I Distinguishing classical physics vs. quantum physics

[PeterDonis]

The randomness is already an axiom of the fundamental math of QM

The existence of no collapse interpretations like the MWI would seem to indicate that this can't be right. In the MWI, there is no randomness; the quantum state evolves by unitary evolution, which is perfectly reversible and deterministic. And there is no randomness in measurement results, because all measurement results happen. In fact, the challenge of the MWI is to explain how the Born rule for "probabilities" arises since there are no probabilities in the fundamental math.

 

[Nugatory]

The existence of no collapse interpretations like the MWI would seem to indicate that this can't be right. In the MWI, there is no randomness; the quantum state evolves by unitary evolution, which is perfectly reversible and deterministic. And there is no randomness in measurement results, because all measurement results happen. In fact, the challenge of the MWI is to explain how the Born rule for "probabilities" arises since there are no probabilities in the fundamental math.

As I see it, MWI just moves the randomness around. No matter which interpretation I choose the mathematical formalism will not allow me predict the outcome of my measurement even with complete knowledge of the initial conditions. Yes, with MWI I don't have the wave function collapsing to a random value with probabilities given by the Born rule, but instead I'm left wondering why I'm looking at this measurement result instead of one of the others that also happened.

 

[secur]

The existence of no collapse interpretations like the MWI would seem to indicate that this can't be right. In the MWI, there is no randomness; the quantum state evolves by unitary evolution, which is perfectly reversible and deterministic. And there is no randomness in measurement results, because all measurement results happen. In fact, the challenge of the MWI is to explain how the Born rule for "probabilities" arises since there are no probabilities in the fundamental math.

You're right: probability in MWI - demonstrating Born rule - is still an unsolved challenge. But for the sake of argument let's suppose it can be solved (FWIW,IMHO it can be). Then MWI would be a complete consistent interpretation. But that still doesn't disprove inherent randomness.

MWI says that from the observer's point of view fundamental math of QM is correct. (Note the observer can be thought of as an "Information Gathering and Utilizing System", and the issue of consciousness completely ignored). IOW MWI agrees precisely with the "naïve" collapse theory.

But MWI adds an extra superstructure: many worlds in a Block Universe. That is indeed, deterministic, but not from any point of view we can have. BU depends on, or assumes, a "super-observer" (sometimes called "God's-eye view"). At the moment, as far as we know, that can't possibly be observed or detected. It's irrelevant to humans, unless there's some new breakthrough.

So what MWI actually proves is that determinism is possible - which we already knew. It doesn't prove determinism is real.

 

[PeterDonis]

No matter which interpretation I choose the mathematical formalism will not allow me predict the outcome of my measurement even with complete knowledge of the initial conditions.

Yes, it will. The formalism tells you that all possible outcomes occur. So obviously it can't tell you "which one" will occur, since it's telling you they all occur.

instead I'm left wondering why I'm looking at this measurement result instead of one of the others that also happened.

There is a "you" who is looking at all of those other results, just a slightly different one--each of "you" has exactly the same history up to that point, so you're all almost identical, you just have that one last observation that differs. And each of "you" is wondering the exact same thing, because "you're" all forgetting that there isn't just one of "you".

Bear in mind, I'm not saying I agree with the MWI; I'm just saying that I don't see how it includes any randomness. It just requires a drastic rethinking of what the QM formalism is actually telling us.

 

[PeterDonis]

MWI says that from the observer's point of view fundamental math of QM is correct.

No, it doesn't. It says there is one wave function and it evolves by unitary evolution. It says nothing at all about "observers" or "points of view".

MWI adds an extra superstructure: many worlds in a Block Universe.

No, MWI just recognizes that that structure is already there in the QM formalism. As soon as you realize that, according to the formalism, there is one wave function and it evolves by unitary evolution, the "many worlds" are there; nothing else has to be added. They're there because that one wave function can't possibly be an eigenstate of all operators, which is what would have to be the case for there to be "just one world".

 

[secur]

@PeterDonis, I don't agree, but it's not worth arguing about.

