Why can't SR explain why electrons do not crash into the nucleus?

[DrChinese]

To clarify, I am not trying to question the validity of QM. I am trying to identify the reason classical physics (including SR) fails to explain why an electron cannot orbit a proton without crashing into it.

So far the only reason seems to be that, according to classical physics, the electron would radiate all of its energy as it orbited because of its acceleration. All I am saying is that whether classical physics requires electrons to radiate in orbital motion about a proton seems to be a matter of some dispute still. So let's leave that argument to the side for the moment.

We know that electrons do not radiate energy while accelerating in the vicinity of a proton. The explanation for this is that electrons can only emit energy in packets. That is quite well proven. But it seems to me that does not explain why the electron doesn't keep getting closer to the proton and keep emitting more energy until it crashes into the proton. The evidence is that the coulomb force applies between protons and electrons down to the level of the size of the proton (approx 1 Fermi or 10e-15 m.).

My understanding is that the uncertainty principle provides the only explanation as to why the electron does not crash into the nucleus. I am just trying to see why the Special Theory of Relativity would not also come into play here.

AM

Why should a "failed" classical theory be able to explain Bohr's atomic model?
And what does SR have to do with the quantum model? You are starting from the assumption it should have some significant connection in answering the question, when you already know it doesn't. All classical models have the election either going into the nucleus or orbiting at any specific place outside the nucleus, depending on the model, and neither of these things actually happen.

You can't bring in the price of tea in China as a factor either. So the idea of trying to explain quantum behavior using a non-quantum concept like SR is off the mark.

 

[reilly]

WOW. How revisionist can you get?

If any of you wish to understand the dilemma faced by classical physics in regard to atomic stability and and atomic spectra, study the history, and learn the facts. As succinct a statement as any can be found in Pais' bio of Bohr, Neils Bohr's Times, ..., p 119., " Could these circuits not simply be electrons moving inside atoms? By a general classical theorem (post-dating Ampere) such orbits are unstable, however, since the electrons will necessarily lose energy by emission of electromagnetic radiation" There's absolutely no doubt about the matter.

Such masters of classical physics as J.J. Thomson could not figure out how to get around the problem. (In fact, Pais titles the section on Bohr's atomic model: Triumph over Logic: the Hydrogen Atom.) If you want to get a sense of thinking about E&M and radiation just prior to the First World War, get and read The Mathematical Analysis of Electrical and Optical Wave-Motion by H. Bateman (My copy is published by Dover, and I would suspect the book is still available. ) It's highly mathematical, discussed the then cutting edge of research, but there's a lot of accessible physics -- fields of moving singularities, diffraction, various ways to attack the wave equation, and so forth. Bateman, some 10 years after the birth of Special Relativity, gives Einstein just a single footnote Then there's Sir E. Whittaker's wonderful History of the Aether and Electricity. Far better, and more productive to study such material than to pursue paths that history shows lead to blind alleys -- but if you don't understand the history...

As an accelerator physicist, who should know better than ZapperZ about radiation from accelerated charges? Radiation losses in accelerators, or one of Bohr's favorite topics, the stopping of charged particles going through matter, should be, today, no-brainer topics (at least for physicists).

One of the ways I measured my success as a teacher was the degree to which the questions my students asked became more sophisticated and more knowledgeable. That they did so reflected their own serious efforts to learn physics, rather than dabble. Not that there's necessarily anything wrong with dabbling -- it's just a different ballgame, or something along the lines of air guitar -- with all due respect.

Regards,
Reilly Atkinson

 

[Antiphon]

You can find a derivation of the E field of a moving, accelerating charge here:

http://fermi.la.asu.edu/PHY531/larmor/

See formula 19 which is equal to Jacksons Equation 14.14. which is
also the one used in your refs.

If you now simplify (19) to that of a non moving particle then you get this:

E = \frac{q\hat{r}}{4 \pi \epsilon_0 r^2} - \frac{q}{4 \pi \epsilon_0 r} \frac{\vec{a}}{c^2} cos (\phi)

Where the first term is the usual Coulomb term and the second term
is caused by the acceleration a. Now if you go back to (19) then you'll
see that there's no way to get rid of the second term by choosing an
arbitrary speed.

Non radiating charges would need a modified EM theory at small distances.


Regards, Hans.

Hans,

The confusion stems from the fact that a charge in uniform acceleration
does not radiate *in that accelerated frame*.

It does radiate when viewed from other frames in uniform motion, as your
equations correctly state.

