Does Acceleration of Matter Lead to Gravitational Dilation?

[tvscientist]

As mass approaches C it also approaches infinite mass. As it acquires mass, does it also accumulate gravitational forces? I believe this is important when considering the conservation of angular momentum of mass as it spirals towards a Black Hole.

 

[Vorde]

As an object gains more energy it gains mass, therefore it would produce a stronger gravitational attraction.

 

[Drakkith]

An object at a high velocity would NOT gain any mass in it's rest frame, and therefor never gain any gravity in that frame either. I don't know how it looks to an outside frame however. I don't believe gravity would increase, as that would require all gravity for everything else in the universe not moving with the object to appear to increase in the moving objects frame, which obviously doesn't happen as far as I know. I think that a moving object gains MOMENTUM, but not mass.

 

[Vorde]

An object at a high velocity would NOT gain any mass in it's rest frame, and therefor never gain any gravity in that frame either. I don't know how it looks to an outside frame however. I don't believe gravity would increase, as that would require all gravity for everything else in the universe not moving with the object to appear to increase in the moving objects frame, which obviously doesn't happen as far as I know. I think that a moving object gains MOMENTUM, but not mass.

I'm torn on this one. When I first saw your comment I saw an obvious flaw in my thinking and I thought you had the correct answer. The problem in my head is that in answering the question I thought that an acceleration of an object implies energy is being transferred to that object. If that is a generalization which does not apply to gravitation then you are correct, but if not then I believe the mass would increase.

The key difference is that (in my mind at least, I probably look like an arrogant idiot if I'm wrong) its not an object at high velocity, but an object undergoing acceleration.

 

[Drakkith]

I don't know enough to explain the details, as I don't really know them myself. Maybe someone else could elaborate or correct me?

 

[darkhorror]

No it will not create more gravity, as rest mass doesn't increase. Mass only seems to increase because of how you see velocity at high speeds. I never like the saying that mass increases as you go faster.

 

[Vorde]

No it will not create more gravity, as rest mass doesn't increase. Mass only seems to increase because of how you see velocity at high speeds. I never like the saying that mass increases as you go faster.

Ok, thanks for clearing that up for me. Sorry about the misunderstaing Drakkith

 

[Drakkith]

Ok, thanks for clearing that up for me. Sorry about the misunderstaing Drakkith

No need to apologize, you did nothing wrong. Hell, I'm still not even sure on the details myself. I just know from a couple of previous posts here on PF.

 

[PAllen]

Well one observation, even though Newtonian concepts are only approximate in GR, is that an object spiralling into black hole brings in its mass plus its potential energy plus the angular momentum it acquires. The the mass equivalent of its KE increase is just the transformation of its potential energy (at great distance); an object falling in from far away will bring in more total energy than one falling from nearby, if they both start out stationary with respect to the black hole.

The case of matter infalling into a black hole is different from frame dependent effects of an isolated object. Consider the trivial case of one object versus two objects with high relative speed. In the former case, KE is strictly frame dependent. In the latter case, no frame can erase the high relative motion of the two objects. Thus the invariant mass of the single isolated object is the same as its rest mass; the invariant mass of the two objects as a system is much larger than the sum of their rest masses.

Thus KE and angular momentum of infalling matter relative to the black hole are essentially invariant, real contributions to the state of the black hole. They don't disappear in any frame (they may change from being attributable to the infalling matter versus the black hole itseld, but the result is the same).

 

[Drakkith]

Does that mean that to see the increase in energy/mass you would need to be viewing two or more objects as one system instead of viewing one object at high velocity? If that makes any sense...

 

[PAllen]

Does that mean that to see the increase in energy/mass you would need to be viewing two or more objects as one system instead of viewing one object at high velocity? If that makes any sense...

Basically, yes. Having multiple particles with different relative speeds introduces a frame invariant component of their KE.

Another example is a beam of atoms. If they are near perfectly uniform in velocity, even if it it is a high velocity, the beam has a temperature of near absolute zero. There exists a frame in which they collectively have almost no KE. The same atoms, with the same speed, but random directions, has high temperature. Even in center of momentum frame, the atoms have large total KE.

In each of these cases, you could compute curvature invariants (for the atoms a source of gravity) in the COM frame. For the collimated beam, the (frame dependent) KE would not contribute at all to the curvature invariants. For the 'ball of gass' case, it (the atom's KE) would contribute to the curvature invariants. Even in the ball of gas case, one can imagine the ball as a whole having a larger KE in some frame compared to the KE in the COM frame. In this case, as well, only the COM KE would contribute to curvature invariants.

 

[tvscientist]

Assume a mass X is accelerated by a constant application of energy. Specify .5 g. As the mass reaches something like .66c, that .5 g force is now acting upon mass dilation of 100 percent. Time is reduced by 50 percent. G force is reduced to .25.

The mass then encounters our atmosphere. Its kinetic energy released is not in proportion to its mass time speed, which only increased from zero to .66c. It is increased by .66 plus 100 percent increase in mass imparted by the constant application of energy before it got here. [Accelerating decreased from .5g to .25g when it reached a mass dilation of 100 percent at about .66c.]

The question is this. Is the increase in potential kinetic energy accompanied by an increase in gravity of the mass? Or is the kinetic energy stored in such a way that it does not interact as if it also had more mass. Only more kinetic energy?







