Distinguishing classical physics vs. quantum physics

[PeterDonis]

I need a specific reference to your method.

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

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

 

[secur]

For some time I've been wondering 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.

... but I'm not sure a freshman who has never taken physics would understand it.

If you really want to address someone "who has never taken physics" few of these answers will do it. If you tell them that "$qp-pq=i\hbar$" 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!

This is alright for a layperson: "quantum has inherent randomness classical doesn't", and a couple other attempts also.

can I get some help from the wisemen?

If there's one word that describes, quite precisely, what almost all physicists aren't, it's "wise".

Since only 37% of high school students have taken a physics class, "any college freshman" is a standard that will probably be harder to meet than you intend.

Good point. But really it's not that hard, if you happen to be a teacher.

With a person who has never had any physics, the first thing to tell them is "QM is mainly about very small things like atoms. Classical is about bigger things". Then, "QM generally gives uncertain answers, classical gives exact, certain answers". And "QM is the real truth, classical is an approximation to it".

I can for example distinguish Newtonian Theory from GR by saying, "A clock on a mountain top runs faster than one at sea level according to tests and GR, but NT says they run the same.". I consider this both simple and short, while also providing a concrete, simple example of different predictions. I would like something similar for CT v QT.

These two are good: "QT is consistent with the stability of the matter surrounding us (a prerequisite for our very existence!), while classical physics isn't" (@vanhees71) and "A radioactive atom decays according to QM but not according to classical mechanics" (@A. Neumaier).

I'm not saying which of these is "best", or even that they're entirely accurate. I just want to emphasize, this is how to talk to non-physicists.

Finally this would also be appropriate for a layman: "The basic ideas of QM are easier to understand than a lot of classical physics, contrary to what you may have heard."

 

[ftr]

I thought the standard answer would be that we do not know of any sharp boundary between QM and CM. However, we have some ideas about how CM arises from QM via Correspondent principle and Ehrenfest theorem. As a matter of fact I have been looking into Ehrenfest theorem of Dirac's relativistic equation for altogether a different reason but it also takes QM vs CM arguments to a different height.

http://physics.lnu.edu.ua/jps/2015/1/pdf/1003-10.pdf

In some other sense both QM and CM have action at distance and invisible fields of sorts.

 

[vanhees71]

There is no boundary between QM and CM. CM is an approximation to QM, referring to "macroscopic observables", i.e., coarse grained "microscopic observables". Today there are no known boundaries of validity of QT. One also shouldn't say that QT doesn't make accurate predictions about the behavior of nature since there are no known contradictions between observations and the predictions of QT, and as far as QT is tested (and it's the best tested and most challenged physical theory ever) it is astonishingly accurate (in some cases 16 or more significant digits of accuracy in the comparison between theory and experiment).

 

[secur]

One also shouldn't say that QT doesn't make accurate predictions about the behavior of nature since there are no known contradictions between observations and the predictions of QT...

Sure, but some of the predictions are probabilistic. "It might be spin up or spin down" is 100% verified by observation. It's always one or the other.

I've accurately predicted the results of every U.S. election since 1960! There was never a contradiction between my predictions and the actual result! - Because I always predicted that either the Democratic or the Republican candidate would win. But for some reason, no one is very impressed with my political analysis skills.

 

[maline]

(in some cases 16 or more significant digits of accuracy in the comparison between theory and experiment).

Wow! The most I had heard about till now was 10 digits. Would you mind providing links?

 

[vanhees71]

Well, QT tells us that that the probabilities are inherent in nature and not just our ignorance about the future. Don't be to critical against your political analysis skills. Most polls over the last elections were wrong. At least your predictions are save ;-).

 

[Zafa Pi]

A radioactive atom decays according to QM but not according to classical mechanics.

Hold on a minute. Are you saying CM forbids atomic decay? Decay was certainly known before QM.

 

[secur]

Decay was indeed known towards the end of the 19th century, before QM. (In fact the phenomenon was noticed long before that.) But CM had, and has, no way to explain it - although they tried. To say it "forbids" it wouldn't be exactly correct, CM just has no theory to deal with it. Of course once you postulate the basic fact you can analyze it statistically, for large samples, without understanding the mechanism; you might call that a "classical" analysis.

 

[Zafa Pi]

Well, QT tells us that that the probabilities are inherent in nature and not just our ignorance about the future.

