Relativistic Physics: Gravitational & Inertial Mass

[Lee Sung Bin]

In Newtonian mechanics, both gravitational mass and inertial mass is m. This principle is known as the principle of equivalence. However, I heard that in Relativity, gravitational mass is γm instead of m because total energy of the particle is γmc². But in special relativity, it is widely known that F=γ³ma while a is acceleration. Does that means inertial mass and gravitational mass is different in general and only approximately same at non-relativistic situation? Or is inertial mass also γm? Or is the answer totally different?

 

[Orodruin]

However, I heard that in Relativity, gravitational mass is γm instead of m because total energy of the particle is γmc2.

"I heard that" is not a valid reference. Where did you hear that? How are we supposed to examine a reference that we have not been given? Either way, what you "heard" is not correct.

But in special relativity, it is widely known that F=γ3ma while a is acceleration.

Again, where did you get this information? It is not generally correct so any inference you take from it is not going to be correct.

See also https://www.physicsforums.com/insights/what-is-relativistic-mass-and-why-it-is-not-used-much/

 

[Ibix]

However, I heard that in Relativity, gravitational mass is γm

Where did you hear this? There is no such thing as "gravitational mass" in relativity, except in the sense that one can derive approximations like Newtonian gravity.

The source term in relativity is the stress-energy tensor, which does not include a $\gamma m$ term. Test objects follow geodesics determined by the geometry of spacetime; their own mass does not enter into it. In other words, gravity is not a force, so relativistic force equations aren't relevant.

 

[Dale]

I heard that in Relativity, gravitational mass is γm

No, most definitely not. Whatever source you heard this from is wrong and you should discard it entirely or treat everything it says with extreme skepticism.

 

[Lee Sung Bin]

what you "heard" is not correct.

No, most definitely not. Whatever source you heard this from is wrong and you should discard it entirely or treat everything it says with extreme skepticism.

If gravitational mass is not γm, then what is? Or is there no gravitational mass in relativity?

 

[m4r35n357]

If gravitational mass is not γm, then what is? Or is there no gravitational mass in relativity?

The source of gravitation in General Relativity is the Stress-Energy Tensor.

 

[Vanadium 50]

r is there no gravitational mass in relativity?

Look up:

There is no such thing as "gravitational mass" in relativity

 

[Dale]

If gravitational mass is not γm, then what is? Or is there no gravitational mass in relativity?

There is no active gravitational mass, the source of gravity in GR is the stress energy tensor. Sometimes people also talk about passive gravitational mass, but the concept doesn’t work in GR since gravity is not a force.

 

[SiennaTheGr8]

... But in special relativity, it is widely known that F=γ³ma while a is acceleration.

FYI, that equation only holds if the force vector is parallel (or antiparallel) with the object's velocity vector.

 

[Herman Trivilino]

But in special relativity, it is widely known that F=γ³ma while a is acceleration.

Just to add a bit to what @SiennaTheGr8 said, $\gamma^3 m$ was called the longitudinal mass. Likewise, and for the same reason, $\gamma m$ was called the transverse mass. It really is better to abandon any hope of finding a proportionality constant between $\vec{F}$ and $\vec{a}$, especially because those two vectors don't generally have the same direction!

It is much better to speak of only one kind of mass $m$, and realize that the departures from $\vec{F}=m \vec{a}$ are not due to some error in the way $m$ is defined, but instead are due to the geometry of spacetime.