This cosmic ray will have been accelerated according to e=mc2, not Newtonean. Accordingly, its kinetic energy will not be linear as to its increased speed relative to us. For instance, at something like .66c its acceleration

 

[Drakkith]

Tvscientist, you're saying the kinetic energy of an object isn't 1/2MV^2 at relativistic speeds?

The question is this. Is the increase in potential kinetic energy accompanied by an increase in gravity of the mass? Or is the kinetic energy stored in such a way that it does not interact as if it also had more mass. Only more kinetic energy?

From previous posts I would say that it does not have more mass or gravity from the frame of the Earth, but the Earth plus the object does have more mass/gravity when you look at the Earth and the object as one system.

 

[tvscientist]

DR

I have been thinking about a better way to express the question. So. We apply 1g to a given mass. As the mass accelerates it 'gains' mass in the sense that more and more energy would be required to sustain 1g.

The mass collides with our atmosphere. Does the kinetic energy released approximately equal the total amount of energy put into the acceleration? If energy released is only measured by the velocity and subsequent deceleration of the original mass, where did the extra relativistic energy go?

If the mass DOES carry the extra kinetic energy of a more massive particle, does that particle also exhibit increased gravity? One way or the other we need to account for the extra energy required to accelerate to mass to relativistic velocities. And one way or another we need to reconcile the energy delivered with its inherent gravitational force.

 

[Drakkith]

The kinetic energy is equal to the energy input to accelerate it to that velocity. If it took you a million joules of energy to get an object up to that speed, then the energy released when you slow the object down is also a million joules. Not using the relativistic formula WILL result in an inaccurate calculation of the energy. The classical formula for kinetic energy is accurate enough for low velocities, but the relativistic formula is ALWAYS more accurate. There is nothing weird going on here, no missing or extra energy or mass or anything like that.

 

[twofish-quant]

As mass approaches C it also approaches infinite mass.

No it doesn't. There was a scientist in the 1950's named George Gamow who wrote a popular book on relativity in which he described relativity as increasing mass as speed increases. Most scientists now wish he hadn't done that since it makes things more confusing.

As thing get closer to the speed of light, the equations for momentum and energy change, and but "rest mass" stays the same.

As it acquires mass, does it also accumulate gravitational forces?

No it doesn't. That's why it's now considered a bad description of what relativity does.

 

[mrspeedybob]

Would it be correct to say that relativistic momentum increase is just another way of looking at time dilation?

If a rocket is accelerating at 1 meter per second per second in it's own reference frame, but time is dilated so that 1 second on the rocket is 2 seconds on my clock, then I see it accelerating at 1 meter per 2 seconds per 2 seconds.

 

[PAllen]

Would it be correct to say that relativistic momentum increase is just another way of looking at time dilation?

If a rocket is accelerating at 1 meter per second per second in it's own reference frame, but time is dilated so that 1 second on the rocket is 2 seconds on my clock, then I see it accelerating at 1 meter per 2 seconds per 2 seconds.

No. Nothing is accelerating in its own frame, by definition.

 

[mrspeedybob]

So what do you call it if there is an accelerometer on the rocket and it reads 1 m per sec^2 ?

 

[PAllen]

So what do you call it if there is an accelerometer on the rocket and it reads 1 m per sec^2 ?

An accelerometer measures deviation from inertial motion. In relativity, it measures an invariant scalar: proper acceleration, which is the norm of acceleration 4-vector, which is derivative of 4-velocity by proper time.

In the frame of an accelerated object, coordinate acceleration is zero, as is coordinate velocity. However, 4-velocity, 4-acceleration, and proper acceleration are not zero.

Relativistic momentum applies to inertial observers and inertial bodies as well as accelerating bodies, so your argument doesn't make sense. How do you apply it to the fact that an inertial proton moving at .99 c has 3 times the momentum as one moving at .9c? Any accelerometer moving with each proton would read zero; each proton is stationary in its frame, and everything in its frame is indistinguishable from the lab frame.

 

[DNMock]

An accelerometer measures deviation from inertial motion. In relativity, it measures an invariant scalar: proper acceleration, which is the norm of acceleration 4-vector, which is derivative of 4-velocity by proper time.

In the frame of an accelerated object, coordinate acceleration is zero, as is coordinate velocity. However, 4-velocity, 4-acceleration, and proper acceleration are not zero.

Relativistic momentum applies to inertial observers and inertial bodies as well as accelerating bodies, so your argument doesn't make sense. How do you apply it to the fact that an inertial proton moving at .99 c has 3 times the momentum as one moving at .9c? Any accelerometer moving with each proton would read zero; each proton is stationary in its frame, and everything in its frame is indistinguishable from the lab frame.

That doesn't make sense though. A particle with a higher velocity has more energy. You must add energy to an object to get it to speed up and the object then gains that energy. This is why all the matter in the universe isn't enough to get an object with mass to actually reach the speed of light. This is simply displayed easily in a particle accelerator. The faster the speed the more energy is released by a collision, and according to the Einstein's E=MC^2, if you increase energy, you increase mass. Or am I seeing this wrong?

 

[Drakkith]

That doesn't make sense though. A particle with a higher velocity has more energy. You must add energy to an object to get it to speed up and the object then gains that energy. This is why all the matter in the universe isn't enough to get an object with mass to actually reach the speed of light. This is simply displayed easily in a particle accelerator. The faster the speed the more energy is released by a collision, and according to the Einstein's E=MC^2, if you increase energy, you increase mass. Or am I seeing this wrong?

Other than mass increasing, that's pretty much correct as far as I know. Mass does not increase as your speed increases, although that is a very common misconception.