The Effects of Gravitomagnetism on Surrounding Particles

[Senlathial]

I haven't thought of physics since I was in college about 10 years ago (I am a biologist today). For some reason, however, last night when I was lying in bed I started thinking about general relativity. My mind settled on a question that caused me to loose several hours of sleep, and I don't want a repeat tonight!

The question settles around the increase in mass when something approaches the speed of light. As I understand it, when something approaches the speed of light its mass increases, until very near the speed of light it reaches very near infinite mass. I learned this is why no spaceship could accelerate faster than light--because it would take infinite energy to move infinite mass past that speed limit.

For some reason, I centered on what effects this increased mass would have on the surrounding environment. I thought about the Earth orbiting the sun and the sun orbiting the center of the galaxy. To an observer above the Milky Way, it would appear that when the Earth is going around the sun in the same direction as the sun is going around the galaxy, then it is going faster than at the opposite time of the year when the Earth's orbit is going against the sun's orbit around the galaxy. Doesn't this mean that the mass of the Earth (or a defined particle on the earth) is increased at one time of the year than at the opposite time of the year? Even a very small amount?

As I thought about this question, I came up with a better one. This is the question that really confounded me: If a particle's mass increases to infinity as it approaches the speed of light, what effect does that increased mass have on particles in the environment that are not traveling at the speed of light?

Let's say there is a man in a spaceship traveling at the speed of light. He flies past a rock in the solar system close enough for his spaceship to gravitationally alter the rock's course. Now, to an outside observer, I seem to recall that the spaceship has near infinite mass because it is moving at near the speed of light. I also recall that the man inside the spaceship would not notice the increased mass--everything would appear normal in his environment. (Correct me if I am wrong on this please.) Now, I thought, if the ship had infinite mass, the path of the rock would be altered much more than if it had the ordinary mass. To the outside observer, the rock would appear to have moved significantly. But if the man in the ship could somehow look behind him, wouldn't he see the rock move only slightly, as he thinks his mass is normal? Maybe the man in the ship can not look behind him, so let's say he stops some distance past the rock and looks behind him. Is the rock in the location the outside observer says it is (moved a lot--infinite mass affected the path of the rock greatly) or is the rock in the location the astronaut thinks it is (hasn't moved much--not much mass to move it)?

Please help me get some sleep tonight! Thanks!

Sen

 

[Dale]

Hi Sen,

Welcome to PF. I hope these links let you get some sleep:
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html
One brief quote "A common example is the mistaken belief that a fast moving particle must form a black hole because of its increase in mass".

The Wikipedia page on the same topic is reasonable as well, but the ucr pages above are more authoritative:
http://en.wikipedia.org/wiki/Mass_in_special_relativity

The bottom line is that the concept of "relativistic mass" fell out of favor in the scientific community a long time ago, but continues to be used popularly. When physicists talk about "mass" they mean "rest mass" or "invariant mass".

 

[Senlathial]

Thanks Dale! I did not understand everything on those pages, but I think I understand a little.

So, in framing my question above, I mistook rest mass for relatavistic mass (which I think is the rest mass plus the energy of its movement). Therefore, if a spaceship flies by a rock at the speed of light, the relativistic mass doesn't really add any more affects to gravity than the invarient mass. Both the outside observer and the astronaut in the ship would see the rock move only due to the invarient mass, and not the near infinite mass I was thinking of.

If this is correct, I will sleep tonight! Thanks again!

 

[pervect]

Thanks Dale! I did not understand everything on those pages, but I think I understand a little.

So, in framing my question above, I mistook rest mass for relatavistic mass (which I think is the rest mass plus the energy of its movement). Therefore, if a spaceship flies by a rock at the speed of light, the relativistic mass doesn't really add any more affects to gravity than the invarient mass. Both the outside observer and the astronaut in the ship would see the rock move only due to the invarient mass, and not the near infinite mass I was thinking of.

If this is correct, I will sleep tonight! Thanks again!

No, motion does have an effect on gravity. However, the effect is not as simple as using the Newtonian formula for gravity and replacing "mass" with "relativistic mass".

A close, but imperfect, analogy for what happens to the gravitational field of a moving mass is what happens to the electric field of a moving charge. The case of the moving charge is considerably easier to understand, however. See for example http://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_15.pdf (and also *_14.pdf).

In words: the electric field becomes concentrated in the transverse direction. A similar effect occurs for gravity.

For more discussion see the following old thread:
https://www.physicsforums.com/showthread.php?t=205073

 

[Dale]

Both the outside observer and the astronaut in the ship would see the rock move only due to the invarient mass, and not the near infinite mass I was thinking of.

In words: the electric field becomes concentrated in the transverse direction. A similar effect occurs for gravity.

My understanding is that the outside observer (at rest wrt the rock) and the astronaut in the ship will reach the same conclusions about the motion of the rock. The outside observer will attribute it to the "concentration in the transverse direction" of the gravitational metric that pervect is referring to. The astronaut will attribute it to the length contraction of the rock.

 

[pervect]

Consider the electromagnetic case. An observer with respect to both charges sees only electric fields. An observer watching both charges move sees both magnetic and electric fields.

Thinking of the only forces between the charges as electrostatic forces leads to wrong conclusions and predictions -one must consider electrostatic and magnetic forces as a combined entity to get the correct physical properties of Lorentz invariance of the force.

The situation in GR is similar, though the idea of gravitomagnetism works a little differently than electromagnetism does. The point is that one cannot take a simple Newtonian model and get a Lorentz invariant force, one needs a more sophisticated model. In the weak field limit, one can think of the additional terms as being a lot like the magnetic force, and this is called gravitoelectromagnetism or GEM.

Thus part of the solution to this problem (a pair of masses and how they interact seen from the viewpoint of a stationary and moving observer) is the existence of what might be called "gravitomagnetic forces".