Can QM be derived from Newton's Laws of motion

[Terry Giblin]

Here is an answer I have just given to a question about the journey of light, which applying its logic you can derive QM and GR.

Newton's first law of motion state

"Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it."

Provided there is nothing to apply an external force to a photon then the above law will not be broken, therefore no additional force is required. It simply follow's the shortist path, where every its journey takes it.

But he has his revenge, with his third law,

"For every action there is an equal and opposite reaction. " - Hence the electron...

Using Newton's own laws of motion, proves the existence of electrons by the properties of photon's...

Now that's an original thought - if I've ever had one....

 

[lavalamp]

Originally posted by Terry Giblin
"For every action there is an equal and opposite reaction. " - Hence the electron...

I'm not sure I followed you around this bend. Do you care to be a little more specific for us less enlightened folk please.

 

[jcsd]

The answer is unequivocally "no", you cannot derive quantum physics wholly from classical physics, hence the division.

 

[arivero]

Now, you can get inspiration for quantum mechanics by reading Newton's principia.

 

[TeV]

Originally posted by arivero
Now, you can get inspiration for quantum mechanics by reading Newton's principia.

?
You mean treating the light in a corpuscular manner,or something else?
Personally,I've never got around to read Pricipia.
(My great sin,I know..)

 

[Chi Meson]

Original thought, yes. But it turns out that Newtonian Physics can be derived as a special case of QM, where we have many many particles all together at relatively low energy levels. In the "macro" world quantum effects are too small to notice. In no way does a deep analysis of Newtonian mechanics lead us to quantum machanics; in fact, it was the application of Newtonian mechanics that led Neils Bohr et al to realize that something was amiss, and a new set of rules was necessary to explain what was going on.

 

[selfAdjoint]

Originally posted by arivero
Now, you can get inspiration for quantum mechanics by reading Newton's principia.

I don't think Newton's corpuscular light theory is in his Principia; it's in his other book, Opticks.

 

[arivero]

Yep but the real issue is in the proof of area law for central potentials. No the proposition, but the proof itself. It is already noticeable it is called to be the core of (Feynman) space-time approach to quantum mechanics.

 

[arivero]

Originally posted by Chi Meson
But it turns out that Newtonian Physics can be derived as a special case of QM, where we have many many particles all together at relatively low energy levels.

Bad grammar here in this statement. Perhaps it should be: But it turns out that Newtonian Physics can be derived as a special case of QM where we have many many particles all together at relatively high energy levels respect to the fundamental one.

 

[Chi Meson]

OK. My mistake was trying to oversimplify again: I was considering thermal and kinetic energy levels.

But I think my grammar wasn't so bad for a forum post. Certainly warn't not worser than yorn.

 

[jcsd]

For the key reason why you can't derive quantum mechanics from classical physics, you have to look at how the Schroedinger equation was derived. Basically it was derived using an inductive rather than deductive method and it is significantly different from a classical wave equation.

 

[jackle]

it was derived using an inductive rather than deductive method

For the less enlightened, what does this phrase mean please?

 

[jcsd]

http://www.ncsu.edu/felder-public/kenny/papers/scientist.html

 

[jackle]

Brilliant, very entertaining, thanks!

 

[jcsd]

Id just add: don't get the impression that I mean classical physics doesn't involve induction. Taking the example of special relativity, Einstein inductively (of course Messrs Michelson, Morley et al deserve more than a little credit for this) derived the postulate that light travels the same speed in all inertial reference frames and then he deductively derived special relativity from previous classical theories. Special relativity is a classical theory.

Schroedinger inductively derived wave-particle duality (though the lionshare of the credit must go to Prince De Broglie for this), but he used induction again to derive his famous equaton (by first considering a classical wave equation then inductively making changes to it).

 

[arivero]

Originally posted by jcsd
For the key reason why you can't derive quantum mechanics from classical physics, you have to look at how the Schroedinger equation was derived. Basically it was derived using an inductive rather than deductive method and it is significantly different from a classical wave equation.

It could be.

Hmm but one should compare quantum mechanics to classical point mechanics, not to classical waves. In origin, classical mechanics was very inductive too.

PS: yep my grammar is completely awful. You guys should hear my Spanish.

 

[TeV]

Originally posted by arivero
It is already noticeable it is called to be the core of (Feynman) space-time approach to quantum mechanics.

Pardon my ignorance,but what is "the core of Feynman spacetime approach to QM"?

