[Mr. Scientist (OP)]

I propose this equation, which is new, but dimensionally-consistent as being;

P^aP^bη_ab=η^2_0 v^2_f(P_μ,η)-η^2_i v^2_i(P_μ,η)

This is mathematically-consistent as being a dispersion formula.

The left-hand side is in fact the physical equivalance of

P^aP^bη_ab=v^2 (\hbar c/G)

so that

E^2/c^2 - ∏_(n=1)^3 |p^2| = v^2 (\hbar c/G)

Then the equation can become:

E^2-|p^2c^2| = (v^2)^2 \hbar c/G

The relation can be found:

G(\hbar c/G)/ \hbar c = Fvt/Mc^2

and

P^aP^bη_ab = E^2/c^2 - p^2

 

[Geezer]

Fantastic!

What exactly is your question?

[Mr. Scientist (OP)]

The question is bold. Due to the invariant relationship between matter and the presence of geometry, are there points on a spacetime metric which yields the exact fluctuation in question? In the case of only having the geometrical sense of the length of a vector, and no other information, might the solution of the length in question hold a physical importance to the structure of the particle in question, since \hbar c/G reverts to the description of a particle with mass M in a relativistically-invariant habitat?

[syhprum]

To me with only "O" level physics education this reads like the results of one of those jargon generating programs (Perhaps I should be off to university to complete my physics degree)

[lightarrow]

if it were P^μP_μ instead of P^aP^b, and without η_ab (what is it? you haven't defined it), then it would have been an obvious relation.
If you don't define the terms and what you exactly mean, it's not so easy to understand your post...

[Mr. Scientist (OP)]

if it were P^μP_μ instead of P^aP^b, and without η_ab (what is it? you haven't defined it), then it would have been an obvious relation.
If you don't define the terms and what you exactly mean, it's not so easy to understand your post...

P^aP^2P_ab - it refers to rest mass, or rest energy M_0c^2.

[lightarrow]

Then it is obvious: you have written E² = (mc²)² + (cp)², which is a well known equation.

[Mr. Scientist (OP)]

Not quite what i was hoping for. Total fail.

I have more to say - but will do so later..

[Mr. Scientist (OP)]

Then it is obvious: you have written E² = (mc²)² + (cp)², which is a well known equation.

Let's do this properly. The answer to your reply is no. I had to look for a corresponding equation to varify it's use. If it had dimensions of E^2, it would not fit the description P^aP^2P_ab - originally i gave this as M_0c^2, which was incorrect - whilst technically P^aP^2P_ab is rest mass, it has the dimensions M^2c^2.

Lorentz covariance - Wikipedia, the free encyclopedia.mht

[lightarrow]

I still don't understand what you mean.
Don't know, maybe it's me...

[Mr. Scientist (OP)]

I still don't understand what you mean.
Don't know, maybe it's me...

You don't know the expression P^2b^2n_ab? Did you follow the link for a reference to it?