Amplitude of a wave and general laws of physics

[quiet]

As a student, I asked why, in some types of waves, the square of the amplitude and the density of energy are directly proportional. I got answers based on general laws of physics.

Then I asked why, in the De Broglie - Schrödinger waves, the square of the amplitude is related to probability and not to energy density. I got a response referring to an idea proposed by Max Born, without mention of the general laws of physics.

If possible, I would like to understand what is the relationship between that idea of Max Born and the general laws of physics.

[Strange]

39 minutes ago, quiet said:

Then I asked why, in the De Broglie - Schrödinger waves, the square of the amplitude is related to probability and not to energy density. I got a response referring to an idea proposed by Max Born, without mention of the general laws of physics.

You are comparing two very different things. The waves describe different types of things so the meaning of the amplitude will, of course, be different. I deleted what I started writing because I came across this which summarises it perfectly:

Quote

Schrödinger's quantum mechanical waves are conceptually different from ordinary physical waves such as water or sound. Ordinary physical waves are characterized by undulating real-number 'displacements' of dimensioned physical variables at each point of ordinary physical space at each instant of time. Schrödinger's "waves" are characterized by the undulating value of a dimensionless complex number at each point of an abstract multi-dimensional space, for example of configuration space.

From: https://en.m.wikipedia.org/wiki/Matter_wave The following text expands further on this distinction and the meaning.

I'm not sure what you mean by "general laws of physics"; the Schroedinger wave equation is (now) one of the general laws of physics. So I guess you mean laws of classical physics but those will never be sufficient to describe quantum system. But the development of quantum theory is solidly based on the preceding laws of physics.

[quiet]

1 hour ago, Strange said:

You are comparing two very different things.

Hello, Strange. Although many times I have read and heard the arguments that you have exposed, I will ask like the first time I heard that, when I was a student.

What physical laws connect this abstract, non-dimensional and non-physical wave with the concrete, dimensional and physical events of the diffraction and the interference of the particle beams? And more, of the particles sent one by one, waiting between shipments times as large as desired.

Edited October 21, 2018 by quiet

[Strange]

2 minutes ago, quiet said:

What physical laws connect this abstract, non-dimensional and non-physical wave with the concrete, dimensional and physical events of the diffraction and the interference of the particle beams?

I don't understand the question. What do you mean by "physical law"? As far as I can see, the wave equation IS the "physical law" that describes the behaviour of quantum events.

 

 

[swansont]

6 hours ago, quiet said:

 
Then I asked why, in the De Broglie - Schrödinger waves, the square of the amplitude is related to probability and not to energy density. I got a response referring to an idea proposed by Max Born, without mention of the general laws of physics.

Schrödinger waves and de Broglie waves are not interchangeable.

I'd say that probability integrating to 1 is based in physical law. But which laws you are relying on depend on what measurements you can do. In some problems, energy is the crucial parameter. In others, it might be momentum.

[quiet]

I would be reassured to hear that Max Born's proposal is simply a way of establishing useful algorithms for practical purposes. But nobody comes to me saying that. It happens that they present a thousand tautological arguments to deny that it is only an algorithmic procedure useful in practice and, collaterally, to situate the probabilistic interpretation in the context of fundamental physical principles.

[Strange]

19 minutes ago, quiet said:

I would be reassured to hear that Max Born's proposal is simply a way of establishing useful algorithms for practical purposes. But nobody comes to me saying that. It happens that they present a thousand tautological arguments to deny that it is only an algorithmic procedure useful in practice and, collaterally, to situate the probabilistic interpretation in the context of fundamental physical principles.

Isn’t that true of all scientific models and laws? They are simply (formalised) ways of describing what happens, whether that is classical light waves, de Broglie’s matter waves or the Schroedinger wave equation. Why are you creating an artificial distinction between them?

What do you mean by “fundamental physical principles”?

And what do you mean by “general laws of physics”?

I’m still not sure what you are asking. 

Edited October 21, 2018 by Strange

[quiet]

Does pure probability fulfill some principle of conservation or, equivalently, does it exhibit some symmetry that enables the application of Noether's theorem?

Can pure probability be expressed vectorially or tensorially?

In the experimental field, is it possible to build an instrument that measures pure probability? I am not thinking of a computerized system that calculates probability based on the data of a situation. I'm thinking of an independent instrument, that does not use computerized calculation, such as an ammeter or a voltmeter does not need a built-in microprocessor.

Can probability be transmitted between two objects, how are heat transmitted, electric charge, amounts of linear and angular movement, etc. ?

The above questions can be summarized in one. Does pure probability have physical existence?

I know that question will elicit arguments of the following kind. Does the electrical charge have a physical existence? Or is the term electric charge referred to the result of a deliberately established procedure, with the intention of obtaining a specific type of numerical data? Foreseeing that such arguments could appear, in the first paragraphs I mentioned magnitudes that are conserved and transmitted, even if they are arbitrarily defined. My mind does not accept to call physical property a mathematical construct based on pure probability.

