Quantum Interpretations history

[vanesch]

If "irreversible measurement" means 'a measurement which leaves a trace of information' (roughly) then I guess this puts MWI and "modern" CI back on the same page in this specific regard.

Yes! That's why it is kind of silly to try to distinguish between them experimentally!
Caveat: at least, that is how *I* understand CI, because you never find two identical accounts of what is exactly CI...

 

[Hans de Vries]

With all the different quantum interpretations out there, which is your favourite " ?

You asked me for my favorite interpretation in a PM, Now, since I use
my own interpretation I'll post the elementary ideas here.


Just to give it a name: Sea-of-particle interpretation


Q: What is a particle?
A: A single surplus/absent particle in the see-of-particles


Q: Why can a particle turn up everywhere in the wave-function?
A: First this:

00_000000000000
000000000000_00

How long does it take for the 'gap' to go from the left to the right?
In principle not more as it takes the ten '0' take to go one step to
the left. There is in principle no SR limitation for the 'gap' to be either
at the left or the right.


Q: What is the wave function?
A: A single absent/surplus particle will distort the whole 'grid'
Instead of a single gap of say '40' there will be many small gaps
like for instance:

1-2-4-6-7-7-6-4-2-1

This is the wave function. The bigger the gap, the higher the chance
of detection. No single gap corresponds to the single deficit particle.
No single 'sea-of-particles' particle corresponds to the one surplus
particle.


Q: What is the detection of a particle?
A: The removal of the single surplus / deficit particle from the sea-of-
gates. Fixed and localized for instance to an atom.


Q: What happens with the wave function?
A: Without the single surplus/absent particle there is nothing anymore
to 'distort' the grid of the sea of particles. The wider wave-function will
die out. The wave-function will become fixed /localized to an atom for
instance.


Q: Shouldn't the wave-function disappear instantaneously? A remaining
gap could be detected as a particle which would violate unitarity.

A: This describes particle-pair creation, it leaves an extra surplus particle.
This happens all the time, temporary, because of energy conservation.
Single particle unitarity does not exist.


Q: What is the physical interaction?
A: The physical interaction is generally with the whole wave-function.

example: In Afshar's experiment there are more than 10^23 interactions
(~Avogadro's number) between the single photon's wave-function and
the dielectric molecules of the lens. These are real physical interactions.
Atoms are displaced back and forward. They detect the wave-function
but they do not -detect- the photon in the sense that they remove a
single surplus/absent particle from the see-of-particles.



For so far, In the hope to give you something which is more acceptable... :^)

Regards, Hans

 

[akhmeteli]

You asked me for my favorite interpretation in a PM, Now, since I use
my own interpretation I'll post the elementary ideas here.


Just to give it a name: Sea-of-particle interpretation


Q: What is a particle?
A: A single surplus/absent particle in the see-of-particles

Interesting. Actually, I discussed a similar interpretation in http://arxiv.org/abs/quant-ph/0509044 .
Could you give references to your (or other people's) publications on this approach?

 

[vanesch]

You asked me for my favorite interpretation in a PM, Now, since I use
my own interpretation I'll post the elementary ideas here.


Just to give it a name: Sea-of-particle interpretation

It is difficult to imagine how this is in 1-1 correspondence with the quantum formalism. After all, what you describe is almost litterally the dynamics of crystal defects in materials (Frenkel defects and all that). For instance, how does one get simply, say, the helium spectrum out of such a picture ?

 

[Hans de Vries]

For instance, how does one get simply, say, the helium spectrum out of such a picture ?

That shouldn't be so difficult.

The atomic spectra arise when the Laplacian is combined with a central potential
and the Laplacian occurs almost everywhere where you have particle assembles
since it's part of the classical wave equation.


Regards, Hans

 

[Hans de Vries]

Could you give references to your (or other people's) publications on this approach?

I don't have anything serious written up in Latex yet. it's a developing
idea and I would like to fill in more of the details.



Regards, Hans

 

[Count Iblis]

Many worlds interpretation is my favorite, but I'm not 100% conviced.
If you take unitary time evolution serious, then some of the intuitive ideas about quantum randomness etc. are wrong. E.g., unitary time evolution implies that there exists an observable for observing the position of a particle some time into the future. If you could somehow measure that observable, you could tell exactly where the particle will be in the future.

And, of course, you can make this as crazy as you like. There exists an observable for measuring the contents of your newspaper in the year 2100. The universe will then effective collapse into a specially prepared state which will evolve to some state consistent with the contents of the newspaper.

 

[vanesch]

That shouldn't be so difficult.

The atomic spectra arise when the Laplacian is combined with a central potential
and the Laplacian occurs almost everywhere where you have particle assembles
since it's part of the classical wave equation.

Let us not forget that (hence my *helium* and not *hydrogen*) a significant part of the spectrum of helium is determined by configuration interaction, which is due to the entanglement of the two orbitals (that is, is due to the deviation from the true ground state from a Slater determinant). Very many "quantum interpretations" which are in fact naive hidden variable field theories are quite OK as long as one looks at single-particle states, or product states (or Slater determinants for Fermions), but break down when coming to "real quantum mechanics" where actual entanglement takes place (that is, when the wavefunctions are essentially not factorisable). One thinks of course of EPR situations, but there are many more "entanglements" in quantum phenomena, and the one that comes most obviously to mind is the Helium spectrum.

 

[vanesch]

If you take unitary time evolution serious, then some of the intuitive ideas about quantum randomness etc. are wrong. E.g., unitary time evolution implies that there exists an observable for observing the position of a particle some time into the future. If you could somehow measure that observable, you could tell exactly where the particle will be in the future.

This is the quantum analogon of the classical canonical variable change in Hamilton-Jacobi theory, where the "canonical variables" simply become the "initial conditions" which don't evolve in time anymore (up to the angle variable, which has a linear time variation).

However, it is just as irrealistic in MWI as it is in classical physics (except for simple toy systems), or even more so, because in order to be able to construct that observable, you have to know unitary evolution well enough, INCLUDING all "observer" and "environment" interactions.

 

[peter0302]

Since this thread is _still_ alive :) I thought I'd ask another related question, and this is generally directed to Vanesch but anyone who also has an opinion is welcome to jump in.

When distinguishable fermi particles are scattered, the probability of finding one or the other in a particular state is simply what one would expect with classical physics. However, when _indistinguishable_ bose particles are scattered, it is more likely that a bose particle will end up in a paritcular state if the other particles did.

Does this not intuitively support a many-worlds theory? The rationale would be that because the particles are completely indistinguishable, the universes simply do not "split" (because they're indistinguishable!) and consequently the probability amplitude of a paritcular branch of the wavefunction is higher (the universe is "thicker") than it would be if the particles were distinguishable. This is reflected in seeing a higher probability of viewing the bose particles in particular states.

