# What is the experimental evidence for mass relativity?

I've been looking for the specific experimental evidence as to why we know mass increases with velocity. The only way I can think of is with gravitation. If so how do we experimentally know that (as I've been told) increase in observed mass relies on the total relative velocity of the moving object and not simply the component of velocity in the direction of the gravitational field?

PeterDonis
Mentor
2020 Award
I've been looking for the specific experimental evidence as to why we know mass increases with velocity. The only way I can think of is with gravitation.
Gravitational mass does not increase with velocity. Velocity is frame-dependent, but the way an object acts as a source of gravity is not.

We know inertia increases with velocity because when we design particle accelerators, the strength of the magnetic fields in them has to be varied according to the velocity of the particles. This is what the common pop science statement that "mass increases with velocity" means, physically.

Gravitational mass does not increase with velocity. Velocity is frame-dependent, but the way an object acts as a source of gravity is not.

We know inertia increases with velocity because when we design particle accelerators, the strength of the magnetic fields in them has to be varied according to the velocity of the particles. This is what the common pop science statement that "mass increases with velocity" means, physically.
So for clarification the gravitational attraction between two objects doesn't depend on whether one of them is moving or not?

Things only move relatively to other things.
Any object is not moving in relation to itself, it's mass doesn't change whatever other any objects might be doing.

Ibix
2020 Award
Gravitational attraction is a rather complex beast in relativity, and motion of the source does come into it. For example, a rotating mass does have a different effect from a non-rotating one - you may wish to look up the "frame dragging" effect verified by Gravity Probe B.

However the "relativistic mass" that you are talking about is not related to gravity. In fact, the concept has largely fallen out of use (you'll notice Peter was quite careful to avoid the term) due, among other things, to misconceptions like yours. Here's a simple way to see why it is not relevant. Two small masses are close to one another. The gravitational attraction between them is almost nil so they are effectively stationary with respect to each other. An alien zips by at near light speed. According to relativity, the alien can treat itself as being at rest and the two masses as travelling at near light speed. If gravitational attraction depended on speed, the alien would argue that the two masses ought to be crashing together hard due to their "relativistic mass". The two descriptions are contradictory - something is wrong. It turns out that the mistake is "gravity depends on speed" in any naive sense.

Nugatory
Mentor
The only way I can think of is with gravitation.
As Ibix says above, gravitation won't show this effect. However, there are many other possible experiments, and some of these were among the earliest successful experimental tests of relativity. An easy one is to shoot an electron at relativistic velocity through a strong electrical field, see how much the electron accelerates in response to the electrical force. You'll find this and some others described in much greater detail here.

You'll also want to take a look at this FAQ.

As Ibix says above, gravitation won't show this effect. However, there are many other possible experiments, and some of these were among the earliest successful experimental tests of relativity. An easy one is to shoot an electron at relativistic velocity through a strong electrical field, see how much the electron accelerates in response to the electrical force. You'll find this and some others described in much greater detail here.

You'll also want to take a look at this FAQ.
As Ibix says above, gravitation won't show this effect. However, there are many other possible experiments, and some of these were among the earliest successful experimental tests of relativity. An easy one is to shoot an electron at relativistic velocity through a strong electrical field, see how much the electron accelerates in response to the electrical force. You'll find this and some others described in much greater detail here.

You'll also want to take a look at this FAQ.
I've been informed now of the paradoxes, but how do we know why gravity isn't impacted by special relativity? Why doesn't the additional energy get affected by gravitational force?

Nugatory
Mentor
Why doesn't the additional energy get affected by gravitational force?
As Ibix said above, "Gravitational attraction is a rather complex beast in relativity....".

First you need to separate out the things that are an artifact of a particular observer or frame of reference - these don't belong. For example, let's say a 1000kg elephant is struck by a .01 kg bullet fired with a muzzle velocity of 1000 meters/sec. How much energy is involved in the collision between the two? Any high-school physics student will answer that one without hesitation - ##E_k=(mv^2)/2##, ##m=.01##, ##v=1000##, the kinetic energy is 5000 Joules. But I could just as easily have adopted coordinates in which the bullet is at rest and the elephant is moving towards it at 1000 meters/sec - and now the kinetic energy is 500,000,000 Joules. Because the physics of the elephant-bullet interaction is the same either way (and works to rather to the disadvantage of the unfortunate elephant) this huge discrepancy has to be an artifact of the point of view we've taken.

