Understanding the Paradox of Mass in Relativity | Physics World

[pmb_phy]

I normally don't post a web page until I've worked out all possible problems with a concept. It led to less flames that way. But to be honest - I don't care anymore about that nonsense. So here's the page I just made

http://www.geocities.com/physics_world/sr/mass_mag_field.htm

In my constant pursuit of the meaning of mass in relativity I came across what at first sight appears to be a paradox (paradox - problem that really isn't there. It just seems like it). I may have a resolution to it but am as yet unsure. I think its simply that the definition regarding certain things can be meaningless in some instances (regardless of whether you refer to 'mass' as 'rest mass' or 'relativistic mass' - this paradox does not address that notion per se).

If youy have any notions as to the resolution to this paradox I'm all ears.

Pete

ps - I've cross posted this to another forum.

 

[mitchellmckain]

Just some superficial thoughts...

Well isn't this consistent with the description of magnetic fields in terms of photons. Isn't the result simply saying that this magnetic field in the second case has no momentum in the direction of motion.

Furthermore for the magnet field to be purely in one direction you would have to have an infinitely long solenoid. In which case, I am not sure you can say that the magnetic field is moving just because the infinitely long solenoid is moving (when that motion is parallel to the axis.

 

[pmb_phy]

Just some superficial thoughts...
Well isn't this consistent with the description of magnetic fields in terms of photons. Isn't the result simply saying that this magnetic field in the second case has no momentum in the direction of motion.

It'd be nice if that were the case. But if you take another look at the example then you'll notice that it is assumed that since the Poynting vector is zero in S then we can take S as the zero momentum frame of the element of matter (i.e. that which we are attempting to assign a mass density to). Can this be referred to as the "rest frame" for this element of matter"? If you notice the results of the first case then you'lll see a speed in there where I wrote The mass is given by M = P/v, ...[/quote] where "v" is the speed of the element with respect to S. So it will be assumed that the element is "at rest" in S for the time being. In the later example we find that there is no frame in which the momentum has any value so we can't look at the S frame as a rest frame"

I will revise to make this explicit. Thank you very much for your comment! It demonstrates that I had a total lack of explanation of what the problem is!

Pete

 

[pmb_phy]

I have modified the page and update the webite to reflect this change. I believe that I have solved the paradox. That really suprises me big time. I had no idea I could take a shot at a resolultion for a very long time! It may be wrong but I'm a very happy camper that I was able to take a crack at it so soon.

Pete