics approach to mathematics and how mathematics is used in physics to derive laws from principles and vice versa, is as far from formalist mathematician-type axiomatic mathematics as can be.
I feel I need to expand on this by explaining what exactly the difference is between a formal axiomatization as is customarily used in contemporary mathematics since the late 19th/early 20th century and a derivation from first principles as was invented by NewtonNewton – first principles – well lets look at those shall we:
Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time …
What utter nonsense, and there is zero doubt Feynman would agree. I know those vireos you posted very well and they say nothing of the sort.
With all due respect to Newton of course who as Einstein said was really the only path a man of the highest intellect could take in his time.
But things have moved on.
Thanks
Bill
… one of the most important features of the development and the analysis of modern physics is the experience that the concepts of natural language, vaguely defined as they are, seem to be more stable in the expansion of knowledge than the precise terms of scientific language, derived as an idealization from only limited groups of phenomena. To be fair he did not write that in light of future development that shows the exact opposite to an even greater degree than was then known. But even then they knew the work of Wigner and Noether that showed it most definitely is NOT true. It can only be expressed in the language of math.
If you think otherwise state Noether's theorem in plain English without resorting to technical concepts that can only be expressed mathematically. Here is the theorem: Noether's first theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law.
Mathematical concepts used – diferrentiable symmetry and action. If you can explain it in plain English – be my guest.
Thanks
Bill
As for the axiomatic treatment a la Ballentine, I believe the others have answered that adequately, but I will reiterate my own viewpoint: that is a mathematical axiomatization made in a similar vein to measure theoretic probability theory, not a physical derivation from first principles.@bhobba I feel I need to expand on this by explaining what exactly the difference is between a formal axiomatization as is customarily used in contemporary mathematics since the late 19th/early 20th century and a derivation from first principles as was invented by Newton and is practically unaltered customarily used in physics up to this day. I will once again let Feynman do the talking, so just sit back and relax:
I hope this exposition makes things somewhat more clear. If it doesn't, well…
From Physics and Philosophy by Werner Heisenberg
… one of the most important features of the development and the analysis of modern physics is the experience that the concepts of natural language, vaguely defined as they are, seem to be more stable in the expansion of knowledge than the precise terms of scientific language, derived as an idealization from only limited groups of phenomena. This is in fact not surprising since the concepts of natural language are formed by the immediate connection with reality; they represent reality. It is true that they are not very well defined and may therefore also undergo changes in the course of the centuries, just as reality itself did, but they never lose the immediate connection with reality. On the other hand, the scientific concepts are idealizations; they are derived from experience obtained by refined experimental tools, and are precisely defined through axioms and definitions. Only through these precise definitions is it possible to connect the concepts with a mathematical scheme and to derive mathematically the infinite variety of possible phenomena in this field. But through this process of idealization and precise definition the immediate connection with reality is lost. The concepts still correspond very closely to reality in that part of nature which had been the object of the research. But the correspondence may be lost in other parts containing other groups of phenomena.Well, I think the opposite is true. With the refined means of the scientific effort we come closer and closer to reality. Our senses and "natural language" are optimized to survive under the specific "macroscopic" circumstances on Earth but not necessarily to understand realms of reality which are much different in scale than the one relevant for our survival like the microscopic scale of atoms, atomic nuclei, and subatomic/elementary particles or the very large scale of astronomy and cosmology. It's very natural to expect that our "natural language" is unsuitable to describe, let alone in some sense understand, what's going on at these vastly different scales. As proven by evidence the most efficient way to communicate about and to some extent understand nature on various scales is mathematics, and as with natural languages to learn a new language is never a loss but always a gain in understanding and experience.
Bohr and Heisenberg were confronted with simple materialistic views that prevailed in the natural science of the nineteenth century and which were still held during the development of quantum theory by, for example, Einstein. What you call “philosophical ballast“ are at the end nothing else but attempts to explain to Einstein and others that the task of “Physics” is not to promote concepts of materialistic philosophy.What's funny (to me) about the anti-philosophy bent of so many physicists is that many of them actually do have deeply-held philosophical beliefs, but they prefer to only use the word "philosophy" to apply to philosophies that are different from their own.
