Why quantum effects disappear at the classical level

[g.lemaitre]

I forget where I read it but one author said that mountains of ink have been spilled debating why quantum effects disappear at the quantum level. I don't understand why this is a problem, I think the answer is rather obvious. One poster on another thread wrote: "Technically - classical physics is what QM does on average ... so the math is different."
https://www.physicsforums.com/showpost.php?p=4158638&postcount=2
That seems to be the answer. If the Planck length were roughly the size of a human being and a scientist was 10 orders of magnitude larger than a human, then if you continually measured a million humans, and your measuring device was rather crude, then each millions of human would be on average the same, even though a quanta (a human being) would not be the same but uncertain.

 

[PhysicsWiz4]

It might have to do with why we don't see Schrödinger's cat ever and we don't encounter wave collapse or entanglement in classical life, but I'm uncertain.

 

[Crazymechanic]

to the OP: Why don't you go in public being naked? Well because there are certain things that we do and that we have when we are alone and different things when we are in a society.
Although some things overlap and some are just used to either one or the other state that a person is in.
I look at quantum physics with this kind of a viewpoint.
Even though not a perfect analogy but one brick is a little different than a wall of brick not to mention a house or a highrise.

Although I must say that it would be a very interesting world if people could "tunnel" through doors before they ever get the chance to open or if humans or cars could "scatter" and so avoid crashing into objects directly.

 

[Dreak]

Shrödinger equation:

-h²/2M psi + Vpsi = Epsi

the higher the mass, the smaller the effect (the wave function becomes more 'difficult' to 'see')if it comes to Heisenberg:
xp > h, p depends on the mass and h is really small. The effects can't be seen for macroscopic items.

And then you got Ernesttheorema (I do believe it's Ernest or Erhnfest, something like that) which is as you say: "classic physics is the 'average' of QM"

 

[Naty1]

g.lemaitre:

I like the first part of your post...I'm not so sure about the second part:

If the Planck length were roughly the size of a human being...

I doubt anybody knows what would result...

If you mean that were the size scale where quantum effects become significant, you are getting close...but a remaining problem would be that Planck time would still be 10^-43 seconds or so...Planck energy would make us wildly unstable,etc,etc 'at human size',,,,
In other words, could this universe even exist??...

Check out the description in the first several paragraphs here:
http://en.wikipedia.org/wiki/Quantum_realm

 

[The_Duck]

All essentially quantum mechanical effects are proportional to hbar, or powers of hbar. hbar is really tiny in normal units (10^-34 Joule-seconds), so quantum mechanical effects are not noticeable at normal scales.

 

[bhobba]

I forget where I read it but one author said that mountains of ink have been spilled debating why quantum effects disappear at the quantum level. I don't understand why this is a problem, I think the answer is rather obvious.

Well actually its a very deep issue that hasn't fully been resolved yet. Quantum effects do not disappear at the macroscopic level eg liquid helium had been described as quantum mechanics writ large and so called bucky balls show quantum effects. The modern view is that macroscopic objects are just as quantum as other scales but due to decoherence behave classically - if you can remove that decoherence - and such is very hard but not impossible - then they will, and in fact do, display quantum effects such as superposition.

The emergence of the classical domain has been given a lot of attention - see for example Roland Omnes - Understanding Quantum Mechanics - Chapter 11. From that chapter evidently the mathematics of that emergence depends on something called the Egorov Theorem. With that theorem the issue is resolvable - trouble is it only has been proved for some restrictive conditions such as an infinitely differentiable Hamiltonian and some bounds on those derivatives. Research has continued and some of those restrictions have been removed but is still not general enough to cover all the cases physicists are interested in. It is thought this will eventually be fixed up and most don't worry about it, but the fact is, some issues still remain.

Thanks
Bill

 

[jon4444]

bhobba's answer is consistent with what I've been reading.

So are the (commonly heard) explanations given by other posters just wrong?

 

[Naty1]

So are the (commonly heard) explanations given by other posters just wrong?

no...except for

Why don't you go in public being naked?

which I'm not so sure about...

the posts represent different viewpoints...

