- #1

- 78

- 1

Two physics professors said two different things about the invariance of mass.

One said that "mass" is a quantity which is always measured in the object rest frame - and therefore invariant to the Lorentz transformation. In additions, laws of motion in "real life" (relativistic motion) aren't the same as in high school. For example, Newton's second law would be [tex]F=\gamma m a[/tex]. Where "m" is what he called "mass" and [tex]\gamma[/tex] is the velocity-related constant.

The other professor said that mass is not invariant, and is given by [tex]m'=\gamma m_0[/tex] (will always be bigger than the self-mass).

And now for the gravity thing:

An object at rest will produce a field of gravity given by [tex]Gm/r^2[/tex].

Now I'm at rest and some object (say a spaceship) is moving near me, and I want to measure its mass by the gravitational force it applies on me.

I know that my own mass, at my own frame, is [tex]m_{me}[/tex] so the force between us (if the spaceship were at rest) would be [tex]F=Gm_{me} m/r^2[/tex]. The mass of the spaceship, as I see it, would be [tex]m=F r^2/G m_{me}[/tex].

Which 'm' did I find? Is it the same mass I would measure if I took the spaceship and weighed it in my frame, or is it [tex]\gamma[/tex] times that mass?

Thank you.