From another post:

A charge at rest in a gravitational field is accelerated (assume uniformly)
yet does not radiate. Therefore (by equivalence) a charge at rest in a
uniformly accelerating reference frame does not radiate *in that frame*.

Thus if you suppose you are next to a charge in an elevator that is
undergoing uniform 1 G acceleration, it will not appear to emit radiation
to *you*.

But an observer in a nearby non-accelerated frame will measure the
presence of both electric and magnetic fields changing as a function
of time. Time-changing fields (in free space) will result in radiation.
There IS radiation coming from the accelerating charge which can be observed in other frames. The energy for this radiation comes from the mechanical source which is accelerating the charge, it's prime mover.


The observer in the elevator sees no radiation, but *does* measure
an anisotropic field in the elevator *and through all of space*.
That is, the static electric Coulomb field at the top of the elevator
is different than at the bottom. There is a time-static spatial potential
energy variation in this Coulomb field that has an equivalent mass which
takes work by the elevator's prime mover to accelerate.

If you transform this time-static spatial variation of the Coulomb field
back into the uniformly moving reference frame, you will recover the
radition fields.

 

[Andrew Mason]

WOW. How revisionist can you get?

Please explain. I am not trying to revise history. I am just trying to understand something.

If any of you wish to understand the dilemma faced by classical physics in regard to atomic stability and and atomic spectra, study the history, and learn the facts. As succinct a statement as any can be found in Pais' bio of Bohr, Neils Bohr's Times, ..., p 119., " Could these circuits not simply be electrons moving inside atoms? By a general classical theorem (post-dating Ampere) such orbits are unstable, however, since the electrons will necessarily lose energy by emission of electromagnetic radiation" There's absolutely no doubt about the matter.

Such masters of classical physics as J.J. Thomson could not figure out how to get around the problem. (In fact, Pais titles the section on Bohr's atomic model: Triumph over Logic: the Hydrogen Atom.) If you want to get a sense of thinking about E&M and radiation just prior to the First World War, get and read The Mathematical Analysis of Electrical and Optical Wave-Motion by H. Bateman (My copy is published by Dover, and I would suspect the book is still available. ) It's highly mathematical, discussed the then cutting edge of research, but there's a lot of accessible physics -- fields of moving singularities, diffraction, various ways to attack the wave equation, and so forth. Bateman, some 10 years after the birth of Special Relativity, gives Einstein just a single footnote Then there's Sir E. Whittaker's wonderful History of the Aether and Electricity. Far better, and more productive to study such material than to pursue paths that history shows lead to blind alleys -- but if you don't understand the history...

This is all very interesting. However, I am not aware of anyone applying special relativity to the problem. If the ionization energy of an H atom is sufficient to bring an electron to a relativistic speed, why would it not be reasonable to ask such a question?

As an accelerator physicist, who should know better than ZapperZ about radiation from accelerated charges? Radiation losses in accelerators, or one of Bohr's favorite topics, the stopping of charged particles going through matter, should be, today, no-brainer topics (at least for physicists).

I don't think you have to be an accelerator physicist to know that charges accelerated by magnetic fields radiate energy. But that doesn't mean that the accelerated charge radiates because it is accelerated.

The question is whether it is the interaction of the fields of the charge and magnet that cause the radiation (and, because the charge has mass, also the charge's acceleration) or whether the interaction just causes the charge's acceleration and that acceleration, in turn, causes the radiation. Big difference.

One of the ways I measured my success as a teacher was the degree to which the questions my students asked became more sophisticated and more knowledgeable. That they did so reflected their own serious efforts to learn physics, rather than dabble. Not that there's necessarily anything wrong with dabbling -- it's just a different ballgame, or something along the lines of air guitar -- with all due respect.

You can't always tell when someone is dabbling or persuing a serious inquiry. It is better to err on the side of reserving judgment. One of the ways I measured the success of my teachers was their willingness to treat questions, even those that might appear to be dumb questions, seriously. As you know, there is no scientist alive who has not asked a dumb question. And there are few good scientists who have not asked what he or she thought might be a dumb question, only to realize later that it wasn't -- with all due respect.

AM

 

[reilly]

Mr. Mason -- I never said anything about dumb questions. Much of what you say about dumb questions is quite correct. But you apparently have not paid much attention to answers to your questions, which many have provided in this thread.

Of course relativity has been applied to the problem of the hydrogen atom. Read about it in Dirac's elegant and justly famous book, Quantum Mechanics, or most any book on atomic physics. History.