Indeed, everyone seems to think so. In post #1 I even said as much, "quantum has inherent randomness classical doesn't", but I rejected it.
It's funny, I look through various QT axiom schema and I can't find inherent anywhere. I do find axioms that say that measurements are random variables, and I am unable to find any cause for the random nature of of measurements of entangled photons, but so what. Hence it would be really nice to see a proof (that convinces one who believes in super-determinism).

 

[Zafa Pi]

Decay was indeed known towards the end of the 19th century, before QM. (In fact the phenomenon was noticed long before that.) But CM had, and has, no way to explain it - although they tried. To say it "forbids" it wouldn't be exactly correct, CM just has no theory to deal with it. Of course once you postulate the basic fact you can analyze it statistically, for large samples, without understanding the mechanism; you might call that a "classical" analysis.

At first I went along with Neumaier"s statement; "A radioactive atom decays according to QM but not according to classical mechanics.", but now I have problems.
1st off a radioactive atom is one where we notice decay, so the first half of his statement is a tautology.
2ndly CT didn't have an explanation for why masses produced gravitational forces, but there was Newton's formula and gravity was apart of CT.
3rdishly As you point out, CT had statistical laws for decay and acknowledges it does occur, but was silent for why decay occurred. Well for that matter so is QT.
What is the cause of radioactive decay?
(sorry but I don't know how to condense a link into a word)

 

[secur]

Indeed, everyone seems to think so. In post #1 I even said as much, "quantum has inherent randomness classical doesn't", but I rejected it.

It's funny, I look through various QT axiom schema and I can't find inherent anywhere. I do find axioms that say that measurements are random variables, and I am unable to find any cause for the random nature of of measurements of entangled photons, but so what. Hence it would be really nice to see a proof (that convinces one who believes in super-determinism).

There can never be a proof, either theoretical or experimental, that QM randomness or uncertainty is truly "inherent". As far as we know right now, it is. That's shown by the fact that representing measurements as RV's gives the right answer. But we might someday find a way to predict the RV's value. If so it would no longer be an RV - instead it would be a deterministic equation of some sort. This possibility can never be ruled out.

However it is sensible to look for a proof of this nature: given some other facts of physics (symmetry, conservation laws, etc) show that inherent randomness logically follows from them. For instance uncertainty principle is easily proved given the (current) fundamental math of QM (due to Dirac), which represents complementary observables such as position and momentum as Fourier transforms. That's a "conditional proof" that uncertainty is inherent. Bell's theorem is of this nature also, but conversely.

It's also sensible to continue to experimentally check that randomness is still inherent under new experimental conditions not previously tested. For instance, (just off the top of my head), someday check whether radium half-life is affected by strong gravity waves. No reason it should be but you don't know until you try.

In these ways we can expect to become more and more sure that the randomness is truly inherent. But obviously it can never be proven for certain. Someday we might get a surprise.

Uncertainty of the truth value of physical theories is inherent.

 

[Zafa Pi]

There can never be a proof, either theoretical or experimental, that QM randomness or uncertainty is truly "inherent". As far as we know right now, it is.

Here is the short version of your two sentences: "We can't prove it, but we know it's true."
vanhees71 is a little more sure about things than you, I'm still hoping for a proof.

Uncertainty of the truth value of physical theories is inherent.

Are you sure about that?

 

[Nugatory]

However it is sensible to look for a proof of this nature: given some other facts of physics (symmetry, conservation laws, etc) show that inherent randomness logically follows from them. For instance uncertainty principle is easily proved given the (current) fundamental math of QM (due to Dirac), which represents complementary observables such as position and momentum as Fourier transforms. That's a "conditional proof" that uncertainty is inherent.

Is it? The randomness is already an axiom of the fundamental math of QM, so it's to be expected that any conclusion based on that fundamental math is going to be consistent with that axiom and randomness. The current state of affairs is "QM is inherently random. We don't know whether QM is the last word"; to move beyond that we would need to find a theory that underlies QM so that it is no longer the last word. When and if we have that theory we can consider whether it is deterministic or random, but as long as QM is the only game in town the randomness is already an axiom.

 

[Nugatory]

Here is the short version of your two sentences: "We can't prove it, but we know it's true."
vanhees71 is a little more sure about things than you, I'm still hoping for a proof.

You won't find one within the framework of QM, because it's already an axiom there.

 

[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.