 

[Zafa Pi]

When a determinist says, "The outcome of a coin flip in a wind tunnel is not inherently random, but is in principle determined by the conditions prior and during the flip."

Or when a quantumist says,

The current state of affairs is "QM is inherently random.

Or when a godist says, "There is a god."
It's all the same to me. I'm an apatheist .

 

[secur]

@Zafa Pi, you remind me of ...

I don't believe in magic
I don't believe in I-ching
I don't believe in Bible
I don't believe in Tarot
I don't believe in Hitler
I don't believe in Jesus
I don't believe in Kennedy
I don't believe in Buddha
I don't believe in Mantra
I don't believe in Gita
I don't believe in Yoga
I don't believe in Kings
I don't believe in Elvis
I don't believe in Zimmerman
I don't believe in Beatles

I just believe in me, Yoko and me, and that's reality

I'm even more apatheistic than John Lennon: I don't believe in Yoko either :-)

 

[Zafa Pi]

@Zafa Pi, you remind me of ...
I'm even more apatheistic than John Lennon: I don't believe in Yoko either :-)

As an apatheist, it isn't that I don't believe in, say inherent randomness or god, it's that I'm apathetic, I just don't care.
Question: When Lennon mentioned Zimmerman was he referring to Dylan?
BTW, I believe in Lennon, Ali, and Einstein.

 

[A. Neumaier]

Are you saying CM forbids atomic decay? Decay was certainly known before QM.

but is cannot be modeled using classical mechanics. Spectrosdcopy was also known before QM, but classical mechanics has no explanation or even place for it.

 

[A. Neumaier]

1st off a radioactive atom is one where we notice decay, so the first half of his statement is a tautology.

One can predict with QM the rate of decay. If this is a tautology then all theoretical physics is, since one can notice everything it predicts correctly!

 

[A. Neumaier]

how to eloquently distinguish classical and quantum physics. What I mean by eloquent is both simple and short. By simple I mean understandable to any college freshman, and with that caveat, as short as possible.

QM predicts spectra, CM doesn't.

 

[vanhees71]

In QM Born's rule is a postulate. It's unlikely that one can proof it somehow from the other postulates (see Weinberg, Lectures on Quantum Mechanics, Cambridge University Press 2012). So far I don't know of any evidence that there is anywhere the classical determinism left. I guess, if one can find a deterministic theory, then it will be even less comprehensible than quantum theory, because given the fact that Bell's inequality is violated as predicted by QT one must give up locality, and this will be a big challenge to be made compatible with the relativistic space-time structure and causality.

Concerning radioactive decay, I've no clue, how it could be understandable within classical mechanics beyond a purely statistical ("random walk") rule: The decay probabilities are given and then implemented in terms of a rate equation, in the most simple case leading just to radioactive decay of A to B+X (like one of the three usual decay mechanisms of radioactivity, called $\alpha$, $\beta$, and $\gamma$, because it was just not understood what's really going on).

With quantum (field) theory it's easy to describe as interactions causing transitions from one state to another, and thus the only microscopic mechanism to "explain" the radioactive decays known today. With "explain" I mean to finally trace it back to the interactions that we take as "fundamental" today,i.e., those described by the Standard Model of Elementary particles; the three decay forms correspond to the strong interaction (cluster formation within nuclei "preforming" $\alpha$ particles, i.e., $\text{He}^4$ nuclei within the nucleus which then tunnel through the potential barrier a la Gamav), the weak interaction ($\beta$ decay of one quark flavor to another quark flavor and leptons like $\text{n} \rightarrow e^-+\bar{\nu}_e + \text{p}$, i.e., the decay of a down quark to an up-quark and the leptons within the neutron, and the electromagnetic interaction, which is nothing else than an electromagnetic transition of an excited nuclei leading to the decay to a less excited nucleus (maybe even to its ground state) and a photon. This is all described in terms of quantum field theory by taking the unstable particles/nuclei as resonances and calculating perturbatively their width, i.e., lifetime which figures into the decay rates to be put into the phenomenological rate equations.