Acceleration and radiation? Read any book on E&M; they have all said the same thing for over a century. For the physics community, it's a done deal, and has been for over a century. Why fight it? The connection between acceleration and radiation was good enough for JJ Thomsen, Heinrik Lorenz, Harry Kramers, Schrodinger, Einstein, Dirac, Heisenberg, Fermi, Oppenheimer, Weinberg, GellMan, Feynman --except apparently in a weak moment, Bohr, Pais, Lev Landau, J.H. Van Vleck (my teacher) Lee and Yang, A. Sommerfeld... These are smart guys, who insist in getting it right. In statistical terms, their agreement provides the correctness of classical radiation theory at the 99.99999 confidence level.(If you can prove them all wrong, you'll get a Nobel Prize for sure.)

Not only that, but the classical theory of radiation is and has been enormously successful -- radio and TV, and radar, particle accelerators for example. What's to argue?

For practical purposes, atoms are stable because to a substantial degree, following Bohr, QM is designed to insure that stability. It is remarkable that QM does such a magnificent job in describing atomic phenomena. Check out the theory of the hydrogen atom, take your choice of Dirac or Schrodinger, and you will find out why electrons do not crash into the nuclei. It is basic, well understood, taught in undergraduate physics all over the world, and is fundamentally quantum mechanical in nature.

Yours is a good question, no doubt about it. And, the answer is well known throughout the physics community, without controversy. Go read about it, study the matter; hit a library, do a Google. When I was teaching, some of my students asked similar questions, and I always pointed them in a direction where they could figure out the answer themselves. That's the best way.To that end, I've suggested several books -- if you read them, you will learn a great deal about physics, and you'll be able to answer your own question. Is that such an onerous task? Good luck.

Regards,
Reilly Atkinson

 

[quantumdude]

Andrew, I know you want to set aside the radiation question, but that really is what is at issue here. It is the unequivocal testimony of physics textbooks everywhere that an orbiting charge radiates, and derivations of the energy flow rate abound at varying levels of rigor. You can't just brush it off like that.

But at the same time, I think you deserve an answer on this alleged controversy, which is why I am looking forward to reading those papers you cited. I'm sure I'll learn a great deal from them, so thank you for bringing them to my attention.

 

[jtbell]

The question is whether it is the interaction of the fields of the charge and magnet that cause the radiation (and, because the charge has mass, also the charge's acceleration) or whether the interaction just causes the charge's acceleration and that acceleration, in turn, causes the radiation. Big difference.

But how do you tell the difference, in practice? How do you cause a charge to accelerate, without using electric or magnetic fields? Before you answer, "gravity", consider that in the context of general relativity, gravity isn't really a force at all, but "merely" a consequence of curved spacetime.

 

[Andrew Mason]

But how do you tell the difference, in practice? How do you cause a charge to accelerate, without using electric or magnetic fields? Before you answer, "gravity", consider that in the context of general relativity, gravity isn't really a force at all, but "merely" a consequence of curved spacetime.

That may be so, but acceleration is acceleration. And GR says that an accelerating mass (including a charged mass) and the same mass at rest in a gravitational field are equivalent. If, in fact, it is uniform acceleration that causes the charge to radiate, then it would have to radiate in a gravitational field.

I haven't read Feynman's Lectures on Gravitation (2002), although I am looking for a copy, but he starts one of those lectures, apparently, by saying:

'For example, in Feynman's "Lectures on Gravitation" he says "we have inherited a prejudice that an accelerating charge should radiate", and then he goes on to argue that the usual formula giving the power radiated by an accelerating charge as proportional to the square of the acceleration "has led us astray" because it applies only to cyclic or bounded motions.'​

See: http://www.mathpages.com/home/kmath528/kmath528.htm

AM

 

[Andrew Mason]

Andrew, I know you want to set aside the radiation question, but that really is what is at issue here. It is the unequivocal testimony of physics textbooks everywhere that an orbiting charge radiates, and derivations of the energy flow rate abound at varying levels of rigor. You can't just brush it off like that.

But at the same time, I think you deserve an answer on this alleged controversy, which is why I am looking forward to reading those papers you cited. I'm sure I'll learn a great deal from them, so thank you for bringing them to my attention.

