Quantum Mechanics without Measurement

stevendaryl

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There's unfortunately a tendency to take a particular way of explaining quantum weirdness and assuming that it's the heart of quantum mechanics. Then you can find nonquantum analogies, and feel comforted (or disappointed, depending on your personality) that things aren't really so weird, after all.

The one that people latched onto from the very beginning was Heisenberg's "disturbance" interpretation of his uncertainty principle. To try to measure position of a tiny particle very precisely, you have to "see" it with a very small-wavelength light ray. But since light carries momentum as well, this changes the trajectory of the electron in an uncontrolled way. So no experiment can precisely determine the position and momenta of a particle. Similarly, measuring the z-component of an electron's spin invariably changes the x-component of spin in an uncontrollable way. So you think of the uncertainty principle in terms of the existence of incompatible properties where the set-up to measure one necessarily prevents you from measuring the other.

But the genius of the EPR experiment is that it gets around this problem. If you have two particles that have opposite spins, then you can measure the z-component of spin for one particle, and measure the x-component of spin for the other particle. Since the spins are correlated perfectly, this allows us to know the spins in the x-direction and z-direction simultaneously. But quantum mechanics doesn't allow us to make that conclusion (which would be perfectly justified from the point of view of classical probability and logic).
 
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This has got me thinking. Is anyone working on a meta-interpretation? By this, I essentially mean a single mathematical expression of all possible interpretations of quantum physics.

What we have at the moment are many interpretations that select aspects of classicality to lock down and allow those remaining to have non-classical features in a hypothetical world, but conververgence in observable cases. It seems that it should, in theory at least, be possible to express this combination of features in a mathematical form. I'm going to go as far as suggesting that we should be able to derive such an expression.

I'm going to make a wild conjecture here, but imagine if such a meta-interpretation provided a hint on how to unite gravity with QM. Can anyone demonstrate that such a hint couldn't exist?
 
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martinbn

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I don't think the Feynman example is very good. I think you need to add a moment of time. Say, "F. is going to be a good physicist tomorrow at 5pm" is meaningful. So is "F. is going to be a good lover tomorrow at 5pm". But when you connect them with an "and" to form "F. is going to be a good physicist tomorrow at 5pm and F. is going to be a good lover tomorrow at 5pm" you get a meaningless statement.
 

Demystifier

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I sort of get the analogy. However, in the case of Feynman, we could bring the framework into the question, for example:

"If we were speaking from within the framework of physics, would you say that Feynman was a good physicist?"

"If we were speaking from within the framework of lovemaking, would you say that Feynman was a good lover?"

So it's possible that both of these questions can have the answer "yes" simultaneously. Feynman can't demonstrate the truth of both of these at the same time, because the demonstration of one requires a setting that is incompatible with the demonstration of the other. But it still makes sense to ask if both are true simultaneously.

This is sort of like "contrafactual definiteness" in discussions of Bell's inequality. Measuring the spin of an electron in the x-direction is incompatible with measuring the spin in the z-direction. So we can't, with a single experiment, know the answer to the questions:

"Is the electron spin-up in the z-direction?"
"Is the electron spin-up in the x-direction?"

However, you could make the questions into hypotheticals as follows:

"If I were to measure the z-component of spin, would I get spin-up?"
"If I were to measure the x-component of spin, would I get spin-up?"

By analogy with the Feynman case, one might think that it makes sense to ask the two questions simultaneously, even if there is no way to determine the answers (by a single experiment). You might think that a question whose answer cannot be know might as well be meaningless. But that's not exactly true, because people can do case-based analysis. For example, in logic, you can reason

  • If A is true, then B is true.
  • If A is false, then C is true.
  • Therefore, B or C must be true.
The violation of Bell's inequality in EPR type experiments shows, in a sense, that certain conjunctions whose truth values are unknown cannot consistently be given a truth value. It's not just that we can't know or demonstrate the truth of the conjunction, but that it really doesn't have a consistent truth value.
I agree with everything you say above. But in your opinion, what (if anything) does it tell us about the Griffiths interpretation?
 

Demystifier

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But when you connect them with an "and" to form "F. is going to be a good physicist tomorrow at 5pm and F. is going to be a good lover tomorrow at 5pm" you get a meaningless statement.
Fine. But suppose you want to EXPLAIN why F. (or anybody else) is never a physicist and a good lover at the same time. Would you count the assertion above (that it is meaningless) as an explanation?
 

