pervect said:
I think the idea that "energy is being put into length contraction" in the first place is most likely based on a false idea of how the electric and magnetic fields transform relativisticaly.
Because the electric field in the direction of motion is unchanged, the force between charges does not increase even though the charges are closer together.
See
http://en.wikipedia.org/wiki/Classical_electromagnetism_and_special_relativity for a non-tensor explanation of how the E and B fields transform relativisticaly.
This is making me wonder about something else actually, but at the moment I have to run, alas, no time to get into it.
Okay so I looked into the wikipedia page and also some linked pages that it had to better understand everything. I've also watched this video which explains the some of the math which I found quite helpful.
However I don't understand how it is a false idea that a magnetic field is actually an electric field viewed from a different frame of reference. Unless I misinterpreted what you wrote.
Also none of the equations I saw related to the energy required to contract the length viewed from a frame. It is as if they never consider it, unless I just haven't recognized or encountered the formula or if I'm still seeing this incorrectly.
jartsa said:
Let's consider accelerating two electrons using an electron gun. Acceleration takes place along the line connecting the electrons.
If electrons come out of the gun closer to each other than originally, then we might say that some "extra" energy was used, because electrons close to each other have more energy than electrons far away from each other.
Thank you for the analogy Jartsa. However I'm unclear of how I can relate it to my question. Could you maybe clarify on the "extra" energy used and how it relates to relativity? Thanks.
Drakkith said:
I've given some considerable thought to this thread, and in the end I decided that whether you say the energy is stored in the length contraction or whether you say it's stored in the magnetic field makes little difference for most cases since length contraction occurs at the same time as the magnetic field. The one area I'm unsure about is in the case of EM waves. EM waves involve changing magnetic and electric fields, yet there are no length contracted particles around to generate them.
I can't agree Drakkith because it seems to me that it makes all the the difference. I shoot a bullet from a gun, the energy from the gun transferred to the kinetic energy of the bullet. The bullet slows down by transferring it's energy to the air (assuming it doesn't hit anything). Same as electrons flowing in a wire, the energy given to the electrons stays within the electrons to cause it to flow until it dissipates into surrounding atoms which we can call friction.
Now consider Lenz's Law. If I give energy to electrons in a wire to flow in a certain direction relativity "occurs" at the same time. However I did not put energy into relativity, I put energy into the electrons just as I did with the bullet from the gun. Relativity as far as I know just happens, as a phenomenon. As soon as the electrons move, simultaneously length contraction occurs causing the charge imbalance. The change in field will affect electrons in a neighboring wire. HOWEVER, this energy is NOT from the electrons because the electrons are analogous to the bullet where it is not dissipating its energy through the magnetic field, it is dissipating its energy through opposing charges within the wire its flowing through. This energy comes from relativity causing the length contraction to create the charge imbalance.
The reason why we don't measure "extra energy" is thanks to Lenz's law. As soon as the electrons in a neighboring wire experience the induction, they will send out their own magnetic field that opposes the electrons I originally gave energy to. And once again this opposing magnetic field is also caused by relativity.
So in essence there would be 2 sources of energy being seen as 1. What if we find a way to separate the two sources and use length contraction in some sort of clever way to produce power. Lastly, I am not saying energy is being created by relativity, because I don't know where the energy is coming from, it may very well be conserved in a manner that is not clearly shown until relativity is understood.