QED meets GR

[kcdodd]

1. You assume that the outer shell can have zero thickness and has thus zero volume. This requires that the charge-density must be infinite. What you should do is to also assume a charge density for this opposite charge. There is thus also electric-field energy within this shell. What now happens when you let R(1) go to R(0) is that the electric-field energy between the shell and the central sphere becomes zero (One can even see that from your equation). What remains is the electric-field energy within the central sphere plus the electric field within the shell having a thickness of R(2)-R(0)>0. Not a Twinkie as you call it above. Nonetheless, the fact remains that it is not physically possible to generate such a shell of distributed charge within "free space". So the whole derivation is only a mathematical game with no physics-relevance.

First you say to change the shell so it has thickness, but then you say it doesn't matter because one cannot make it anyway? The original point of the exercise was that simply asserting that q_total = 0 would not change the physics because one can put a shell of charge around the experiment to meet such a requirement, changing q_total, but which will not give rise to any forces inside the shell. It only goes to change the fields outside the shell where the experiment is not being conducted.

Around and near the center of such a wave, the charge density can thus be approximated by a parabolic expression. One can thus write that (rho)=C*(1-(alpha)*r^2). Now let us return to the electric field around a solitary electron and not trust our belief in Coulomb's law, but rather use the differential expression divE=(rho)epsi0. Writing this in terms of spherical coordinates it is elementary to calculate the electric field within a sphere using the parabolic expression for the charge-density. You will then find that the electric field is zero at the origin, increases to go through a maximum and then decreases again to become zero at a critical distance R(0). You can now normalize your calculation by choosing C and alpha so that the total charge within the volume with radius R(0) is equal to -e.

If you have done this mathematically I would be impressed to see it. Since rho is spherically symmetric the electric field at R is equivalent to a point charge with total Q = integral of rho from 0 to R. So, if the electric field is zero at R(0), then the integral of rho from 0 to R(0) must also be zero (ie Q = 0). So, how can you normalize Q to equal -e? And besides that, the electric field only has two roots; R = 0 and R = R(0) = sqrt(5/(3*alpha)). So even if you did this, the electric field will be non-zero everywhere else, unless you are saying rho is zero when R > R(0). Otherwise the distribution would have infinite self energy.

[johanfprins]

If you have done this mathematically I would be impressed to see it. Since rho is spherically symmetric the electric field at R is equivalent to a point charge with total Q = integral of rho from 0 to R. So, if the electric field is zero at R(0), then the integral of rho from 0 to R(0) must also be zero (ie Q = 0).

When you do the calculation you will see that this is not the case

So, how can you normalize Q to equal -e? And besides that, the electric field only has two roots; R = 0 and R = R(0) = sqrt(5/(3*alpha)). So even if you did this, the electric field will be non-zero everywhere else, unless you are saying rho is zero when R > R(0). Otherwise the distribution would have infinite self energy.

If you give me an e-mail address to which I can attach a document I will make the time to type out the proof and send it to you. Although I know you are competent enough to the calculation on your own.

I hope you will be impressed and that I did not slip up somewhere. Doing physics, the latter is always possible, and one must always be willing to admit it or else you become a bigot like the crackpots who are at present in charge of main stream physics.

The normalization is required since you are using the intensity of a Gaussian matter wave which must be normalized to represent the charge-distribution.

I want to thank you that you forced me to return to some off my old notes which I have kept on the back burner for far too long.

[kcdodd]

I sent you a pm.

[johanfprins]

I sent you a pm.

You will have the calculation within a couple of days.

[kcdodd]

I received your derivation. There are a couple issues I see.

1.

You say C can be normalized so that q_total = e, but you don't actually bother to plug in R0 to find out what C would be. I got C = e/(4*pi*R0*(1/3 - alpha*R0^2/5)). But R0 = sqrt(5/(3*alpha)) from solving E(R0) = 0. You can see that if you plug in R0 to C you get C = e/0 = infinity. So, C cannot be normalized so that the total charge is e while maintaining E(R0) = 0. This is simply the fact of what I said earlier that the total charge is zero, and so you cannot then normalize to make it not-zero.