There has been quite a bit written on the subject. I have compiled this rather incomplete summary:

D. Boulware, "Radiation from a uniformly accelerated charge", Annals of Physics 124 , 169-187 (1980)

Kirk T. Mcdonald, "Hawking-Unruh Radiation and Radiation of a Uniformly Accelerated Charge", http://www.hep.princeton.edu/~mcdonald/accel/unruhrad.pdf (1998)

S. Parrott, "Radiation from a particle uniformly accelerated for all time", General Relativity and Gravitation 27 1463-1472, http://arxiv.org/PS_cache/gr-qc/pdf/9711/9711027.pdf (1995)

S. Parrott, "Radiation from Uniformly Accelerated Charge and the Equivalence Principle", Foundations of Physics, Volume 32, Number 3
March 2002, http://arxiv.org/abs/gr-qc/9303025

S. Parrott, "Relativistic Electrodynamics and Differential Geometry", New York: Springer Verlag, 1987.

A. Shariati, and M. Khorrami, "Equivalence Principle and Radiation by a Uniformly Accelerated Charge", Found. Phys. Lett. 12 427-439 (1999) http://arxiv.org/PS_cache/gr-qc/pdf/0006/0006037.pdf

Alfonso Rueda, Bernhard Haisch, "Contribution to inertial mass by reaction of the vacuum to accelerated motion" http://arxiv.org/abs/physics/9802030

A. K. Singal, "The Equivalence Principle and an Electric Charge in a Gravitational Field", General Relativity and Gravitation 27 953-967 (1995)

A. K. Singal, "The Equivalence Principle and an Electric Charge in a Gravitational Field II. A Uniformly Accelerated Charge Does Not Radiate", General Relativity and Gravitation 27 1371-1390 (1997)

"Abstract:The electromagnetic field of a charge supported in a uniform gravitational field is examined from the viewpoint of an observer falling freely in the gravitational field. It is argued that such a charge, which from the principle of equivalence is moving with a uniform acceleration with respect to the (inertial) observer, could not be undergoing radiation losses at a rate implied by Larmor's formula. It is explicitly shown that the total energy in electromagnetic fields, including both velocity and acceleration fields, of a uniformly accelerated charge, at any given instant of the inertial observer's time, is just equal to the self-energy of a non-accelerated charge moving with a velocity equal to the instantaneous “present” velocity of the accelerated charge. At any given instant of time, and as seen with respect to the “present” position of the uniformly accelerated charge, although during the acceleration phase there is a radially outward component of the Poynting vector, there is throughout a radially inward Poynting flux component during the deceleration phase, and a null Poynting vector at the instant of the turn around. From Poynting's theorem, defined for any region of space strictly in terms of fixed instants of time, it is shown that a uniformly accelerated charge does not emit electromagnetic radiation, in contrast to what is generally believed. Contrary to some earlier suggestions in the literature, there is no continuous passing of electromagnetic radiation from a uniformly accelerated charge into the region inaccessible to a co-accelerating observer."​

William E. Baylis, " Electromagnetic Radiation from an Accelerated
Charge[/url]" June 2003.

AM

 

[Locrian]

Does an argument that electrons uniformly accelerated by gravity (which is unarguably a very different phenomenon than being uniformly accelerated by electromagnetic forces) do not emmit radiation meaningful in an atom where it could not possibly be bound by gravitational forces?

I'm having a hard time understanding the relevance of those papers. What have I missed?

 

[Andrew Mason]

Does an argument that electrons uniformly accelerated by gravity (which is unarguably a very different phenomenon than being uniformly accelerated by electromagnetic forces) do not emmit radiation meaningful in an atom where it could not possibly be bound by gravitational forces?

I'm having a hard time understanding the relevance of those papers. What have I missed?

You cannot make a distinction between gravitation and acceleration due to electromagnetic force without violating the principle of equivalence under GR. If GR is valid, then either a charge in the electromagnetic field does not radiate, or it does and we should be able to detect it. No one has been able to detect it.

AM

 

[ZapperZ]

You cannot make a distinction between gravitation and acceleration due to electromagnetic force without violating the principle of equivalence under GR. If GR is valid, then either a charge in the electromagnetic field does not radiate, or it does and we should be able to detect it. No one has been able to detect it.

AM

NO one has been able to detect that a charge in an EM field radiate? I don't understand. HOw many times do you need to be told that a charge in an EM field radiate?

It's like talking to a WALL!

Zz.

 

[Andrew Mason]

NO one has been able to detect that a charge in an EM field radiate? I don't understand. HOw many times do you need to be told that a charge in an EM field radiate?