stevendaryl

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I don't think the Feynman example is very good. I think you need to add a moment of time. Say, "F. is going to be a good physicist tomorrow at 5pm" is meaningful. So is "F. is going to be a good lover tomorrow at 5pm". But when you connect them with an "and" to form "F. is going to be a good physicist tomorrow at 5pm and F. is going to be a good lover tomorrow at 5pm" you get a meaningless statement.
Maybe. Except that you can imagine letting Feynman do a coin toss at the last minute to do physics or to make love. Then before the coin toss, it is certainly meaningful to say "If the result is heads, then Feynman will be a good physicist." and it is meaningful to say "If the result is tails, then Feynman will be a good lover." I don't see any reason for the conjunction to be meaningless. They could both be true. Presumably, a detailed theory of what makes a good physicist or a good lover would be able to say whether the statement "If the result is heads, then Feynman will be a good physicist" is true before actually tossing the coin.
 

stevendaryl

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I agree with everything you say above. But in your opinion, what (if anything) does it tell us about the Griffiths interpretation?
Only that Griffiths' approach seems to be the same kind of abandonment of classical logic for histories that quantum logic is for properties at a single moment. He's able to recover classical logic only by restricting statements to a collection of "compatible" statements.
 

atyy

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Fine. But suppose you want to EXPLAIN why F. (or anybody else) is never a physicist and a good lover at the same time. Would you count the assertion above (that it is meaningless) as an explanation?
But maybe that is not the right criticism of CH. When they say "Copenhagen done right", I assume they mean the possibility that quantum mechanics is truly weird and there cannot be hidden variables (let's say QM and Lorentz invariance are exact, so that dBB is ugly; and also there is no arrow of time, so many-worlds is also ugly). Then doesn't CH solve the measurement problem within an unrealistic framework?

(I guess your answer is "no", because there is no single framework in CH?)
 

Demystifier

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Only that Griffiths' approach seems to be the same kind of abandonment of classical logic for histories that quantum logic is for properties at a single moment. He's able to recover classical logic only by restricting statements to a collection of "compatible" statements.
Fine. But in your opinion, does the physicist/lover complementarity can help us to better understand the Griffiths approach? And if it does, would you say that it increaes or decreses the value of his approach?
 

Demystifier

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But maybe that is not the right criticism of CH. When they say "Copenhagen done right", I assume they mean the possibility that quantum mechanics is truly weird and there cannot be hidden variables (let's say QM and Lorentz invariance are exact, so that dBB is ugly; and also there is no arrow of time, so many-worlds is also ugly). Then doesn't CH solve the measurement problem within an unrealistic framework?

(I guess your answer is "no", because there is no single framework in CH?)
My answer is indeed "no", but for a different reason. If I cannot solve a problem by other means, then accepting it's weirdness will not resolve the problem either. At best it may make me stop thinking about the problem, which perhaps is not bad at all, but just because I stopped thinking about the problem doesn't mean I have solved it.
 
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Fine. But suppose you want to EXPLAIN why F. (or anybody else) is never a physicist and a good lover at the same time. Would you count the assertion above (that it is meaningless) as an explanation?
No, I wouldn't. F. being a classical dude can exist in an eigenstate of being a good lover and a good physicist at the same time. Whenever you measure each attribute you will get a consistent result which ever order to measure them in and how many times (within reason!). Hence it is not meaningless to say he is both at the same time. They are not mutually incompatible.

However if the spin of a spin 1/2 particle with S^2 = s(s+1)} has a component 1/2 along the z axis it cannot also have a component of 1/2 along the x axis at the same time. The geometry of a triangle would say that the most it can be would be 1/√2 so the eigenstates are mutually incompatible.
 

atyy

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My answer is indeed "no", but for a different reason. If I cannot solve a problem by other means, then accepting it's weirdness will not resolve the problem either. At best it may make me stop thinking about the problem, which perhaps is not bad at all, but just because I stopped thinking about the problem doesn't mean I have solved it.
If Bell's theorems are correct, and if the inequalities can be shown to be violated, then we are left with nonlocal realism or local nonrealism or superdeterminism or variables over which a probability distribution does not exist. dBB solves the measurement problem in nonlocal realism. Would you accept CH as a solution to the question of what local nonrealism might be in a way that solves the measurement problem (eg. solipsism is local nonrealism, but it has a measurement problem)?
 
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martinbn

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Maybe. Except that you can imagine letting Feynman do a coin toss at the last minute to do physics or to make love. Then before the coin toss, it is certainly meaningful to say "If the result is heads, then Feynman will be a good physicist." and it is meaningful to say "If the result is tails, then Feynman will be a good lover." I don't see any reason for the conjunction to be meaningless. They could both be true. Presumably, a detailed theory of what makes a good physicist or a good lover would be able to say whether the statement "If the result is heads, then Feynman will be a good physicist" is true before actually tossing the coin.
So! There is not claim that all conjunctions are meaningless. But you have completely changed the experimental set up. This is a different scenario.
 

martinbn

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Fine. But suppose you want to EXPLAIN why F. (or anybody else) is never a physicist and a good lover at the same time. Would you count the assertion above (that it is meaningless) as an explanation?
Yes, if it is a logical necessity it is a good explanation. But what is your point? If it is something is meaningless it is meaningless, saying the opposite cannot be a part of a good explanation.
 

atyy

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Here are some of the criticisms of CH I've heard. Have these been resolved or are they non-problems?