Can a pilot wave or other hidden variable interpretation account for this?

 

[akhmeteli]

It is difficult to imagine how this is in 1-1 correspondence with the quantum formalism. After all, what you describe is almost litterally the dynamics of crystal defects in materials (Frenkel defects and all that). For instance, how does one get simply, say, the helium spectrum out of such a picture ?

Let us not forget that (hence my *helium* and not *hydrogen*) a significant part of the spectrum of helium is determined by configuration interaction, which is due to the entanglement of the two orbitals (that is, is due to the deviation from the true ground state from a Slater determinant). Very many "quantum interpretations" which are in fact naive hidden variable field theories are quite OK as long as one looks at single-particle states, or product states (or Slater determinants for Fermions), but break down when coming to "real quantum mechanics" where actual entanglement takes place (that is, when the wavefunctions are essentially not factorisable). One thinks of course of EPR situations, but there are many more "entanglements" in quantum phenomena, and the one that comes most obviously to mind is the Helium spectrum.

It may well be that no 1-1 correspondence with the quantum formalism can be achieved. However, that would not be the end of the story. Strictly speaking, what we need is not 1-1 correspondence with the formalism, but agreement with the existing body of experimental data. That is, we need agreement with the formalism up to the experimentally achievable accuracy. However, that accuracy can be extremely high, so maybe I am hair-splitting. The reason I emphasize this distinction is that, for example, the results of Barut's self-field electrodynamics seem to emulate those of QED with high accuracy. To the best of my knowledge, it is not clear if Barut's theory is in disagreement with the body of experimental data. Thus, the Dirac sea interpretation (or you may call it "plasma interpretation", or "vacuum polarization interpretation") may be just added to Barut's theory or to some version of that theory.

 

[reilly]

See any E&M text dealing with E&M radiation, Landau and Lifschitz, for example. Diffraction is diffraction is scattering is interference no matter what blocks or impedes the radiation.

As long as the detector is any distance from the slit, there's a probability that the photon detected "came" from the other slit. So, who knows?

Certainty is hard to come by.

Regards,
Reilly Atkinson

But the slits don't cause diffraction like a lens or prism does. The slits merely pick out photons in such a way as to make it ambiguous which slit they went through. But I still say they only went through one slit or another, as evidenced by the fact that if you put detectors immediately beyond the slits before any interference pattern can show up, you only see one detector or the other go off.

 

[reilly]

Think for a moment about a volt meter. To be sure, we know how such a voltmeter works. Even with AC, we can assert that a voltage measurement will pick out one and only one value at any time whenever it is used -- up to the limits of measurement errors. Why just one value? Who knows? But, not many seem to worry about this basic property of Nature. Among other things, this "one per measurement", when appropriate, is fundamental to all empirically based science -- along with the idea that the physics of the immediate future is as it is now. No one worries much about this idea either. So, there's really a lot we choose not to question or understand. For some of us QM fits right in there with other stuff we don't know much about -- like, what's an electric charge?.

Humans need interpretations and meanings. This certainly true in physics, and the field is somewhat hung-up on QM. Having a strong sense of how QM came to be, and a long background in all manner of statistics and probability, I see many solid, practical reasons for a QM interpretation that's as simple as possible, Occamized if you will. I should note that my interest is in the application of QM to physical problems. So, what is the minimum set of ideas and stipulations that will allow us to deal with the demands of day-to-day physics?

A short version is: Key Experiments, Schrodinger, Born, Dirac.

Why do you need more if you do? It's can't be in search of a better description/theory of Nature, because the most fundamental questions of science are never asked, nor answered. You want better? Don't forget electric charge, don't forget that we perceive in 3D, why? QM is just the tip of the iceberg.
Regards,
Reilly Atkinson

(Key experiments -- black body radiation, atomic spectra, photoelectric, Davisson Germer, etc.)

 

[peter0302]

I think the main reason QM holds a special place in the hearts of those looking for physical interpretations is because it is so drastically different than anything humanity had seen before. Until the HUP, physics was really taking a slow but steady journey in one direction, namely, that there was a physical reality and no fundamental limits in our ability to describe and predict it. People truly believed that it was possible, in theory, to know _everything_ about the universe, including the future. Even Relativity did not contradict this; in fact, in some ways it helped reinforce this, because it placed a fundamental limiti on action, i.e., locality.

QM threw all this out the window. It really was a huge step _backwards_ in the formulation of a theory of everything. Where we thought we were "getting there", now we don't even know where "there" is.

So I think the quasi-obsession that is seen in finding intuitive interpretations of QM stems from a desire to recapture that feeling that we were actually on the right track in terms of completing our knowledge of the universe. Obviously nobody believes that we can understand everything there is to understand anytime soon, or ever, but we want to be going in the right direction!

I think, personally, that interpreting QM is very important because beneath the philosophical babble, it encourages scientists to search for ways to challenge the rpedictions of QM, and every challenge, even the ones that fail (which is so far ALL of them!) is valuable. Rarely, in the search of interpretation, someone finds a theory that agrees with every experimental test of QM performed thus far but yet still disagree somewhere else. Eventually, some needle in a haystack experiment may come along that does disprove some aspect of QM. That will be an historic day.

Until then, I think we really need to recognize that physics did, in fact, have to take a step backwards before it could move forward, which it did, dramatically, after the discovery of QM.

We're in a state now not too unlike where we were in 1905. Let's not forget that Einstein originally thought his "corpuscles" of light were just an "Interpetation", a mathematical trick that happened to fit the data. It took Bohr and others to realize that the mathematical "trick" had profound implications. I believe someone "interpreting" QM will eventually make a similarly profound realization and build from that an even deeper understanding than we have now.

 

[reilly]

Bohm's work has not produced any new physics in over 50 years; MWI similarly for more like 40. These approaches, however, are excellent producers of controversy. In the meantime, QM has totally transformed our world.
Regards,
Reilly Atkinson

Interpretations are more than "just" interpretations: they have consequences for future research. I've read from proponents of both Bohm's interpretation as well as of MWI, that a future development of their theories will lead to additional predictions which will be verifiable.

 

[akhmeteli]

Bohm's work has not produced any new physics in over 50 years.

In https://www.physicsforums.com/showpost.php?p=1565868&postcount=8 I asked you the following:

"As for new physics, do the Bell's inequalities qualify as "new physics"? As far as I know, Bohm's interpretation was the inspiration for Bell."

I did not get an answer.

Furthermore, does the Aharonov-Bohm effect qualify as new physics? I know that A-B were not the first to discover it theoretically, but the effect became famous after their work.

I value your thoughtful posts, and I would appreciate your reply.

 

[vanesch]

Can a pilot wave or other hidden variable interpretation account for this?