Hang on Zz. I have never said that a (moving) charge in an EM field doesn't radiate. The question is whether the radiation is caused by acceleration.

If the charge radiates because of the interaction of the two em fields, the charge will necessarily accelerate. But that doesn't mean that it is the acceleration that causes the radiation. If it the charges' acceleration that generates the radiation, you have real problems with GR.

AM

 

[ZapperZ]

Hang on Zz. I have never said that a (moving) charge in an EM field doesn't radiate. The question is whether the radiation is caused by acceleration.

If the charge radiates because of the interaction of the two em fields, the charge will necessarily accelerate. But that doesn't mean that it is the acceleration that causes the radiation. If it the charges' acceleration that generates the radiation, you have real problems with GR.

AM

No I don't. You do.

Accelerating charges radiate. I have verified that EXPERIMENTALLY. This occurs no matter if it is accelerating linearly, or accelerating in a uniform circular motion. If you don't buy this, you have a real problem with experimental observations.

What is causing you to stand on top of your head is the issue that a charge that isn't moving in a gravitatonal field does not radiate.

If you are in the same reference frame as the charge, and the charge is accelerating, can you prove that you do see a radiation coming from the charge? And please, make sure you use the Lorentz covariant form of Maxwell Equations to do this.

Zz.

 

[Hans de Vries]

Hans,

The confusion stems from the fact that a charge in uniform acceleration
does not radiate *in that accelerated frame*.

It does radiate when viewed from other frames in uniform motion, as your
equations correctly state.

From another post:

Antiphon.

It seems indeed true that, when using the Lienard Wiechert potentials, a
charge in uniform acceleration does not radiate *in that accelerated frame*.

One does get a non-zero vector potential because the relative velocity of
the retarded charge seen in the accelerated frame increases the longer
ago the EM potentials left the charge.

The vector potentials however stay constant in time in the case of, and
only in the case of, uniform acceleration. As a result there are no
fields which are associated with the acceleration.

These radiative fields re-appear again if observed from a reference frame
in uniform motion. At 90 degrees angles from the charge they have the
form of a E vector opposing the field that has caused the acceleration
of the charge.


Regards, Hans

 

[Andrew Mason]

What is causing you to stand on top of your head is the issue that a charge that isn't moving in a gravitatonal field does not radiate.

If you are in the same reference frame as the charge, and the charge is accelerating, can you prove that you do see a radiation coming from the charge? And please, make sure you use the Lorentz covariant form of Maxwell Equations to do this.

How am I to interpret this statement (cited above)?:

"From Poynting's theorem, defined for any region of space strictly in terms of fixed instants of time, it is shown that a uniformly accelerated charge does not emit electromagnetic radiation, in contrast to what is generally believed. Contrary to some earlier suggestions in the literature, there is no continuous passing of electromagnetic radiation from a uniformly accelerated charge into the region inaccessible to a co-accelerating observer."​

Is the author wrong?

AM

 

[ZapperZ]

How am I to interpret this statement (cited above)?:

"From Poynting's theorem, defined for any region of space strictly in terms of fixed instants of time, it is shown that a uniformly accelerated charge does not emit electromagnetic radiation, in contrast to what is generally believed. Contrary to some earlier suggestions in the literature, there is no continuous passing of electromagnetic radiation from a uniformly accelerated charge into the region inaccessible to a co-accelerating observer."​

Is the author wrong?

AM

... How did you managed to continually overlook the statement "... there is no continuous passing of electromagnetic radiation from a uniformly accelerated charge into the region inaccessible to a co-accelerating observer"?

How is this even anywhere close or applicable to "charge orbiting in a central potential"? Are YOU and the charge "co-accelerating" so much so that you are in this "inaccessible region" that would get no radiation?

This is VERY confusing because (i) you keep ignoring (or maybe you didn't understand) the stuff you're citing and (ii) you're applying different things to different situations that are not equivalent. For some odd reason, even after all this time and after all those replies, you still somehow do not see this.

Zz.

 

[Andrew Mason]

... How did you managed to continually overlook the statement "... there is no continuous passing of electromagnetic radiation from a uniformly accelerated charge into the region inaccessible to a co-accelerating observer"?