2.

Now, going back to the beginning, you say you are approximating a Gaussian function with the parabolic function. However, when you solve for R0 = sqrt(5/(3*alpha)), and plug that into rho, then rho(R0) = -2*C/3, but rho(0) = C. However a Gaussian cannot change sign. So the quadratic approximation is well outside an acceptable approximation of the Gaussian. Because the density changed sign and integrating to R0 you get positive and negative canceling out so that q_total = 0 as above. A true Gaussian would not do that and so you could normalize it so that q = e, but then E would not go to zero anywhere else but r = 0.

[johanfprins]

I received your derivation. There are a couple issues I see.

1.

You say C can be normalized so that q_total = e, but you don't actually bother to plug in R0 to find out what C would be. I got C = e/(4*pi*R0*(1/3 - alpha*R0^2/5)). But R0 = sqrt(5/(3*alpha)) from solving E(R0) = 0. You can see that if you plug in R0 to C you get C = e/0 = infinity. So, C cannot be normalized so that the total charge is e while maintaining E(R0) = 0. This is simply the fact of what I said earlier that the total charge is zero, and so you cannot then normalize to make it not-zero.

I was just sitting down to e-mail to you that I also picked up this mistake: that owing to the parabolic approximation the electric-field is not zero where the charge-distribution ends. Sorry for that one.

2.Now, going back to the beginning, you say you are approximating a Gaussian function with the parabolic function. However, when you solve for R0 = sqrt(5/(3*alpha)), and plug that into rho, then rho(R0) = -2*C/3, but rho(0) = C. However a Gaussian cannot change sign. So the quadratic approximation is well outside an acceptable approximation of the Gaussian. Because the density changed sign and integrating to R0 you get positive and negative canceling out so that q_total = 0 as above. A true Gaussian would not do that and so you could normalize it so that q = e, but then E would not go to zero anywhere else but r = 0.

You are totally correct, I should not have approximated the charge-distribution with a parabolic distribution and then normalized the parabolic distribution. The problem is a little bit more complex than that. Sorry for this. I will get back to you on this one in future.

[kcdodd]

Heh, ok.

I have completed the relativistic dipole problem.

http://www.youtube.com/watch?v=ZYsv7S2QS00

Now, keep in mind this whole thing was to show that there is a magnetic field for a moving dipole, even though the charges in the dipole do not move relative to one another. The dipole moment is P = d*q, where d is the separation distance between the charges in the rest frame, and so my derivation using this moment should be accurate for r >> d.

[icarus]

kcdodd:

I have completed the relativistic dipole problem.

Good one, thnx for that.

[rcain]

... likewise. really well explained, thanks for that KCD. even i managed to follow it.

[kcdodd]

Thanks. I'm glad someone enjoyed it. hehe.

[johanfprins]

Heh, ok.

I have completed the relativistic dipole problem.

http://www.youtube.com/watch?v=ZYsv7S2QS00

Thank you. You really know how to handle your mathematics: I am impressed; since I have mostly done experimental research and only used mathematics to try and explain experimental results. This is in contrast to our modern day theoretical physicists who first do mathematics and then try and find experimental data to fit what they have calculated; as is done at CERN with the Higg's boson. I personally believe that the latter approach is fraught with danger:

To paraphrase a Goldwynism: A theoretical derivation without any experimental verification is like a verbal contract: It is not worth the paper it is written on.

What I want to point out is that your calculations on YouTube do not really address my initial remarks and questions about the electron; which are in essence the following:
1. Can you measure an electric field-energy around a solitary electron;
and
2. Can you measure a stationary magnetic field being left behind in the wake of an electron when it passes you with speed v.