I would think so, but I have to admit not to have worked out any of this in detail, nor having it seen worked out. If it is true that Bohmian mechanics reproduces ALL of quantum mechanical statistical predictions, then this must be part of it. But I admit never having given it much thought of how indistinguishable particles are dealt with in BM.

 

[vanesch]

It may well be that no 1-1 correspondence with the quantum formalism can be achieved. However, that would not be the end of the story. Strictly speaking, what we need is not 1-1 correspondence with the formalism, but agreement with the existing body of experimental data. That is, we need agreement with the formalism up to the experimentally achievable accuracy. However, that accuracy can be extremely high, so maybe I am hair-splitting. The reason I emphasize this distinction is that, for example, the results of Barut's self-field electrodynamics seem to emulate those of QED with high accuracy. To the best of my knowledge, it is not clear if Barut's theory is in disagreement with the body of experimental data. Thus, the Dirac sea interpretation (or you may call it "plasma interpretation", or "vacuum polarization interpretation") may be just added to Barut's theory or to some version of that theory.

There are two different questions here. The first question is: in a toy world where quantum mechanics is supposed to hold strictly, how to give some sense or some intuitive understanding of the workings of that world ? That's the question one asks when dealing with an interpretation of the quantum formalism.

The other question is: in what measure is our actual world described, or not, by quantum theory ? That's a scientific question of the validity of quantum theory.

In as much as it is of course useful to probe eventual limits of the applicability of quantum theory to the real world, one shouldn't mix both. It is not because one has interpretational problems (that one is intellectually unsatisfied with the picture that quantum theory offers you) that you should bet on the other horse. That's a bit like "hoping the problem will go away".

Of course, doing so might suggest challenges to quantum theory where both differ, in order to find potential ways to find ultimate limits to the applicability of quantum theory. So as a "generator of challenges", this might be a useful exercise.

Personally, I'm affraid that Barut's theory is a kind of "semiclassical" approach to QFT. We know many instances of semiclassical approximations in quantum theory which give very good results, and in some cases, exactly the same results as the full-blown quantum machinery. In fact, this is the case each time when at no point, quantum interference is an essential component in the setup, and one is allowed to interchange statistical mixtures and superpositions. As such, I'm not a priori impressed by a semi-classical calculation that is in full agreement with a quantum result. It is always nice to know, of course, but the existence of the semi-classical explanation of a result in full agreement with the quantum prediction doesn't necessarily mean that this will be the case in all generality. There are too many results known where there IS a genuine difference between a semi-classical approach and a full-blown quantum calculation. The challenge is more on that side. There's no real difficulty in reproducing semi-classically the hydrogen spectrum. But once there are more electrons, things become harder. For instance, the helium spectrum. Configuration interaction in quantum chemistry. Things like that.

 

[vanesch]

I think the main reason QM holds a special place in the hearts of those looking for physical interpretations is because it is so drastically different than anything humanity had seen before. Until the HUP, physics was really taking a slow but steady journey in one direction, namely, that there was a physical reality and no fundamental limits in our ability to describe and predict it. People truly believed that it was possible, in theory, to know _everything_ about the universe, including the future. Even Relativity did not contradict this; in fact, in some ways it helped reinforce this, because it placed a fundamental limiti on action, i.e., locality.

QM threw all this out the window. It really was a huge step _backwards_ in the formulation of a theory of everything. Where we thought we were "getting there", now we don't even know where "there" is.

So I think the quasi-obsession that is seen in finding intuitive interpretations of QM stems from a desire to recapture that feeling that we were actually on the right track in terms of completing our knowledge of the universe. Obviously nobody believes that we can understand everything there is to understand anytime soon, or ever, but we want to be going in the right direction!

I think, personally, that interpreting QM is very important because beneath the philosophical babble, it encourages scientists to search for ways to challenge the rpedictions of QM, and every challenge, even the ones that fail (which is so far ALL of them!) is valuable. Rarely, in the search of interpretation, someone finds a theory that agrees with every experimental test of QM performed thus far but yet still disagree somewhere else. Eventually, some needle in a haystack experiment may come along that does disprove some aspect of QM. That will be an historic day.

Until then, I think we really need to recognize that physics did, in fact, have to take a step backwards before it could move forward, which it did, dramatically, after the discovery of QM.

We're in a state now not too unlike where we were in 1905. Let's not forget that Einstein originally thought his "corpuscles" of light were just an "Interpetation", a mathematical trick that happened to fit the data. It took Bohr and others to realize that the mathematical "trick" had profound implications. I believe someone "interpreting" QM will eventually make a similarly profound realization and build from that an even deeper understanding than we have now.

I'm very much in tune with what you wrote here...

 

[akhmeteli]

Personally, I'm affraid that Barut's theory is a kind of "semiclassical" approach to QFT. ... There are too many results known where there IS a genuine difference between a semi-classical approach and a full-blown quantum calculation. ... There's no real difficulty in reproducing semi-classically the hydrogen spectrum. But once there are more electrons, things become harder. For instance, the helium spectrum. Configuration interaction in quantum chemistry. Things like that.

I am not sure Barut's is a semiclassical theory. The reason is as follows. He eliminates the electromagnetic field from his theory using a causal Green function. I believe this is equivalent to quantization of electromagnetic field (please correct me if I am wrong). You may say that this procedure used by Barut stinks to heaven, and I may have a hard time looking for objections, but this does not look like your typical semiclassics.

As for identical particles, Barut uses another trick, introducing an antisymmetrized expression for the current into the action. As a result, it looks like he should not have problems, say, with helium. Again, you may question this procedure, but technically it may actually work.

Again, if you say that there is no fully satisfactory solution so far, I'll have to agree, but I still don't think the Dirac sea interpretation is clearly indefensible.

 

[Fra]

human intuition?

It keeps getting back that quantum behaviour is non-intuitive, but is that really so? or is it just due to the way we were used to think?

Last night I watched some tv program on cognitive psychology, where they pondered over models of the brains decisions making, and while watching it I striked me hard how strong parallells you could make to physics. The human brain behaves as it is RATING all options, and then using that to determine what actions to make in order to get maximum benefit. And once feedback is received, of the result of the actions. The brain doesn't seem to question it. The new facts are simply faced, and a new decision is made from that new initial condition.

Anyone who has been thinking about the quantum stuff couldn't see that program without a smile. And this was intuitive alright, because it was about how the human brain works.

The concept of rating system, actions, are right from physics. And I think for me at least, these types of intuitive analogies are far more appropriate to searching for intuition about quantum theory than is the mechanical style and geometric style analogies.

/Fredrik

 

[reilly]

My apologies for my late response.

I won't quibble. But, at best you have mentioned just two possible examples -- that's one every 25 years. But standard QM over that same period of 50 years has produce probably several hundred thousand examples of new physics.

