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General relativity


momo1788
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Hi guys!

 

Before i begin, i apologize for my language, english is not my first language.

 

After an introduction to the special theory of relativity during my mechanical engineering studies, i started to read some stuff about the general one. What i read was that energy deform the space-time continuum and that this property of the geometry of the space-time continuum was the new explanation pour the gravity instead of the concept of "gravitational force" that introduces Newton.

 

Then, I asked myself the following question: According to the equation of einstein that link mass and energy, i though that the kinetic energy of a car going at a very high speed, let say 99.9c, could deform the space-time due to its enormous energy and then increase it's gravity effect around it. So I suppose if I was near this car, i would be attract actually by the car!

 

Is it correct to interpret this experience like this?

 

I also have a second question:

 

I heard that we were looking (well, the physicians) for particles which were "the vector"(i really have no idea about the word i should use about that...) of forces. I also heard that there were looking about the graviton, which should the particle that "create" gravity. But, why? I mean, if the gravity is a geometry result of the space-time, then it should not be a force like the nuclear forces for example, no?

 

Already thanks for the answers!

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Then, I asked myself the following question: According to the equation of einstein that link mass and energy, i though that the kinetic energy of a car going at a very high speed, let say 99.9c, could deform the space-time due to its enormous energy and then increase it's gravity effect around it. So I suppose if I was near this car, i would be attract actually by the car!

 

 

If the car was passing at 99.9c how long would you be near the car?

 

If you were moving along with the car you would not see a relative motion of 99.9c

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If the car was passing at 99.9c how long would you be near the car?

 

If you were moving along with the car you would not see a relative motion of 99.9c

 

okay, but my question is more about the deformation of space-time. Does an object with a high kinetic energy modify the geometry of space-time, thus create a gravitational effect bigger than the same object without kinetic energy?

Edited by momo1788
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According to E=Mc^2 and general relativity theory; yes -

 

As an objects velocity increases so does its mass, and thanks to newtons use of the inverse square law in his gravitational equation, we can conclude that a greater mass means greater gravitational force. Thus a greater warping of spacetime.

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According to E=Mc^2 and general relativity theory; yes -

 

As an objects velocity increases so does its mass, and thanks to newtons use of the inverse square law in his gravitational equation, we can conclude that a greater mass means greater gravitational force. Thus a greater warping of spacetime.

 

Your conclusion is correct, but your logic is flawed. Newton's inverse square law is a statement about rest mass, not relativistic mass. The reason that an object with large kinetic energy would have a greater gravitational influence is because the components of the stress-energy tensor are larger.

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Your conclusion is correct, but your logic is flawed. Newton's inverse square law is a statement about rest mass, not relativistic mass. The reason that an object with large kinetic energy would have a greater gravitational influence is because the components of the stress-energy tensor are larger.

 

Aha, thank you for clearing that up. I thought I'd over looked something a bit :blink:

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Your conclusion is correct, but your logic is flawed. Newton's inverse square law is a statement about rest mass, not relativistic mass. The reason that an object with large kinetic energy would have a greater gravitational influence is because the components of the stress-energy tensor are larger.

 

Thanks, it helps.

 

I also just saw, for my second question about the graviton, that the stress-energy tensor is linked with the graviton. So, I will try to understand what is a tensor^^.

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Thanks, it helps.

 

I also just saw, for my second question about the graviton, that the stress-energy tensor is linked with the graviton. So, I will try to understand what is a tensor^^.

 

The Einstein field equations say that the stress-energy tensor (a mathematical object which contains the information about the energy and momentum distribution of spacetime) is proportional to the Einstein tensor (a mathematical object which contains the information about the curvature of spacetime).

 

As for your second question: physics creates models that represent the physical world. The usual interpretation of General Relativity is a literal one - that spacetime is "really" curved. You can also model gravity as a spin-2 massless field (gravitons) on a flat (non-curved) spacetime background. The math and predictions are equivalent. What is different is how we interpret them.

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The Einstein field equations say that the stress-energy tensor (a mathematical object which contains the information about the energy and momentum distribution of spacetime) is proportional to the Einstein tensor (a mathematical object which contains the information about the curvature of spacetime).

 

As for your second question: physics creates models that represent the physical world. The usual interpretation of General Relativity is a literal one - that spacetime is "really" curved. You can also model gravity as a spin-2 massless field (gravitons) on a flat (non-curved) spacetime background. The math and predictions are equivalent. What is different is how we interpret them.

 

 

 

hum...but, if we found a proof of the graviton's existence, this should be in contradiction with general relativity, isn't it? Or these two theories could be both valid due to there mathematical equivalence?

