On Four Velocity and Four Momentum

[joigus]

8 hours ago, Anamitra Palit said:

Kino seems to have accepted this relation v1.v2>=c^2

 

Well, yes but:

On 1/28/2021 at 6:48 PM, Kino said:

Um... what?!

You already showed on another thread that for two four velocities u and v their inner product satisfies u.v≥c2 , with equality iff u=v . So what you should expect from (15) is that v−ka is not a four velocity, except in the case that ka=0 . In fact, a moment's thought would tell you that v−ka isn't even necessarily timelike. Furthermore, you already know that a is spacelike, so your m must be imaginary and cannot be 1 as you so blithely assert. This whole line of argument is utterly incoherent.

(my emphasis)

Also:

On 12/23/2020 at 9:42 AM, Markus Hanke said:

The mistake you made is assuming that 4-velocities can be any arbitrary 4-vector, but that isn‘t true - all 4-velocities are 4-vectors, but not all 4-vectors are automatically 4-velocities.

(my emphasis)

Also:

On 1/27/2021 at 8:12 AM, Ghideon said:

Please also explain why this is posted in relativity section if your mathematics is not about physics. 

This recurring point is what I mean by off-shell. Can you address any of these questions?

You can get all kinds of weird things by adding 4-vectors, one pointing to the past light-cone, and another pointing to the future light-cone. You can obviously get the 4-vector,

\[\left(u^{0},\boldsymbol{u}\right)+\left(-u^{0},\boldsymbol{u}\right)=\left(0,2\boldsymbol{u}\right)\]

But that's unphysical. That's what we're trying to tell you.

[studiot]

1 hour ago, joigus said:

Well, yes but:

(my emphasis)

Also:

(my emphasis)

Also:

This recurring point is what I mean by off-shell. Can you address any of these questions?

You can get all kinds of weird things by adding 4-vectors, one pointing to the past light-cone, and another pointing to the future light-cone. You can obviously get the 4-vector,

 

(u0,u)+(−u0,u)=(0,2u)

 

But that's unphysical. That's what we're trying to tell you.

Your analysis so clearly demonstrates the dangers of simply playing about with algebra and symbols without  properly understanding what those symbols mean.

+1

[Phi for All]

11 hours ago, Anamitra Palit said:

There is no reason to believe that by discussion is of a speculative nature.Requesting the moderator to restore it to its normal status.

!

Moderator Note

On the contrary, you haven't supported your ideas, nor have you adequately addressed the questions and concerns you've amassed in the last four pages, so you're still pushing against mainstream physics without evidence. You ignore the posts that refute or challenge your thinking, and you keep repeating points that were covered in the posts you ignored. That's not discussion, that's soapboxing, and it's not conducive to meaningful discussion.

This thread is closed, and since you can't support the ideas within the boundaries of our rules, please don't bring it up again.