Just to be clear, David Bohm was a great physicist

And thank you for your kind words.
Regards,
Reilly Atkinson

In https://www.physicsforums.com/showpost.php?p=1565868&postcount=8 I asked you the following:

"As for new physics, do the Bell's inequalities qualify as "new physics"? As far as I know, Bohm's interpretation was the inspiration for Bell."

I did not get an answer.

Furthermore, does the Aharonov-Bohm effect qualify as new physics? I know that A-B were not the first to discover it theoretically, but the effect became famous after their work.

I value your thoughtful posts, and I would appreciate your reply.

 

[akhmeteli]

But, at best you have mentioned just two possible examples -- that's one every 25 years. But standard QM over that same period of 50 years has produce probably several hundred thousand examples of new physics.

Thank you very much for your reply.

Thus, it seems like the Bohmian interpretation might have contributed some new physics. I'd say this is not a bad result for an interpretation. As for the quantitative comparison, I am not sure the Copenhagen interpretation should be credited for all incredible achievements of quantum mechanics - I would think most of them are interpretation-neutral, as, say, the Schroedinger equation is equally valid in the Bohmian interpretation.

You see, I am not a great fan of the Bohmian interpretation, I think I know its weaknesses. However, the Copenhagen interpretation does not seem satisfactory either, as it requires measurements that cannot be described by a unitary evolution operator. On the other hand, any measurements are within the realm of quantum mechanics. I understand that it can be irritating when the same issues are discussed for years and decades without visible progress. However, I don't think this is the reason to pretend the mainstream interpretation is satisfactory. That does not mean I know a fully satisfactory interpretation.

 

[reilly]

Here's the deal. Virtually every paper published about QM aince the 1920s has used one form or other of the Copenhagen interpretation, but always using the Born probability prescription. The worries about measurement are, in my opinion, spurious. Those types of issues transcend QM and occur in almost every effort that involves probability -- cf Kalman Filtering, and Shannon's Communication Theory. Further, the probability theory of the mathematicians, assumes only that measurements can be done.

My point of view is based on the mystery of single values for most measurements -- length, speed, mass, charge, etc. Why is this so?

Regards,
Reilly Atkinson

Thank you very much for your reply.
Thus, it seems like the Bohmian interpretation might have contributed some new physics. I'd say this is not a bad result for an interpretation. As for the quantitative comparison, I am not sure the Copenhagen interpretation should be credited for all incredible achievements of quantum mechanics - I would think most of them are interpretation-neutral, as, say, the Schroedinger equation is equally valid in the Bohmian interpretation.

You see, I am not a great fan of the Bohmian interpretation, I think I know its weaknesses. However, the Copenhagen interpretation does not seem satisfactory either, as it requires measurements that cannot be described by a unitary evolution operator. On the other hand, any measurements are within the realm of quantum mechanics. I understand that it can be irritating when the same issues are discussed for years and decades without visible progress. However, I don't think this is the reason to pretend the mainstream interpretation is satisfactory. That does not mean I know a fully satisfactory interpretation.

 

[reilly]

Here's the deal. Virtually every paper published about QM aince the 1920s has used one form or other of the Copenhagen interpretation, but always using the Born probability prescription. That indicates to me that, at a practical level, working physicists use Born, etc. because it's the best game in town. Almost all sciences involve consensus -- covering definitions, experimental procedures, and interpretations of theories, and so forth. So to speak, the electorate has spoken, and the overwhelming majority say . Born is still the guy. Just as Einstein is still the guy in relativity. Alternate interpretations have had almost a century to work -- they have not. If they had, then they would be part of the working physicist's tool box -- they are not.

For example, how do you do the Bohm thing to solve the simple QFT problem of finding the quantized E&M field generated by a classical current?


The worries about measurement are, in my opinion, spurious. Those types of issues transcend QM and occur in almost every effort that involves probability -- cf Kalman Filtering, and Shannon's Communication Theory. Further, the probability theory of the mathematicians, assumes only that measurements can be done.

My point of view is based on the mystery of single values for most measurements -- length, speed, mass, charge, etc. Why is this so?

Regards,
Reilly Atkinson

Thank you very much for your reply.
Thus, it seems like the Bohmian interpretation might have contributed some new physics. I'd say this is not a bad result for an interpretation. As for the quantitative comparison, I am not sure the Copenhagen interpretation should be credited for all incredible achievements of quantum mechanics - I would think most of them are interpretation-neutral, as, say, the Schroedinger equation is equally valid in the Bohmian interpretation.

You see, I am not a great fan of the Bohmian interpretation, I think I know its weaknesses. However, the Copenhagen interpretation does not seem satisfactory either, as it requires measurements that cannot be described by a unitary evolution operator. On the other hand, any measurements are within the realm of quantum mechanics. I understand that it can be irritating when the same issues are discussed for years and decades without visible progress. However, I don't think this is the reason to pretend the mainstream interpretation is satisfactory. That does not mean I know a fully satisfactory interpretation.

Thank you very much for your reply.

Thus, it seems like the Bohmian interpretation might have contributed some new physics. I'd say this is not a bad result for an interpretation. As for the quantitative comparison, I am not sure the Copenhagen interpretation should be credited for all incredible achievements of quantum mechanics - I would think most of them are interpretation-neutral, as, say, the Schroedinger equation is equally valid in the Bohmian interpretation.

You see, I am not a great fan of the Bohmian interpretation, I think I know its weaknesses. However, the Copenhagen interpretation does not seem satisfactory either, as it requires measurements that cannot be described by a unitary evolution operator. On the other hand, any measurements are within the realm of quantum mechanics. I understand that it can be irritating when the same issues are discussed for years and decades without visible progress. However, I don't think this is the reason to pretend the mainstream interpretation is satisfactory. That does not mean I know a fully satisfactory interpretation.

 

[drv]

How did physics get so screwed up?

Here's the deal. Virtually every paper published about QM aince the 1920s has used one form or other of the Copenhagen interpretation, but always using the Born probability prescription. The worries about measurement are, in my opinion, spurious. Those types of issues transcend QM and occur in almost every effort that involves probability -- cf Kalman Filtering, and Shannon's Communication Theory. Further, the probability theory of the mathematicians, assumes only that measurements can be done.

My point of view is based on the mystery of single values for most measurements -- length, speed, mass, charge, etc. Why is this so?



Regards,
Reilly Atkinson

Pardon the interjection, but I just can't hold back. In most all of these conversations, the views of modern physics are noticeably different. Why is this? Partially because of catch words like "quantum", "classical physics" and historically inaccurate statements as to prior efforts.

The Bohr (Copenhagen) atom model is down the tubes, although not entirely. Part of it is stuck in there somewhere. It would help to get rid of the impossibilities before starting to think about the possibilities.

