Any direct evidence of gravitational mass increase?

[hkyriazi]

Is there any evidence that objects moving increasingly closer to light speed gain gravitational mass, in the sense of attracting surrounding (and not co-moving) masses more strongly, rather than solely possessing the increased inertial mass implied by the greater force necessary to accelerate/decelerate it?

I can see that, for the laws of physics to not be noticeably different on, say, a fast-moving, non-accelerating rocket ship, the speed with which objects on the ship gravitate toward one another must be unchanged, so that if those objects' inertial masses increase, so must their gravitational masses. I consider that indirect evidence of gravitational mass increase. But what about the ship's (direct) gravitational effect on passing, more-or-less stationary objects?

 

[PeroK]

Is there any evidence that objects moving increasingly closer to light speed gain gravitational mass, in the sense of attracting surrounding (and not co-moving) masses more strongly, rather than solely possessing the increased inertial mass implied by the greater force necessary to accelerate/decelerate it?

I can see that, for the laws of physics to not be noticeably different on, say, a fast-moving, non-accelerating rocket ship, the speed with which objects on the ship gravitate toward one another must be unchanged, so that if those objects' inertial masses increase, so must their gravitational masses. I consider that indirect evidence of gravitational mass increase. But what about the ship's (direct) gravitational effect on passing, more-or-less stationary objects?

Mass in GR is more complicated than rest mass/relativistic mass. Relativistic mass is not generally used much any more. See:

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

 

[hkyriazi]

Mass in GR is more complicated than rest mass/relativistic mass. Relativistic mass is not generally used much any more. See:

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

Thank you. I appreciated that page's statement that the internal structure of any object moving near c speed is unchanged, as observed by those in its inertial frame. Also, that using energy, rather than mass, is more straightforward and less prone to misunderstanding. My question remains, though: would objects moving at near c speed, having more energy and thus more mass, be expected to exert a greater gravitational effect than would be observed for the same object at "rest"? I can't say I've read of experiments to test this, and assume such would be difficult to perform, but there may be astronomical evidence based on binary star systems, rapidly orbiting white dwarf stars/black holes, etc.

 

[Nugatory]

My question remains, though: would objects moving at near c speed, having more energy and thus more mass, be expected to exert a greater gravitational effect than would be observed for the same object at "rest"?

No.
Consider a massive star and a spaceship (mass negligible compared to the mass of the star) flying past it at close to the speed of light. The mass of the star produces some gravitational effects on the spacetime around it, pretty much what we'd expect from a star at rest in space with its gravity keeping a bunch of planets in orbit around it.
Now consider how someone in the spaceship describes this situation: they're at rest while the star is zooming past them at close to the speed of light. But describing the same situation from a different point of view can't change how the star is interacting with the spacetime around it - it's the same interaction, just being described by a different person.

 

[jartsa]

Is there any evidence that objects moving increasingly closer to light speed gain gravitational mass, in the sense of attracting surrounding (and not co-moving) masses more strongly, rather than solely possessing the increased inertial mass implied by the greater force necessary to accelerate/decelerate it?

So the question is about a gravitating mass that passes a test mass at high speed, not about a gravitationally bound system passing an observer at high speed.

Well, if we went to the rest frame of a light pulse (this light pulse is made of smaller light pulses that aren't perfectly parallel to each other, so said frame does exist), then we could observe a very fast moving sun exerting a force on the light, the force would be such that it would cause a quite abrupt change of momentum of the light.

So then a person that does not know general relativity might say that the sun exerted a large force on the light, or the force was quite small, but the inertial mass of the light was very small. (General relativity says that there is no such thing as "force of gravity", right?)

(I don't know what a person that knows general relativity would say. Maybe the experts can tell us.)Oh yes, whatever the reason for the abrupt change of momentum is, it is something else than "relativistic mass" ... because the total change of momentum of the light does not get very large when the "relativistic mass" of the sun gets very large.

 

[m4r35n357]

My question remains, though: would objects moving at near c speed, having more energy and thus more mass, be expected to exert a greater gravitational effect than would be observed for the same object at "rest"?

