Distinguishing classical physics vs. quantum physics

[Zafa Pi]

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.

Something like: "quantum has inherent randomness classical doesn't", I don't think works because "inherent randomness" isn't simple and I'm not even convinced the statement is valid. It is short.

"Quantum violates Bell's inequality classical doesn't." could possibly be made simple , but then no longer short.

What about: "In classical, outcomes depend on the past, in quantum they don't" I'm not sure it's true, does this need freewill? (Conway-Kochen) Is "outcome" simple? Probably.

I've been toying with:
Alice and Bob are too far apart to communicate and neither knows what the other is doing.
If Alice and Bob both perform experiment X they will get the same result.
Alice performs X and gets result 1, while Bob performs Y and gets 2.
If Bob had performed X instead would he have necessarily gotten 1?
Yes is classical, no is quantum.

It's xmas time can I get some help from the wisemen?

 

[vanhees71]

The most simple statement for me is that QT is consistent with the stability of the matter surrounding us (a prerequisite for our very existence!), while classical physics isn't.

 

[rubi]

The difference between classical physics and quantum physics is that quantum physics is contextual. Mathematically, this is a consequence of the fact that the algebra of yes/no questions is no longer a $\sigma$-algebra and hence, the functional that assigns probabilities to yes/no questions is no longer a probability measure, i.e. you get a generalization of classical probability theory.

 

[A. Neumaier]

how to eloquently distinguish classical and quantum physics. What I mean by eloquent is both simple and short.

The simplest (3 characters only) is $$(1)~~~~~\hbar=0?$$ Next simple (5 characters) is $$(2)~~~~~qp=pq?$$ In more words (equivalently but less eloquently, according to your definition), do position $q$ and momentum $p$ commute? This follows from (1) and $$(3)~~~~~qp-pq=i\hbar.$$ This really is the essence of the difference between classical and quantum mechanics, and indeed, this was the starting point of modern quantum mechanics (Heisenberg 1925).

But many here seem to hold the view that the most eloquent distinction is intelligible vs. weird...

 

[Vanadium 50]

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.

 

[bhobba]

QM is based on the following axiom (or two axioms if you do not want to invoke Gleason):
https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

The dynamics follows from symmetry - see chapter 3 Ballentine.

The Principle Of Least Action follows from those axioms and using that plus exactly the same symmetry principles you get classical physics - see Landau Mechanics.

The basis of classical mechanics is QM but both use exactly the same symmetry principles (specifically the principle of relativity)

Interestingly one of the fundamental basics of Quantum Field Theory is also least action principles and even deeper symmetry principles (gauge symmetries for example) - but here its not derived from anything - its just the way nature is. This is a great mystery right now.

Thanks
Bill

 

[Strilanc]

Scott Aaronson is fond of saying quantum mechanics just preserves the 2-norm instead of the 1-norm.

 

[Nugatory]

I don't know of any short'n'sweet way of expressing it... But the fact that otherwise identical particles cannot be distinguished by their classical trajectories has very important non-classical consequences.

 

[Zafa Pi]

The most simple statement for me is that QT is consistent with the stability of the matter surrounding us (a prerequisite for our very existence!), while classical physics isn't.

Thanks. It is short and I find it simple, but I'm not sure a freshman who has never taken physics would understand it. What's important to me is that your post shows I didn't formulate my question very well. Even: "Classical Theory is is not valid (doesn't agree with observations), whereas CT is valid as far as we know." which is simpler yet, but is not what I'm after.

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.

The posts above are all interesting, but not what I had in mind. The Alice and Bob story at the bottom of my OP is as close as I have gotten. Is it valid? Can it be beaten?

 

[PeterDonis]

The Alice and Bob story at the bottom of my OP is as close as I have gotten. Is it valid?

I'm not sure it is. For one thing, you start out specifying, by hypothesis, that if Bob runs experiment X he will get the same result as Alice. Then you end up asking whether, if Bob had run experiment X, he would get the same result that Alice got. This doesn't seem like a way to distinguish classical from quantum physics; it seems like a way to test whether the reader was paying attention.

I would focus on violations of the Bell inequalities, particularly if you use forms in which the violations are not probabilistic, but simple yes/no tests: Alice and Bob could each make a particular yes/no measurement, and if they both get the same result, you have quantum physics, whereas if they get opposite results, you have classical physics. See, e.g., here:

https://en.wikipedia.org/wiki/GHZ_experiment

 

[bhobba]

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.

That is really BAD. In the Australian curriculum physics is required, along with all the other sciences including Earth science in grade 7,8,9 and 10 so that by the end of year 10 they have done the equivalent of at least one year of physics. Specialist science schools of course do more, but its not required in grade 11 and 12. The only issue I have is 11 and 12 physics is not calculus based despite the fact virtually everyone that takes it does calculus in 11 and 12. Its sad though that once its not compulsory very few students elect to do it these days. When I did 11 and 12 everyone did it along with calculus to US calculus BC standard. Even politicians out here are VERY worried by this - and rightly so.

The future belongs to STEM areas - at least our politicians understand it - but doing something about it is proving very difficult. You get extra points for university entrance doing those subjects, and we have specialist schools, they are looking at science teacher quality, all sorts of things are being tried but nothing seems to work.