QED

 

[reilly]

1. What is historically inaccurate?
2.Why are Bohr at.al. down the tubes?
3. What are the impossibilities?
Regards,
Reilly Atkinson

Pardon the interjection, but I just can't hold back. In most all of these conversations, the views of modern physics are noticeably different. Why is this? Partially because of catch words like "quantum", "classical physics" and historically inaccurate statements as to prior efforts.

The Bohr (Copenhagen) atom model is down the tubes, although not entirely. Part of it is stuck in there somewhere. It would help to get rid of the impossibilities before starting to think about the possibilities.

QED

 

[drv]

Answers

1. What is historically inaccurate?
2.Why are Bohr at.al. down the tubes?
3. What are the impossibilities?
Regards,
Reilly Atkinson

1. There are many things about the history of physics that are presently misquoted. To take just one example, see http://plato.stanford.edu/entries/qm-copenhagen/ . Let me go through this paper and pick out some inaccuracies:

a."But Planck's suggestion was that if black bodies only exchange energy with the radiation field in a proportion equal to hv that problem would disappear."

The truth is that the state equation that he derived, in which the falloff of state energy with frequency is exponential, was derived by Planck before any thought of hf. Based on Boltzmann's prior work, Planck deduced that there must be stable energy states, and that the change between any two energy consecutive energy states is fixed at hf.

b."According to classical mechanics and electrodynamics one might expect that the electrons orbiting around a positively charged nucleus would continuously emit radiation so that the nucleus would quickly swallow the electrons."

This is in contradiction with measured data and the laws of physics. Charges moving in a circle do not emit radiation. They produce a stable electromagnetic field.

c. The following "postulates" are attributed to Neils Bohr:

1. "An atomic system is only stable in a certain set of states, called stationary states, each state being associated with a discrete energy, and every change of energy corresponds to a complete transition from one state to another."

Planck's efforts were completed long before Bohr completed his model.

"The possibility for the atom to absorb and emit radiation is determined by a law according to which the energy of the radiation is given by the energy difference between two stationary states being equal to hv."

This is what Planck's radiation model was based on, again occcuring long before Bohr's efforts.

d. "Some features of Bohr's semi-classical model were indeed very strange compared to the principles of classical physics. It introduced an element of discontinuity and indeterminism foreign to classical mechanics:" (four examples given)

The definition of "classical physics" is not clear. If you don't believe this statement, then Google it. It is true, however, that the classical methods of that time were not believed to be applicable. Keep in mind that those methods generally involved second-order differential equations, which has its limitations. In today's world, the concept of "jump functions", which are related to the later efforts of Oliver Heaviside and Cauchy are well-suited to handling these types of situations. Example (1.) conflicts directly with Planck's model, the Planck state equation allows a great number of energy states. Example (2.) is ridiculous. Example (3.) is highly presumptive, and Example (4.) is simply silly.

e. The author of this paper goes on to state some of the principles of classical analysis, which I believe are quite correct. His comments, however, were well-covered by Planck in his definitions of the concepts of reversibility and irreversibility. Reversible systems obey the laws of thermodynamics, while the atom is a reversible system in which any of the energy states are possible.

f." Furthermore, the observation of a system does not affect its later behavior or, if observation somehow should influence this behavior, it is always possible to incorporate the effect into the prediction of the system's later state. Thus, in classical physics we can always draw a sharp distinction between the state of the measuring instrument being used on a system and the state of the physical system itself. It means that the physical description of the system is objective because the definition of any later state is not dependent on measuring conditions or other observational conditions."

This seems to me to be a very naive statement. Any measurement is affected by the instrument of measurement. However, that does not mean that the error of the measurement cannot be taken into consideration in order to get an accurate measurement. This requires the process of "characterization", derived from many typical measurements.

This covers the first quarter of this reference paper. Enough for now?

 

[reilly]

Th problems you cite don't have much to do with current physics

Classical physics? You know it when you see it.


Planck did not generate the stationary state hypothesis - at least according to A.Pais in his bio of Bohr.


We use Cauchy and Heavyside on a daily basis -- just like electrical engineers.

Try telling someone who works with cyclotrons about your claim of no radiation from circular orbits.
Regards,
Reilly Atkinson

1. There are many things about the history of physics that are presently misquoted. To take just one example, see http://plato.stanford.edu/entries/qm-copenhagen/ . Let me go through this paper and pick out some inaccuracies:

a."But Planck's suggestion was that if black bodies only exchange energy with the radiation field in a proportion equal to hv that problem would disappear."

The truth is that the state equation that he derived, in which the falloff of state energy with frequency is exponential, was derived by Planck before any thought of hf. Based on Boltzmann's prior work, Planck deduced that there must be stable energy states, and that the change between any two energy consecutive energy states is fixed at hf.

b."According to classical mechanics and electrodynamics one might expect that the electrons orbiting around a positively charged nucleus would continuously emit radiation so that the nucleus would quickly swallow the electrons."

This is in contradiction with measured data and the laws of physics. Charges moving in a circle do not emit radiation. They produce a stable electromagnetic field.

c. The following "postulates" are attributed to Neils Bohr:

1. "An atomic system is only stable in a certain set of states, called stationary states, each state being associated with a discrete energy, and every change of energy corresponds to a complete transition from one state to another."

Planck's efforts were completed long before Bohr completed his model.

"The possibility for the atom to absorb and emit radiation is determined by a law according to which the energy of the radiation is given by the energy difference between two stationary states being equal to hv."

This is what Planck's radiation model was based on, again occcuring long before Bohr's efforts.

d. "Some features of Bohr's semi-classical model were indeed very strange compared to the principles of classical physics. It introduced an element of discontinuity and indeterminism foreign to classical mechanics:" (four examples given)

The definition of "classical physics" is not clear. If you don't believe this statement, then Google it. It is true, however, that the classical methods of that time were not believed to be applicable. Keep in mind that those methods generally involved second-order differential equations, which has its limitations. In today's world, the concept of "jump functions", which are related to the later efforts of Oliver Heaviside and Cauchy are well-suited to handling these types of situations. Example (1.) conflicts directly with Planck's model, the Planck state equation allows a great number of energy states. Example (2.) is ridiculous. Example (3.) is highly presumptive, and Example (4.) is simply silly.

e. The author of this paper goes on to state some of the principles of classical analysis, which I believe are quite correct. His comments, however, were well-covered by Planck in his definitions of the concepts of reversibility and irreversibility. Reversible systems obey the laws of thermodynamics, while the atom is a reversible system in which any of the energy states are possible.

f." Furthermore, the observation of a system does not affect its later behavior or, if observation somehow should influence this behavior, it is always possible to incorporate the effect into the prediction of the system's later state. Thus, in classical physics we can always draw a sharp distinction between the state of the measuring instrument being used on a system and the state of the physical system itself. It means that the physical description of the system is objective because the definition of any later state is not dependent on measuring conditions or other observational conditions."

