Would classical physics not exist without probability?

  • #1
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Main Question or Discussion Point

Quantum mechanics is a highly statistical theory. Classical physics is usually regarded as deterministic, that probability is not nearly as fundamental concerning measurement and interrelation of variables.

Might it be so that classical physics is just as reliant on probability, albeit in different form, as quantum mechanics? The non-quantum realm relies on interpolation and extrapolation; linear and nonlinear error; precision and accuracy; standards of measurement; the correspondence principle; hypothesis and prediction; the eventual horizon to and mutability of classical laws.

Would classical physics not exist without probability?
 

Answers and Replies

  • #2
russ_watters
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None of those things (error sources, etc) show up in the equations or theories - they are all just limitations in our ability to verify the theories.
 
  • #3
Andrew Mason
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Quantum mechanics is a highly statistical theory. Classical physics is usually regarded as deterministic, that probability is not nearly as fundamental concerning measurement and interrelation of variables.

Might it be so that classical physics is just as reliant on probability, albeit in different form, as quantum mechanics? The non-quantum realm relies on interpolation and extrapolation; linear and nonlinear error; precision and accuracy; standards of measurement; the correspondence principle; hypothesis and prediction; the eventual horizon to and mutability of classical laws.

Would classical physics not exist without probability?
You may want to read Murray Gell-Mann's The Quark and the Jaguar to explore this further. The classical world is explained as decoherence of the quantum world. It is well written and entertaining - but a challenging read.

AM
 
  • #4
The biggest problem with classical physics is that it generally doesn't take probability into account. For some classical theories, gases, heat, etc, there is some lip service paid to the concept of things being random and then "averaging out", but overall, classical physics more or less ignores any kind of advanced probability theory.

This isn't very surprising, because when classical physics theories were being developed, classical statistics as we know it either didn't exist or was in it infancy.
 
  • #5
Danger
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I'm not sure that this is the proper sort of response to the OP, but it seems to me that nothing (including classical physics) would exist without probability. It's the basis of reality. The veracity of that statement might be a matter of interpretation, though.
 
  • #6
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Andrew,

I had read "The Quark..." once upon a spacetime. How does he define decoherence?
 
  • #7
Andrew Mason
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Andrew,

I had read "The Quark..." once upon a spacetime. How does he define decoherence?
I was afraid you'd ask that.

Gell-Mann explains the quantum mechanics "alternative histories" concept, and how at the quantum level these are not independent, but interfere. The analogy is to a photon going through a double slit screen. The photon passing through has two possible histories, which interfere with each other. It is not possible or meaningful to say which slit it passed through. Decoherence occurs when interference (or the sum of the interference terms between all the alternative histories") is effectively zero. That would occur when the slits are wide enough and far enough apart that we can determine which slit it came through - but then the interference pattern would disappear.

I have concluded that decoherence is either not really useful in explaining anything or it is really useful in explaining everything. I am not sure which it is. But, as I said, Gell-Mann's book is an interesting read.

AM
 
  • #8
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I'm not sure that this is the proper sort of response to the OP, but it seems to me that nothing (including classical physics) would exist without probability. It's the basis of reality. The veracity of that statement might be a matter of interpretation, though.
Another interpretation of the same thought is to say that probability applies to everything, because all human knowledge is uncertain; but I would disagree and say that probability is a mode of description, not a basis for reality but a basis for human knowledge of reality.
 
  • #9
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Probability is a psychological construct, an idea to make sense of the dice rolling, where we can't be certain what the outcome will be.

It does not have any physical existence beyond that. No one has, or ever will measure a probablity because there's no such thing.

So, to ask if the world can exist without probability can only expect the answer 'yes'.
 
  • #10
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Probability is a psychological construct, an idea to make sense of the dice rolling, where we can't be certain what the outcome will be.

It does not have any physical existence beyond that. No one has, or ever will measure a probablity because there's no such thing.

So, to ask if the world can exist without probability can only expect the answer 'yes'.
What about Heisenberg's uncertainty principle? If there is no way of knowing both where an electron is and how fast it is going, does that mean that if we know how fast an electron is going, it has a definite location in space time, but we just don't know where it is? Or does it not really exist in one distinct location, and where it could be must be determined by probability?

See also http://http://www.newtonphysics.on.ca/HEISENBERG/Chapter2.html" [Broken].

I believe this proves that at least quantum mechanics cannot exist without probability. Classical physics, however, probably can.
 
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  • #11
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Hi Izzhof,

actually HUP makes no mention of probability. But that's not at issue here.
Indeterminacy is the issue. All our quantum theories use probablity because there's something which will affect the outcome of any experiment that cannot be determined by us (phase, maybe ?)
But that does not mean that the indeterminacy is fundamental. Some physicists of standing believe that the universe must be deterministic.
Before you ask, I don't have a view on this.

Also, the waves of probablity amplitude are in phase space, which is itself imaginary.

Classical physics has at least one branch which uses probablity - statistical mechanics.
 
  • #12
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Hi Izzhof,

actually HUP makes no mention of probability. But that's not at issue here.
Indeterminacy is the issue. All our quantum theories use probablity because there's something which will affect the outcome of any experiment that cannot be determined by us (phase, maybe ?)
But that does not mean that the indeterminacy is fundamental. Some physicists of standing believe that the universe must be deterministic.
Before you ask, I don't have a view on this.