Thanks
Bill

 

[Eye_in_the_Sky]

The posts above are all interesting, but not what I had in mind.

How about this?
_____

Keep a one-world picture.

Keep the counters (i.e. measuring instruments of Alice and Bob) and the source (i.e. instrument of preparation) as classical objects in spacetime.

Keep the normative causal structure of spacetime (i.e. cause precedes effect, and no faster-than-light propagation).

[So far, this is all just standard classical physics.]
_____

Now ask the question:

Can the influence of the source upon the counters be construed as a propagation within spacetime?

In CM the answer is always YES.

In QM the answer is sometimes NO.

 

[Zafa Pi]

I'm not sure it is. For one thing, you start out specifying, by hypothesis, that if Bob runs experiment X he will get the same result as Alice. Then you end up asking whether, if Bob had run experiment X, he would get the same result that Alice got. This doesn't seem like a way to distinguish classical from quantum physics; it seems like a way to test whether the reader was paying attention

I would focus on violations of the Bell inequalities, particularly if you use forms in which the violations are not probabilistic, but simple yes/no tests: Alice and Bob could each make a particular yes/no measurement, and if they both get the same result, you have quantum physics, whereas if they get opposite results, you have classical physics. See, e.g., here:

https://en.wikipedia.org/wiki/GHZ_experiment

Yes indeed, it does seem "like a way to test whether the reader was paying attention." However we are at the meat of the Bell inequality.
Alice got 1 when Bob chose experiment Y. How do you know she would have have gotten 1 if he had chosen X instead? The usual argument goes like: Well the reality confronting Alice would have been the same what ever Bob did (they were sufficiently separated) so she would have had to get 1, and thus so would he. This is the argument from realism and is exactly what is needed to prove the Bell inequality (or the GHZ equality). And what QM measurements of entangled photons show is false.

My Alice and Bob story at post #1 doesn't need all the rest of the extra details for a simple proof of a Bell inequality (including GHZ).

BTW, my favorite Bell like result is GHZ, however I've presented 7 different versions with proofs to freshman math students and though GHZ is the shortest the most convincing regularly turned out to be a simplified version of CHSH.

 

[PeterDonis]

Alice got 1 when Bob chose experiment Y. How do you know she would have have gotten 1 if he had chosen X instead?

Because you said that Alice performed X and got 1. It's really, really hard to deal with counterfactuals; that's why I suggested picking a setup where you don't need them.

 

[Zafa Pi]

Can the influence of the source upon the counters be construed as a propagation within spacetime?

In CM the answer is always YES.

In QM the answer is sometimes NO.

It seems valid to me, but would a freshman lit major understand? This is the problem I had with the other posts.

 

[Zafa Pi]

Because you said that Alice performed X and got 1. It's really, really hard to deal with counterfactuals; that's why I suggested picking a setup where you don't need them.

I agree that the uninitiated will find a no answer to my story really strange (QM is weird), but counterfactuals are necessary to prove Bell inequalities and the GHZ result.

 

[PeterDonis]

counterfactuals are necessary to prove Bell inequalities

No, they're not. The Bell inequalities just show that no theory whose mathematical model for generating probabilities for measurement results has a certain form can reproduce the predictions of QM. Some people interpret the mathematical model that obeys the inequalities using counterfactuals, but that's not required.

 

[Eye_in_the_Sky]

It seems valid to me, but would a freshman lit major understand? This is the problem I had with the other posts.

Okay. Maybe then along Peter's line:

I would focus on violations of the Bell inequalities, particularly if you use forms in which the violations are not probabilistic, but simple yes/no tests: Alice and Bob could each make a particular yes/no measurement ...

... But with Hardy's example:

Each of the instruments of Alice and Bob have two settings, 1 and 2, for which the outcomes can be YES or NO.

Then:

(0) For the configuration <a₁,b₁>: the outcome (NO,NO) is sometimes obtained.

(1) For the configuration <a₁,b₂>: if a₁ gives NO, then b₂ gives YES with certainty.

(2) For the configuration <a₂,b₁>: if b₁ gives NO, then a₂ gives YES with certainty.

(3) For the configuration <a₂,b₂>: the outcome (YES,YES) is forbidden.

 

[Zafa Pi]

No, they're not. The Bell inequalities just show that no theory whose mathematical model for generating probabilities for measurement results has a certain form can reproduce the predictions of QM. Some people interpret the mathematical model that obeys the inequalities using counterfactuals, but that's not required.

Oh boy, we've gone around on this in another thread. A Bell inequality arises from a theorem whose hypothesis contains certain values (like the 4 values in CHSH) Where do those values come from? That's the classical part.

 

[Zafa Pi]

Okay. Maybe then along Peter's line:... But with Hardy's example:

Each of the instruments of Alice and Bob have two settings, 1 and 2, for which the outcomes can be YES or NO.

Then:

(0) For the configuration <a₁,b₁>: the outcome (NO,NO) is sometimes obtained.

(1) For the configuration <a₁,b₂>: if a₁ gives NO, then b₂ gives YES with certainty.