This seems to me to be a very naive statement. Any measurement is affected by the instrument of measurement. However, that does not mean that the error of the measurement cannot be taken into consideration in order to get an accurate measurement. This requires the process of "characterization", derived from many typical measurements.

This covers the first quarter of this reference paper. Enough for now?

 

[drv]

Th problems you cite don't have much to do with current physics

Classical physics? You know it when you see it.


Planck did not generate the stationary state hypothesis - at least according to A.Pais in his bio of Bohr.


We use Cauchy and Heavyside on a daily basis -- just like electrical engineers.

Try telling someone who works with cyclotrons about your claim of no radiation from circular orbits.
Regards,
Reilly Atkinson

"You know it when you see it"? That is a non-answer. Do as I suggested and you will get a thousand answers to the definition of what constitutes "classical analysis".

Planck described his theory in his Columbia Lectures in 1908. Any writings after Bohr are decades later. A. Pais was either or wrong or unintentionally making a misstatement. Planck describes his energy states in his sixth lecture. I quote: "In order to find the entropy S of the resonator [he describes the atom as a "resonator"] we will use the general connection between entropy and probability, which we have extensively discussed in the previous lectures, and inquire then as to the existing probability that the virating resonator possesses the energy U. ...[next page] If we now have to find the existing probability that the energy of a resonator shall lie between U and delta-U we have to calculate the magnitude of that state domain in the (phi,psi)-plane, which is bounded by the curves U= const. and U + delta-U = const. ..." In this analysis, phi and psi and the state variables in state space, which is the same procedure utilized in today's state space analysis. If you want to get more details, see "Planck's Columbia Lectures" (2005), Chapter 6, p.201. You are proving my point by citing a flawed reference.

I am very pleased that you use Cauchy and Heaviside analysis, since we will be able to communicate more intelligently.

The cyclotron, as I understand it, does not produce a stable orbit. According to my reference, the circulating protons spiral outward from the source, which is a quite different situation. In the electronic analog of the atom as a resonator, there is no power loss or radiation. The analysis of Planck also produces the same result.

 

[akhmeteli]

Here's the deal. Virtually every paper published about QM aince the 1920s has used one form or other of the Copenhagen interpretation, but always using the Born probability prescription. That indicates to me that, at a practical level, working physicists use Born, etc. because it's the best game in town. Almost all sciences involve consensus -- covering definitions, experimental procedures, and interpretations of theories, and so forth. So to speak, the electorate has spoken, and the overwhelming majority say . Born is still the guy. Just as Einstein is still the guy in relativity.

Born's probability prescription is really great. The question is what its final status will be. Let me give an example. Thermodynamics and statistical physics have provided a mind-boggling lot of first-class results. However, they have their own place and do not substitute microscopic dynamics, be it classical or quantum. A lot of first-class physicists rejected the idea of atoms until the beginning of the 20th century. Consensus in physics is a rather flimsy thing - new experimental results can destroy any consensus and erode any majority. Furthermore, there has never been a consensus on the interpretation of quantum mechanics, if you ask me. Of course, nobody cares and should not care what I might think on this issue, but the mere existence of such "dissidents" as Einstein, Plank, Schroedinger, de Broglie, pretty much relieves me of any obligations towards the Copenhagen interpretation.

Alternate interpretations have had almost a century to work -- they have not. If they had, then they would be part of the working physicist's tool box -- they are not.

For example, how do you do the Bohm thing to solve the simple QFT problem of finding the quantized E&M field generated by a classical current?

Again, I have not pledged allegiance to the Bohmian interpretation. That does not mean I have to swallow anything the Copenhagen interpretation might wish to push down my throat.

The worries about measurement are, in my opinion, spurious. Those types of issues transcend QM and occur in almost every effort that involves probability -- cf Kalman Filtering, and Shannon's Communication Theory. Further, the probability theory of the mathematicians, assumes only that measurements can be done.

Again, I have nothing against probabilities, but the questions are the same: "What is their place?", "Is there anything beyond the probabilities?" And I would like to emphasize again, that even if I agreed that there is nothing beyond the probabilities of quantum mechanics, I could not swallow the Copenhagen interpretation for the simple reason that it requires measurements as something that cannot be described by quantum mechanics. Again, I cannot see how measurements can be different from everything else, which scrupulously follows the laws of quantum mechanics. By the way, I tend to believe, following some authors, that measurements of the Copenhagen interpretation are not possible without irreversibility, which suggests that the final status of the Copenhagen interpretation is the same as that of statistical physics.

My point of view is based on the mystery of single values for most measurements -- length, speed, mass, charge, etc. Why is this so?

I am afraid I just don't quite understand this passage (or its relevance to interpretation of quantum theory). Could you explain?

 

[reilly]

You have not dealt with all my questions.

Nonetheless, I'll do my best to respond to your various points.



Looks to me like Planck is doing a standard computation of phase space a la statistical mechanics A la Boltzman and Gibbs. I see nothing about discrete states and radiation.

I am ever so relieved and flattered that a small portion of my mathematical background is satisfactory to you. Also note, however, that physicists use the Fourier rather than the Laplace transform in most circumstances.

One major reason for the great utility of Cauchy's integral theorems are their great utility in the representation of special functions. So I imagine that you are ready for a discussion of complex angular momentum based on Sommerfeld's analytic continuation of a multipole expansion (circa 1900) which was rediscovered by Tulio Regge and applied to scattering problems(1960s) But who knows, you might find my mathematical background lacking, in which case, who knows

So, where do you claim you can find stable circular orbits for charge particles? You will be doing physics a great service if you can show us a real, live charged particle orbiting in a circular path with no radiation. (I should have said synchrotron rather than cyclotron.)
Regards,
Reilly Atkinson

"You know it when you see it"? That is a non-answer. Do as I suggested and you will get a thousand answers to the definition of what constitutes "classical analysis".

Planck described his theory in his Columbia Lectures in 1908. Any writings after Bohr are decades later. A. Pais was either or wrong or unintentionally making a misstatement. Planck describes his energy states in his sixth lecture. I quote: "In order to find the entropy S of the resonator [he describes the atom as a "resonator"] we will use the general connection between entropy and probability, which we have extensively discussed in the previous lectures, and inquire then as to the existing probability that the virating resonator possesses the energy U. ...[next page] If we now have to find the existing probability that the energy of a resonator shall lie between U and delta-U we have to calculate the magnitude of that state domain in the (phi,psi)-plane, which is bounded by the curves U= const. and U + delta-U = const. ..." In this analysis, phi and psi and the state variables in state space, which is the same procedure utilized in today's state space analysis. If you want to get more details, see "Planck's Columbia Lectures" (2005), Chapter 6, p.201. You are proving my point by citing a flawed reference.

I am very pleased that you use Cauchy and Heaviside analysis, since we will be able to communicate more intelligently.