Also, the waves of probablity amplitude are in phase space, which is itself imaginary.

Hmm... so you're saying these physicists of standing believe that everything has a definite place and motion, but it's just not possible for us to know all these things?

Classical physics has at least one branch which uses probablity - statistical mechanics.
Statistical mechanics does not mean classical physics can't exist without probability; statistical mechanics itself is just a way to approximate the motion of individual particles without having to take into account each one into account separately. Since statistical mechanics is an approximation, "true" classical physics doesn't need it, because, even though we aren't taking all the particles into account separately, they still have definite places and momentums (according to classical physics).
 
  • #13
Classical physics is based upon our observations. It uses limits but it is not a statistical model. There is an exception and that has to do with wave motion.
Perhaps, you want to know how and why probability and statistics entered into physics. It all has to do with the nature and motion of electrons. The underlying problem is a description of the atom. Bohr's model of the atom suggests that electrons are projectiles that move around a central nucleus in a specific orbit. Unfortunately, Bohr's theory was only ever able to account for Hydrogen, and specifically, the evolution of line spectra from Hydrogen and H-like atoms. He did show, however, that the mechanism for generating photons was related to the quantum states of an electron. Once it was proven that electrons behave as waves, Shrodindger and Heisenberg decided to treat the motion of the electron as a wave, using a classical wave-equation.
Heisenberg theorized that it was impossible to measure the exact position of an electron without altering the measurement during the process. "Heisenberg's Uncertainty principle". He decided to alter our perception of the electron from a particle with a trajectory to a probability. If we can't know the exact motion of an electron, perhaps we can know its probable location... This model suggests that electrons are smeared out, into electron clouds, and quantum mechanics then describes the probability of finding electrons in certain regions around a nucleus.

I believe that quantum physics is a time consuming, sophisticated, and abstract probability theory. I don't like it. It should be noted that Einstein didn't like it either, and that he osticized himself from the main scientific commmunity as a result. He spent 20 years of his life trying to find a solution.
"God does not play dice"-Einstein.

If your having difficulty understanding how probability enters into the very foundation of science, you are not alone. Given that all of the diversity of our world reduces down to 114 or so elements, and then to protons, neutrons, and electrons in the atoms, it is hard to believe that suddenly we need a probability theory to understand that realm...
Quantum physics is valid as a probability theory, and it is highly succesful. And it should be. Given that any theory which is probable, has a degree of latitude, inherent in its construction. But is it close enough?
 
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  • #14
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Hmm... so you're saying these physicists of standing believe that everything has a definite place and motion, but it's just not possible for us to know all these things?
Prof. t'Hooft in particular has published several papers in recent years proposing exactly this. They are available in the ArXiv.

I take the point about statistical mechanics not being probablistic in the same way as QM.

The De Broglie-Bohm theory of quantum motion does not have probability amplitudes but relies on an 'ensemble' interpretation. The indeterminacy comes from our inability to know the initial conditions for any single partcle.
 
  • #15
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What physics is not of random origin?

What known physical phenomena could not exist in a random, infinite universe?
 
  • #16
turbo
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What known physical phenomena could not exist in a random, infinite universe?
If you mean by "random" a universe that has no rules, or at least has rules that are malleable and can change with time and/or location, you can safely exclude the observation of a universe that is homogeneous or isotropic. Since the universe looks pretty much the same no matter where we look (in direction and look-back time), we can assume that the universe has a very simple set of rules that hold everywhere.
 
  • #17
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We humans frequently encounter situations in which the outcome cannot be accurately predicted, and to our antecedents it could be a matter of survival to make the best choice. We have evolved a language and a set of concepts to deal with what we call randomness, indeterminacy, probability and so on. It would be a mistake to jump to the conclusion from this experience that the universe was not deterministic.
We can't be sure on the existing evidence, can we ?
 
  • #18
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We humans frequently encounter situations in which the outcome cannot be accurately predicted, and to our antecedents it could be a matter of survival to make the best choice. We have evolved a language and a set of concepts to deal with what we call randomness, indeterminacy, probability and so on. It would be a mistake to jump to the conclusion from this experience that the universe was not deterministic.
We can't be sure on the existing evidence, can we ?
That's not the only evidence we're basing this on, unless you're only talking about classical physics, in which case I completely agree with you.

If you are referring to quantum mechanics as well, see post #10.
 
  • #19
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Please see post #11.
 
  • #20
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What about Heisenberg's uncertainty principle?
Nobody,asked would "quantum physics not exist without probability".
Classical physics would exists without probability but some of its important parts (like thermodinamics) would be severely cripled I think.
 
  • #21
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Perhaps, you want to know how and why probability and statistics entered into physics. It all has to do with the nature and motion of electrons. The underlying problem is a description of the atom.

The key is to realise that the atom works differently from a vortex, particles created in a vortex are compacted in one plane (radial) but expand in another (spiral) plane; they retain the same volume.
In an atom the electron shells compact in all planes resulting in a change in volume.
Experiments involving particle collision create a vortex leaving the volume unchanged. FQHEs compress in one plane only and again the volume remains unchanged. Only the atom changes volume.
 

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