classical physics vs relativity: parallel electron beams

[engineer]

Dear physicist.
In another paper in the appendix http://wbabin.globat.com/physics/hynecek17.pdf, Hynecek derives equation for the force on the plates of a parallel moving capacitor. Since the force does not depend on the plate's spacing the energy is thus just the force multiplied by the spacing a. So, it is clear that the energy is the same for both cases. Also there is no transformation or boosts necessary, both moving and stationary cases are observed from the laboratory system in rest. For the moving case Maxwell equations are used. Only thing that is used from "relativity" is the Lorentz length contraction.

[Physicist]

engineer - is the spacing the same in the two cases, in your opinion?

[mharratsc]

Physicist said:

Without knowing anything about the specifics of the experiment, I would think that if "other influences" were significant, you'd just see the capacitor twirling all over the place. Unless the "other influences" conspired to exactly cancel out the torque from the ether. Seems a bit unlikely, no?

I don't understand how the notion that a nigh-massless 'aether' would cause 'friction' or 'drag' on anything at all, actually. I would think that any torque on the plates would be induced by Lorentz force of the current moving through the thing, miniscule as it might be from just the fair-weather field. I'm no scientist, and I've never done the experiment or anything, but that's just what occurs to me from thinking about it. :\

Wal Thornhill suggests a model of a 'sea' of neutrinos existing as the lowest-energy state of matter that could conceivably be 'dragged' by large bodies (hey why not- everyone thinks that 'frames' can drag, right? ) so in such an instance, an experiment to detect motion of an 'aether' over the surface of a planet might show a null, while one outside a plasmasphere might show some positive result (hence my comment from before.)

Just saying- this stuff is outside of my normal 'mental stomping grounds' usually...

[Aristarchus]

Which is [for the benefit of Aristarchus] to use his equation (5) for the energy without transforming it properly into the boosted frame.

This is what you wrote previously:

If you don't do it correctly, you end up with what's called the "Trouton - Noble paradox" - which asserts that a parallel plate capacitor has a torque on it that depends on your frame of reference.

I think those involved are aware of what you assert. In a paper citing Hynecek, it states the following:

http://78.90.51.94/Home/materiali/OLUP/ ... ticalA.pdf

The parallel-plate capacitor formula isn’t adequate for the pads, so we have to do a few measurements of the actual capacitance, and we find that it’s 0.2 pF per pad. By (16.4), the two bits of trace look like 8.0 nH of inductance and 0.95 pF of capacitance. This model is only valid far below resonance, so to leading order it doesn’t matter where we put them in the model; since the circuit is symmetrical, we’ll add them symmetrically, so our final low frequency model is as shown in Figure 16.3.

You might consider this outside the topic, but it clearly demonstrates that those involved are aware of the problems associated with the parallel-plate capacitor formula and the research it involves. Again, you're assuming text-book examples without considering the overall research or the specifics in the Hynecek paper. We might eventually discuss aspects of Hynecek's paper dealing with the Fermat Principle. Your attempt to undermine Hynecek's paper and credentials have not really hit the mark.

[engineer]

physicist: simple formula from electrical engineering is for the energy: W=QQ/2C where C is the capacitance: C=eWL/a. (e=epsilon) Capacitance is a pure geometry and Q is an absolute invariant. When the plates are moving in parallel direction there is also a current that needs to be considered (see the appendix of the previously cited paper). Simply stated it does not matter how the capacitor is oriented the energy in it transforms as m=mo*Sqrt(1-vv/cc). There cannot be any doubt about this simple fact. Of course "a" as the original plate's spacing and is constant, but for the perpendicular motion it undergoes the Lorentz contraction. Similarly the plate's length undergoes the Lorentz contraction for the parallel motion. Hope that this satisfies you and you can agree with conclusions in the papers and we can move on on the topic of the light speed constancy in the gravitational field where you are also wrong.

[Physicist]

engineer - spank me with a wet kipper but it seems to me that you didn't address my objection.

The a goes in the numerator of your formula for W, but the L goes in the denominator. So if you Lorentz contract a, you'll decrease W. But if you Lorentz contract L, you'll increase W.

How do you plead?

[engineer]

Dear physicist, I have answered your question. However, you need to read the page in the appendix of the paper I am referencing: http://wbabin.globat.com/physics/hynecek17.pdf. There is a derivation in it where it is shown that for the parallel moving capacitor it is necessary to also consider the currents that the moving plates generate. When this is correctly done, the same formula is obtained. The force of current effect cannot be neglected. Please read again carefully what I am saying. It is hard to repeat the same thing now for the third time.

[Aristarchus]

is a derivation in it where it is shown that for the parallel moving capacitor it is necessary to also consider the currents that the moving plates generate. When this is correctly done, the same formula is obtained. The force of current effect cannot be neglected. Please read again carefully what I am saying. It is hard to repeat the same thing now for the third time.

engineer,

Is the following an example of what you're stating?