The cyclotron, as I understand it, does not produce a stable orbit. According to my reference, the circulating protons spiral outward from the source, which is a quite different situation. In the electronic analog of the atom as a resonator, there is no power loss or radiation. The analysis of Planck also produces the same result.

 

[drv]

You have not dealt with all my questions.

Nonetheless, I'll do my best to respond to your various points.



Looks to me like Planck is doing a standard computation of phase space a la statistical mechanics A la Boltzman and Gibbs. I see nothing about discrete states and radiation.

I am ever so relieved and flattered that a small portion of my mathematical background is satisfactory to you. Also note, however, that physicists use the Fourier rather than the Laplace transform in most circumstances.

One major reason for the great utility of Cauchy's integral theorems are their great utility in the representation of special functions. So I imagine that you are ready for a discussion of complex angular momentum based on Sommerfeld's analytic continuation of a multipole expansion (circa 1900) which was rediscovered by Tulio Regge and applied to scattering problems(1960s) But who knows, you might find my mathematical background lacking, in which case, who knows

So, where do you claim you can find stable circular orbits for charge particles? You will be doing physics a great service if you can show us a real, live charged particle orbiting in a circular path with no radiation. (I should have said synchrotron rather than cyclotron.)
Regards,
Reilly Atkinson

Planck did not do a computation of "phase space", nor is that what I stated. The parameters of the "state space" were given in my second paragraph. Since you evidently are not familiar with state space, let me explain. The two variables are a state variable, say x, and its derivative dx/dt. Planck referred to these two variables as phi and psi, respectively. When these two variables are plotted against one another and form a closed curve, that defines one "steady state". In the case of an oscillator (Planck's model of the atom), the steady-state curve is an ellipse (or circle). The stored energy, U, is proportional to the area of the ellipse. That is one stead state. The next steady state is (U + delta-U). Planck maintained that the steady states of the atom form a series of ellipses, and that delta-U is constant for adjacent ellipses. He solved for the delta-U, which turned out to be hf, where h is Planck's constant, and he derived an exact value for h, which had never before been accomplished. So please don't distort the truth. This was an enormous accomplishment, and one of the few laws of physics that have stayed the course of time. Please do read my paragraphs before you try to comment. I had thought the answer was stated quite clearly

Yes, we all use both the Fourier and Laplace transforms. Did you know that the Fourier transform can be easily determined from the resulting pole-zero plot of the Laplace transform?

No, it is not necessary to consider an "analytic continuation of a multi-pole expansion". However, we will have to work in complex vector space.

The hydrogen atom is an example of an electron orbiting the proton in a circular and/or spherical path with no detection of radiation. We will have to give credit to Bohr for this bit of theory. They now call it the "Bohr Magneton", which is a steady-state magnetic field vector that does not radiate energy, similar to a small magnet.

The synchrotron will definitely radiate energy. It uses a very powerful oscillator in order to operate.

No, I didn't answer all of your questions yet. Are you sure you want me to?

 

[Hans de Vries]

b."According to classical mechanics and electrodynamics one might expect that the electrons orbiting around a positively charged nucleus would continuously emit radiation so that the nucleus would quickly swallow the electrons."

This is in contradiction with measured data and the laws of physics. Charges moving in a circle do not emit radiation. They produce a stable electromagnetic field.

The synchrotron will definitely radiate energy. It uses a very powerful oscillator in order to operate.

The laws of physics describing the EM field of arbitrary moving charges were
derived by Liènard and Wiechert in 1900. They show that:

1) A charge moving in a circle does radiate energy.

2) A constant charge-current density with the charge continuously distributed
over the QM orbital does not radiate energy.Regards, Hans

 

[drv]

The laws of physics describing the EM field of arbitrary moving charges were
derived by Liènard and Wiechert in 1900. They show that:

1) A charge moving in a circle does radiate energy.

2) A constant charge-current density with the charge continuously distributed
over the QM orbital does not radiate energy.


Regards, Hans

I would like to inspect the derivation you cite, if possible. Do you have an exact reference? (I do not understand where the reference number you gave comes from)

1. The question is whether or not the derivation is based on ordinary mechanics or the laws of moving charges.

2. Please note that mass is asymmetrical when in motion. The transverse mass approaches zero as the speed approaches the speed of light. Therefore, the forces acting on high-velocity electrons will vary.

3. What you seem to be inferring is that the electrons are fixed in space with respect to the proton. This is in contradiction to the Bohr model, which successfully correlates with coherent radiation from atoms, since the Bohr model was based on moving electrons. If the only force acting on the electron is the Coulomb force from the proton. Where is the opposing force that conteracts the Coulomb forece?These is are just more problems with QM, which is full of contradictions.

4. Another contradiction has to do with the energy attained by the electron, and the forces acting on it by the proton. As an electron approaches the proton, it gains energy in the amount of Ke/R. If R does not vary, or if it does not vary enough, then how would the radiation correlate with measured values? If the electron rotates and loses energy, then the radius must slowly decrease, which produces a varying electromagnetic field (radiation). There is no evidence to support this mechanism. The concept of an "orbital" is not clear. In my view, the electrons may be moving or they could be fixed at certain point on the shell. If they are fixed, then it would take a considerable amount of energy to get them moving fast enough to create coherent radiation, and coherent radiation is indeed emitted by excited atom.

5. When the "Lorentz Force" equation is utilized, rather than ordinary mechanics, then any moving electrons will assume circular or helical paths. That is the nature of electromagnetics, and it has not been fully exploited, and it will never be advanced until the methods of QM allow it. Unfortunately, QM theory is very frigid and closed to new thoughts and ideas.

6. According to Planck ("Planck's Columbia Lectures", 2005 - p. 196), "In accordance with Maxwell's theory, the energy U of the oscillator (atom) does not generally remain constant and sends out spherical waves in all direction into the surrounding field. If no actions from without are exerted upon the oscillator, then there must be a loss in energy, and the oscillations are damped. Howere, the energy generally flows both outward and inward in a manner that may, or may not be periodic. ...". This argument is somewhat in agreement with your contention. However, the problem with the assumptions. As unlikely it may seem, electromagnetic radiation does not occur in the form of spherical waves. The Mesny antenna radiation equations, which are based on exact measurements, show this to be the case ("A New Picture of Radiation", Antennas and Propagation Society International Symposium 2003).

7. It has been shown that Einstein's energy equation is very simply derived from the hydrogen atom electromagnetic model, based on the Lorentz force equation, for a rotating atom. The force opposing the Coulomb force is a magnetic force.

Further comments invited.



drv

 

[Valery]

Check another quantum interpretation. Tetrahedral stacking !
Perhaps, it will clarify something:
www.perfectperiodictable.com. Go to 3D Image page. Read other pages too.