 

[arivero]

Originally posted by TeV
Pardon my ignorance,but what is "the core of Feynman spacetime approach to QM"?

I'd say, path discretization and consideration of the process of limit.

Feynman approach has two process of limit: "small time step", which drives one back to Schroedinger equation, and "small Planck constant", which let's one to go back to Newton equations (Euler Lagrange if you prefer).

 

[jcsd]

Originally posted by arivero
It could be.

Hmm but one should compare quantum mechanics to classical point mechanics, not to classical waves. In origin, classical mechanics was very inductive too.

PS: yep my grammar is completely awful. You guys should hear my Spanish.

Disagree, wave mechanics was the first real quantum theory and it comes straight from considering the form of classical wave equations.

Yes classical physics involves a lot of induction, but if quantum mechanics was derived as a classical theory Schroedinger would of had his starting point of matter waves and the HUP and then he would of been able to deductively derive his equation from these (and classical physics), but didn't and he couldn't do this.

Simlairly you can't derive relativistic quantum mechanics from non-relativistic quantum mechanics and you apparently can't derive quantum gravity from quantum field theory, etc.

 

[Terry Giblin]

When is the speed of light not!

Gentlemen,

Has anyone heard the joke,

"When is the speed of light, not the speed of light?"

"When it's an electron!"

In the quantum tunnelling effect, does the electron or photon pass through the potential barrier, based on probability alone - in a real world or chaos world?

Unless the 'infinitesimal volume element' is satified by the restrictions of the experiment, as predicted by the underlying harmonic equations.

In the YDSE does an electron not transform into an intereference pattern.

In the quantum tunnelling effect, does and electron or photon entering and existing a quantum barrier an electron emerging on the other side when tested for.

"The path of an electron is only created when tested for..."

 

[TeV]

Originally posted by arivero
I'd say, path discretization and consideration of the process of limit.

Feynman approach has two process of limit: "small time step", which drives one back to Schroedinger equation, and "small Planck constant", which let's one to go back to Newton equations (Euler Lagrange if you prefer).

I was actually thinking that your point was Newton had been the first who had introduced Field as physical entity in theories (through the law of central potentials in conservative fields and Lagrangian it is indicative).From mathematical point ,space discretitation,was treated by "fluxions" (spelling?) in Newton's case I would think and is more closer to space continuum.Leibnitz looks closer to quanization of space by his math metodology and his notation in calculus was more convenient to operate with (albeit both methods are equivalent).
Note: Space-time in my first posts would be better expression than spacetime;-)

 

[arivero]

Hmm, TeV I had nor really thought explicitly about the notion of field, but it is true that the principia needs to introduce the notion of a force field. In fact there are two close notions: a "impulse sequence", discrete, and a "force field" which is the result of smoothing impulses towards the continuum limit.

 

[TeV]

One way or another ,I should better look for one copy of Newton's Principia.This way would be just my wild guessing, without actually knowing what is in.Momentum conservation law in a particle system expained by methodology of absorber theory was a crucial step for development of QED.Basic idea was "stolen" from classical Maxwell equation with exploiting time symmetry in it.So,the suggestion is physical reality of the EM field has no sense without the presence of at least two particles photon way interacting.
Newton of course didn't know of EM eqs. and quanta,but I was wondering if he pondered about space with gravitational potential as kind of excited and different than usual in phyisical reality,or just he treated problems in purely mathematical way?

 

[arivero]

Originally posted by TeV
Momentum conservation law in a particle system expained by methodology of absorber theory

This is interesting by itself. Can you suggest some reading about?
I am currently under the impression that the distance between interacting particles happens to be "about" the wavelength of the virtual photon.

 

[TeV]

Arivero,
There are many books presenting formalism of QED and math methods,but very few discuss what is behind ,and there are other QED models today (equivalent to Feynman model) that give in many aspects the same results.
However,it seems Feynman view and his approach to QED (includung Feynman rules and strickt development of perturbation theory) got more touching points with classical theory and that's the reason it is advantageous for people to use it.I find it to have more "naive" simplicity in it.
The root of Feynman approach to QED lays more in a classical theory than in the bases of QM !
During the development of its' formalism,the theory gradually lost the trace of original idea ( prescription principle) and it is curious for one to know the mechanism of prescription principle wasn't considered firstly by Feynman or even Wheeler.
One another person on Princeton tryed to link EM with Gravity in 1930's,using some quite unusual hypotesis (It is easy to guess who.But he went in big troubles..)
But the idea as starting point proved to be fruitful for QED.
Little while ago I found this link:
http://www.nobel.se/physics/laureates/1965/feynman-lecture.html
Hope you will find it useful.

