Equivalence of mass, energy and gravity

[xchaos01]

Hi guys, I'd like to hear what you think about a little thing I did talking about the equivalence of mass, energy and gravity. I used planet Earth as an example.

Here's the link to the .docx Word file:
http://www.angelfire.com/bug/chaos1/Gravity_Rotation.docx"

My premise is that the more energy an object has the more mass, and the more mass the more gravity.

Thanks. P.S. If you have any problems with the file let me know.

 

[xchaos01]

I'll try and find a way to paste the document "as is" so you don't have to go through downloading it. If you know a way to convert it, specifically referring to the equation editor objects in Word please let me know. Thanks.

 

[xchaos01]

Alright, I put it picture format, so here it is:
(Please Comment)

[PLAIN]http://img72.imageshack.us/img72/7392/gravityrotation.gif

 

[xchaos01]

Anyone care to comment?(bump)

 

[ZikZak]

Why, after discussing the Relativistic concept of mass-energy equivalence, are you then reverting to Newton's explicitly non-Relativistic theory of gravity?

Unfortunately, General Relativity is more complicated than replacing "m" by "E" in Newton's equations.

 

[xchaos01]

Verry good observation, I'll have to revisit the gravity equations...

But still, on the main premise, does it add to the gravitational force or not?

 

[Rasalhague]

Taylor/Wheeler: Spacetime Physics:

Does Einstein's statement that mass and energy are equivalent mean that energy is the same as mass? No. Value of energy depends upon inertial frame of reference from which the particle (or system of particles) is regarded. Value of rest mass is independent of inertial frame. Energy is only the time component of a 4-vector. The time component gives the magnitude of the 4-vector only in the special case in which that 4-vector has no space component; that is when the [3-]momentum of the particle (or the total [3-]momentum of the system of particles) is zero. Only in this special case does energy have the same value as rest mass.

[...]

The distinction between mass and energy is this: mass measures the magnitude of a 4-vector and energy measures the time component of the same vector. Any feature of any discussion that emphasizes this contrast is an aid to understanding. Any slurring of terminology that obscures this discinction is a potential source of error or confusion.

Perhaps the expression "mass-energy equivalence" should be numbered among such slurrings.

The famous equation E = mc² can be understood in two ways. Einstein's own preference was to treat mass here as the coordinate-independent kind, sometimes called rest mass; in that case, the equation says that the energy of a system is equal to its mass, times c squared, in a reference frame where the system has no 3-momentum, i.e. its rest frame ( http://physics.princeton.edu/~mcdonald/examples/EM/hecht_ajp_77_804_09.pdf ); this is the viewpoint recommended by Taylor and Wheeler who say it's best to dispense with the concept of relativistic mass. Others interpret the famous equation as saying the energy of a massive system equals its relativistic mass times c squared.

A more revealing equation is m²=E/c²-p², where m is (rest) mass, E total energy, and p the Euclidean norm (magnitude) of 3-momentum. This also applies to systems with no mass, so the energy of a photon is equal to the magnitude of its 3-momentum.

 

[xchaos01]

Thanks for the replies guys.

Ok, I'll just leave with this simple question: Does the rotational kinetic energy add to a body's gravity?

 

[Antiphon]

Thanks for the replies guys.

Ok, I'll just leave with this simple question: Does the rotational kinetic energy add to a body's gravity?

Yes. Angular momentum would show up along with pressure and shear stresses.
The sources of gravity are found in the 16 terms of the Stress-Energy tensor.
There is part of it that has your mc^2 in it. Other parts capture every other
kind of energy that will create gravity.

They are all depicted here: http://en.wikipedia.org/wiki/File:StressEnergyTensor.svg
Get a good book on General Relativity and it should spell it out for you.

 

[Passionflower]

...
Value of rest mass is independent of inertial frame.
...

But on the other hand the saying is actually nothing more than a tautology. The rest mass of a body is simply the mass measured by an inertial frame at rest with this body.

By the way, elementary particles, which are allegedly the source of rest mass are seldom at rest.