I'm not quite clear on why it is that if "we can never make deterministic predictions about the results of quantum experiments" that this implies non-reality, as opposed, for example, to a system that is chaotic (in the sense of having dynamics that are highly sensitive to slight changes in initial conditions) with sensitivity to differences in initial conditions that aren't merely hard to measure, but are inherently and theoretically impossible to measure because measurement is theoretically incapable of measuring both location and momentum at the scale relevant to the future dynamics of a particle.Well, Bell's theorem was the result of investigating exactly this question: How do we know that the indeterminacy of QM isn't due to some unknown dynamics that are just too complicated to extract deterministic results from? The answer is: As long as the dynamics is local (no instantaneous long-range interactions), you can't reproduce the predictions of QM this way.
The use of the word "realism" is a little confusing and unclear. But if you look at Bell's proof, a local, realistic theory is one satisfying the following conditions:
Why is the word "realism" associated with these assumptions? Well, let's look at a classical example from probability to illustrate:
Suppose you have two balls, a red ball and a black ball. You place each of them into an identical white box and close it. Then you mix up the two boxes. You give one box to Alice, and another box to Bob, and they go far apart to open their boxes. We can summarize the situation as follows:
If you consider the probability distribution to be a kind of "state" of the system, then this system violates locality: The probability that Bob will find a red ball depends not only on the state of Bob and his box, but also on whether Alice has already found a red ball or a black ball. So this is a violation of condition 2 in my definition of a local realistic theory.
However, the correct explanation for this violation is that classical probability is not a realistic theory. To say that Bob's box has a 50% probability of producing a red ball is not a statement about the box; it's a statement about Bob's knowledge of the box. A realistic theory of Bob's box would be one that describes what's really in the box, a black ball or a red ball, and not Bob's information about the box. Of course, Bob may have no way of knowing what his box's state is, but after opening his box and seeing that it contains a red ball, Bob can conclude, using a realistic theory, "The box really contained a red ball all along, I just didn't know it until I opened it."
In a realistic theory, systems have properties that exist whether or not anyone has measured them, and measuring just reveals something about their value. (I wouldn't put it as "a measurement reveals the value of the property", because there is no need to assume that the properties are in one-to-one correspondence with measurement results. More generally, the properties influence the measurement results, but may not necessarily determine those results, nor do the results need to uniquely determine the properties).
Bell's notion of realism is sort of the opposite of the idea that our observations create reality. Reality determines our observations, not the other way around.
…..superfluous philosophical balastBohr and Heisenberg were confronted with simple materialistic views that prevailed in the natural science of the nineteenth century and which were still held during the development of quantum theory by, for example, Einstein. What you call “philosophical ballast“ are at the end nothing else but attempts to explain to Einstein and others that the task of “Physics” is not to promote concepts of materialistic philosophy.
Yes, and in 1926ff we learnt that this is a misleading statement. The explanation of the photoelectric effect on the level of Einstein's famous 1905 paper does not necessitate the quantization of the electromagnetic field but only of the (bound) electrons.
https://www.physicsforums.com/insights/sins-physics-didactics/I didn' want to be the one to say that and I was pretty sure you or Arnold would have corrected me :smile:
Thanks.
—
lightarrow
From Physics and Philosophy by Werner Heisenberg
… one of the most important features of the development and the analysis of modern physics is the experience that the concepts of natural language, vaguely defined as they are, seem to be more stable in the expansion of knowledge than the precise terms of scientific language, derived as an idealization from only limited groups of phenomena. This is in fact not surprising since the concepts of natural language are formed by the immediate connection with reality; they represent reality. It is true that they are not very well defined and may therefore also undergo changes in the course of the centuries, just as reality itself did, but they never lose the immediate connection with reality. On the other hand, the scientific concepts are idealizations; they are derived from experience obtained by refined experimental tools, and are precisely defined through axioms and definitions. Only through these precise definitions is it possible to connect the concepts with a mathematical scheme and to derive mathematically the infinite variety of possible phenomena in this field. But through this process of idealization and precise definition the immediate connection with reality is lost. The concepts still correspond very closely to reality in that part of nature which had been the object of the research. But the correspondence may be lost in other parts containing other groups of phenomena.
I find the different perspectives interacting here truly entertaining.
We can probably agree that physics is not logic, nor mathematics, nor is it philosophy. But all ingredients are needed, this is why i think physics is so much more fun than pure math.
