What does v represent in Einstein's equation with c²-v²?

[Raparicio]

Hello All,

I have a question about photons. In A. Einstein ecuation (about Lorenzt transformation), there's a square root of c^2-v^2. My question is about what is the v represented: a vector? Only one direction vector? Only his module?

best reggards.

R.apaparioscios.

 

[Nylex]

Do you mean (1 - β^2)^1/2, where β = v/c? It's just the size of the velocity, so the modulus.

 

[Raparicio]

Ok

Do you mean (1 - β^2)^1/2, where β = v/c? It's just the size of the velocity, so the modulus.

It's right. Is the modulus, but: could be a paravector?

 

[Nylex]

What's a paravector?

 

[Raparicio]

Paravector

Hello now,

A paravector is a generalization of a vector, with a non-vectorial part and a vectorial part (like complex numbers have Real + Complex number). There are more generenalizations of vectors, like hypercomplex of hamilton, and the most general interesting now is Clifford Algebras and Geometric Algebra.

Could say that a vector is a paravector without escalar part in this example.

my best reggards.

 

[dextercioby]

You'd need a new theory for that.For the Theory of Relativity developed over the last exactly 100 years,that "v" from $\beta$ or $\gamma$ is a scalar,namely $\left|\vec{v}\right|$...That "v" has nothing to do with photons,of course...

Daniel.

 

[marlon]

Hello All,

I have a question about photons. In A. Einstein ecuation (about Lorenzt transformation), there's a square root of c^2-v^2. My question is about what is the v represented: a vector? Only one direction vector? Only his module?

best reggards.

R.apaparioscios.

the v is just an ordinary velocity-vector. It has three dimensions or equivalently it has three components, just like in the case of Lorentz transformations. That's all. The v² is the magnitude of this vector which is determined by calculating the scalar product of this vector with itself.

The v is the velocity of one frame of reference to another...
marlon

 

[Raparicio]

Paravector

the v is just an ordinary velocity-vector. It has three dimensions or equivalently it has three components, just like in the case of Lorentz transformations. That's all. The v² is the magnitude of this vector which is determined by calculating the scalar product of this vector with itself.

The v is the velocity of one frame of reference to another...
marlon

Could be the velocity, a paravector or multivector, and this 'v' its module?

 

[dextercioby]

It could iff u changed the whole theory.It could be pseudovector,the trace of a rank 658 tensor,etc...

Daniel.

 

[Raparicio]

Whole theory?

It could iff u changed the whole theory.It could be pseudovector,the trace of a rank 658 tensor,etc...
Daniel.

Daniel,

What whole theory?

 

[Nylex]

Maybe he means SR, I dunno.

 

[dextercioby]

Yeah,change SR,you'll need to change GR as well.For the time being,they are successful theories and these theories address the velocity in the "gamma-factor" as the modulus of an ordinary 3-vector...

Daniel.

 

[Raparicio]

Dear Daniel and forum,

Have you seen this:

https://www.physicsforums.com/showthread.php?t=69849

Is related about the present post.

best reggards.

 

[Raparicio]

Meaning of SR and GR

Yeah,change SR,you'll need to change GR as well.For the time being,they are successful theories and these theories address the velocity in the "gamma-factor" as the modulus of an ordinary 3-vector...
Daniel.

I'm sorry for my ignorance. What means SR and GR?

 

[dextercioby]

Special Relativity and General Relativity.


Daniel.

 

[Raparicio]

Ok

Special Relativity and General Relativity.
Daniel.

Dear Daniel,

What I say is, what to unify SR an GR, we need to think the same way in both, and Geometrical Algebra provides a new tools to face it. If we take a multivector and apply a generalization of the Bertrand Russell circle, there are very interesting insights.

But this is very confusing to me.

Thanks another time.