1. Dowker and Kent say that it isn't obvious that there is any quasiclassical realm in CH. http://arxiv.org/abs/gr-qc/9412067

2. Laloe says that in CH there are consistent histories in which the cat is both dead and alive. http://arxiv.org/abs/quant-ph/0209123 (p88)
 

Demystifier

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Yes, if it is a logical necessity it is a good explanation.
Yes, but CH is not a logical necessity. For instance, nonlocal hidden variables are logically not excluded.

But what is your point? If it is something is meaningless it is meaningless, saying the opposite cannot be a part of a good explanation.
Generaly, something can be meaningless only within a certain predefined rules of language. The CH interpretation proposes one such set of rules, and within this language some statements are meaningless. But they still have meaning outside of this language, i.e., in some other interpretation of quantum mechanics. So the real question is: Should we accept the rules of language proposed by CH? My point is that we shouldn't.
 

Demystifier

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Would you accept CH as a solution to the question of what local nonrealism might be in a way that solves the measurement problem
No I wouldn't.

(eg. solipsism is local nonrealism, but it has a measurement problem)?
In an attempt to understand local nonrealism as a kind of solipsism WITHOUT a measurement problem, I have constructed my own model of solipsistic local hidden variables:
http://lanl.arxiv.org/abs/1112.2034 [Int. J. Quantum Inf. 10 (2012) 1241016]
 

DevilsAvocado

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Some people think that such an emphasis on measurement is appropriate, since physics is an empirical science, and empirical science is founded on measurements, experiments, observations, etc. However, I find it very unsatisfactory for measurement to play a key role in the formulation a of fundamental theory because measurements are not fundamental.
I absolutely agree, and so do J. S. Bell in his last article – Against ‘Measurement’ (1990).

[PLAIN said:
http://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf]Here[/PLAIN] [Broken] are some words which, however legitimate and necessary in application, have no place in a formulation with any pretension to physical precision: system, apparatus, environment, microscopic, macroscopic, reversible, irreversible, observable, information, measurement.

The concepts 'system', 'apparatus', 'environment', immediately imply an artificial division of the world, and an intention to neglect, or take only schematic account of, the interaction across the split. The notions of 'microscopic' and 'macroscopic' defy precise definition. So also do the notions of 'reversible' and 'irreversible'. Einstein said that it is theory which decides what is 'observable'. I think he was right – 'observation' is a complicated and theory-laden business. Then that notion should not appear in the formulation of fundamental theory. Information? Whose information? Information about what?

On this list of bad words from good books, the worst of all is 'measurement'. It must have a section to itself.
A measuring device is, after all, a physical object, presumably governed by the same physical laws that govern atoms and molecules and light and gravity. What makes a particular physical object suitable to be considered a "measuring device" is pretty complicated:

  • There must be an interaction between the system being measured and states of the measuring device.
  • The measuring device must act as an "amplifier", so that microscopic properties of the system being measured can trigger macroscopic changes in the state of the device.
  • The measuring device must have states that are sufficiently "orderly" to interpret easily. Either, there must be a number of discrete states in the measuring device that are observably different, or else there must be a continuous sets of states that can readily be interpreted as a linear scale.
  • The act of measurement should result in a "record", an irreversible change that can be reliably checked later.
Yes, and to be picky (and maybe make things worse), there are also quantum "measuring devices", for example a beamsplitter; where we do have an interaction and measurement of states, but no microscopic amplification or irreversibility (i.e. quantum measurements could easily be undone).

It seems that the root of the 'confusion' is the Schrödinger wavefunction vs. the Born rule |ψ|2, which afaik is just a 'hack', without any rigorous mathematical 'explanation'. Bell seems to agree even on this point.

[PLAIN said:
http://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf]In[/PLAIN] [Broken] the beginning, Schrodinger tried to interpret his wave- function as giving somehow the density of the stuff of which the world is made. He tried to think of an electron as represented by a wavepacket – a wavefunction appreciably different from zero only over a small region in space. The extension of that region he thought of as the actual size of the electron - his electron was a bit fuzzy. At first he thought that small wavepackets, evolving according to the Schrodinger equation, would remain small. But that was wrong. Wavepackets diffuse, and with the passage of time become indefinitely extended, according to the Schrodinger equation. But however far the wavefunction has extended, the reaction of a detector to an electron remains spotty. So Schrodinger's 'realistic' interpretation of his wavefunction did not survive.