If you search these forums you'll find a lot of other viewpoints...for example, you can get an idea about 'macroscopic quantum mechanics' from solid state electronics ...semiconductors...

 

[g.lemaitre]

Well actually its a very deep issue that hasn't fully been resolved yet. Quantum effects do not disappear at the macroscopic level eg liquid helium had been described as quantum mechanics writ large and so called bucky balls show quantum effects.

Thanks for that info, I didn't know that.

The modern view is that macroscopic objects are just as quantum as other scales but due to decoherence behave classically - if you can remove that decoherence

Does decoherence require the many world interpretation?

 

[g.lemaitre]

Well actually its a very deep issue that hasn't fully been resolved yet.

But the duck's answer

All essentially quantum mechanical effects are proportional to hbar, or powers of hbar. hbar is really tiny in normal units (10^-34 Joule-seconds), so quantum mechanical effects are not noticeable at normal scales.

looks so obvious and easy to understand. I guess liquid helium and bucking balls are anamolies, right?

 

[mfb]

Does decoherence require the many world interpretation?

No, but if you do not want to add collapses or other stuff, you get MWI.

I guess liquid helium and bucking balls are anamolies, right?

Metals, semiconductors, superconductors, Bose-Einstein condensates, vibrating cantilevers... quantum effects on macroscopic scales are common. The true distinction between "microscopic" and "macroscopic" in that respect is not the size, but the "unordered" (leading to decoherence) interaction with the environment.

 

[Maui]

Metals, semiconductors, superconductors, Bose-Einstein condensates, vibrating cantilevers... quantum effects on macroscopic scales are common. The true distinction between "microscopic" and "macroscopic" in that respect is not the size, but the "unordered" (leading to decoherence) interaction with the environment.

The environment is just as 'unordered' and unclassical as the system being measured.
The is no such thing as classical environment that causes some systems to decohere upon interaction.

 

[Maui]

I forget where I read it but one author said that mountains of ink have been spilled debating why quantum effects disappear at the quantum level. I don't understand why this is a problem, I think the answer is rather obvious. One poster on another thread wrote: "Technically - classical physics is what QM does on average ... so the math is different."
https://www.physicsforums.com/showpost.php?p=4158638&postcount=2
That seems to be the answer. If the Planck length were roughly the size of a human being and a scientist was 10 orders of magnitude larger than a human, then if you continually measured a million humans, android your measuring device was rather crude, then each millions of human would be on average the same, even though a quanta (a human being) would not be the same but uncertain.

For all practical purposes it can be assumed that interactions cause systems to lose their coherence. But this is misleading and not entirely true. The issue is complicated and unreslved/certainly not in a manner that most would find acceptable/.

 

[mfb]

The environment is just as 'unordered' and unclassical as the system being measured.

Not if you prepare your system careful enough to see quantum effects, but don't do the same with the remaining world.

The is no such thing as classical environment

I agree.

 

[Naty1]

For nice insights into some fundamental mathematical differences between QM and classical physics, give this Leonard Susskind quantum mechanics youtube lecture a try...

tune in at 1 hr and 17 minutes...



A sample:
In classical three dimensional space, vectors are over REAL numbers;
in QM, vectors are over COMPLEX NUMBERS> you can multiply vectors by complex numbers.

 

[bhobba]

So are the (commonly heard) explanations given by other posters just wrong?

No. Its often the case in any field of endeavor that the explanation at a deeper level is different to what is said at a more superficial level. For example in studying electronics they say a current is electrons flowing through conductors but that is not true - its actually electrons and holes where holes are the absence of electrons but due to quantum effects they actually act like particles. Its just not necessary to get caught up in this for basic electronics - but the jig is up when you want to understand how transistors work - then its of vital importance. The same here - most textbooks don't give the full modern answer because it not really required in most applications. But when discussing fundamental issues the jig is up - you need to be more careful.

Thanks
Bill

 

[bhobba]

Does decoherence require the many world interpretation?