Edited October 22, 2018 by quiet

[Markus Hanke]

4 hours ago, quiet said:

Does pure probability fulfill some principle of conservation or, equivalently, does it exhibit some symmetry that enables the application of Noether's theorem?

Yes, it is invariant under rotation about some real-valued angle (i.e. under a U(1) symmetry); the corresponding conserved current in Noether‘s theorem is called the probability current.

[Strange]

7 hours ago, quiet said:

In the experimental field, is it possible to build an instrument that measures pure probability?

Is it possible to build an instrument to (directly) measure potential energy? Or even kinetic energy - this has to be “collapsed” and converted to something else that can be measured. 

7 hours ago, quiet said:

My mind does not accept to call physical property a mathematical construct based on pure probability.

That is a problem with your mind not a problem with the physics. 

[quiet]

5 hours ago, Markus Hanke said:

Yes, it is invariant under rotation about some real-valued angle (i.e. under a U(1) symmetry); the corresponding conserved current in Noether‘s theorem is called the probability current.

Thanks Markus! This is interesting.

[studiot]

12 minutes ago, quiet said:

6 hours ago, Markus Hanke said:

Yes, it is invariant under rotation about some real-valued angle (i.e. under a U(1) symmetry); the corresponding conserved current in Noether‘s theorem is called the probability current.

Thanks Markus! This is interesting.

Yes but be careful what you call a fundamental principle of Physics.

By definition a fundamntal principle cannot rest upon anything else (more fundamental).

 

10 hours ago, quiet said:

Can pure probability be expressed vectorially or tensorially?

No probability is a pure number.

 

10 hours ago, quiet said:

My mind does not accept to call physical property a mathematical construct based on pure probability.

 

There are  circumstances where we cannot do without it.

For instance consider the breaking  load or stress of a rope.

The only certain method to know this is to break the rope and measure it.

But that leaves us with a broken rope.

So we employ statistical methods, including  probability to use the rope without breaking it.

[Rob McEachern]

On 10/21/2018 at 10:30 AM, quiet said:

Then I asked why, in the De Broglie - Schrödinger waves, the square of the amplitude is related to probability and not to energy density.

Probability and energy density are related. Whenever the energy arrives within a detector, in equal quanta of energy, then the number of quanta detected by any given detector, can be inferred, from the ratio of total energy detected, divided by the energy per quanta. This fact is independent of the nature of the quanta; the debate about particle vs. wave is irrelevant. All that matters is that the quanta have equal energy. Which is why the experiments are always designed to ensure that is the case.

[studiot]

Like it Rob.

Some further things might be pointed out.

 

Energy is also a function of frequency.

Classical waves and other periodic phenomena, Schrodinger and De Broglie phenomena can be travelling or stationary.

Classical waves of interest are perhaps more often travelling, the latter two perhaps more often stationary.

Energy formulae are different for travelling and stationary 'waves'

Edited October 22, 2018 by studiot

[swansont]

1 hour ago, Rob McEachern said:

Probability and energy density are related. Whenever the energy arrives within a detector, in equal quanta of energy, then the number of quanta detected by any given detector, can be inferred, from the ratio of total energy detected, divided by the energy per quanta. This fact is independent of the nature of the quanta; the debate about particle vs. wave is irrelevant. All that matters is that the quanta have equal energy. Which is why the experiments are always designed to ensure that is the case.

I'm not sure what experiment you have in mind here, nor how probability is coming into play. You've said that E_tot = N*E_photon

If we're talking about the probability of detecting a photon in detector A vs B, there isn't (or need not be) any explicit energy dependence. You can have a 50/50 beamsplitter that works on red photons and blue photons, or one that works at a single frequency but is not dependent on the flux of the photons. In either case, probability does not depend on the energy density.

At best, you might be able to say "Probability and energy density can be related" but I don't think you've described a situation where that happens.

[quiet]

If possible, I would like to enter the same party through another door.

Suppose that in the near future a valid model of elementary particle is proposed, which agrees with the quantum theory, with relativity, with the thermodynamic treatment of the blackbody radiation, with the weak interaction, with the strong interaction, with the electromagnetic interaction and with everything necessary.

That model would describe how it is made and what an elementary particle is made of. It would explain in what they agree and in what they differ a particle and its antiparticle. It would explain how and why the photon has rest mass equal to zero. I know that rest mass is an archaic expression, but I want to use very explicit language at this time. It would also explain how and why other kinds of particles and antiparticles have rest mass other than zero. It would allow to theoretically state the conditions of the particle that has the minimum rest mass compatible with subsistence. I refer that to subsist without decomposing after being created. And it would allow to deduce from the model the theoretical value of the minimum rest mass compatible with subsistence. (One would expect that theoretical value to coincide with the rest mass of the electron.)

Let's open the other door now. If a valid model of elementary particle appeared, could it be advantageously replacing the probabilistic formulation?

[Rob McEachern]

3 hours ago, swansont said:

I'm not sure what experiment you have in mind here, nor how probability is coming into play. You've said that E_tot = N*E_photon

Any experiment in which a multi-channel detector, responds to a mono-energy input (quanta) within each individual channel. That is what every Fourier transform's power spectrum describes. Thus, since wave-functions are mathematically described via Fourier transforms, it is true of every wave-function, whenever each "bin" in the transform receives only entities (quanta) with a single energy, E_photon ,which may differ from one channel to the next. That is the origin of the Born rule.