Note that this is an approximation, which is strictly speaking contradicting basic principles of quantum field theory, namely the unitarity of the S-matrix, according to which there cannot be any strictly exponential decay law (see the textbook of Sakurai, 2nd edition). In the energy domain that's the statement that the spectral function of the unstable state cannot be a strict Lorentzian.

 

[houlahound]

Is this too simple;

The experimental outcomes of QT depend on the integer parameter "n", CM the outcomes do not vary.

 

[Zafa Pi]

Is this too simple;

The experimental outcomes of QT depend on the integer parameter "n", CM the outcomes do not vary.

Not too simple for me. I don't get it.

 

[houlahound]

Trying a different approach;

re the OP - a quantum particle requires the specification of a set of numbers to define the state of the particle and its observable properties that have no counterpart in CM eg: n, l, m, z, s.

 

[Zafa Pi]

One can predict with QM the rate of decay. If this is a tautology then all theoretical physics is, since one can notice everything it predicts correctly!

I agree that saying, "One can predict with QM the rate of decay." is not a tautology. But your earlier statement, "A radioactive atom decays according to QM" is what I was referring to.
I also agree that your statement in post #62, "QM predicts spectra, CM doesn't." is is accurate and elegantly short, but I doubt a freshman lit major would be familiar with the concept "spectra".

 

[houlahound]

Tunnelling in general is pure QM.

 

[Zafa Pi]

Note that this is an approximation, which is strictly speaking contradicting basic principles of quantum field theory, namely the unitarity of the S-matrix, according to which there cannot be any strictly exponential decay law (see the textbook of Sakurai, 2nd edition). In the energy domain that's the statement that the spectral function of the unstable state cannot be a strict Lorentzian.

Wow, I always thought that lifetime till decay was governed by an exponential distribution and was well documented by experiment. I'm not familiar with your explanation, but what is the law in that case?

 

[Zafa Pi]

Tunnelling in general is pure QM.

True enough, and nicely short. But what I was after in my OP was something a college freshman would understand.

 

[houlahound]

I think you are short changing the intelligence of the average freshman. Tunnelling is the conceptually simplest thing to visualise with a simple sketch yet it is classically impossible that nobody would argue.

 

[ftr]

True enough, and nicely short. But what I was after in my OP was something a college freshman would understand.

I am an EE who is interested in physics from the early days of college and spent many many hours investigating the subject. Even with good background in classical electromagnetic being part of my field, I still struggle to have a good mental picture of what QM is as related to CM or on its own. Moreover, the conceptual difference ( not necessarily the weird things like ERP.. etc) are also interpretation dependent. But I also think with any science student who is interested in QM today with vast amount of knowledge on the internet and libraries at his fingertip should not have much problem getting the hang of it.

Ya, it is an interesting exercise, but I wouldn't worry about it.

 

[Zafa Pi]

Ya, it is an interesting exercise, but I wouldn't worry about it.

You got a pill for that? I've been dwelling about it on and off for months.

 

[secur]

Wow, I always thought that lifetime till decay was governed by an exponential distribution and was well documented by experiment. I'm not familiar with your explanation, but what is the law in that case?

Exponential decay takes over when decoherence has separated the decay modes / states, by sending off-diagonal elements of density matrix (correlations) to zero. After that happens probabilities are classical and we get exponential decay. But before they decohere, right at the beginning of the decay event ... I don't really know what it does but it's not exponential, due to interference between potential decay states.

The tail of the distribution also isn't exactly exponential. I'd be interested to hear why that is.

This non-exponentiality hasn't yet been verified experimentally AFAIK. But no doubt QM will turn out to be right, as usual.

 

[Zafa Pi]

If you really want to address someone "who has never taken physics" few of these answers will do it. If you tell them that "qp−pq=iℏqp−pq=iℏqp-pq=i\hbar" or "Alice and Bob are too far apart to communicate and neither knows what the other is doing, etc" they'll give a totally blank look - and never again ask you anything about physics!

Over the past three days I've given my story in post #1 to several high school graduates and they seem to understand it, but can not fathom a no answer. Just what I expected and wanted. Maybe you think I should want something else.