 

[Terry Giblin]

TeV,

Thank you, absolutely correct - execellent site.

It would appear that I have had similar idea and train of thoughts, as others in the past.

"Insanity is a measure of how many people believe you."

"I don't suffer from insanity, I enjoy every moment of it, especially when you realize your not alone"

But as I said to several Physics and Maths Prof's, "It is still an original thought - provided it came from your own knowledge and intuition."

- Even if someone has had the same thought and idea, but arrived at different interpretations and solutions.

For example

E = mc2 c=h/t, assume h=1, c= 1/t

E = mt^-2

Or m=c or c=m (YDSE and QT)

E = mc^2 m=c=1/t

E = t^-3

E = h^3.t^-3

Therefore if the electrical impedence, is zero, t must be infinite, unless h under these circumstances tends to c or m depending on which external forces are applied.

 

[TeV]

Originally posted by Terry Giblin


Therefore if the electrical impedence, is zero..

He,he formula as a starting point is irrelevant for scientific discovery.What is important is the principle.Here in your post is indicated condition of electrical resonance.And what happens under condition of resonance in the system?Best transfer of energies.In a overall picture it doesn't matter wether it is mechanical,electromagnetic,or nuclear resonance.It is the principle of resonce important in nature.Maybe even in arrivero's post there is indication of wavelenght resonance principle as well ("..distance between interacting particles happens to be about the wavelenght of virtual photon")

 

[cartuz]

Yes, of cause. We can to describe the quantum objects by classical Newton’s gravitation.
But we must to consider the random gravitational field background, which we can name the Stochastic Gravitational Fields. It may be static fields, changing gravitation fields or gravitation waves. It is not important. Important that it must be random. Quantum objects we can consider as test particles in random gravitation fields. Then quantum property is not property of microobjects. It is property of Stochastic fields, i.e. random gravitation background fields.
All quantum effects it is possible to explain by statistical physics.
But experiment of electron’s diffraction classical physics cannot explain without random gravitation fields. For our case with gravitation random fields we have coherent test particles and its will be interference!
You can read this in paper How to Complete the Quantum-Mechanical Description? http://xxx.lanl.gov/abs/quant-ph/0212139.

 

[jcsd]

Last time I looked there wasn'y any quantum field theory of gravity carutz

 

[cartuz]

P.S. In this paper (http://xxx.lanl.gov/abs/quant-ph/0212139) used General Relativity Theory with Newton’s gravitation as particular case. It is classical description with random classical fields. Microobjects here consider as classical test particles and will have Quantum properties in Gravitation Background which classical too. In this description the Word is Classical with Quantum properties as follows case.

 

[jcsd]

You mean treating gravity semi-classically, it's just that 'stochastic gravitational fields' implies to me that some attempt to quantize the gravational field.

 

[cartuz]

Hi, jcsd.
No. Only classically. Not quasi-classically. In classical physics there are discrete sizes and discrete quantities. Quantum quantities can be described with the help of statistical physics.

 

[Janitor]

Time is a valid dimension and should be given its own baryon number. - Terry Giblin

Baryon number is a function of the quark content of particles which respond to the strong force. What do you mean when you suggest assigning baryon number to time? What would that amount to? What would happen to the principle of baryon number conservation, which at least to a very good approximation is a valid physical law?

 

[Terry Giblin]

Time respects baryon number cons.

Baryon number is a function of the quark content of particles which respond to the strong force. What do you mean when you suggest assigning baryon number to time? What would that amount to? What would happen to the principle of baryon number conservation, which at least to a very good approximation is a valid physical law?

Perhaps its is exactly this reason Time has been ignored too long as a Dimension, although the reflection is actually traveling back in time the experiment is constantly moving forward in real time.

Therefore the baryon number conservation is maintained.

Where is the problem?

 

[Terry Giblin]

This demonstrates the power of the www

Baryon number is a function of the quark content of particles which respond to the strong force. What do you mean when you suggest assigning baryon number to time? What would that amount to? What would happen to the principle of baryon number conservation, which at least to a very good approximation is a valid physical law?

Janitor I followed your advice and looked up what the baryon number conservation rule was and found this site.

http://www.lns.cornell.edu/spr/2003-03/msg0049916.html

It would appear the jury is still out..