It turns out that there is mathematical machinery for describing physical systems in a way that is independent of the observer's point of view (and also allows us to calculate back to how any given observer would describe the system - otherwise it wouldn't be very useful). This goes by the name "tensor calculus", and to get a proper description of the way that energy produces gravitational effects you need to start with something called the "stress-energy tensor". Einstein's field equations basically relate the curvature of spacetime (which leads to gravitational effects) to this tensor. There's a fairly gentle introduction at http://preposterousuniverse.com/grnotes/grtinypdf.pdf [Broken]

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• James Nelson
Nugatory
Mentor
how do we know why gravity isn't impacted by special relativity?
If we take the equations of general relativity and apply them to the special case in which the curvature of spacetime is zero so there is no gravity... we get special relativity. In fact, that's why it's called "special" relativity, because it only applies in the special case in which gravitational effects are negligible, whereas general relativity applies there and also in the more general case of non-negligible gravitational effects. Thus, it's something of a tautology to say "gravity isn't impacted by special relativity" - it's part of the definition of special relativity.

Ibix
2020 Award
I've been informed now of the paradoxes, but how do we know why gravity isn't impacted by special relativity? Why doesn't the additional energy get affected by gravitational force?
Well, paradoxes following from an idea are a pretty strong hint that it's wrong. The best answer I can give is to say that every experimental test of gravity that we've done has agreed with the predictions of GR (gravitational deflection of light, the precession of Mercury, orbital decay of the Taylor Hulse pulsars, the GPS clocks, Gravity Probes A and B, and the Pound-Rebka experiment to name a few), and the source term in GR is the stress-energy tensor, which does not include a term that looks like ##\gamma m##.

Well, paradoxes following from an idea are a pretty strong hint that it's wrong. The best answer I can give is to say that every experimental test of gravity that we've done has agreed with the predictions of GR (gravitational deflection of light, the precession of Mercury, orbital decay of the Taylor Hulse pulsars, the GPS clocks, Gravity Probes A and B, and the Pound-Rebka experiment to name a few), and the source term in GR is the stress-energy tensor, which does not include a term that looks like ##\gamma m##.
Well, paradoxes following from an idea are a pretty strong hint that it's wrong. The best answer I can give is to say that every experimental test of gravity that we've done has agreed with the predictions of GR (gravitational deflection of light, the precession of Mercury, orbital decay of the Taylor Hulse pulsars, the GPS clocks, Gravity Probes A and B, and the Pound-Rebka experiment to name a few), and the source term in GR is the stress-energy tensor, which does not include a term that looks like ##\gamma m##.
I know now that experimentally it works, and that it's not in his general theory. But I desire to know why he didn't put gamma in the equation in the first place. Is there some term that cancels making gamma and therefore the effects of velocity go away? Or some other reason that the additional energy doesn't affect gravity? Special relativity applies in other situations so it seems odd that gravity isn't affected.

PeterDonis
Mentor
2020 Award
the gravitational attraction between two objects doesn't depend on whether one of them is moving or not?
It can depend on the relative motion of the two objects; but it doesn't depend on whether either of them is moving relative to the coordinates we choose.

For example, the gravitational interaction between the Sun and the planet Mercury is a little bit different from what it would be if Mercury were at rest relative to the Sun, instead of moving around it. (This small difference is responsible for the precession of Mercury's perihelion, which was one of the classic tests that distinguished GR from Newtonian gravity.) But the interaction is the same regardless of whether we choose a frame in which the Sun is at rest, or a frame in which Mercury is at rest, or a frame in which they are both moving.

I desire to know why he didn't put gamma in the equation
Because gamma is an artifact of the choice of coordinates. In the example above, gamma would be different in a frame in which the Sun is at rest, vs. a frame in which Mercury is at rest, vs. a frame in which both were moving. But the gravitational interaction is the same. So gamma, and other frame-dependent quantities, can't affect the gravitational interaction.

• James Nelson
Ibix
2020 Award
I know now that experimentally it works, and that it's not in his general theory. But I desire to know why he didn't put gamma in the equation in the first place. Is there some term that cancels making gamma and therefore the effects of velocity go away? Or some other reason that the additional energy doesn't affect gravity? Special relativity applies in other situations so it seems odd that gravity isn't affected.
As Nugatory noted earlier, if there's gravity, SR does not apply. Seriously, just forget about relativistic mass. It was mostly dropped in professional circles decades ago (two to four decades, depending who you ask), although it persists in pop-sci (mostly because it sounds cool, I think). It just confuses things. There is no "extra mass" because the notion of "extra mass" only makes sense if you try to treat special relativistic equations as if they were a correction to Newton rather than a fundamental re-write which Newton only ever approximated. That treatment is extremely strained for special relativity, and is completely untenable for general relativity.

If you want to understand the development of GR you are going to have to find a book. Nugatory already referenced Carroll. If memory serves, @bcrowell 's book Relativity for Poets, which can be freely downloaded from lightandmatter.com covers some of it, and does not require advanced maths. But one can see easily one reason why Einstein did not include relativistic mass as a source - doing so would lead to contradictions of the type I pointed out earlier.