 

[Zafa Pi]

Exponential decay takes over when decoherence has separated the decay modes / states, by sending off-diagonal elements of density matrix (correlations) to zero. After that happens probabilities are classical and we get exponential decay. But before they decohere, right at the beginning of the decay event ... I don't really know what it does but it's not exponential, due to interference between potential decay states.

The tail of the distribution also isn't exactly exponential. I'd be interested to hear why that is.

This non-exponentiality hasn't yet been verified experimentally AFAIK. But no doubt QM will turn out to be right, as usual.

I like it, it sounds cool, but I don't understand, "but it's not exponential, due to interference between potential decay states."

 

[secur]

Maybe you think I should want something else.

Not at all.

I like it, it sounds cool, but I don't understand, "but it's not exponential, due to interference between potential decay states."

I don't really know what it does but it's not exponential, due to interference between potential decay states.

But the basic idea is clear. When the decay states are decohered, and obey classical probabilities, each decays at its own unique (except for degeneracy) decay rate eigenvalue. But when there's interference you get some hard-to-calculate semi-random mix of the different decay rates. It wouldn't look exponential; it might even increase at times. If you can get data at that granularity, 10^-20 seconds (typical), the graph would start off irregular. But soon it would become smooth exponential decay, because, according to MWI, this particular instance of you has become entangled with one of the decohered eigenstates. And if you believe that I've got a great deal on Nigerian gold mines you might be interested in. Please PM.

 

[vanhees71]

I think the non-exponential decay due to quantum effects has been observed in atomic transitions.

For a detailed discussion about theory on non-exponential decay, see the following paper

https://arxiv.org/abs/1110.5923

 

[houlahound]

Wooh, that is a tough paper.

 

[A. Neumaier]

I also agree that your statement in post #62, "QM predicts spectra, CM doesn't." is is accurate and elegantly short, but I doubt a freshman lit major would be familiar with the concept "spectra".

Replace ''spectra'' by ''spectral lines in a rainbow pattern obtained by shining sun light through a prism'', and they will understand. (Or they won't understand anything about classical and quantum mechanics anyway.)

 

[A. Neumaier]

Tunnelling in general is pure QM.

except that the name is completely spurious. If it were really tunneling, the rate should be independent of the height of the barrier. But is goes to zero as the barrier gets larger and larger.

 

[houlahound]

Mr Nuemaier an you comment on tunnelling of EM waves. I get confused because it was observed before QM and has a full classical explanation - is it a quantum thing?

 

[A. Neumaier]

tunnelling of EM waves. I get confused because it was observed before QM and has a full classical explanation

Please give a reference so that I can comment.

 

[houlahound]

https://en.m.wikipedia.org/wiki/Total_internal_reflection#Frustrated_total_internal_reflection

It is leakage/tunnelling across a forbidden gap by my reckoning. Sorry about the basic level link.

 

[A. Neumaier]

https://en.m.wikipedia.org/wiki/Total_internal_reflection#Frustrated_total_internal_reflection

It is leakage/tunnelling across a forbidden gap by my reckoning. Sorry about the basic level link.

This is mathematically the same as quantum 1-photon tunneling. In both cases, the barrier height affects the tunneling efficiency, and an astromomically high barrier would produce negligible tunneling.

 

[bhobba]

In QM Born's rule is a postulate. It's unlikely that one can proof it somehow from the other postulates (see Weinberg, Lectures on Quantum Mechanics, Cambridge University Press 2012).

Just to elaborate a bit. Weinberg is of course correct. But, via Gleason, can be reduced to something that at first sight seems to have nothing to do with it, and within the formalism of QM seems almost trivial. In fact when you go through Gleason its so obvious its easy to miss - but its there. But it isn't trivial. In fact its telling us something very very deep about QM - but that requires a whole new thread.

The key point was reformulated as the Kochen-Specker theorem, but its really a simple corollary to Gleason. That it went this way has an interesting history:
https://plato.stanford.edu/entries/kochen-specker/

I believe this obscures its main import - its really the reason for the Born-Rule.

