Relativistic Mass as Gravitational Charge

[Arcon]

Relativistic Mass as "Gravitational Charge"

I've just made a new page for the GR portion of my web site. In it I derived Einstein's field equation but with a different slant. I've decided to go with the "relativistic mass" as source of the gravitational field rather than the "energy as source" view. As such I used the mass tensor, M, that I defined here
http://www.geocities.com/physics_world/sr/mass_tensor.htm

The difference being only a constant of proportionality. The relationship between the mass tensor M and the energy-momentum tensor T is analogous to the relation E = mc². The difference in meaning of these tensors is analogous to the question as to whether 4-momentum should be defined as

P = (mc,p)

or as

P = (E/c,p)

http://www.geocities.com/physics_world/gr/einsteins_field_equations.htm

Relativistic mass, aka mass-energy, plays the role of a gravitational charge in general relativity.

Of course this is exactly what is meant in Gravitation, Misner, Thorne and Wheeler, on page 404

Mass is the source of gravity.

 

[Arcon]

Invariance of relativistic mass

In the page listed above there is mention of relativistic mass density as an invariant. To see what this means please see

http://www.geocities.com/physics_world/ma/invariant.htm

and note that when one is speaking of energy/relativistic mass in relativity then one is neccesarily speaking of a particular Lorentz observer since the concept of energy relativity has no meaning until a frame of referance has been chosen. Each frame of reference defines an observer and to each observed there is a 4-velocity and to each 4-velovity of an observer there is a relativistic mass which is an invariant such as the scalar product of the observers 4-velocity with a particle's 4-momentum or the contraction of the mass-tensor, i.e. (energy-momentum tensor)/c[sup2[/sup], with the observer's 4-velocity.

The link I posted above in this post makes clear the exact meaning of this.

Arcon

 

[DW]

Originally posted by Arcon
...I derived Einstein's field equation but with a different slant. ...I used the mass tensor, M...

Changing the units of the stress energy tensor and inappropriately calling it a mass tensor in a typical textbook presentation of the field equations is hardly deriving them with a new slant.

 

[Arcon]

Originally posted by DW
Changing the units of the stress energy tensor and inappropriately calling it a mass tensor in a typical textbook presentation of the field equations is hardly deriving them with a new slant.

Then you failed to understand the topic of this thread.

Mass is defined one way

Energy is defined another way

It is proven that Energy = mass*c²


Therefore your comment about renaming is bogus. Your comment about it being "inappropriately called" a mass tensor is also bogus. Please refrain from making such claims unless you're prepared to back them up with something more than Cuz I says so! kind of arguements. Prove it or don't mention it.

Please read the topics and derivations more carefully before you try posting again.

 

[selfAdjoint]

And you please don't use flame words like "bogus". The burden is upon you to support your novel approach, not upon others to disprove it.

 

[Arcon]

Originally posted by selfAdjoint
And you please don't use flame words like "bogus".

The term bogus is not a flame word. Why would you say it was?

The term bogus is defined as not genuine. When waite (aka "dw") made the claim that it's "inappropriate" and does not back his claim up then he's not making a genuine claim. He's commenting on a proof of something and making a claim that something is wrong and making no effort to support his claim that there is an error (e.g. "inappropriate") in that proof.

If you prefer then I'll change from "bogus" to "not genuine" but I don't see the point.

And what I've posted is not a novel approach by any means whatsoever. In fact Misner, Thorne and Wheeler defined a similar tensor in their text. While I call mine the "mass tensor" they refer to theirs as the "inertial mass tensor." Plus I'm not the first to use the term "mass tensor." I think its defined in other places each having a different meaning.


If you've never seen it its because the mass-energy relation has been employed when it never really has been before. waite has never seen the T^ab referred to as anything other than "energy-momentum tensor" or "stress-energy tensor" or "stress-energy tensor" etc. However it does go by different names in the physics literature and the components are called different things in the literature. The reason for these different names is Einstein's mass-energy equivalence relation, which waite is claiming that it's all just a meaningless multiplication by a constant. These other names are just not used that often. As explained in the derivation the quantity T^ab was referred to as the material energy tensor by Dirac. I've just placed the in a different form. Also in that derivation I employed the Newtonian tidal force tensor - something waite told me that he never heard of (i.e. he claimed it doesn't exist) so that's probably why he was making these non-genuine claims.


The link I provided in the first post is the derivation. It is there that I back up what I said. Of course this is nothing new since MTW do the same thing. i.e. rho = T(U,U). I suggest that anyone who is going to claim that it's wrong prove what they say rather than simply say "You're wrong". Do you consider "You're wrong." a valid argument if they don't back it up with a valid argument why they claim that it's wrong?

I.e. prove which equation is incorrect and prove how it led to an error or show why an error led the to a correct result.


Again - what I did was nothing new. Just rarely seen nowadays. In fact this is in some of the best physics texts that their are. Plus - I've already supported this in the page that I posted with the derivation. The only thing that is different is a different view. i.e. instead of defining T⁰⁰ as energy density[/sup] Einstein's mass-energy equivalence E = mc² is employed to write T⁰⁰ = c[su]2[/sup] rho. But that's widely done in the physics literatur which has been pointed out to waite hundreds of times. In all those hundreds of response in the past all he did was to repeat his claim with no effort made of backing it up.

For a similar approach see
http://assets.cambridge.org/0521422701/sample/0521422701WS.pdf

The burden is upon you to support your novel approach, not upon others to disprove it.

To be precise - If I have a "novel approach" and I support it then the burden shifts to those who claim that its wrong to prove their claim.

 

[treat2]

Originally posted by Arcon
Then you failed to understand the topic of this thread.

Mass is defined one way

Energy is defined another way

It is proven that Energy = mass*c²


Therefore your comment about renaming is bogus. Your comment about it being "inappropriately called" a mass tensor is also bogus. Please refrain from making such claims unless you're prepared to back them up with something more than Cuz I says so! kind of arguements. Prove it or don't mention it.

Please read the topics and derivations more carefully before you try posting again.

I'm but a lowly Software Developer, but I think what might have been missed in the original equation posted: E = M*C^2,
is that, that is NOT Einstein's ACTUAL Equation.

It is my understanding that Einstein's Equation is often misunderstood because of a missing Subscript of Zero for the "E".
I could be wrong about this, but I recall his equation to be:
Eo = M*C^2

(Sorry, I'm not certain how to make a subscript. I'd be interested in knowing though, how all those neat symbols are being created in the math posts I've seen. It would be of some use to my posts, if anyone cares to enlighten me how to do it. Thanks in advance, if you do. PM me, if you wish.)

 

[Phobos]

Welcome to Physics Forums, treat2!

Sorry to come down on this thread, but I'd prefer not to revive this particular Arcon-DW debate.

Your question is welcome...please start a new topic/thread for it if you want.