Gravity and relativity
- Thread starter Votorx
- Start date
No.*Votorx said:
I'm fuzzy on this stuff, but less fuzzy than most physics teachers. Here's my understanding:
Person B must apply a strong force outward in order to maintain their circular motion.
In B's reference frame, B is motionless, but they are still applying this force... So in B's frame there is a pseudo-force directed outward from person A which exactly counter-acts the real force B is applying in order to keep B motionless.
This pseudo-force is called the centrifugal force. Note that it only exists in B's reference frame, and (unlike gravity) is directed away from A.
In general relativity, gravity itself is a pseudo-force that doesn't exist in free-falling reference frames. In this way, "centrifugal force" and "gravity" can be grouped together as pseudo-forces... but this does not mean that centrifugal force = gravity.
* At a large distance from A, the combined gravity of A and B will be stronger a B goes faster B, because B's kinetic energy adds to the mass-energy density of the system.
Umm... yes, I think.
I should stop there, because I really dont' know what I'm talking about, but I can't help giving my vague understanding of the matter anyway...
An accelerating mass produces a gravity wave or waves. If the acceleration is fast and repetitive, the combined gravity waves will look like a uniform gravitational field from a distance. The gravitational field will have the same strength as that produced by an object with the same mass/energy as the sum of the accelerating mass and its average kinetic energy*.
*The mass's average kinetic energy for this purpose should be taken in the mass's average inertial rest frame, ie the inertial frame in which it "jiggles" but doesn't "travel". This will be the minimum average kinetic energy of the mass. I'd like to call it the non-removable kinetic energy, since it can't be transformed away by switching reference frames, but I really don't know the right terminology.
PhysicsMonkey, how close to the truth am I?
I should stop there, because I really dont' know what I'm talking about, but I can't help giving my vague understanding of the matter anyway...
An accelerating mass produces a gravity wave or waves. If the acceleration is fast and repetitive, the combined gravity waves will look like a uniform gravitational field from a distance. The gravitational field will have the same strength as that produced by an object with the same mass/energy as the sum of the accelerating mass and its average kinetic energy*.
*The mass's average kinetic energy for this purpose should be taken in the mass's average inertial rest frame, ie the inertial frame in which it "jiggles" but doesn't "travel". This will be the minimum average kinetic energy of the mass. I'd like to call it the non-removable kinetic energy, since it can't be transformed away by switching reference frames, but I really don't know the right terminology.
PhysicsMonkey, how close to the truth am I?
Well lets say the statement I made was true...untill someone can verify it completely.
If what I said was true, and a large amount of acceleration over a short amount of time will create a gravitational field, then why did you say no to my first scenerio?
Relative to Person B, Person A is spinning at .9c. That's an extremely large amount of accelaration over a very short amount of time. So doesn't it make sence to say Person A would create that gravitational field?
If what I said was true, and a large amount of acceleration over a short amount of time will create a gravitational field, then why did you say no to my first scenerio?
Relative to Person B, Person A is spinning at .9c. That's an extremely large amount of accelaration over a very short amount of time. So doesn't it make sence to say Person A would create that gravitational field?
Because the gravitational field of A is unchanged. It is the gravitational field of B that is increased.Votorx said:
I don't think so.
I don't know how to analyse it properly, but I think that Person A is not producing gravity waves because their nonremovable kinetic energy is zero - ie there exists an inertial reference frame in which A's kinetic energy is zero.
Properly, you'd have to know how to determine the stress-energy tensor of spacetime around A... but I have no idea how to do that!
Hi Votorx,
The answer to your question depends, unfortunately, on the details. If you imagine a situation where person A is massive while person B is essentially massless then the answer is, of course, no. Don't laugh at me though, massless people are an important idealization in the theory. Let me explain why. In this case we would call person B a "test particle", and the role of a test particle is always to sample the gravitational field produced by another system without influencing the field. The test particle, person B, could move in a circle around person A due to the curved spacetime set up by person A, but person B doesn't effect the field created by person A in this situation. Also, strictly speaking the true effects of gravity are only observable in the separation of two nearby test particles initially moving parallel to one another.