I think Neumaier said this already elsewhere but there is also a difference in progressing science or creating new sensible hypothesis, and applying mature science to technology. Its not a coincidence that the founders of quantum theory seemed to be very philosophical, and the people that some years later formalized and cleaned up the new ideas was less so. I think it is deeply unfair to somehow suggest that the founders like Bohr or Heisenberg was someone inferior physicists than those that worked out the mathematical formalism better in an almost axiomatic manner. This is not so at all! I think all the ingredients are important. (Even if noone said the word inferior, its easy to get almost that impression, that the hard core guys to math, and the others do philosophy)
On the other hand, RARE are those people that can span the whole range! It takes quite some "dynamic" mindset, to not only understand complex mathematics, but also the importance or sound reasoning and how to create feedback between abstraction and fuzzy reality. If you narrow in too much anywhere along this scale you are unavoidable going to miss the big picture.
As for "wild", I think for some pure theorists and philosophers even a soldering iron my be truly wild stuff! Who knows what can go wrong? You burn tables books and fingers. Leave it to experts ;-)
/FredrikI'd say Bohr (in 1912) and Heisenberg (in 1925) were very important in discovering the new theory to give the more mathematically oriented people the idea to work out. To study Bohr and Heisenberg is historically very interesting but it's not a good way to learn quantum theory since their writings tend to clutter the physics with superfluous philosophical balast which confuses the subject more than it helps to understand it. Of course, you need all kinds of thinkers to make progress in physics, and the philsosophical or more intuitive kind like Bohr and Heisenberg is in no way inferior to the physics/math or more analytical type like Dirac or Pauli. A singular exception is Einstein, who was both since on the one hand he was very intuitive, but he also knew about the necessity of the clear analytical mathematical formulation of the theory, for which part he usually had mathematical help from his collaborators (like Großmann in the case of GR).
If the experimental-physicist tells the theoretical-physicist /how/ to measure something, the latter tells the former /what/ he is actually measuring. :-)
Example: before 1905, experimental-physicists performing photoelectric effect were measuring "light"; after, with A. Einstein, they were measuring "photons" .
—
lightarrowYes, and in 1926ff we learnt that this is a misleading statement. The explanation of the photoelectric effect on the level of Einstein's famous 1905 paper does not necessitate the quantization of the electromagnetic field but only of the (bound) electrons.
https://www.physicsforums.com/insights/sins-physics-didactics/
My viewpoint is that deduction and induction are a false dichotomy, for there is an excluded middle, namely Pierce's abduction. Abduction has historically gotten a bad reputation due to it actually being an example of fallacious reasoning, but even so, it seems to be an effective way of thinking; only a puritan logicist would try to insist that fallacious reasoning was outright forbidden, but I digress.
…
Induction may be necessary to generalize and so generate hypotheses, but inference to the best explanation, i.e. abduction or just bluntly guessing (in perhaps a Bayesian manner) is the only way to actually select a hypothesis from a multitude of hypotheses which can then be compared to experiment; if the guessed hypothesis turns out to be false, just rinse and repeat.You are right of course there are much to elaborate here! (my focus was not on strict dichotomies or not, just a quick comment that this question belongs to a general analysis of inferences)
But a more elaborated treatment would risk diverging. In science indeed abductive reasoning is the right term for "induction of a rule". The exact relation here, and the relevance to physical law and interaction between information processing agents is exactly my core focus. But that whole discussion would quickly go off topic, and off rules.
/Fredrik
Just for reference the more convetional terminology for the various kinds of inferences here are, deductive vs inductive inference.
"hard contradictions" are typically what you get in deductive logic, as this deals with propositions that are true or false.
"soft contradictions" are more of the probabilistic kind, where you have various degrees of beliefs or support in certain propositions.
The history or probability theory has its roots in inductive reasoning and its philosophy. The idea was that in order to make inductive reasoning rational and objective, one can simply "count evidence", and construct a formal measure of "degree of belief". That is one way to understanding the roots of probability theory. Probability theory is thus one possible mathematical model for rational inference.
Popper was also grossly disturbed by the fact that science seemed to be an inductive process, and he wanted to "cure this" buy supress the inductive process of how to generate a new hypothesis from a falsified theory in a rational way, and instead focus on the deductive part: falsification. Ie. his idea was that the progress of science is effectively made at the falsification of a theory – this is also the deductive step – which popper liked! But needless to say this analysis is poor and inappropriate.
Obviously deductive reasoing is cleaner and easier. So if its possible, its not hard to see the preference. But unfortunately reality is not well described by pure deductive reasoning. Propositions corresponding to precesses in nature are rarely easily characterised as true or false.