Something in your two posts gives me the impression that you are asking about gravitation in the context of Special Relativity, which does not deal with gravitation. If you are really asking about General Relativity, my apologies.

 

[PAllen]

It is true in GR that if you imagine two small massive bodies passing ( at small relative speed ) close enough to each other that their mutual gravity produces a small deflection, then as you consider the same initial condition except for higher and higher relative speed, the deflection will deviate further and further from Newtonian expectation, as relative speed approaches c. Further it will be larger than the Newtonian expectation, growing nonlinearly, extremely rapidly, close to c.

I do not think this prediction has been tested because getting high enough relative speeds between macroscopic objects has not been achieved. Further, there aren’t any known natural instances of this scenario that could be observed.

I don’t think anyone would doubt the prediction, even so, because GR has been tested so many other ways, including rapid co-orbits of neutron star binaries.

 

[hkyriazi]

Something in your two posts gives me the impression that you are asking about gravitation in the context of Special Relativity, which does not deal with gravitation. If you are really asking about General Relativity, my apologies.

Your impression was 100% correct. I wasn't looking for a GR explanation, though, but one couched in terms of gravitational "force" exerted. It does seem, from your and a subsequent response (that by PAllen), that an increased gravitational effect would indeed be expected.

 

[Nugatory]

I wasn't looking for a GR explanation, though, but one couched in terms of gravitational "force" exerted.

Unfortunately, there can be no such explanation. The Newtonian ##F=GMm/r^2## is inconsistent with SR and cannot be made consistent by allowing for varying masses, incorporating the relativistic mass increase into the theory, or otherwise tweaking things. This was one of the major motivations for the development of GR as a new theory of gravity.

It does seem, from your and a subsequent response (that by PAllen), that an increased gravitational effect would indeed be expected.

There is indeed an increased gravitational effect but you have to use GR to explain it; as @m4r35n357 says, SR doesn't deal with gravity.

 

[PeroK]

Your impression was 100% correct. I wasn't looking for a GR explanation, though, but one couched in terms of gravitational "force" exerted. It does seem, from your and a subsequent response (that by PAllen), that an increased gravitational effect would indeed be expected.

One of the reasons that relativistic mass is an awkward concept is that the acceleration and force measured in two reference frames depends on the direction of the acceleration.

It's difficult to attribute that to an increased mass of the particle. In particular, you cannot simply replace mass with relativistic mass and recover ##\vec{F} = m\vec{a}##.

Moreover, once you introduce the concept of four vectors, which really gets at the heart of SR - and generalises to GR - then you do get:

##f=ma##

Where ##f## and ##a## are the four-force and four-acceleration and ##m## is the rest mass.

 

[PAllen]

Your impression was 100% correct. I wasn't looking for a GR explanation, though, but one couched in terms of gravitational "force" exerted. It does seem, from your and a subsequent response (that by PAllen), that an increased gravitational effect would indeed be expected.

But note, the nonlinear increased deviation (compared to Newtonian expectations) I mentioned is definitively not even approximately obtained by putting relativistic mass into Newton's Law of gravitation.

 

[1977ub]

No.
Consider a massive star and a spaceship (mass negligible compared to the mass of the star) flying past it at close to the speed of light. The mass of the star produces some gravitational effects on the spacetime around it, pretty much what we'd expect from a star at rest in space with its gravity keeping a bunch of planets in orbit around it.
Now consider how someone in the spaceship describes this situation: they're at rest while the star is zooming past them at close to the speed of light. But describing the same situation from a different point of view can't change how the star is interacting with the spacetime around it - it's the same interaction, just being described by a different person.

The star - and its orbiting planets - will be noted to have slower clocks as determined in the frame of the spaceship. Doesn't this end up implying that the forces and masses must be different?

 

[PAllen]

The star - and its orbiting planets - will be noted to have slower clocks as determined in the frame of the spaceship. Doesn't this end up implying that the forces and masses must be different?

Forces are frame dependent, mass is not, so yes and no, to your questions.

 

[PeroK]

Your impression was 100% correct. I wasn't looking for a GR explanation, though, but one couched in terms of gravitational "force" exerted. It does seem, from your and a subsequent response (that by PAllen), that an increased gravitational effect would indeed be expected.