I am not sure what makes you think I overlooked it. My understanding is that this is a reference to the 'co-moving observer exception'. To explain why no radiation is detected from a charge in a gravitational field, the 'co-moving observer exception' has been developed. According to this theory, the lack of radiation from a stationary charge in a gravitational field is that it is there but not detected - that it is not accessible to a co-moving observer (ie. another observer who is at rest in the same gravitational field). What this paper seems to say - at least according to the abstract which I have quoted fully - is that there is no radiation period. There is no radiation detected by the co-moving observer and there is no "passing of electromagnetic radiation from a uniformly accelerated charge into the region inaccessible to a co-accelerating observer"

How is this even anywhere close or applicable to "charge orbiting in a central potential"? Are YOU and the charge "co-accelerating" so much so that you are in this "inaccessible region" that would get no radiation?

This is VERY confusing because (i) you keep ignoring (or maybe you didn't understand) the stuff you're citing and (ii) you're applying different things to different situations that are not equivalent. For some odd reason, even after all this time and after all those replies, you still somehow do not see this.

Well, it has been about 30 years since my last quantum physics and electromagnetism courses. But I think I am capable of understanding from the literature that the issue is still not satisfactorily resolved for some. In any event, the ad hominem approach to discussion and argument doesn't work any better in physics than in law.

AM

 

[ZapperZ]

I am not sure what makes you think I overlooked it. My understanding is that this is a reference to the 'co-moving observer exception'. To explain why no radiation is detected from a charge in a gravitational field, the 'co-moving observer exception' has been developed. According to this theory, the lack of radiation from a stationary charge in a gravitational field is that it is there but not detected - that it is not accessible to a co-moving observer (ie. another observer who is at rest in the same gravitational field). What this paper seems to say - at least according to the abstract which I have quoted fully - is that there is no radiation period. There is no radiation detected by the co-moving observer and there is no "passing of electromagnetic radiation from a uniformly accelerated charge into the region inaccessible to a co-accelerating observer"

Well, it has been about 30 years since my last quantum physics and electromagnetism courses. But I think I am capable of understanding from the literature that the issue is still not satisfactorily resolved for some. In any event, the ad hominem approach to discussion and argument doesn't work any better in physics than in law.

AM

1. You are doubting the EM model, in which an electron in a "circular orbit around a nucleus" would radiate EM radiation.

2. You used THIS paper that you are citing as an "example" that an accelerating charge need not radiate.

3. I asked you why would you think this two would make a fair comparison? One is where the observe is in the SAME accelerating frame, while the other, the observer is in a different frame where the electron is observed to be in a circular motion. The observe isn't IN the same frame as the accelerating electron.

If you cannot argue why those two situations are equivalent to each other, then this whole thread that you started is MOOT. They are different! They are SUPPOSED to be different from each other. This isn't unusual. If I'm moving at the same constant velocity as a bunch of moving charges, I see no current! I also detect no magnetic field! Are you then going to argue that classical E&M is wrong? Or some other principles are faulty?

The fact that you have been told EARLY on a few times that these are different (I see at least a couple of postings indicating accelerating reference frame of the observer and the charge) makes me wonder if you either did not understand what was meant by that, or you simply refuse to put any validity on such arguments.

Unless you can show me an example of a charge particle moving in a circular motion that does NOT radiate, this thread is finished.

Zz.

 

[reilly]

In classical E&M, as written in hundreds of books, the radiation field-- the 1/r part-- is proportional to A, the acceleration of the charge (modulo some vector expressions) And, wonder of wonders, all these books agree. There is nothing in the derivation to suggest that uniform A is to be excluded.

So what's the problem? This standard, well verified derivation does not include gravitation in the General Relativistic fashion -- it could not, originally, as GR had not been developed when the derivations of radiation were first done. When GR is included, Maxwell's equations in general covarient form automatically involve the metric structure of space, and that's a different ball game, and a difficult one at that. We live in a flat space, to a good approximation, so the usual form of the radiation formulas are valid.

Regards,
Reilly Atkinson

 

[Andrew Mason]

Unless you can show me an example of a charge particle moving in a circular motion that does NOT radiate, this thread is finished.

First of all, this thread was supposed to be about special relativity. My question related to the reason the electron does not collide with the proton and whether there was something other than QM (the uncertainty principle), that could possibly explain it.

Let's forget about orbits and just look at an electron colliding with a proton. If you confine the electron to a space the size of a several proton diameters - 10^{-14} m, then according to the uncertainty principle,

\Delta p\Delta x > \hbar /2
So \Delta p > 5\times 10^{-35}/10^{-14} = 5\times 10^{-21} kg. m/sec

Since m = 9.1 x 10^-31 kg., this means that the uncertainty in speed is:

\Delta v > 5.5\times 10^{9}m/sec^2 which is 18 x the speed of light.

