|Jan26-04, 06:15 AM||#1|
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
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)
P = (E/c,p)
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
|Jan26-04, 07:04 AM||#2|
In the page listed above there is mention of relativistic mass density as an invariant. To see what this means please see
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.
|Jan26-04, 08:06 AM||#3|
|Jan26-04, 09:37 AM||#4|
Relativistic Mass as "Gravitational Charge"
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.
|Jan26-04, 10:10 AM||#5|
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.
|Jan26-04, 10:31 AM||#6|
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 Tab refered 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 Tab 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 arguement if they don't back it up with a valid arguement 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 [i]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
|Feb7-04, 07:18 AM||#7|
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.)
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