Well, in fact, there is a decreased gravitational effect. We could analyse the motion of a falling body using just SR and ignore GR:

First, we can look At the kinematic acceleration. If the object is falling in the y-direction with acceleration ##a_y## and the system is analysed in a frame moving at velocity ##v## in the x-direction, where the acceleration is ##a'_y##, then:

##a'_y = \frac{a_y}{\gamma^2}##

This difference is in fact due to time dilation of the system, measured in the moving frame.

I.e. the acceleration in the frame in Which the two-body system is moving is less than in the rest frame of the system.

As there is no length contraction in the y-direction, we have:

##g' = \frac{GM}{\gamma^2 r^2}##

This would be consistent with a decrease in the mass of the large moving body and not at all consistent with an increase attributable to relativistic mass.

Your experiment, if carried out, would suggest the opposite of an increase in gravitational mass with relative velocity.

The situation is worse for gravitational mass in the case of the object falling in the x-direction. In This case we have:

##a'_x \approx \frac{a_x}{\gamma^3}##

But, we also have length contraction in the x-direction so the bodies are closer together in the moving frame. Hence:

##g' = \frac{GM}{\gamma^5 r^2}##

Again this can be understood from length contraction and time dilation: in the moving frame the objects are closer together and the small object falls a shorter distance in greater time, which all adds up to five gamma factors.

Again, quite the opposite of what an advocate of relativistic mass might expect.

 

[PAllen]

Well, in fact, there is a decreased gravitational effect. We could analyse the motion of a falling body using just SR and ignore GR:

First, we can look At the kinematic acceleration. If the object is falling in the y-direction with acceleration ##a_y## and the system is analysed in a frame moving at velocity ##v## in the x-direction, where the acceleration is ##a'_y##, then:

##a'_y = \frac{a_y}{\gamma^2}##

This difference is in fact due to time dilation of the system, measured in the moving frame.

I.e. the acceleration in the frame in Which the two-body system is moving is less than in the rest frame of the system.

As there is no length contraction in the y-direction, we have:

##g' = \frac{GM}{\gamma^2 r^2}##

This would be consistent with a decrease in the mass of the large moving body and not at all consistent with an increase attributable to relativistic mass.

Your experiment, if carried out, would suggest the opposite of an increase in gravitational mass with relative velocity.

The situation is worse for gravitational mass in the case of the object falling in the x-direction. In This case we have:

##a'_x \approx \frac{a_x}{\gamma^3}##

But, we also have length contraction in the x-direction so the bodies are closer together in the moving frame. Hence:

##g' = \frac{GM}{\gamma^5 r^2}##

Again this can be understood from length contraction and time dilation: in the moving frame the objects are closer together and the small object falls a shorter distance in greater time, which all adds up to five gamma factors.

Again, quite the opposite of what an advocate of relativistic mass might expect.

The most specific case asked in the OP was the effect of a rapidly moving rocket on stationary test bodies. This is actually well known to produce a deflection, per GR, of (1 + β²)γ times the Newtonian expectation.

What you are deriving, is if the particles were initially comoving with the rocket. Looking back at the OP, I see this case was mentioned in passing as well, but the final question asked was the one I have answered.

I’m glad you analyzed the ‘in passing’ observation, as well, because you’ve shown it was incorrect.

 

[PeterDonis]

This is actually well known to produce a deflection, per GR, of (1 + β2)γ times the Newtonian expectation

I don't think the ##\gamma## in this formula as it appears in GR textbooks refers to the SR ##\gamma## factor, does it? I thought it referred to the ##\gamma## PPN parameter, which is something quite different.

 

[PAllen]

I don't think the ##\gamma## in this formula as it appears in GR textbooks refers to the SR ##\gamma## factor, does it? I thought it referred to the ##\gamma## PPN parameter, which is something quite different.

No, it is the SR gamma. @pervect has frequently cited the historic paper that derived this. There is an identical result for dust beams, with this same factor applying to oppositely moving dust beams, while for comoving ones, there is no such augmentation. In fact, there is a decrease relative to expectation for comoving beams.