To achieve that level of uncertainty of position, there would have to be a non-zero probability that the electron is traveling at a speed greater than c, which would seem to violate SR and, in any event, would require infinite energy.

One cannot confine the electron to a space that small. And it is not the uncertainty principle that is the limiting factor. It is special relativity and, ultimately, energy.


As far as your request for an example is concerned, what about a charge in gravitational orbit? If it is the centripetal acceleration that causes the charge to radiate, then a charge in gravitational orbit should radiate. But if it does radiate, then gravitational orbit is not equivalent to uniform motion (ie. I can tell the difference locally between an electron in gravitational orbit and an electron at rest in an inertial frame of reference).

AM

 

[Hurkyl]

\vec{p} \neq m \vec{v}

As far as your request for an example is concerned, what about a charge in gravitational orbit?

It's traveling in a straight line. (More precisely, geodesic)

 

[ZapperZ]

Let's forget about orbits and just look at an electron colliding with a proton. If you confine the electron to a space the size of a several proton diameters - 10^{-14} m, then according to the uncertainty principle,

\Delta p\Delta x > \hbar /2
So \Delta p > 5\times 10^{-35}/10^{-14} = 5\times 10^{-21} kg. m/sec

Since m = 9.1 x 10^-31 kg., this means that the uncertainty in speed is:

\Delta v > 5.5\times 10^{9}m/sec^2 which is 18 x the speed of light.

To achieve that level of uncertainty of position, there would have to be a non-zero probability that the electron is traveling at a speed greater than c, which would seem to violate SR and, in any event, would require infinite energy.

One cannot confine the electron to a space that small. And it is not the uncertainty principle that is the limiting factor. It is special relativity and, ultimately, energy.

It looks like you "forgot" MORE than just orbits. You forgot that when you get to that speed, you can no longer use the rest mass! Or maybe you also intend to forget special relativity...;

As far as your request for an example is concerned, what about a charge in gravitational orbit? If it is the centripetal acceleration that causes the charge to radiate, then a charge in gravitational orbit should radiate. But if it does radiate, then gravitational orbit is not equivalent to uniform motion (ie. I can tell the difference locally between an electron in gravitational orbit and an electron at rest in an inertial frame of reference).

AM

Let me get this right. You are STILL insisting that (i) a charge in a gravitational orbit is IDENTICAL to (ii) a charge that is stationary in a gravitational field??!

You not only have problems with E&M, you also have problems with classical mechanics! And I'm not even going to ask you where you have seen a charge particle moving in a gravitational orbit that does NOT emit radiation.

Zz.

 

[juvenal]

As far as your request for an example is concerned, what about a charge in gravitational orbit? If it is the centripetal acceleration that causes the charge to radiate, then a charge in gravitational orbit should radiate. But if it does radiate, then gravitational orbit is not equivalent to uniform motion (ie. I can tell the difference locally between an electron in gravitational orbit and an electron at rest in an inertial frame of reference).

AM

I haven't really had time to sort through the arguments in this thread, but if you read some of the papers you linked to, some physicists have indeed proposed that charged particles do violate the weak Equivalence Principle. So there is some degree of controversy when dealing with charged particles and gravity. (Also - there's the problem that no one has experimentally been able to answer the question whether an unsupported electron accelerated by gravity radiates). But you'll notice that none of the papers you cited ever mention that this means that there is a potential problem in electrodynamics itself. Because there is none.

Also in another post, you also seem to be separating out "acceleration" and "electromagnetic interaction/force". Something about the electromagnetic interaction causing the radiation, but not the acceleration per se, if I understand you correctly. I don't think you can do this, from a theoretical standpoint. Or at least, it seems somewhat meaningless to do so.

You're by no means obligated to believe the modern theories and interpretative frameworks of classical and quantum physics, but unless you have better alternatives which explain experimental phenomenon just as well if not better, few others will be in your camp.

 

[Andrew Mason]

It looks like you "forgot" MORE than just orbits. You forgot that when you get to that speed, you can no longer use the rest mass! Or maybe you also intend to forget special relativity...;

Quite right, as Hurkyl quickly pointed out. The point is that a huge amount of energy is required to confine the electron to such a small space, and that energy is simply not available.

Let me get this right. You are STILL insisting that (i) a charge in a gravitational orbit is IDENTICAL to (ii) a charge that is stationary in a gravitational field??!