If you cannot, which is the actual fact, then by doing theoretical calculations to prove that there is such energies is nothing else but writing a verbal contract.

The fact is that there is no way in which one can confirm experimentally that a solitary electron actually does have electric field-energy in the space around it; no matter how logical it seems that it might be so from Maxwell's equations. Only experimental data stands as the final arbiter in physics and if you cannot back your theoretical data up by experiment you are not doing real physics.

The very act of measuring or observing can alter what you are measuring. Heisenberg even came up with the crackpot statement that the classical path of an electron only comes into being when the electron is being observed. I believe that observation is the same as "making a measurement". According to Heisenberg's uncertainty principle he concluded that it is impossible to see an electron at a position x if you know anything about its momentum or seeing its momentum if you know anything about its position; but if you "look correctly" you can suddenly see its classical path; which requires that you to see both its momentum and position at the same time. This, in turn, led to the crackpot Copenhagen interpretation according to which, before you observe anything, there are only possibilities of which only one actualizes when you look.

I agree partially with Heisenberg; namely that there are situations in Nature where you cannot conclude what is out there before you measure.

Thus there is no way to know experimentally if a solitary electron has an electric field energy around it without making a measurement, and to make a measurement, you must use another charge so that the electron is not solitary anymore. Accepting that experimental information is the arbiter, a physicist is mandated to conclude from this factual situation that there is a 50/50 probability that there is such a field or that there is not such a field. The measurement might induce the charges and electric field between the charges, and the latter electric field is definitely not a radial symmetric field around a point.

One must thus take both possibilities into account when doing calculations and reject the one that leads to inconsistencies that, for example, require one to rape mathematics to get what you want to get: e.g. renormalization.

Thus I thank you for you calculations, but they did not change what I have argued on this thread all along. God speed!

[ladajo]

Without having read Johan's book yet, I am somewhat mentally flubbuxed right now. On one hand we have solid math, on the other we have math does not matter if you can't prove it physically. I think I am ging to fall somewhere in the middle on this for my personal sanity.

[johanfprins]

Without having read Johan's book yet, I am somewhat mentally flubbuxed right now. On one hand we have solid math, on the other we have math does not matter if you can't prove it physically. I think I am ging to fall somewhere in the middle on this for my personal sanity.

All I am doing is to follow the official guidelines which should be followed by physicists since the Royal Society laid them down at their founding during the 17th century. It is a pity that physics, including the Royal Society of London, has strayed so far away from these principles that it would be better to start all over again. The rule of experimental philosophy MUST be that if you cannot measure it, no calculation is trustworthy. Unfortunately Paul Dirac was the pied piper who led us away from this very fundamental principle into the wilderness!

[ladajo]

Johan,
I agree with your points regarding the philosphy of experimental science, and as I have said in another thread, philospher I am not. But I also must consider that mathmatical musings by theorists have lead to a search and discovery of new things.
In this thread, you have raised some great points, as has Carter. Very educational on all aspects. So in the final analysis, in my humble personal opinion, I think that the middle ground is the best place for me to land.
That said, if you are game, I would humbly suggest you offer Carter a gratis copy of your book, and ask of him to give it a read and critic (if he is game). I think that the exchanges you guys have had have been and are valuable for both (no tto mention the rest of us). As you yourself have said, this discussions are valuable for you to refine your own understandings, as well as position.
After all, is not true science not only experimentation and proof, as well as the free exchange of ideas and thoughts that make it all possible?

[Giorgio]

The suggestion is logic Ladajo, but I do not think it can solve the fundamental different starting point that is at the base of this discussion.
Accepting one of the 2 starting points authomatically excludes the other.

Not that I am saying that one of the 2 must be wrong. For what we know both starting points could be valid within certain boundaries and/or limits.

On a different note, it was quite an interesting exchange of ideas. Too bad we have not been able to implement a solid Math formula system on the board. These discussions could become more frequent and interesting.