Mechanical and electromagnetic relations involved in the Trouton–Noble paradox are analysed on the basis of special relativity theory as well as on the basis of Maxwellian electrodynamics. It is shown that the paradox only arises when not all dynamical effects associated with the moving capacitor used by Trouton and Noble are considered. Crucial for the resolution of the paradox is the fact that the forces and torques in an electromagnetic system involving moving charge distributions are associated with both the mechanical momentum and electromagnetic momentum of the system. Once the electromagnetic momentum of the moving capacitor is properly taken into account, the paradox disappears.

http://www.physics.princeton.edu/~mcdon ... 755_99.pdf

[Physicist]

Forgive me engineer, but you still haven't answered my objection. I set it out very explicitly in my last post. Where am I going wrong? Did I get my numerator and denominator mixed up? Did I miss out a term?

[engineer]

Aristarchus: this is correct.
Physicist: Hmm, I am lost with my explanative powers. As I have said several times before there is also a Lorentz force between the moving plates that needs to be included into the consideration not only the electrostatic force. The Lorentz force causes additional repulsive contribution amounting to (1-vv/cc) in the numerator. This cancels part of the Sqrt(1-vv/cc) in the denominator that you are repeatedly mentioning resulting in the same energy-mass equation. . If this is not good enough explanation, then I must give up. Perhaps go back to work in engineering, which deals with reality not with some texbook dogmas .

[Physicist]

engineer-

I agree entirely with that last part. We should deal with reality, and the reality is that our capacitor does not have a torque on it, as I think you would agree.

That is precisely Mr Hynecek's problem. Because if one uses his formula for the energy [(5) in his paper], one arrives at the inescapable conclusion that there should be a torque on the capacitor. If you don't believe my math (and again I encourage you to point out where I've gone wrong), check out section 1 of

http://muj.optol.cz/~richterek/data/med ... er1958.pdf

where the erroneous calculation is outlined. Note their energy formula in equation (1) is what Mr Hynecek is using. Note also that taking into account magnetic effects doesn't help you get rid of the torque.

The conclusion is that the usual engineer's energy formula can't be correct in the case of moving charges. However, if you use a correct (covariant) version [see (18) in the paper above] you arrive at 2 conclusions:

1. No torque on our capacitor, in agreement with experiment;
2. The usual relativistic transformation for mass-energy - not Mr Hynecek's.

When I get a chance I'll take a look at the 3rd Hynecek paper you referenced - maybe he does a better job with the forces than he does with the fields.

[engineer]

Physicist.

Hynecek's paper does not talk about torque, only about energies. Nevertheless,

"Note also that taking into account magnetic effects doesn't help you get rid of the torque."

Of course, this is the whole point. Considering the magnetic field resolves the issue, energies become identical, no torque.

[Physicist]

engineer - torque is basically just the derivative of the energy with respect to the orientation angle - so if you know the energies, then you know the torque too.

Again, I urge you to look at equations (10) and (11) in Butler.

They use the method you are suggesting to find the two energies, taking magnetic effects into account, and STILL come up with different energies. This is the famous paradox. It wouldn't be much of a paradox if it were as simple as remembering to include the energy in the magnetic field.

http://muj.optol.cz/~richterek/data/med ... er1958.pdf

[engineer]

Physicist: Hmm, then there is a paper brought up by Aristarchus: http://www.physics.princeton.edu/~mcdon ... 755_99.pdf, where the paradox is eliminated by properly including the mag. field. Perhaps it is better to use your own brain instead of quoting all kinds of papers. Perhaps returning to basic physics (should not be a problem for a physicist) and making your own derivations would show us what you mean. Not all the published papers are correct including the papers on relativity. So, instead of selecting which ones to follow and believe in show us your derivation. At least Hynecek's papers are simple to follow without any nul vectors and boosts obfuscations. Again, no relativity is necessary, just Maxwell's equations and one reference frame, but including thje Lorentz length contraction. By the way forces are the same as fields, since the field is the force divided by charge (as far as I know). Again a strange comment from a physicist.

[Physicist]

engineer - the thing is that by using our brains we can immediately tell that Hynecek's energy formula must be wrong. From a theoretical standpoint, we see that he has a factor of gamma in the denominator, and so his energy isn't what we call covariant. From a more practical engineering standpoint, we can deduce lots of silly behavior from that - for instance, the total energy DECREASES with speed. The kinetic energy is negative! I leave it to you to figure out all the daft behavior that results from that.

At least Hynecek's papers are simple to follow without any nul vectors and boosts obfuscations. Again, no relativity is necessary, just Maxwell's equations and one reference frame, but including thje Lorentz length contraction.

I agree - and it's interesting to go back and see why that approach doesn't work. The solution is sufficiently subtle that people have gotten papers out of explaining it - already in this thread we have found 2 of them. It seems strange to me that Hynecek appears not to have checked the literature.

By the way forces are the same as fields, since the field is the force divided by charge (as far as I know). Again a strange comment from a physicist.

Well, not quite. They have different transformation properties, for a start. But if we're talking freshman electrostatics, then sure: F=qE