When did I say that? I said it is equivalent to a charge at rest in an inertial frame. A charge at rest in a gravitational field is equivalent to an accelerating charge.

And I'm not even going to ask you where you have seen a charge particle moving in a gravitational orbit that does NOT emit radiation.

Then you are saying that a charge in circular orbit is not equivalent to a charge at rest in an inertial frame?

AM

 

[reilly]

Mr. Mason -- If you could confine an electron in a sphere of just several proton radii, you certainly will get a free trip to Stockholm. You are perfectly free to invent your own brand of physics. You seem to avoid any study of the issues with which you are concerned, and you do not listen(read). With all due respect, I get the strong sense that you are mainly concerned with pushing your own agenda, and, unfortunately, too many of us have ended up playing your game. Bye.

Reilly Atkinson

 

[Andrew Mason]

Also in another post, you also seem to be separating out "acceleration" and "electromagnetic interaction/force". Something about the electromagnetic interaction causing the radiation, but not the acceleration per se, if I understand you correctly. I don't think you can do this, from a theoretical standpoint. Or at least, it seems somewhat meaningless to do so.

Is it? If it is acceleration that causes radiation, then acceleration in a gravitational field should cause the same radiation (which would necessarily mean that the radiation arises due to the interaction of the electron's field with itself). This seems to create a serious GR problem. If it is not the acceleration there is no GR problem.

You're by no means obligated to believe the modern theories and interpretative frameworks of classical and quantum physics, but unless you have better alternatives which explain experimental phenomenon just as well if not better, few others will be in your camp.

I don't have a camp. I don't have a theory. I am not challenging QM. I am just asking a question.

AM

 

[Andrew Mason]

Mr. Mason -- If you could confine an electron in a sphere of just several proton radii, you certainly will get a free trip to Stockholm.

Well isn't that the point? You can't confine the proton to such a small space. Special relativity says that it requires too much energy. If you can't confine it to such a space, it can't crash into the nucleus.

You are perfectly free to invent your own brand of physics. You seem to avoid any study of the issues with which you are concerned, and you do not listen(read). With all due respect, I get the strong sense that you are mainly concerned with pushing your own agenda, and, unfortunately, too many of us have ended up playing your game. Bye.

I am sorry that you seem to take a personal affront to the discussion. I am just trying to gain some insight into an interesting area by asking a question. I can assure you that I am not smart enough and will never be knowledgeable enough to have an agenda to push when it comes to quantum mechanics.

AM

 

[quantumdude]

To all:

Is it really all that important to have an answer to this right this second? Why don't all the interested parties just take their time with the papers that have been cited, and see if the results really are applicable to the problem. Then we can get to the bottom of this without being so frustrated, and we can learn something in the process.

 

[juvenal]

Is it? If it is acceleration that causes radiation, then acceleration in a gravitational field should cause the same radiation (which would necessarily mean that the radiation arises due to the interaction of the electron's field with itself). This seems to create a serious GR problem. If it is not the acceleration there is no GR problem.
AM

You seem to have neglected the first part of my response when I said that the GR part is controversial. And you keep using the controversial GR part as a way to discount electrodynamics, no? That's why this argument has become circular - your only valid point seems to be that there is a controversy about charged particles radiating in GR. Do you agree?

The problem I see is that we're venturing off into the philosophy of science at this point.

Physicists come up with models, and these models are always effective models of reality. Even if string theory turns out to be right, it will be an effective model up to the highest energies that are experimentally testable. And with each of these models there involves some interpretation of what the models actually mean. And the question of to what extent such a model represents "reality".

In the classical theory of electrodynamics (as detailed by Jackson's textbook), acceleration and radiation go hand-in-hand when we're talking about an observer at rest watching an accelerated electron. This model works for almost all cases where electromagnetic interactions are involved, and in the cases where it breaks down, we rely on quantum mechanics and/or quantum electrodynamics. To separate acceleration and EM interaction in these models is meaningless.

You make the point that maybe in some other model, one can separate out acceleration and EM interaction, and that this is necessary due to the possible problem in GR you mention above. The answer that the majority of us, I believe, have, is first, that it isn't necessary since some general relativist may be able to resolve things. And second, we honestly don't care given that classical EM and QM work just fine otherwise, and are the best models we have given the energy scales and laboratory conditions that are typical. There is no doubt, for example, that QM explains atomic and molecular physics. Maybe, like Einstein, you don't believe in QM, but most of us are perfectly happy with it, in the sense that we are happy with its predictions of experimental phenomenon.