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hum...but, if we found a proof of the graviton's existence, this should be in contradiction with general relativity, isn't it? Or these two theories could be both valid due to there mathematical equivalence?

 

No more of a contradiction that electric/magnetic fields and waves, and photons. The quantum nature of gravity is only important at small distances and/or strong gravity; otherwise both descriptions have to give the same result.

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elfmotat wrote ------------------------

Your conclusion is correct, but your logic is flawed. Newton's inverse square law is a statement about rest mass, not relativistic mass.

--------------------------------------------

Newton's inverse square law is merely an approximation to the gravitational field. It's Einstein's General Theory of Relativity which is the correct statement for all values of stress, energy and momentum. It is more correct to place relativistic mass in place of rest mass rather than rest mass which seems to be what you're doing. There is an illustrating example from the American Journal of Physics.

 

Measuring the active gravitational mass of a moving object, D.W. Olson and R.C.Guarino, Am. J. Phys. 53(7), July 1985. The abstract reads

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Abstract - If a heavy object with rest mass M moves past you with a velocity comparable to the speed of light, you will be attracted gravitationally towards its path as thought it had an increased mass. If the relativistic increase in active gravitational mass is measured by the transverse (and logintudinal) velocities with which a moving moving mass induces in test particles initially at rest near its path, then we find, with this definition, tha M_rel = gamma[ 1 + (v/c)^2]M. Therefore , in the ultrarelativistic limit, the active gravitational mass of a moving body, measured in this way, is not gamma*M but is approximately 2*gamma*M.

--------------------------------------------

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elfmotat wrote ------------------------

Your conclusion is correct, but your logic is flawed. Newton's inverse square law is a statement about rest mass, not relativistic mass.

--------------------------------------------

Newton's inverse square law is merely an approximation to the gravitational field. It's Einstein's General Theory of Relativity which is the correct statement for all values of stress, energy and momentum. It is more correct to place relativistic mass in place of rest mass rather than rest mass which seems to be what you're doing. There is an illustrating example from the American Journal of Physics.

 

Measuring the active gravitational mass of a moving object, D.W. Olson and R.C.Guarino, Am. J. Phys. 53(7), July 1985. The abstract reads

--------------------------------------------

Abstract - If a heavy object with rest mass M moves past you with a velocity comparable to the speed of light, you will be attracted gravitationally towards its path as thought it had an increased mass. If the relativistic increase in active gravitational mass is measured by the transverse (and logintudinal) velocities with which a moving moving mass induces in test particles initially at rest near its path, then we find, with this definition, tha M_rel = gamma[ 1 + (v/c)^2]M. Therefore , in the ultrarelativistic limit, the active gravitational mass of a moving body, measured in this way, is not gamma*M but is approximately 2*gamma*M.

--------------------------------------------

 

I've never seen the inverse square law applied to relativistic bodies before, since it's generally only accurate at low velocities. This is interesting though.

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I've never seen the inverse square law applied to relativistic bodies before, since it's generally only accurate at low velocities. This is interesting though.

I'm delighted to see that you found it interesting. What are you refering to when you said above since it's generally accurate at low velocities.

This can be found in the general relatiivity way back. Since it was already done by the time the 60's had come along, nobody had thought it worth while to do since it was alredy well known. Then things started to change and the literature became more and more different than the past and so the body of the material had changed quite a lot. For example; things like the gravitational field of a directed beam of light came into the literature. See http://home.comcast..../grav_light.htm

 

I had seen these things becomming less and less popular so I put them on my own website. But on my site I decided to make things like a long moving rod. See http://home.comcast...._moving_rod.htm

 

They're very interesting to see and play with. Take the metrics from the web site and copy them on a sheet of paper. The slow the particles down and make the field very very week. You should then see that the results become the Newtonian limit. There's the beginning for one for a sheet of matter.

 

On this page you can see the active gravitational mass in the equations. See http://home.comcast....e_grav_mass.htm If you look carefully you can see the proper mass density and the pressure and how it fits into the equations. If you were to compare this equation with the ones found in general relatvity texts that is what you'll see. Perhaps you might even see it in Schutz's book Gravity From the Ground Up. Some of it is online at Gravity From the Ground Up at http://www.gravityfromthegroundup.org/. You'll see those equations in his GR book as well as Peebles book on Cosmology too. If you take a look at inertial mass you'll see only one term for gravity whereas for a black hole there are there terms. Want to guess why?:) I've see general relativity experts miss that. This is a very good reason for knowing the hows and whys of relativistic mass. You have to know why the answer you get is the way it is. If you see the term "2" instead of, say, "3" you might miss the correct answer. You see, it's not enough to merely get the answer to a problem, but you have to know whether the answer you got is the correct answer. :)

 

Pete

Edited by pmb
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