No. Many modern interpretations that are not of the MW type such a decoherent history's use it:
http://quantum.phys.cmu.edu/CHS/histories.html

Thanks
Bill

 

[bhobba]

But the duck's answer looks so obvious and easy to understand. I guess liquid helium and bucking balls are anamolies, right?

No - QM operates at all levels - even when planks constant can be taken as zero for all practical purposes which suppresses many - but not all effects. Quantum effects can still remain eg the existence of holes. Most of the time you will not notice them but under some circumstances you can eg if you put a conductor in a magnetic field and measure what is called the hall effect you simply can't explain it without holes.

Thanks
Bill

 

[Charles Wilson]

I've already gummed up the works today so one more post won't hurt.
If the question is something like, "Why do Quantum effects morph into Classical stuff?", I'll try to get another quote from a physics book I use, maybe tomorrow.

Consider an infinite square well with an ideal classical marble bouncing back and forth. Where are we MOST LIKELY to find the marble?
At the sides: It approaches one side, is reflected, goes to the other side, approaches, is reflected.
4 times vs 2 times in the middle.

Where does QM say we'll find the marble? Most likely IN THE MIDDLE with the first "ground state wave".
As we consider greater numbers of "Excited" waves, the amplitudes begin to make appearances at different parts of the well and the result begins to look like the classical form.

Bohr's correspondence principle states that the behavior of systems described by the theory of quantum mechanics (or by the old quantum theory) reproduces classical physics in the limit of large quantum numbers.

G'Night,

CW

 

[bhobba]

Bohr's correspondence principle states that the behavior of systems described by the theory of quantum mechanics (or by the old quantum theory) reproduces classical physics in the limit of large quantum numbers.

Yea - that's correct - but must be used with care - quantum effects can, and sometimes do, remain. For example liquid helium is an entirely macro object but requires QM to explain its weird counter intuitive behavior eg:
-It carries no thermal energy (no entropy): all of the heat energy is in the normal component
-It has no viscosity: it can flow through tiny holes.
-It flows towards areas where the helium II is heated. Heat causes superfluid to convert to normal. A flow of superfluid into the heated area cools that area and restores the uniform mixture of normal and superfluid.

None of this can be explained classically.

Thanks
Bill

 

[Charles Wilson]

See what happens when I bring up Bohr. I always get into trouble.
I have a better version I'll try to get to tomorrow.

Thanx,
Insomniacally yours,

CW

PS: You can bring Low Temperature Helium into any QM discussion anytime, I'll probably believe whatever is said. Simply mind boggling material.

 

[Naty1]

g.lemaitre: a quick change of perspective for illustration:

Why [do]quantum effects disappear at the classical level...

is of course valid, but could be considered 'backwards'... it seems the traditional view because most people learn classical first then quantum...but it IS valid to say:

Why do classical effects disappear at the quantum level...

If each state has a probability via QM considerations... in classical physics the probability [uncertainty] 'disappears' and becomes an 'exact' measurement [state]...and we have an 'exact point'...so with QM we have less information that we otherwise might.

edit: upon reconsideration, I don't like this description all that much...but it is fun to turn stuff for a different perspective so I'll leave it posted...

 

[mfb]

Consider an infinite square well with an ideal classical marble bouncing back and forth. Where are we MOST LIKELY to find the marble?
At the sides: It approaches one side, is reflected, goes to the other side, approaches, is reflected.
4 times vs 2 times in the middle.

I think this should be a harmonic potential, otherwise classical mechanics predicts the same probability everywhere. In addition, you need something like a harmonic potential to get the highest probability at the borders in QM.


@Naty1: But if you start with QM, how can you ask how classical effects (what is that) disappear at the quantum level (which was your baseline anyway)? Shouldn't you ask how classical effects emerge?

