Understanding the Paradox of Mass in Relativity | Physics World

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In summary, Pete posted a web page on the topic of mass in relativity and encountered a paradox. He asked for others' thoughts and received comments suggesting that the magnetic field in the second case has no momentum in the direction of motion. Pete revised his page to reflect this and claims to have solved the paradox.
  • #1
pmb_phy
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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.
 
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  • #2
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.
 
  • #3
mitchellmckain said:
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! :approve:

Pete
 
  • #4
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. :tongue:

Pete
 

What is the paradox of mass in relativity?

The paradox of mass in relativity refers to the contradiction between Newtonian mechanics, which states that mass is constant, and Einstein's theory of relativity, which suggests that mass can change depending on the speed of an object.

How does relativity explain the paradox of mass?

According to Einstein's theory of relativity, mass and energy are equivalent and can be converted into each other. This means that as an object increases in speed, its kinetic energy also increases, causing its mass to increase as well.

Why is the concept of mass important in relativity?

The concept of mass is important in relativity because it is a fundamental property of matter and is used to calculate other physical quantities, such as energy and momentum. Understanding the paradox of mass allows for a more accurate understanding of the behavior of objects at high speeds.

What implications does the paradox of mass have for space travel?

The paradox of mass has significant implications for space travel, as it means that as objects reach high speeds, their mass increases, making it more difficult to accelerate and travel long distances. This is a major challenge for space exploration and requires careful calculations and engineering to overcome.

Is the paradox of mass in relativity still a topic of debate?

While the concept of mass in relativity is generally accepted by the scientific community, there are still ongoing debates and discussions about its implications and applications. Further research and experiments are being conducted to better understand this paradox and its effects on our understanding of the universe.

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