# Increase of Mass With Relative Velocity Proven?

It was only in 2004 with the launch of Gravity Probe B that spacetime curvature was physically ascertained to exist, previous to that, it was a simply an extremely elegant proposition underlying GR.

Similarly, has the increase of mass with relative velocity been physically proven to exist or does it remain an extremely elegant proposition underlying SR?

Would this increase in mass be effected by more physical matter somehow lumping itself onto the moving object or by the object's inertia simply increasing with velocity?

IH

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Bill_K
Mass does not increase with velocity. The so-called "relativistic mass" is an artificial quantity M = γm, defined because the momentum for a relativistic particle is p = γmv, thus one can write it as p = Mv. The only mass with actual physical significance is the rest mass m.

The relativistic formula for momentum has been verified at least a trillion times, every time the LHC accelerates a proton.

The relativistic formula for momentum has been verified at least a trillion times, every time the LHC accelerates a proton.
But for a mathematician, it is still not proof :rofl:

But for a mathematician, it is still not proof :rofl:
But you can never mathematically prove anything in physics, it is all based of off observation and experiment.

But you can never mathematically prove anything in physics, it is all based of off observation and experiment.

Mathematically you can only devise hypotheses, yes. These must be proven within the realm of the physical. However if your hypothesis is (mathematically) consistent with more than one established theory, there is a presumption that it stands a better chance at physical reality.

And let us not forget that mathematics derives from physics: the abstract notion of numbers evolved naturally from our physical perception of the quality of "oneness", "twoness, "threeness", etc of sets of objects all around us.

IH

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has the increase of mass with relative velocity been physically proven to exist
The increase of mass (as used in Newton's definition of momentum) with velocity has already been proven even before it was predicted by relativity [Kaufmann, W. (1901), 'Die magnetische und elektrische Ablenkbarkeit der Becquerelstrahlen und die scheinbare Masse der Elektronen.', Gött. Nachr. , 143-155 .]

And let us not forget that mathematics derives from physics: the abstract notion of numbers evolved naturally from our physical perception of the quality of "oneness", "twoness, "threeness", etc of sets of objects all around us.

Pray to that, although I once argued about "i" and physical measurements in the Math forum, and that was quite disturbing - I ended up in disbelief of everything real (including real numbers).

Mass does not increase with velocity. The so-called "relativistic mass" is an artificial quantity M = γm, defined because the momentum for a relativistic particle is p = γmv, thus one can write it as p = Mv.

Wow, that's a fantastically clear way of explaining that - thank you. I actually thought that a particle at high speed would have a greater attraction due to gravity - I reckon it remains the same, right?

I actually thought that a particle at high speed would have a greater attraction due to gravity - I reckon it remains the same, right?
No, not right. There is no universal relationship between velocity and gravity. Sometimes gravitational attraction increases at high velocities and sometimes it remains unchanged. It depends on the circumstances.

jtbell
Mentor
I actually thought that a particle at high speed would have a greater attraction due to gravity - I reckon it remains the same, right?
Actually it doesn't. What happens is somewhat like the electromagnetic force exerted by a moving charge versus a stationary one.

With a stationary charge, you have the 1/r^2 electrostatic force described by Coulomb's Law, very similar to the classical law of gravitation.

With a moving charge, two things happen: (a) the electric field that it "produces" is no longer uniform in all directions, but becomes relatively stronger in the directions perpendicular to the motion and weaker along the direction of motion; (b) you now have a magnetic field which also contributes to the electromagnetic force when the "target" particle is moving.

In general relativity you have similar sorts of things going on with the gravitational field of a very fast-moving object (the mathematical details are different). The result can't be described simply by plugging the so-called "relativistic mass" into the classical formula for gravitational force.

PAllen
2019 Award
Actually it doesn't. What happens is somewhat like the electromagnetic force exerted by a moving charge versus a stationary one.

With a stationary charge, you have the 1/r^2 electrostatic force described by Coulomb's Law, very similar to the classical law of gravitation.

With a moving charge, two things happen: (a) the electric field that it "produces" is no longer uniform in all directions, but becomes relatively stronger in the directions perpendicular to the motion and weaker along the direction of motion; (b) you now have a magnetic field which also contributes to the electromagnetic force when the "target" particle is moving.

In general relativity you have similar sorts of things going on with the gravitational field of a very fast-moving object (the mathematical details are different). The result can't be described simply by plugging the so-called "relativistic mass" into the classical formula for gravitational force.
To add one more point to this explanation, just like the EM case, if you are dealing with measuring the field of an isolated particle, these effects are frame dependent. Switch to a frame where the charge is moving slowly or stationary, and you measure different mix of electric vs. magnetic field, and different spatial distribution of field. The same is true of the gravitational case.

Similarly, has the increase of mass with relative velocity been physically proven to exist or does it remain an extremely elegant proposition underlying SR?
If you replace the expression "relativistic Mass" with relativistic Momentum or energy, then the answer is yes. (Kaufmann, Bertozzi, and all particle accelerators).

Tests of relativistic energy and momentum

Thank you, DrStupid, jtbell and PAllen. Another thing learned from the forums - that's awesome.

Mass does not increase with velocity. The so-called "relativistic mass" is an artificial quantity M = γm, defined because the momentum for a relativistic particle is p = γmv, thus one can write it as p = Mv. The only mass with actual physical significance is the rest mass m.

The relativistic formula for momentum has been verified at least a trillion times, every time the LHC accelerates a proton.

Then isn't relativistic mass somewhat of a misleading notion?

I recall in Feynmann's "Six not so Easy Pieces" that he wrote that if all one wanted to know was how to account for SR in making predictive calculations, like for engineering for example, then the whole corpus of SR boiled down to the one 'observation' of objects gaining mass as they speed up. You need not know anything more than this to take SR into account for predictive computations.

I suppose he meant to say (relativistic) momentum increases with speed, which can be treated *metaphorically* as if mass is increasing when physically it isn't.

IH

Fredrik
Staff Emeritus