• bcrowell
PeroK
Homework Helper
Gold Member
2020 Award
I know now that experimentally it works, and that it's not in his general theory. But I desire to know why he didn't put gamma in the equation in the first place. Is there some term that cancels making gamma and therefore the effects of velocity go away? Or some other reason that the additional energy doesn't affect gravity? Special relativity applies in other situations so it seems odd that gravity isn't affected.
Instead of using good physics, let me fight fire with fire, so to speak. In classical physics the equation for Kinetic Energy of a particle is ##KE = \frac{1}{2}mv^2##. Let's say we are suspicious of what that ##\frac{1}{2}## is doing there, so we try to redefine mass so that for an object in motion ##m = \frac{1}{2}m_0## where ##m_0## is the rest mass. Then we have ##KE = mv^2##.

We then decide (fairly quickly) that this isn't a very good idea, and abandon it. We go back to ##m = m_0##: the mass of a particle in motion is equal to its rest mass.

But, unfortunately, there's this guy that heard of our idea and he won't let it go. He says, where's the experimental evidence for the mass halving when an object starts to move? Why isn't the gravity of an object halved when it starts to move? Why did you come up with that idea in the first place? It can't have been just a way to make some equations look simpler! There must be more to it than that.

Instead of using good physics, let me fight fire with fire, so to speak. In classical physics the equation for Kinetic Energy of a particle is ##KE = \frac{1}{2}mv^2##. Let's say we are suspicious of what that ##\frac{1}{2}## is doing there, so we try to redefine mass so that for an object in motion ##m = \frac{1}{2}m_0## where ##m_0## is the rest mass. Then we have ##KE = mv^2##.

We then decide (fairly quickly) that this isn't a very good idea, and abandon it. We go back to ##m = m_0##: the mass of a particle in motion is equal to its rest mass.

But, unfortunately, there's this guy that heard of our idea and he won't let it go. He says, where's the experimental evidence for the mass halving when an object starts to move? Why isn't the gravity of an object halved when it starts to move? Why did you come up with that idea in the first place? It can't have been just a way to make some equations look simpler! There must be more to it than that.
I'm sorry, I'm not at all trying to use bad physics. It's just that I need extra help to get a satisfying answer and truly understand it.

PeterDonis
Mentor
2020 Award
I need extra help to get a satisfying answer
What would make an answer "satisfying" for you? You have already gotten several good answers in this thread. It looks to me like your response to those answers is to keep changing the question; but if the question you end up with is basically "why are the equations of GR the way they are?", that isn't going to be answered in a PF thread; you need to, as others have said, take the time to learn GR from a textbook.

pervect
Staff Emeritus
I've been looking for the specific experimental evidence as to why we know mass increases with velocity. The only way I can think of is with gravitation. If so how do we experimentally know that (as I've been told) increase in observed mass relies on the total relative velocity of the moving object and not simply the component of velocity in the direction of the gravitational field?
The reason that many popularizations describe "mass" as increasing with velocity is based on special relativity, and has nothing to do with gravity. I suppose I should look up what's been done in the way of formal experiments more carefully, bu at this point t instead I'll just remark that CERN, for instance, simply wouldn't work if the relativistic effects on "mass" weren't accounted for properly.

As far as your question goes, it's wrong to think of applying Newton's gravitational law with a modified expression for "mass" to get a relativistic version of gravity. To explain the right approach takes a book. The good news is that there are explanations available at the advanced undergraduate level, the topic used to be accessible only to graduate students. The bad news is it turns out that the simple model of gravity as a "force" is insufficient to explain the effects of relativistic gravity, one needs to get into the geometrical aspects of space-time. For instance, time dilation due to gravity is well known and experimentlly verified, but does not follow from any model of "gravity" as a force.

• Ibix
The reason that many popularizations describe "mass" as increasing with velocity is based on special relativity, and has nothing to do with gravity. I suppose I should look up what's been done in the way of formal experiments more carefully, bu at this point t instead I'll just remark that CERN, for instance, simply wouldn't work if the relativistic effects on "mass" weren't accounted for properly.

As far as your question goes, it's wrong to think of applying Newton's gravitational law with a modified expression for "mass" to get a relativistic version of gravity. To explain the right approach takes a book. The good news is that there are explanations available at the advanced undergraduate level, the topic used to be accessible only to graduate students. The bad news is it turns out that the simple model of gravity as a "force" is insufficient to explain the effects of relativistic gravity, one needs to get into the geometrical aspects of space-time. For instance, time dilation due to gravity is well known and experimentlly verified, but does not follow from any model of "gravity" as a force.
Thank you! That's what I was looking for.