3 hours ago, swansont said:

I don't think you've described a situation where that happens.

It happens with every experiment, that can be described mathematically via a Fourier transform's power spectrum (as are all wave-functions-squared), since it is a mathematical property of a Fourier transform, having nothing to do with physics. The only experimental condition that must be met, for the Born rule to be valid, is that each bin of the power-spectrum/histogram be obtained by a mono-chromatic integration of quanta. In other words E_photon must be the same for all the photons detected in a bin, but can differ from bin-to-bin. For example, a diffraction grating or prism, will deflect photons of different energies/frequencies at different angles. Consequently, detectors placed at different angles will each receive photons within a single, narrow band of energies, thus ensuring the validity of the Born rule. On the other hand, if you remove the grating or prism, and let white-light hit the detectors, the mono-energy condition is not met and the Born rule does not apply - nor will you observe an "interference" pattern behind any slits, for that very reason. In the case of white light passing through slits, there is no longer a single, unique value for E_photon , at each deflection angle, so the ratio E_tot/E_photon no longer yields a correct inference of N; you still get a spectrum (AKA interference pattern) but it no longer yields a correct inference of probability, or even looks anything like the more familiar interference patterns obtained with mono-chromatic inputs.

35 minutes ago, quiet said:

That model would describe how it is made and what an elementary particle is made of.

 

“The important thing about electrons and protons is not what they are but how they behave, how they move. I can describe the situation by comparing it to the game of chess. In chess, we have various chessmen, kings, knights, pawns and so on. If you ask what a chessman is, the answer would be that it is a piece of wood, or a piece of ivory, or perhaps just a sign written on paper, or anything whatever. It does not matter. Each chessman has a characteristic way of moving and this is all that matters about it.”   P.A.M. Dirac

[Markus Hanke]

5 hours ago, quiet said:

Suppose that in the near future a valid model of elementary particle is proposed, which agrees with the quantum theory, with relativity, with the thermodynamic treatment of the blackbody radiation, with the weak interaction, with the strong interaction, with the electromagnetic interaction and with everything necessary.

That model would describe how it is made and what an elementary particle is made of. It would explain in what they agree and in what they differ a particle and its antiparticle. It would explain how and why the photon has rest mass equal to zero. I know that rest mass is an archaic expression, but I want to use very explicit language at this time. It would also explain how and why other kinds of particles and antiparticles have rest mass other than zero. It would allow to theoretically state the conditions of the particle that has the minimum rest mass compatible with subsistence. I refer that to subsist without decomposing after being created. And it would allow to deduce from the model the theoretical value of the minimum rest mass compatible with subsistence. (One would expect that theoretical value to coincide with the rest mass of the electron.)

We already have such a framework: quantum field theory.

[Strange]

7 hours ago, quiet said:

That model would describe how it is made and what an elementary particle is made of.

There are models that attempt to describe elementary particles as being made up of more fundamental components, such as prions. But that just raises the question, what are they made from. You are chasing a rainbow. 

 

[studiot]

27 minutes ago, Strange said:

There are models that attempt to describe elementary particles as being made up of more fundamental components, such as prions. But that just raises the question, what are they made from. You are chasing a rainbow. 

 

 

8 hours ago, quiet said:

Suppose that in the near future a valid model of elementary particle is proposed,

 

I have always understood the definitionof an elementary particle to be

Quote

Elementary particle - Wikipedia

 

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

In particle physics, an elementary particle or fundamental particle is a subatomic particle with no substructure, thus not composed of other particles.

 

 

Elementary particles have no model or substructure, that is the nature of the beast.

 

Models are made in terms of something more fundamental that that which is being modelled.

So a model of an elemnetary particle would of necessity be non particulate.

3 hours ago, Markus Hanke said:

We already have such a framework: quantum field theory.

QFT goes a long way towards this goal.

[Strange]

40 minutes ago, studiot said:

I have always understood the definitionof an elementary particle to be

I should probably have put “elementary particles” in quotes. Or said something like “what are currently thought of as elementary particles...”

 

Edited October 23, 2018 by Strange
grammer and spylling

[studiot]

1 hour ago, Strange said:

Or said something like “what are currently thought of as elementary particles...”

Yes that would be an excellent clarification, especially in relation to your good point about a never ending trail.

[quiet]

2 hours ago, studiot said:

a model of an elemnetary particle would of necessity be non particulate.

On this I think as a way of to search a model of that we currently call elementary particle. Agree with semantic definition of elementary particle, withou internal components.

Edited October 23, 2018 by quiet

[Strange]

2 minutes ago, quiet said:

On this I think as a way of to search a model of that we currently call elementary particle.

We have such a model.

What do you think is wrong with it? (Scientifically, rather than aesthetically)

[quiet]

55 minutes ago, Strange said:

We have such a model.

Can You tell a little more about such a model?

Edited October 23, 2018 by quiet