Thanks
Bill

 

[Zafa Pi]

Bell's original papers. See, for example, equation (2) here:

http://www.drchinese.com/David/Bell_Compact.pdf

Sorry for taking so long to get back to you, though you were always in my thoughts. I finally got around to perusing Bell's paper you recommended, thank you.
His proof that expectation value (e.v.) generated via hidden variables (2) cannot capture the e.v. from QM (3) (page 404) does in fact require CFD. This is in opposition to your posts #21 and #14.

For a given trial of the experiment only two measurements are made A(a,λ) and B(b,λ) = -A(b,λ) (1). However on the way to proving his nifty (15) the first equation at the top of page 406 we see three measurements A(a,λ), A(b,λ), and A(c,λ). The only way to get a third measurement in a single formula is employing CFD, we get the value of a measurement that wasn't made. That's what hidden variables allows one to do.

His proof is cute because it is short and only employs three measurements instead of the usual four as in CHSH, beside beating everyone to the punch, for which his name rings loud in the halls of QM.
I attended the - 50th anniversary of his paper - symposium in Vienna. The world came, it was was truly wonderful.

 

[PeterDonis]

The only way to get a third measurement in a single formula is employing CFD, we get the value of a measurement that wasn't made.

This is not correct. P(a, b) and P(a, c) in the formula at the top of p. 406 refer to probability distributions obtained from two sets of runs--one set with settings a, b for the two measuring devices, the other with settings a, c for the two measuring devices. Similarly, P(b, c) in equation 15 and the equation just above it refers to a third set of runs, where the settings are b, c for the two measuring devices. There are no counterfactuals at all; everything is in terms of statistics done on actual observed results. And of course when these experiments are actually done, that is exactly how they are done and how they are analyzed; nobody assumes any results for measurements that are not made.

 

[Zafa Pi]

This is not correct. P(a, b) and P(a, c) in the formula at the top of p. 406 refer to probability distributions obtained from two sets of runs--one set with settings a, b for the two measuring devices, the other with settings a, c for the two measuring devices. Similarly, P(b, c) in equation 15 and the equation just above it refers to a third set of runs, where the settings are b, c for the two measuring devices. There are no counterfactuals at all; everything is in terms of statistics done on actual observed results. And of course when these experiments are actually done, that is exactly how they are done and how they are analyzed; nobody assumes any results for measurements that are not made.

Would you say that the usual CHSH or GHZ uses CFD? If so where? If not then we have a fundamental disagreement on the nature of CFD that I can foresee may be very difficult to resolve.

BTW P(a,b) is not a probability distribution it is a number, an expectation value, allegedly = -a•b

 

[PeterDonis]

Would you say that the usual CHSH or GHZ uses CFD?

If you can give a specific reference I will take a look at it.

 

[Zafa Pi]

If you can give a specific reference I will take a look at it.

For CHSH try page 114 of Quantum Computation and Quantum Information by Nielsen and Chuang (favorite of mine and Demystifier).
I looked on the internet for GHZ and was appalled at how long and clumsy all the presentations were. I posted a presentation during a dialogue with rubi. It was simple and very short, but I can't recall the thread. Do you know of a way I can go about finding it?

 

[Zafa Pi]

If you can give a specific reference I will take a look at it.

I rewrote it for your viewing pleasure (or not).

Physical set up for GHZ:
Alice, Bob, Carol, and Eve are all mutually one light minute apart. At noon Eve simultaneously sends a light signal to each of A, B, and C. When A receives her signal she flips a fair coin. If it comes up heads she selects (via some objective process) a value of either 1 or -1 and calls that Ah. If she flips tails she selects 1 or -1 and calls it At. This takes her less than ½ minute. Each of B and C do the same, calling their selections Bh, Bt, and Ch, Ct.

If we assume that no influence or information can go faster than the speed of light (called locality) then none of the three know what the others flipped, nor can one's selection influence another's.

GHZ Theorem: Let's assume that if only one of A, B, or C flipped a head then the product of their selections equals -1.
I.e., we assume -1 = Ah•Bt•Ct = At•Bh•Ct = At•Bt•Ch.
Then we may conclude if all three flipped heads their product would be -1. I.e., -1 = Ah•Bh•Ch.