The intereresting part (IMO) is the RELATION between deductive and inductive reasoning WHEN you take into acount the physical limits of the "hardware" that executes the inferences. This is exactly my personal focus, and how this relates to foundational physics, and the notion of physical law, which is deductive vs the inductive nature of "measurement", which merely "measures nature" by accounting for evidence, in an inductive way.
But almost no people think along these line, ive learned, so this is why i am an oddball here.
/FredrikMy viewpoint is that deduction and induction are a false dichotomy, for there is an excluded middle, namely Pierce's abduction. Abduction has historically gotten a bad reputation due to it actually being an example of fallacious reasoning, but even so, it seems to be an effective way of thinking; only a puritan logicist would try to insist that fallacious reasoning was outright forbidden, but I digress.
Induction may be necessary to generalize and so generate hypotheses, but inference to the best explanation, i.e. abduction or just bluntly guessing (in perhaps a Bayesian manner) is the only way to actually select a hypothesis from a multitude of hypotheses which can then be compared to experiment; if the guessed hypothesis turns out to be false, just rinse and repeat.
Here is where my viewpoint not just diverges away from standard philosophy of science, but also from standard philosophy of mathematics: in my view not only is Pierce's abduction necessary to choose scientific hypotheses, abduction seems more or less at the basis of human reasoning itself. For example, if we observe a dark yellowish transparant liquid in a glass in a kitchen, one is easily tempted to conclude it is apple juice, while it actually may be any of a million other things, i.e. it is possibly any of a multitude of things. Yet our intuition based on our everyday experience will tell us that it probably is apple juice; if we for some reason doubt that, we would check it by smelling or tasting or some other means of checking and then updating our idea what it is accordingly. (NB: contrast probability theory and possibility theory).
But if you think about this even more carefully, we can step back and ask if the liquid was even a liquid, if the cup was even a glass, and so on. In other words, we seem to be constantly be abducing without even being aware that we are doing so or even mistakenly believing we are deducing; the act of merely describing things we see in the world around us in words already seems to require the use of abductive reasoning.
Moreover, much of intuition also seems to be the product of abductive reasoning, which would imply that abduction lays at the heart of mathematical reasoning as well. There is actually a modern school of mathematics, namely symbolism, which seems to be arguing as much although not nearly as explicitly as I am doing here (here is a review paper on mathematical symbolism). In any case, if this is actually true it would mean that the entire Fregean/Russellian logicist and Hilbertian formalist schools and programmes are hopelessly misguided; coincidentally, since @bhobba mentioned him before, Wittgenstein happened to say precisely that logicism/formalism were deeply wrong views of mathematics; after having carefully thought about this issue for years, I tend to be in agreement with Wittgenstein on this.
I like that terminology. I'll have to file it away for future use.Just for reference the more convetional terminology for the various kinds of inferences here are, deductive vs inductive inference.
"hard contradictions" are typically what you get in deductive logic, as this deals with propositions that are true or false.
"soft contradictions" are more of the probabilistic kind, where you have various degrees of beliefs or support in certain propositions.
The history or probability theory has its roots in inductive reasoning and its philosophy. The idea was that in order to make inductive reasoning rational and objective, one can simply "count evidence", and construct a formal measure of "degree of belief". That is one way to understanding the roots of probability theory. Probability theory is thus one possible mathematical model for rational inference.
Popper was also grossly disturbed by the fact that science seemed to be an inductive process, and he wanted to "cure this" buy supress the inductive process of how to generate a new hypothesis from a falsified theory in a rational way, and instead focus on the deductive part: falsification. Ie. his idea was that the progress of science is effectively made at the falsification of a theory – this is also the deductive step – which popper liked! But needless to say this analysis is poor and inappropriate.
Obviously deductive reasoing is cleaner and easier. So if its possible, its not hard to see the preference. But unfortunately reality is not well described by pure deductive reasoning. Propositions corresponding to precesses in nature are rarely easily characterised as true or false.
The intereresting part (IMO) is the RELATION between deductive and inductive reasoning WHEN you take into acount the physical limits of the "hardware" that executes the inferences. This is exactly my personal focus, and how this relates to foundational physics, and the notion of physical law, which is deductive vs the inductive nature of "measurement", which merely "measures nature" by accounting for evidence, in an inductive way.