 

[reilly]

In fact, I've taken lessons in distorting the truth...What in the wortld are you talking about? How did I do it? Justify your accusation or withdraw it. ra

. So please don't distort the truth.

 

[drv]

In fact, I've taken lessons in distorting the truth...What in the wortld are you talking about? How did I do it? Justify your accusation or withdraw it. ra

. So please don't distort the truth.

Here is your quote: "Looks to me like Planck is doing a standard computation of phase space a la statistical mechanics A la Boltzman and Gibbs."

To say that Planck's quantum theory is a "standard computation" is a gross distortion of the truth. It is perhaps the greatest example of an important fundamental scientific theory in history.

 

[drv]

Check another quantum interpretation. Tetrahedral stacking !
Perhaps, it will clarify something:
www.perfectperiodictable.com. Go to 3D Image page. Read other pages too.

Very interesting!

Here are some facts that may apply to your "interpretation":

1. The distance between the centers of metals varies from 2 to 3 Angstroms. Copper, for instance has d = 2.343 Angstrom. Since the size of the hydrogen atom is one Angstrom. It makes one wonder where the ions are situated, especially since the lowly hydrogen atom has a diameter of about one Angstrom.

2. Metals have a lattice that is closely packed. The strongest metals have cubic close-packing, and the atoms are believed to touch adjacent atoms.

This doesn't leave much room to maneuver in determining geometric configurations for the various atoms and molecules.

Good luck in your efforts.

Best regards
drv

 

[Hans de Vries]

I would like to inspect the derivation you cite, if possible. Do you have an exact reference? (I do not understand where the reference number you gave comes from)

1. The question is whether or not the derivation is based on ordinary mechanics or the laws of moving charges.

The Liènard Wiechert potentials can be derived from the assumption that they (the
four components V, Ax, Ay, Az) obey the classical wave equation (Poisson's equation)
and that the charge is the source for V and current is the source for A.

2. Please note that mass is asymmetrical when in motion. The transverse mass approaches zero as the speed approaches the speed of light. Therefore, the forces acting on high-velocity electrons will vary.

You'll find the term "Transverse mass" only in very old text. In both non-relativistic
and relativistic mechanics the force is proportional the change of momentum. In
non-relativistic physics this happens to be proportional to the acceleration.

If you apply a force on an ultra-relativistic particle in the direction of the speed,
to push it closer to c, then you'll increase its momentum but you'll hardly increase
its speed. you'll only achieve a very small acceleration.

If you apply the same force transversal to the direction of motion then you change
the momentum proportional to the force by the same amount. However, the change
in speed will be much bigger, the acceleration will be much larger.

The acceleration is asymmetrical but it is not true that, as suggested, that the
transversal acceleration will tend to infinity. It doesn't get easier to accelerate
a faster moving object transversely to its motion.

3. What you seem to be inferring is that the electrons are fixed in space with respect to the proton. This is in contradiction to the Bohr model, which successfully correlates with coherent radiation from atoms, since the Bohr model was based on moving electrons. If the only force acting on the electron is the Coulomb force from the proton. Where is the opposing force that conteracts the Coulomb forece?These is are just more problems with QM, which is full of contradictions.

A wave function has a constant charge density and current density at each point
of the wave-function. The current density can be associated with moving charge
which can be associated with motion.



Regards, Hans

 

[drv]

The Liènard Wiechert potentials can be derived from the assumption that they (the
four components V, Ax, Ay, Az) obey the classical wave equation (Poisson's equation)
and that the charge is the source for V and current is the source for A.




You'll find the term "Transverse mass" only in very old text. In both non-relativistic
and relativistic mechanics the force is proportional the change of momentum. In
non-relativistic physics this happens to be proportional to the acceleration.

If you apply a force on an ultra-relativistic particle in the direction of the speed,
to push it closer to c, then you'll increase its momentum but you'll hardly increase
its speed. you'll only achieve a very small acceleration.

If you apply the same force transversal to the direction of motion then you change
the momentum proportional to the force by the same amount. However, the change
in speed will be much bigger, the acceleration will be much larger.

The acceleration is asymmetrical but it is not true that, as suggested, that the
transversal acceleration will tend to infinity. It doesn't get easier to accelerate
a faster moving object transversely to its motion.



A wave function has a constant charge density and current density at each point
of the wave-function. The current density can be associated with moving charge
which can be associated with motion.



Regards, Hans

Poisson's wave equation is based on spherical waves. This does not apply to electrons moving at high velocity.

Your assertion that "transverse mass" is found only in very old text is quite incorrect. It is currently used in particle physics, for instance in analyzing the characteristics of quarks. I suggest that you do some Googling on this subject. The transverse mass relates directly to the Lorentz equations and was derived therefrom. The Lorentz equations show that the transverse mass decreases with velocity, and therefore the acceleration in the transverse direction is much faster. When an electron is moving through space, a transverse force acts on it, as is shown by the Lorentz force equation. This is simply basic electromagnetic analysis that is quite commonly used.

Your quote: "A wave function has a constant charge density and current density at each point of the wave-function." completely baffles me. An electromagnetic wave has no charge densite or current density. It consists of an E-field and and H-field, both of which are smoothly distributed through space.

Perhaps we have a little communications problem regarding languages?

 

[Hans de Vries]

I presume "drv" stands for dr. (Weldon) Vlasak?

http://www.science-site.net/
http://www.science-site.net/books.htm

anyway:

Poisson's wave equation is based on spherical waves. This does not apply to electrons moving at high velocity.

Check for instance Jackson's Classical Electrodynamics, section 1.7
equation (1.28) for Poisson's equation of the electrostatic potential
and section 5.4 equation (5.31) for Poisson's equation of the
magnetic vector potential.

These equations are fully compatible with special relativity.

Your assertion that "transverse mass" is found only in very old text is quite incorrect. It is currently used in particle physics, for instance in analyzing the characteristics of quarks. I suggest that you do some Googling on this subject. The transverse mass relates directly to the Lorentz equations and was derived therefrom. The Lorentz equations show that the transverse mass decreases with velocity, and therefore the acceleration in the transverse direction is much faster. When an electron is moving through space, a transverse force acts on it, as is shown by the Lorentz force equation. This is simply basic electromagnetic analysis that is quite commonly used.

You can find the relation between force and acceleration longitudinal and
transversal to the motion of a relativistic particle here:

http://en.wikipedia.org/wiki/Mass_i...evelopments:_transverse_and_longitudinal_mass

You see that this "effective transversal mass" does not tend to zero but increases
with gamma.

Your quote: "A wave function has a constant charge density and current density at each point of the wave-function." completely baffles me. An electromagnetic wave has no charge densite or current density. It consists of an E-field and and H-field, both of which are smoothly distributed through space.

Perhaps we have a little communications problem regarding languages?

A charged wave-function belongs to a charged particle...



Regards, Hans