Does Relativistic Mass Affect Gravitational Force in SR? | SR & GR Comparison

[AWolf]

I have a straight forward question that hopefully somebody can answer.

In SR, does the relativistic mass of an object exert an increased gravitational force and if so has it been proven ?

All the information that I've found concerning SR discounts its effects when in GR as being irrelevant and inaccurate.

 

[pmb_phy]

Originally posted by AWolf
I have a straight forward question that hopefully somebody can answer.

In SR, does the relativistic mass of an object exert an increased gravitational force and if so has it been proven ?

In SR there are no gravitational forces so I'll respond using GR. In GR - The faster a body moves the larger the (relativistic) mass. For simplicitly I'll assume the gravitational field is not time dependent.

The larger the mass the larger the gravitational force. Therefore the increase in mass with speed means an increase in the gravitational force. Any "local" observer at rest in a gravitational field may locally consider himself to be at rest in a uniformly accelerating frame frame of referance. As such the relationship between the magnitude of the gravitational force, F, the relativistic mass, m, and the magnitude of the local acceleration due to gravity, g is

F = mg

All the information that I've found concerning SR discounts its effects when in GR as being irrelevant and inaccurate.

Not directly that I know of.

 

[franznietzsche]

Originally posted by AWolf

All the information that I've found concerning SR discounts its effects when in GR as being irrelevant and inaccurate.

SR is simply a spcial case of GR, one with no gravity. If there is no space time warping due to a large mass, then SR holds. The problem lies in the mathematical basis of SR which is based upon the minkowski metric for the spacetime manifold. The minkowksi metric has space as universally flat and unwarped. However, as GR shows us this is not necessarily the case. So when space is warped the GR equations must be used, however if you are in a locally lorentzian frame (meaning either there is no gravity or you are in freefall (includes being in orbit)) then SR holds just fine.

 

[AWolf]

Correct me if I'm wrong - happens occassionaly.

SpaceTime is compressed in SR due to velocity in the minkowski metric, and in GR, with an already warped/compressed SpaceTime, SpaceTime is further compressed due to velocity.

Surely, the very presence of an object in a gravitational field, which is already compressed SpaceTime, would cause it to have additional relativistic mass.

 

[franznietzsche]

Originally posted by AWolf
Correct me if I'm wrong - happens occassionaly.

SpaceTime is compressed in SR due to velocity in the minkowski metric, and in GR, with an already warped/compressed SpaceTime, SpaceTime is further compressed due to velocity.

Surely, the very presence of an object in a gravitational field, which is already compressed SpaceTime, would cause it to have additional relativistic mass.

Not exactly. The lorentz transformations of SR are based on velocity, however gravity in GR is equivalent to a uniformly accelerating frame of reference. The two phenomenon have simliar effects but are not identical.

 

[GRQC]

Originally posted by franznietzsche
SR is simply a spcial case of GR, one with no gravity. If there is no space time warping due to a large mass, then SR holds.

General Relativity describes more than just the warping of spacetime time due to "large masses". The FRW metric, for example, allows for universes which possesses intrinsic gaussian curvature.

 

[AWolf]

Originally posted by franznietzsche
Not exactly. The lorentz transformations of SR are based on velocity, however gravity in GR is equivalent to a uniformly accelerating frame of reference. The two phenomenon have simliar effects but are not identical.

Gravity is the equivalent of velocity between GR and SR - accepted.

If an object is not uniformly accelerating, maintains a constant distant, then the relativistic effects of velocity/acceleration would be nil.
The object is still within the compressed space of the object producing the gravitational field.

Wouldn't this result in a 'stationary' relativistic mass in GR due to the compressed space ?

 

[franznietzsche]

Originally posted by AWolf

Wouldn't this result in a 'stationary' relativistic mass in GR due to the compressed space ?

The way i understand potential energy does not add to effective mass like kinetic energy does...but i could be wrong. I'm not really sure.

 

[AWolf]

I'll put it another way.

A rocket moving at a relative velocity of 1 metre/second away from a massive star, at a (safe) distance.

The time on the rocket, relative to an external observer would be slower because of it location within the gravitational field / compress space of the star - velocity is insignificant.

The further the rocket moves away from the star, the quicker time would become.

In SR, the increase in mass is proportional with the velocity, as is time.

In GR, time is altered due to compressed space , but is mass subject to the same proportional change ?

Relativistic Mass = Time Dilation = Relativistic Mass

Does the rocket loose relativistic mass as it travels away from the star and out of its compressed space ?

I hope that's clear

 

[franznietzsche]

Originally posted by AWolf
I'll put it another way.

A rocket moving at a relative velocity of 1 metre/second away from a massive star, at a (safe) distance.

The time on the rocket, relative to an external observer would be slower because of it location within the gravitational field / compress space of the star - velocity is insignificant.

The further the rocket moves away from the star, the quicker time would become.

In SR, the increase in mass is proportional with the velocity, as is time.

In GR, time is altered due to compressed space , but is mass subject to the same proportional change ?

Relativistic Mass = Time Dilation = Relativistic Mass

Does the rocket loose relativistic mass as it travels away from the star and out of its compressed space ?

I hope that's clear

The reason it gains mass with high velocity in SR is because Kinetic Energy adds to mass, its really the mass-energy that dilates, the effective mass, not the mass itself.

In order for it to gain relativistic mass, i.e. inertia, then potential energy(energy due to presence in a gravitational field) would have to add to mass, and I'm not sure that it does. But i could be wrong.

 

[AWolf]

Thanks for that Franz.

I was trying to work through a problem with regards to gravity and mass using a completely new, as yet unpublished, theory.
If you're right in saying that the mass will not gain energy and subsequently there will be no increase in its own graviational field, then I suppose that is the answer I was after.

The problem was to do with an object in a gravitational field of a large star, for example. As the object moved closer to the star, it would encountered a increased graviational field, the gravitational force being more compressed the closer to the star.
The numbers seemed to imply that there was no increase in energy of the object, but an increase in mass and subsequent time dilation, but no increase in the objects gravitational field.
This seemed to disagree with Newton and gravity being directly related to mass.

Hence the questions about GR relativistic mass and increase in gravity in relation to position in a gravitational field.

 

[franznietzsche]

Originally posted by AWolf

I was trying to work through a problem with regards to gravity and mass using a completely new, as yet unpublished, theory.
If you're right in saying that the mass will not gain energy and subsequently there will be no increase in its own graviational field, then I suppose that is the answer I was after.

Now that i think about it, if potential energy does add to mass in that manner, then the mass of an object in a gravitational field would increase, increasing the field it generates, this ouwl cause an increase in the force exerted on the larger object that created the first fiel (say a star) Its mass would then increase which would increase its gravitational field, increasing the amass of the object, etc. ad absurdum.

By extending this process you would have any two objects that exert a gravitational force on each other posessing divergent relativistic masses. This makes me believe more so that potential energy does not add to effective mass.

 

[AWolf]

By extending this process you would have any two objects that exert a gravitational force on each other posessing divergent relativistic masses. This makes me believe more so that potential energy does not add to effective mass.

This all seems to verify what I was finding that the gravitational force is proportional to the kinetic energy, the effect of which is an increase in mass.
Mass can increase due to an objects environment, but unless the increase in mass is caused by an increase in kinetic energy it does not increase the graviational force.
To add to the effective mass, potential energy must be converted to kinetic energy.