(2) For the configuration <a₂,b₁>: if b₁ gives NO, then a₂ gives YES with certainty.

(3) For the configuration <a₂,b₂>: the outcome (YES,YES) is forbidden.

Yes, Hardy's example is cool. The state of the entangled photons is more complicated than usual, but so what. Nonetheless you still must say that Alice and Bob are appropriately separated and they flip coins to not allow the other to know what is being selected, etc. When all is said and done you have a nice Bell result, but it will turn out to be longer than my story and I suspect even more confusing for the lit major. But that is just an opinion.

 

[PeterDonis]

A Bell inequality arises from a theorem whose hypothesis contains certain values (like the 4 values in CHSH)

No, that's just a particular example to illustrate the theorem. The theorem itself does not assume any particular values; it assumes that the probabilities for measurement results are generated by a function which is factorizable in a particular way. The theorem then proves that probabilities generated by such a function must obey certain inequalities. The probabilities generated by QM violate those inequalities; hence, no model which generates probabilities using such a function can match the predictions of QM.

 

[Zafa Pi]

No, that's just a particular example to illustrate the theorem. The theorem itself does not assume any particular values; it assumes that the probabilities for measurement results are generated by a function which is factorizable in a particular way. The theorem then proves that probabilities generated by such a function must obey certain inequalities. The probabilities generated by QM violate those inequalities; hence, no model which generates probabilities using such a function can match the predictions of QM.

OK, I'm lost. Are you talking about CHSH? If not then I don't know what you are referring to. One needs to show that classical can't produce the QM correlations, I need a specific reference to your method.

 

[zonde]

For some time I've been wondering how to eloquently distinguish classical and quantum physics.

I would put it like that:
In classical physics particles are self contained while in quantum physics they are not.

 

[Zafa Pi]

I would put it like that:
In classical physics particles are self contained while in quantum physics they are not.

Well that is short and only uses simple words, but I don't know what self contained means. I'm not being picky, I really don't know.

 

[vanhees71]

I agree that the uninitiated will find a no answer to my story really strange (QM is weird), but counterfactuals are necessary to prove Bell inequalities and the GHZ result.

This for sure is the wrong discouraging message. QT is not weirder than any other mathematical description of nature. Only when philosophers and other soft science afficionados get their hands on it, it becomes weird, but these guys can do this with the most simple facts about our world too ;-)).

 

[vanhees71]

I would put it like that:
In classical physics particles are self contained while in quantum physics they are not.

What do you want to say with that? I have no clue. In relativistic physics particles are not "self contained". It's even difficult if not impossible to formulate a fully selfconsistent model of interacting classical particles in relativistic physics, while relativistic QFT leads to a consistent description at least in terms of perturbation theory or lattice gauge theory.

 

[zonde]

Well that is short and only uses simple words, but I don't know what self contained means. I'm not being picky, I really don't know.

Look up the words in dictionary: http://www.thefreedictionary.com/self-contained

 

[zonde]

In relativistic physics particles are not "self contained". It's even difficult if not impossible to formulate a fully selfconsistent model of interacting classical particles in relativistic physics,

But non-interacting particles are self-contained in relativistic physics.

 

[Zafa Pi]

This for sure is the wrong discouraging message. QT is not weirder than any other mathematical description of nature. Only when philosophers and other soft science afficionados get their hands on it, it becomes weird, but these guys can do this with the most simple facts about our world too ;-)).

Ok, I admit you are technically correct that "QT is not weirder than any other mathematical description". But the real world = nature that it is attempting to model is weird. And that's what I think Feynman meant when he said, "Nobody understands QM". People confuse the map with the territory on a regular basis. (not to be confused with a Hilbert space basis )

 

[Zafa Pi]

But non-interacting particles are self-contained in relativistic physics.

Is an electron independent of the magnetic field in which it resides?

 

[vanhees71]

Ok, I admit you are technically correct that "QT is not weirder than any other mathematical description". But the real world = nature that it is attempting to model is weird. And that's what I think Feynman meant when he said, "Nobody understands QM". People confuse the map with the territory on a regular basis. (not to be confused with a Hilbert space basis )

Physics is about the objectively observable quantitative behavior of nature and its description. The only adequate language today is that of mathematical theory. Calculus free physics is a contraditio in adjecto. Anybody who is promoting such a thing is a false prophet, and we have to fight against this tendency in modern STEM didactics as vigorously as we can, which is a pest (at least in Germany). It's a step backward into the middle ages and particularly dangerous in this era of "post-truism"!

 

[A. Neumaier]

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.".

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

 

[sandy stone]

A suggestion from a non-professional..."In QM energy can only be delivered in discrete packets, which leads to the correct description of blackbody radiation. Classical theory fails."

 

[vanhees71]

But that's wrong even for black-body radiation. There are photons (in the sense of QED not to be mistaken as particles!) of any frequency, and the black-body spectrum is continuous. Correct is that electromagnetic radiation in a definite frequency mode can exchange energy with matter only in discrete portions of $\hbar \omega$.

 

[sandy stone]

Hmm... guess that's why I'm a non-professional.