 

[sweet springs]

Is there any evidence that objects moving increasingly closer to light speed gain gravitational mass, in the sense of attracting surrounding (and not co-moving) masses more strongly, rather than solely possessing the increased inertial mass implied by the greater force necessary to accelerate/decelerate it?

There is two packed gas, say A and B, of the same amount. A is heated so average speed^2 of gas moecule is much higher than that of B. Say,
energy of A amount 1.1 kg c^2 > energy of B amount 1.0 kg c^2.
I reasonably assume that
energy of A as source of gravity 1.1 kg c^2 > energy of B as source of gravity 1.0 kg c^2
Honestly I do not know the experimental evidence achieved.

 

[Tiran]

Correct me if I'm wrong, but I always understood that the "increased mass" thing is just another way of observing that forces like gravitational attraction or acceleration are rates, and rates require a measure of time that is constant - while time has changed at relativistic speeds, changing all rates with it.

 

[Nugatory]

Correct me if I'm wrong, but I always understood that the "increased mass" thing is just another way of observing that forces like gravitational attraction or acceleration are rates, and rates require a measure of time that is constant - while time has changed at relativistic speeds, changing all rates with it.

That sounds logical enough, and indeed I've used it as a handwaving explanation for the non-mathematical... but as soon as you try putting some math behind it, it falls apart. The problem starts with ordinary special relativity, where the acceleration ##\frac{dv}{dt}## (note that ##v## is a coordinate velocity and ##t## is coordinate time) is different when the force is perpendicular to the direction of motion and parallel.

 

[Tiran]

That sounds logical enough, and indeed I've used it as a handwaving explanation for the non-mathematical... but as soon as you try putting some math behind it, it falls apart. The problem starts with ordinary special relativity, where the acceleration ##\frac{dv}{dt}## (note that ##v## is a coordinate velocity and ##t## is coordinate time) is different when the force is perpendicular to the direction of motion and parallel.

I see what you're saying, but is there any circumstance when a fast moving object behaves like mass has changed? If not, that seems like a math application issue.

 

[Ibix]

is there any circumstance when a fast moving object behaves like mass has changed?

Not really, because that would imply something absolute about the concept of "fast". To the object itself it's always stationary.

That said, the interaction between two bodies in high velocity relative motion is different to the interaction between two bodies in low velocity relative motion. This is because momentum terms do enter into the stress-energy tensor. But they don't look like an added mass.

 

[Nugatory]

I see what you're saying, but is there any circumstance when a fast moving object behaves like mass has changed?

Not consistently, which is why trying to model what's going on as "mass has changed" doesn't work. If something works in one situation but not another... well, a stopped clock is right twice a day, but that doesn't make it a working clock.

I'm not sure what you mean by "a math application issue"?

 

[Tiran]

Not consistently, which is why trying to model what's going on as "mass has changed" doesn't work. If something works in one situation but not another... well, a stopped clock is right twice a day, but that doesn't make it a working clock.

I'm not sure what you mean by "a math application issue"?

Just that if something is inconsistent, it isn't the math that is wrong but the way we are looking at the problem. Possibly forgetting a factor, etc. If the dilation thing doesn't net a real world result but the equations show it should, maybe we are leaving some factors out of applying those equations.

Either way, it doesn't sound like an issue.

 

[Nugatory]

If the dilation thing doesn't net a real world result but the equations show it should, maybe we are leaving some factors out of applying those equations.

In this case the equation in question is Newton's ##F=ma## and the starting point is the assumption that it ought to apply; at the turn of the 19th century that was not an unreasonable assumption.

However at high speeds ##F=ma## breaks down; It becomes clear that the ratio between the measured acceleration and the measured force is different at different speeds. Because the acceleration and the force are both measured quantities the only way of saving the equation is to conjecture that ##m##, the constant of proportionality between them, increases with speed: ##F=m(v)a##. And that's the approach that doesn't work except under very limited conditions- you can treat that ##m(v)## as a mass only in the particular case of applying a transverse force to the moving object.

 

[Tiran]

However at high speeds F=maF=maF=ma breaks down; It becomes clear that the ratio between the measured acceleration and the measured force is different at different speeds.

