[puppypower (OP)]

In Einsteins equations for special relativity there is a term called relativistic mass. Since there is an equivalence of mass and energy via the equation E=MC2, relativistic mass should have a connection to energy and energy conservation. If the laws of physics are the same in all references and energy conservation is a law of physics, then it follows that relativistic mass needs to be same in all references or else one would violate energy conservation. The question I pose is, is there a way to directly measure relativistic mass, that is not reference dependent and therefore allow relativistic mass energy to be same in all references?

Let me show the pitfall of not being able to do this. Say we have two rockets one with mass M and the other with mass 2M. These both start in one reference, with the rocket 2M burning sufficient energy to achieve velocity V.

Before lift-off ,we give the crews from both rockets sleeping pills so they can't tell who has the motion. Instead the crew awaken after the fact and each crew assumes relative velocity V. The result is two different energy balances and two different relativistic mass calculations, based on relative reference, velocity and rest masses. The question is, can we directly measure relativistic mass, to avoid this reference illusion problem that can violate energy conservation and make a law of physics not the same in all references?

[evan_au]

relativistic mass needs to be same in all references or else one would violate energy conservation

I think you have this backwards:
- Rest Mass needs to be the same in all reference frames - but it is easiest to measure when it is at rest in your laboratory.
- Relativistic Mass is inherently different in every (relativistic) reference frame. Since the Relativistic Mass increases with relative velocity, observers in different reference frames traveling at different velocities will measure different Relativistic Mass for the same object.

the crew awaken after the fact and each crew assumes relative velocity V

Yes, the crews can both measure their relative velocity (eg from the Doppler shift of a light of known frequency).

Both crews can easily measure the Rest Mass of their own spaceship to determine if it is M or 2M, since they are at rest in the reference frame of their own spacecraft. They could do this by (say) applying 1 Newton of thrust for 1 second, and measuring their acceleration (using F=ma).

However, observers in the other spaceship in a different frame of reference, watching through a telescope would see a different duration for the thrust, a different force of the thrust, and a different acceleration. One reason for these differences is that the Relativistic Mass of the other spacecraft (and the Relativistic Mass of the reaction mass) is different from its Rest Mass.

Back to the original question:

Is it possible to directly measure relativistic mass?

Yes it is, using a cyclotron in the laboratory.

Charged particles (eg electrons or protons) are accelerated up to relativistic speeds in a cyclotron, so their Relativistic Mass becomes greater than their Rest Mass.

The orbital radius of the particles is related to their Relativistic Mass; as their velocity increases, their Relativistic Mass increases, and the orbital radius increases, until they reach the edge of the machine and are emitted at relativistic speeds.

The Rest Mass of these subatomic particles has not changed; if you bring the particles back to rest, they weigh the same as always.

See: https://en.wikipedia.org/wiki/Cyclotron#Principle_of_operation