Then came the Born interpretation. The wavefunction gives not the density of stuff, but gives rather (on squaring its modulus) the density of probability. Probability of what, exactly? Not of the electron being there, but of the electron being found there, if its position is 'measured'.

Why this aversion to 'being' and insistence on 'finding'? The founding fathers were unable to form a clear picture of things on the remote atomic scale. They became very aware of the intervening apparatus, and of the need for a 'classical' base from which to intervene on the quantum system. And so the shifty split.
And the "shifty split" is still there; 24 years later, as Steven Weinberg explains.

[my bolding]
[PLAIN said:
http://scitation.aip.org/content/aip/magazine/physicstoday/article/58/11/10.1063/1.2155755]Bohr’s[/PLAIN] [Broken] version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wavefunction (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?

Considerable progress has been made in recent years toward the resolution of the problem, which I cannot go into here. It is enough to say that neither Bohr nor Einstein had focused on the real problem with quantum mechanics. The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wavefunction, the Schrödinger equation, to observers and their apparatus. The difficulty is not that quantum mechanics is probabilistic — that is something we apparently just have to live with. The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics.
Regarding Griffiths; the urge to 'eradicate' measurements altogether, I think has more to do with the problem that we do have empirical evidence (i.e. EPR-Bell experiments) that do not fit his consistent worldview – and the easiest thing to do is just to get rid of the whole enchilada, by some preposterous word-salad, that no one can take seriously.

And yet it moves -- Galileo Galilei

Griffiths makes two disastrous mistakes:

1)
Bell's theorem is a no-go theorem, which put restrictions on the classical world, not quantum mechanics, and to try to solve this dilemma by 'modifications' on Hilbert space, quantum logic, etc, is just ridiculous. QM works – classical local realism don't!

We can forget everything about Bell's theorem and QM, and instead put "Barnum & Bailey Circus – The Greatest Show on Earth", in its place:

Code:
 Classical      |     Barnum & Bailey              |     Classical
----------------------------------------------------------------------------
 Source  -->    |     Entanglement Circus   -->    |     Measurement data 
----------------------------------------------------------------------------
Now, if we empirically have tested the Barnum & Bailey Circus for almost a hundred years, without finding one single error, we have to assume that this circus is not cheating, right?

And since the outcome is classical, we can inspect the results without any 'influences' from Barnum & Bailey, right?

Then, the only rational way is to check if we can replicate the 'trick' without Barnum & Bailey, and if we can't do this, then the only option left is modifications in our view on the classical part, even if it hurts, right?

Thus, it doesn't really matter what 'trick' Barnum & Bailey performs, because we have checked their business model for almost a hundred years, and Barnum & Bailey are true/compatible to all tests performed this far (which also means that this reputation can never be taken away from them, no matter what happens in the future), right?

Conclusion: We must modify our view* on the classical part in this show; this is the only way out, Griffiths is on the wrong path, leading to a dead end.

*I.e. "Barnum & Bailey" has the capability to perform a 'trick' that is empirical true, but impossible to replicate with only the tools available in the classical part.

2)
Griffiths tries to put science on The Platonic Pedestal of Eternal, Ultimate and Consistent Truth – but he has already lost the game (obviously without even knowing it). Gödel's incompleteness theorem proves that any system that is sufficiently powerful cannot be both consistent and complete.

Thus, Griffiths is using logic – proven to be either inconsistent or incomplete – to prove physics consistent and complete.​

Result = Inconsistent Fairy Tales
 
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atyy

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DevilsAvocado

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This, indeed, is the main problem with the Griffiths interpretation. To avoid EPR "paradox" and consequences of the Bell theorem, Griffiths proposes to abandon the rules of classical LOGIC, replacing them with a kind of quantum logic:
http://lanl.arxiv.org/abs/1105.3932
http://lanl.arxiv.org/abs/1110.0974
Most physicists, mathematicians, and even logicians, find it very unattractive.

In particular, let me quote from http://www.scholarpedia.org/article/Bell's_theorem
"[...] By forbidding the reasoning used to prove inequality (1), the aforementioned rule of CH prevents us from arriving at the contradiction. But a physical theory is not simply a game for which one can impose arbitrary rules about what reasonings are permitted for the propositions of the theory;"
The problem is that Griffiths wants to avoid the Bell theorem, according to which hidden variables (not necessarily deterministic) must necessarily be nonlocal. He avoids Bell theorem not by rejecting assumptions of the Bell theorem, but by rejecting classical LOGIC leading from the assumptions to the theorem.

Indeed, any logical conclusion may be avoided by rejecting the rules of logic. This technique, for instance, is often used by politicians. But should we allow it in science? I don't think so.
Thank you very much for this Demystifier. In an earlier thread, I did find it necessary to defend Griffiths as not being a crackpot. After all, he is a Professor of Physics at Carnegie Mellon University.

But now, I'm not so sure about this...
 

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