# Is mass dependent on the observer?

1. Nov 11, 2005

### Razor436

I recall that an object's mass increases as the the object travels faster through space.
Question:
Imagine observer A is stationary, and observer B & an object move near light speed. When observer A and B measure the mass of the object, do they measure diffenrent masses?

2. Nov 11, 2005

### MichaelW24

I was just sort of debating this in another thread.

If an object travels at two relative speeds in your frame, v and then later u, for v>u, you will observe it's momentum to be equal to gamma*m*v, where m is the mass of the object in its own frame. This added gamma factor allows momentum to increase, since v is limited by v<c, but I guess you can say the total mass can be written as gamma*m; as gamma is a velocity-dependant factor then yes, the mass will appear greater when it travels at v than when it travels at u, using the simple equations:

total mass = gamma*m

gamma(u) < gamma(v) as gamma is an increasing function of the velocity for 0<v<c.

That reply was a bundle of messy random comments but I hope I helped somewhat. I will imagine someone will come along and answer your question concisely in aroughtly 3 words, and I hope one day Ill be able to do that!

3. Nov 11, 2005

### pervect

Staff Emeritus
How are you envisioning them as measuring each others masses?

We can definitely use the principle of relativity to say that there is no absolute velocity, so that if the situation is symmetrical, whatever A measures about B, B measures about A.

Here is one example of how one might go about measuring masses, and the result it gets.

You are on a spaceship, accelerating at 1g, to create what is often called a "uniform gravitational field" throughout all of space. You have a charged particle, and you apply an electric field to the particle that is sufficient to cause it to remain motionless.

You then accelerate the charged particle so it has a velocity of v, perpendicular to the "uniform gravitational field", i.e. in a direction that's at right angles to the rocket's accelration.

For ease of reference, we will call the direction of the ship's acceleration and the gravitational field the 'z' direction, and the direction of the linear velocity of the particle the 'x' direction.

Then we find that we have to increase the electric field (as measured in the ships frame) in order to keep the charged particle at z=0 when it is moving in the x-direction at relativistic velocities.

The increase in the required electric field is by a factor of gamma, i.e 1/sqrt(1-(v/c)^2). You can think of this as "weighing" the particle, because the force on the particle is the product of the electric field E and the charge q, independent of the velocity, and one is finding the force necessary to hold it "stationary" in the "uniform gravitational field" created by the ships acceleration.

For a point particle, this analysis can be done purely within the framework of SR.

Note that the invariant mass of the particle remains equal to 'm', that would be measured by a different technique, simply measuring the energy E and momentum p of the particle and calculating m = sqrt(E^2 - p^2) (in geometric units).

Last edited: Nov 12, 2005
4. Nov 11, 2005

### pmb_phy

re - Is mass dependent on the observer? - Relativistic mass - Yes. Proper mass - No.
Yes. They measure different (relativistic) masses.

Pete