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

[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.

 

[reilly]

Mr. Mattson -- Mr. Mason, apparently without recognition, has had his question answered in this thread numerous times. Further, the issue of the equivalence principle has absolutely nothing to do with the stability of the hydrogen atom, or any other atom for that matter. It should be dealt with in another thread , which I believe has been the case.

The fact that Mr. Mason could state that relativity has not been applied to the issue of atomic stability for hydrogen suggests to me that he does not know enough to recognize a valid answer to his concerns. Particularly as an ex-professor, I say he does not need answers here, rather he should take the enormous amount of info provided, retire to his study, and study so that he can at least recognize correct answers, or better yet, formulate his own answers. Indeed, as I've said in this thread, he's asked an interesting question. Now let him supply an interesting answer. This is what I would say if I were still partipating in this thread, which I am not.

Regards,
Reilly Atkinson

 

[Calculex]

I assumed that this non-QM explanation was wrong and that I was missing something obvious somewhere. I have tried to figure out why this is not at least a plausible explanation. I can't.

I seem to recall that Dirac looked at all this when he developed relativistic quantum mechanics. I am afraid you are barking up an old tree that Dirac has already peed on. Worth a look anyway.

 

[ZapperZ]

Mr. Mattson -- Mr. Mason, apparently without recognition, has had his question answered in this thread numerous times. Further, the issue of the equivalence principle has absolutely nothing to do with the stability of the hydrogen atom, or any other atom for that matter. It should be dealt with in another thread , which I believe has been the case.

The fact that Mr. Mason could state that relativity has not been applied to the issue of atomic stability for hydrogen suggests to me that he does not know enough to recognize a valid answer to his concerns. Particularly as an ex-professor, I say he does not need answers here, rather he should take the enormous amount of info provided, retire to his study, and study so that he can at least recognize correct answers, or better yet, formulate his own answers. Indeed, as I've said in this thread, he's asked an interesting question. Now let him supply an interesting answer. This is what I would say if I were still partipating in this thread, which I am not.

Regards,
Reilly Atkinson

I'm beginning to concur with Reilly. If one cannot see the distinct difference between an acceleration of an object in a circular motion, with an object AT REST in a gravitational field, even after repeated explanation, then there's nothing else that can be said. The continued bastardization of the equivalence principle here is astounding.

As I've said earlier, if I am not shown where a charged particle in a circular motion doesn't radiate, then this thread is finished... and it is.

Zz.

 

[Andrew Mason]

Either people are not fully reading/understanding my posts or I am not fully understanding theirs. I keep telling Zz, for example, that I am NOT saying that an electron in gravitational orbit is equivalent to an electron at rest in a gravitational field. Rather that it is equivalent to an electron at rest in an inertial frame of reference. So I don't understand the last post. We don't seem to be joining issue on the problem here, for some reason.

In any event, we seem to be making little progress. So I will graciously take all of your collective advice and retire to my study to reflect on all these weighty matters. Many thanks for putting up with me.

AM

 

[lightarrow]

I only would like to make a consideration.

We know that charged particles radiates when they accelerates, and I'm totally sure of it.

But when we talk about charged particles in this context, do we mean that they have to be spatially localized?

Since it's not possible to localize an electron in a precise point of its 1s orbit in an atom, maybe it's not possible to say that it accelerates. In a particle accelerator, or even in an high energy atom orbit, it's another story.

The fact the 1s electron could be "spread" around the nucleus, makes me wonder if the electron could be continuously reassorbing the very EM energy it radiates.

 

[ZapperZ]

Are you aware of how OLD of a thread you were replying to? I think the last 2 threads you replied to were all "old" threads that were no longer active.

Zz.

 

[lightarrow]

I know how old they are. If this is a problem, you suggest me to begin a new thread?

 

[ZapperZ]

No, it's not a problem. Sometime people who reply to these old threads don't seem the realize that the "train has left the station", so to speak.

Zz.

 

[lightarrow]

Thanks.
Have you ever heard about some kind of model of electron in an atom emitting and reabsorbing its own energy?

 

[vanesch]

Thanks.
Have you ever heard about some kind of model of electron in an atom emitting and reabsorbing its own energy?

There are "stochastic electrodynamics" models around in which everything is bathing in some background noise radiation, which compensates exactly (stochastically) the loss due to radiation by acceleration, maintaining some kind of dynamical equilibrium which corresponds in many respects to the quantum-mechanical solution:

* Journal of Scientific Computing Volume 20 , Issue 1 (February 2004)
Pages: 43 - 68

* A stochastic electrodynamics interpretation of spontaneous transitions in the hydrogen atom; H M França et al 1997 Eur. J. Phys. 18 343-349

* Daniel C. Cole & Yi Zou, Quantum Mechanical Ground State of Hydrogen Obtained from Classical Electrodynamics, Physics Letters A, Vol. 317, No. 1-2, pp. 14-20, (2003)

*Daniel C. Cole & Yi Zou, Analysis of Orbital Decay Time for the Classical Hydrogen Atom Interacting with Circularly Polarized Electromagnetic Radiation, Physical Review E, 69, 016601, (2004)

You take these results for what you like them to be. I don't know if these are just fancy coincidences or mean anything more.