If you have accelerated to 99% of C from your initial velocity, what sort breakdown would you see in your velocity reference frame from F=ma in terms of engine output vs acceleration?

 

[sweet springs]

You deal with ordinary F=ma matters in your daily life. No extraordinary phenomena should be observed in it by an observer who moves 99% c speed relative to something as well as you.

 

[Ibix]

If you have accelerated to 99% of C from your initial velocity, what sort breakdown would you see in your velocity reference frame from F=ma in terms of engine output vs acceleration?

None. Again, that would imply an absolute meaning to "speed". But if you apply a force to a fast moving object, ##F=ma## does not apply. The acceleration will not typically be parallel to the force, for example.

 

[PAllen]

There is two packed gas, say A and B, of the same amount. A is heated so average speed^2 of gas moecule is much higher than that of B. Say,
energy of A amount 1.1 kg c^2 > energy of B amount 1.0 kg c^2.
I reasonably assume that
energy of A as source of gravity 1.1 kg c^2 > energy of B as source of gravity 1.0 kg c^2
Honestly I do not know the experimental evidence achieved.

The contribution of kinetic energy to mass of a bound system like this has, in fact, been supported experimentally, by re-interpreting prior experiments. See:

https://xxx.lanl.gov/abs/gr-qc/9909014

 

[Dale]

rates require a measure of time that is constant - while time has changed at relativistic speeds,

There is a measure of time which is constant (invariant). It is called “proper time”. The type of time that is frame variant is called “coordinate time”. So all that needs to be done is to express the laws of physics in terms of proper time and other invariant or covariant quantities.

 

[Tiran]

None. Again, that would imply an absolute meaning to "speed". But if you apply a force to a fast moving object, ##F=ma## does not apply. The acceleration will not typically be parallel to the force, for example.

What do you mean it doesn't apply? How could a force applied to a fast moving object not effect the vector of that object?

 

[Nugatory]

What do you mean it doesn't apply? How could a force applied to a fast moving object not effect the vector of that object?

It does have an effect, but the equation ##F=ma## does not properly describe it: the acceleration is not necessarily in the same direction as the force, and the constant of proportionality between the force and acceleration is different for different directions and speeds.

 

[Tiran]

It does have an effect, but the equation ##F=ma## does not properly describe it: the acceleration is not necessarily in the same direction as the force, and the constant of proportionality between the force and acceleration is different for different directions and speeds.

Is this a claim that has anything to do with relativistic speeds, or are you just pointing out how vectors work?

 

[Ibix]

What do you mean it doesn't apply? How could a force applied to a fast moving object not effect the vector of that object?

It affects it, but not according to the Newtonian ##F=ma##. The resultant acceleration is not, in general, even parallel to the force even with constant mass.

 

[Nugatory]

Is this a claim that has anything to do with relativistic speeds, or are you just pointing out how vectors work?

It is a claim about relativistic speeds and it is one of the bigger differences between relativistic and classical kinematics. In classical mechanics the direction of acceleration is always in the same direction as the force (if it weren't, we wouldn't be able to write ##F=ma##, which only makes sense for scalars and vectors pointing in the same direction). In relativistic mechanics it is not.

As an aside, if we use the modern four-vector formulation (which was not known when relativity was first discovered, or no one would have bothered with the idea of mass increasing with speed) we can write the analogous vector equation ##\vec{F}=m\vec{a}## and it does work properly. But it's very different beast:
- The four-vectors are vectors in four-dimensional spacetime instead of three-dimensional space
- The acceleration four-vector ##\vec{a}## is defined as the time derivative of the velocity four-vector ##\vec{v}## as you'd expect, but ##\vec{v}## has a constant magnitude in all coordinate systems, and only its direction changes.
- The time derivative is with respect to a clock moving at the same speed and in the same direction as the object, at the moment that the force is applied. (That would be "proper time along the object's wordline" in the jargon).
- The ##m## that appears in ##\vec{F}=m\vec{a}## is the mass of the object as observed by an observer at rest relative to it, no adjustments for speed or time dilation needed to make everything come out right.