# Kinetic energy and gravity

1. Nov 19, 2008

### WCOLtd

Energy = mass times the speed of light squared

does this mean energy and mass are completely interchangable? Where ever I see energy can I just divide it by c^2 to get that system's mass value?

Take for example two systems;
In the first system there are two bodies of mass moving towards each other at 1 m/s. there is a reference particle, initially at rest and located at large distance (r) from the area at which these two bodies of mass impact each other.

From the time both bodies of mass are away from each other, to the point at which they impact, the displacement of the reference particle is measured and recorded and the the displacement is divided by the time interval between those two events to determine the average gravitational acceleration by the two bodies of mass.

In the second system there are two bodies of mass moving towards each other (of equal mass as the first system) but they are moving towards each other at a much greater rate - .99c. Will the gravitational acceleration of the reference particle (located at distance r) be different than in the first system?

In other words, does the kinetic energy of any system effect it's gravitational field?

2. Nov 19, 2008

### michael879

yes.

also, yes.

This can be thought of in another way (that's not entirely accurate but it illustrates the point). An object moving at .99c will have a much greater observed mass than one traveling at 1 m/s. The gravitational field is proportional to the mass of the object, so the object should have more gravity.

3. Nov 19, 2008

### Staff: Mentor

This is incorrect. The key mistake is the part in bold. In relativity, gravitation is related to the http://en.wikipedia.org/wiki/Stress-energy_tensor" [Broken]

Last edited by a moderator: May 3, 2017
4. Nov 19, 2008

### WCOLtd

I think I've got it now, gravity is proportional to the amount of mass, rest mass, not inertial mass.

What so what is meant by "The mass increases as kinetic energy approaches c" is not the rest mass, but rather the momentum, the inertial mass in the context F = ma, or the amount of force needed to accelerate the body an extra meter/second beyond .99 c (or whatever its relative speed is).

5. Nov 19, 2008

### michael879

notice:

I know the example I gave is wrong, I was just trying to illustrate the point. A moving object does have more gravitation than one at rest tho right? Just because an object approaching c doesn't become a black hole doesn't mean it's gravitational field stays the same.

Last edited by a moderator: May 3, 2017
6. Nov 20, 2008

### Staff: Mentor

Let's say T is the stress-energy tensor of some mass/energy distribution and G=8πT is the resulting curvature from the Einstein field equations. Now, suppose we have some Lorentz transform matrix, L, representing a boost of v, then G'=L.G and T'=L.G are also solutions to the Einstein field equations G'=8πT'.

So boosting an object simply Lorentz transforms its gravitation. The proper force on any test particle remains the same whether it is the particle or the mass that is "moving".

7. Nov 20, 2008

### michael879

what if mass is converted to kinetic energy though? Does the gravitational field actually decrease??

8. Nov 21, 2008

### Staff: Mentor

Well, you will have to be a little more specific on the details of the scenario you are thinking about.

If you convert mass to kinetic energy in a way which does not change the stress energy tensor then the gravitational field will not change. But if you convert mass to kinetic energy in a way which changes the stress energy tensor then the gravitational field will change.

9. Nov 22, 2008

### Vanir

This appears to be right along the lines of something I've been quite wondering about. What exactly do you mean by the bolded sentence?