But almost no people think along these line, ive learned, so this is why i am an oddball here.
/Fredrik
That is really helpful. I've never heard anyone say that quite that clearly before.This surprises me somewhat, I was under the impression that the linearity (or unitarity) of QM was extremely well recognized, i.e. the fact that conventional QM has absolutely nothing to do with nonlinear dynamics; this is exactly why I for example believe that QM can be only at best a provisional theory, because almost all phenomena in nature are inherently non-linear, which is reflected in the fact that historically almost all fundamental theories in physics were special linearized limiting cases which eventually got recast into their more correct non-linear form. This trend continues to this very day; just take a look at condensed matter physics, hydrodynamics, biophysics and so on.
So I have zero idea where you are getting this from – its certainly not from textbooks that carefully examine QM. Textbooks at the beginner/intermediate level sometimes have issues – but they are fixed in the better, but unfortunately, more advanced textsI got this from having read several papers, systematic reviews, conference transcripts and books on the subject. I don't have much time to spare atm but will link to them later if needed.
As for the axiomatic treatment a la Ballentine, I believe the others have answered that adequately, but I will reiterate my own viewpoint: that is a mathematical axiomatization made in a similar vein to measure theoretic probability theory, not a physical derivation from first principles.
That leads to exactly the same situation as QM – a deterministic equation describing a probabilistic quantity. Is that inconsistent too? Of course not. Inconsistency – definition: If there are inconsistencies in two statements, one cannot be true if the other is true. Obviously it can be true that observations are probabilistic and the equation describing those probabilities deterministic. There is no inconsistency at all,Your analogy fails because what you are describing there are internal parts, i.e. a hidden variables theory; for QM these types of theories are ruled out experimentally by various inequality theorems (Bell, Leggett), at least assuming locality, but this seems to be an irrelevant digression.
In any case, what you go on to say here makes it clear that you are still missing my point, namely where exactly the self-inconsistency of QM arises, i.e. not merely of measurement or of the Schrodinger equation, but of full QM: the full theory is not self-consistently captured by a single mathematical viewpoint, like say from within analysis or within geometry. It is instead usually analytic and sometimes stochastically discontinuous. I do not believe that Nature is actually schizofrenic in this manner, and I believe that the fact that QM is displaying these pathological symptoms is due to the physical theory displaying the failure of being merely some linearized limiting case.
Imagine it like this, say you have an analytic function on some time domain, where you artificially introduce in cuts and stochastic vertical translations to the function at certain parts and so manually introduce in discontinuity. Is this new function with artificially added in discontinuities still appropriately something akin to an analytic function? Or is there perhaps a novel kind of mathematical viewpoint/treatment needed to describe such an object, similar to how distribution theory was needed for the Dirac delta? I don't know, although I do have my own suspicions. What I do know is that insisting that 'QM as is is fully adequate by just using the ensemble interpretation; just accept it as the final theory of Nature' does not help us one bit further in going beyond QM.
Lastly, I think Penrose here says quite a few sensible things and extremely relevant things on exactly the topic at hand:
dare I say prescient:That hit the bullseye indeed!
(I had actually never seen that particular clip of feynmann before)
/Fredrik
I'm not quite clear on why it is that if "we can never make deterministic predictions about the results of quantum experiments" that this implies non-realityDefinition of "reality" It's a humain being viewpoint … popper's three worlds, Heisenberg's 3 regions of knowledge, …
If any physical law is merely a bet on action, the scandal of probability ceases: far from being an inadequate substitute for our power to know, it is the springboard of all scientific activity.
It is easier to aknowledge that physical laws are gambles of action when no way of interpreting them as descriptions of an independent, detached, "primary" nature is unanimously accepted … Instead: an inventory of relations-with/withing-natureView attachment 218360
View attachment 218363
Best regards
Patrick
I don't know that my intuition means much; it's extremely difficult for most people who already know a subject in detail to imagine how people who don't have that knowledge will respond to different ways of conveying it. But FWIW, my intuition is that the "shut up and calculate" interpretation is pedagogically the best place to start, because until you understand the underlying math and predictions of QM, trying to deal with any interpretation on top of that is more likely to confuse you than to help you.Feynman's response to this is extremely apt, dare I say prescient:
is there any serious research into which interpretation is most effective pedagogically?I don't know of any, but I'm not at all up to speed on this kind of research.
what is your intuition on that point?I don't know that my intuition means much; it's extremely difficult for most people who already know a subject in detail to imagine how people who don't have that knowledge will respond to different ways of conveying it. But FWIW, my intuition is that the "shut up and calculate" interpretation is pedagogically the best place to start, because until you understand the underlying math and predictions of QM, trying to deal with any interpretation on top of that is more likely to confuse you than to help you.