 

[Charles Wilson]

Try this one. From _Physics_, Wolfson and Pasachoff, ISBN 0-67339836-6:

 

[audioloop]

I forget where I read it but one author said that mountains of ink have been spilled debating why quantum effects disappear at the quantum level. I don't understand why this is a problem, I think the answer is rather obvious. One poster on another thread wrote: "Technically - classical physics is what QM does on average ... so the math is different."
https://www.physicsforums.com/showpost.php?p=4158638&postcount=2
That seems to be the answer. If the Planck length were roughly the size of a human being and a scientist was 10 orders of magnitude larger than a human, then if you continually measured a million humans, and your measuring device was rather crude, then each millions of human would be on average the same, even though a quanta (a human being) would not be the same but uncertain.

maybe macroreality is not quantum.

 

[mfb]

Try this one. From _Physics_, Wolfson and Pasachoff, ISBN 0-67339836-6:

"Harmonic oscillator" (and not infinite square well) is exactly my point.

 

[audioloop]

Macrorealism from entropic Leggett-Garg inequalities
Phys. Rev. A 87, 052103 (2013
http://pra.aps.org/abstract/PRA/v87/i5/e052103

http://arxiv.org/abs/1208.4491

...Yet another foundational concept of classical world that is at variance with the quantum description is macrorealism [4]. The notion of macrorealism rests on the classical world view that (i) physical properties of a macroscopic object exist independent of the act of observation and (ii) measurements are non-invasive i.e., the measurement of an observable at any instant of time does not influence its subsequent evolution. Quantum predictions differ at a foundational level from these two contentions. In 1985, Leggett and Garg (LG) designed an inequality (which places bounds on certain linear combinations of temporal correlations of a dynamical observable) to test whether a single macroscopic object exhibits macrorealism or not...

-----
Entropic Leggett-Garg Inequality:
"This inequality places a bound on the statistical measurement outcomes of dynamical observables describing a macrorealistic system. Such a bound is not necessarily obeyed by quantum systems, and therefore provides an important way to distinguish quantumness from classical behavior."

 

[Dundeephysics]

I myself like to think about it in the way you described, the classical world is an average of the quantum one. Charles Wilson previously gave a nice example. Classical Physics could be described classically and quantum mechanically, however quantum particles can not be described classically (in a Newtonian fashion). This creates the limits of classical physics and was the main reason for the high recognition to the great work that was made by quantum mechanics physicists during the beginning of the 20th century.

As mentioned previously quantum mechanical equations dictate that the greater the mass the smaller the quantum mechanical effects that could happen, e.g. tunneling through a potential

Schrödinger equation can be used not for quantum particles but it could also be used for classical ones, such as tennis balls, however their effects are not very apparent. Consider a tennis ball that is hit by a player, using debroglie equation (lambda = h/p). the wavelength (lambda) is found to be too small (not even enough to make an interference pattern like with electron's or photon's). This could help you think about why large objects don't exhibit good quantum mechanical behaviours like small ones.

 

[bhobba]

This could help you think about why large objects don't exhibit good quantum mechanical behaviours like small ones.

Why are people continually thinking that QM behavior disappears at the macro level? That's simply not true. Consider liquid helium again. Why does it exhibit its strange behavior? It's a complex phenomena but one of the reasons is despite the fact it's not at absolute zero it is in its lowest possible energy state. This is quantum mechanics pure and simple - classically its impossible. It is quantum mechanics writ large. This also shows the limitations of the argument that as planks constant goes to zero at the macro level things like discrete energy states go over to a continuum and quantum effects disappear - often its true - but not always - as liquid helium proves. The argument you find in textbooks to this effect is not of universal validity. This explains some of its strange behavior eg because its in its lowest energy state it can't have vortices because they dissipate energy which since it is in it lowest state it cant.

Quantum behavior can and does appear at the macro level. The reason it is not common is decoherence and entanglement. Macro objects normally are in contact with the rest of an environment and becomes entangled with it - that is the cause of classical behavior at the macro level. The reason the moon is there when you are not looking at it is because it is always being observed by the environment - eg photons. Remove, at least some of that entanglement, such as in the case of liquid helium and quantum effects appear.

Thanks
Bill