Proof: -1 = (Ah•Bt•Ct)•(At•Bh•Ct)•(At•Bt•Ch) = At²•Bt²•Ct²•Ah•Bh•Ch which implies that -1 = Ah•Bh•Ch. QED

If Eve sent each of A, B, C one photon from the entangled triple state |ψ⟩ = √½(|000⟩ + |111⟩) and if flipping a head selects the value obtained by measuring a photon with Pauli X and flipping a tail means measuring with Pauli Y, then X⊗Y⊗Y and Y⊗X⊗Y and Y⊗Y⊗X each operating on |ψ⟩ yield -1, so the hypothesis of the Theorem is satisfied. However, X⊗X⊗X operating on |ψ⟩ gives 1, contradicting the conclusion.

Lab tests show the QM predictions are correct. So what's wrong?

Why other sites take pages of gobbledygook is beyond me. Maybe you see a reason.

 

[PeterDonis]

the entangled triple state |ψ⟩ = √½(|000⟩ + |111⟩)

Your notation is somewhat confusing; earlier you gave the eigenvalues of the measurements as 1 and -1, but in this expression it looks like they are 0 and 1. Also, which basis (X or Y, or something else) is this expression written in?

 

[Zafa Pi]

Your notation is somewhat confusing; earlier you gave the eigenvalues of the measurements as 1 and -1, but in this expression it looks like they are 0 and 1. Also, which basis (X or Y, or something else) is this expression written in?

The eigenvalues are 1 and -1. I am using the standard q-computing notation, see Nielsen and Chuang.
|ψ⟩ = √½(|000⟩ + |111⟩) = √½[1,0,0,0,0,0,0,1] in the 8D tensor product space is an eigenvector of X⊗Y⊗Y with eigenvalue -1 and is an eigenvector of X⊗X⊗X with eigenvalue 1.

 

[PeterDonis]

|ψ⟩ = √½(|000⟩ + |111⟩) = √½[1,0,0,0,0,0,0,1] in the 8D tensor product space

In which basis on that space?

 

[Zafa Pi]

In which basis on that space?

|0⟩ = [1,0], |1⟩ = [0,1] are the basic qubits, |000⟩ = |0⟩⊗|0⟩⊗|0⟩ = [1,0,0,0,0,0,0,0], |001⟩ = |0⟩⊗|0⟩⊗|1⟩ = [0,1,0,0,0,0,0,0], etc. If you don't have access to N & C any reference to q-computing should do. It is the slickest QM notation.

If the QM is a bit obscure it doesn't matter. The point is that QM satisfies the hypothesis but negates the conclusion of the Theorem. So how is that resolved?

 

[PeterDonis]

|0⟩ = [1,0], |1⟩ = [0,1] are the basic qubits

In which basis? Do you understand what that question means? There are an infinite number of possible pairs of basis qubits. Which of them are you using?

 

[zonde]

In which basis on that space?

Here is Zeilingers version in chapter 16.2 (not very long either): https://vcq.quantum.at/fileadmin/Publications/2002-12.pdf

 

[Zafa Pi]

In which basis? Do you understand what that question means? There are an infinite number of possible pairs of basis qubits. Which of them are you using?

The basis in 2D is [1,0] and [0,1], the higher dimensions are built up of tensor products. If you find this inadequate check out N&C.
But your questions are side stepping the crucial question as I said above.
As we pursue this line, I must admit I am nervous that you may use your god like powers to cut out my posts. We are a bit off topic and perhaps we should leave it with I am convinced that Bell used CFD in his argument and you are convinced he didn't.
Or we could start a separate thread on this topic, or whatever you wish.

 

[Zafa Pi]

Here is Zeilingers version in chapter 16.2 (not very long either): https://vcq.quantum.at/fileadmin/Publications/2002-12.pdf

Zeilinger's version and mine are the same. Where he has |H⟩₁ |H⟩₂ |H⟩₃ I have |0⟩|0⟩|0⟩ = |0⟩⊗|0⟩⊗|0⟩ = |000⟩ as per Nielsen & Chaung.