A better way of asking the question you might be trying to ask is, do people care about case 1 vs. case 2 because of the different ways the two cases suggest of looking for a more comprehensive theory of which our current QM would be a special case? The answer to that is yes; case 1 interpretations suggest different possibilities to pursue for a more comprehensive theory than case 2 interpretations do. Such a more comprehensive theory would indeed make different predictions from standard QM for some experiments. But the interpretations themselves are not the more comprehensive theories; they make the same predictions as standard QM, because they are standard QM, not some more comprehensive theory.That was part of the question I was trying to ask.
Going back to one of the other issues that doesn't get into a more comprehensive theory, is there any serious research into which interpretation is most effective pedagogically? If not, what is your intuition on that point?
even if they are indistinguishable in practiceThey aren't indistinguishable "in practice"; they're indistinguishable period.
A better way of asking the question you might be trying to ask is, do people care about case 1 vs. case 2 because of the different ways the two cases suggest of looking for a more comprehensive theory of which our current QM would be a special case? The answer to that is yes; case 1 interpretations suggest different possibilities to pursue for a more comprehensive theory than case 2 interpretations do. Such a more comprehensive theory would indeed make different predictions from standard QM for some experiments. But the interpretations themselves are not the more comprehensive theories; they make the same predictions as standard QM, because they are standard QM, not some more comprehensive theory.
I certainly get the feeling that people who are debating the interpretations feel like they are arguing over more than semantics and terminology.Yes, they do. But unless they draw the key distinction I am drawing between interpretations of an existing theory, standard QM, and more comprehensive theories that include standard QM as a special case, they are highly likely to be talking past each other. Which is indeed one common reason why discussions of QM interpretations go nowhere.
Also, if you find yourself thinking that case 1 and case 2 make different predictions, you are doing something wrong. The whole point of different interpretations of QM is that they all use the same underlying mathematical model to make predictions, so they all make the same predictions. If you have something that makes different predictions, it's not an interpretation of QM, it's a different theory.Isn't the reason that people would care about case 1 v. case 2 that even if they are indistinguishable in practice for the foreseeable future, or at least, even if it is not even theoretically possible to ever distinguish the two even in theory, that one could imagine some circumstances either with engineering that is literally impossible in practice (along the lines of Maxwell's Demon), or (e.g. with Many Worlds) with an observer located somewhere that it is impossible for anyone from the perspective of our universe at a time long after the Big Bang to see, where case 1 and case 2 would imply different things?
Likewise, even if case 1 v. case 2 are indistinguishable in the world of SM + GR core theory, wouldn't a distinction between one and the other have implications for what kind of "new physics" would be more promising to investigate in terms of BSM hypothesis generation?
For example, suppose the "state" of case 2 is "real" (whatever that means). Might that not suggest that brane-like formulations of more fundamental theories might make more sense to investigate than they would if case 1 is a more apt interpretation?
I certainly get the feeling that people who are debating the interpretations feel like they are arguing over more than semantics and terminology. After all, if it really were only just purely semantics, wouldn't the argument between the interpretations be more like the argument between drill and kill v. New Math ways to teaching math: i.e., between which is easier for physics students to learn and grok more quickly in a way that gives them the most accurate intuition when confronted with a novel situation (something that incidentally is amenable to empirical determination), rather than over which is right in a philosophical way?
Again, a theory book or scientific paper has not the purpose to tell how something is measured. That's done in experimental-physics textbooks and scientific papers! Of course, if you only read theoretical-physics and math literature you can come to the deformed view about physics that everything should be mathematically defined, but physics is no mathematics. It just uses matheamtics as a language to express its findings using real-world devices (including our senses to the most complicated inventions of engineering like the detectors at the LHC).If the experimental-physicist tells the theoretical-physicist /how/ to measure something, the latter tells the former /what/ he is actually measuring. :-)
Example: before 1905, experimental-physicists performing photoelectric effect were measuring "light"; after, with A. Einstein, they were measuring "photons" .
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