On the other hand, if person A and person B are both massive objects then the story is more complicated. Whether the system is spinning or not becomes very important. We might again imagine that A and B are gravitationally bound to each other, but now that gravitational binding can itself "produce more gravity". In ordinary situations this extra bit is negligible, but sometimes it can matter a lot. For example, a spinning black hole is very different from a stationary black hole. Back to your case of two massive objects orbiting each other, one of the most famous effects is the emission of gravitational radiation. These gravitational waves carry energy away from the system, and the period of the motion can actually decrease. This decrease has actually been observed precisely as predicted by Einstein's theory.
Hope this helps.
The answer to your question depends, unfortunately, on the details. If you imagine a situation where person A is massive while person B is essentially massless then the answer is, of course, no. Don't laugh at me though, massless people are an important idealization in the theory. Let me explain why. In this case we would call person B a "test particle", and the role of a test particle is always to sample the gravitational field produced by another system without influencing the field. The test particle, person B, could move in a circle around person A due to the curved spacetime set up by person A, but person B doesn't effect the field created by person A in this situation. Also, strictly speaking the true effects of gravity are only observable in the separation of two nearby test particles initially moving parallel to one another.
On the other hand, if person A and person B are both massive objects then the story is more complicated. Whether the system is spinning or not becomes very important. We might again imagine that A and B are gravitationally bound to each other, but now that gravitational binding can itself "produce more gravity". In ordinary situations this extra bit is negligible, but sometimes it can matter a lot. For example, a spinning black hole is very different from a stationary black hole. Back to your case of two massive objects orbiting each other, one of the most famous effects is the emission of gravitational radiation. These gravitational waves carry energy away from the system, and the period of the motion can actually decrease. This decrease has actually been observed precisely as predicted by Einstein's theory.
Hope this helps.
But...in what situation would someone's "nonremovable" kinetic energy be zero? The only situation I can think of is someone going 50 mph, then someone going at the same EXACT speed, then relative to each other their kinetic energy would be zero, right? But work is still being done, even relative to both travelers, therefore kinetic energy couldn't be zero.
But that doesn't make any sense. How can something have kinetic energy yet not have it at the same time in the same reference frame?
(Q) I never saw you responce, I guess I passed over it, but let me rephrase my scenerio...
Both Person A and Person B have mass
Person B is circling around Person A at .9C
Relative to person B, Person A is spinning at .9C. Something that has a great acceleration over a small period of time produces a stronger gravitational field. Wouldn't it be true then that Person A, spinning at a speed of .9C relative to Person B,
would create a greater gravitational field due to the fact that he's accelerating greatly over such a small period of time?
Thanks, PhysicsMonkey!
What I mean by it is "The kinetic energy that can't be removed by switching to a different inertial reference frame", or "the kinetic energy in the inertial reference frame in which the average kinetic energy is smallest".
So the "nonremovable kinetic energy" of any object that is not accelerating is zero... because that object is not moving in its rest frame (obviously), and if it's not accelerating, then its rest frame is inertial, right?
Firstly, I don't think "nonremovable kinetic energy" is a commonly used term, because I just made it up a couple of posts ago.Votorx said:
What I mean by it is "The kinetic energy that can't be removed by switching to a different inertial reference frame", or "the kinetic energy in the inertial reference frame in which the average kinetic energy is smallest".
So the "nonremovable kinetic energy" of any object that is not accelerating is zero... because that object is not moving in its rest frame (obviously), and if it's not accelerating, then its rest frame is inertial, right?
I'm not completely sure what you're thinking here... no work is being done on any object is constant motion.
Again, I'm not sure what you're getting at... You are correct that a given object in a given reference frame at a given time either has kinetic energy or it doesn't.
2 people are moving at the same speed, they both deaccelerate, then accelerate then deaccelerate (by velocity, not direction) over and over again, both at the same time and at the same rate. Throughout all this, relative to each other their kinetic energy is 0, but isn't work being done? If so, how's that possible if kinetic energy remains zero?
Energy is not frame-invariant as you have noticed here, not even in classical physics. So you don't expect energy to be conserved across different frames as you have described here. If you pick any single inertial frame and stick with it then it makes sense to talk about work, KE, and conservation. Otherwise the conservation laws do not apply to your analysis.
Although energy is not frame invariant what is invariant is the magnitude of the four-momentum, which is essentially the rest mass. The four-momentum is comprised of energy and momentum in the same way that an event is comprised of time and space.
-Dale
Although energy is not frame invariant what is invariant is the magnitude of the four-momentum, which is essentially the rest mass. The four-momentum is comprised of energy and momentum in the same way that an event is comprised of time and space.
-Dale
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