- #1

- 392

- 0

[tex]p=\gamma mv[/tex]

If anyone could point me in the right direction, I'd much appreciate it.

- Thread starter NanakiXIII
- Start date

- #1

- 392

- 0

[tex]p=\gamma mv[/tex]

If anyone could point me in the right direction, I'd much appreciate it.

- #2

- 329

- 0

Because this is a definition. And so is the relativistic total energy:

[tex]p=\gamma mv[/tex]

If anyone could point me in the right direction, I'd much appreciate it.

[tex]E=\gamma mc^2[/tex]

- #3

- 392

- 0

Another question on the side: I've seen two different versions of the equation for the mass-energy equivalence, one with and one without the gamma factor. What's the difference?

- #4

- 329

- 0

I explained that to you in the other thread (relativisic mass) a few minutes ago.I see. Why is it defined as such, exactly? There must be a reason for adding the so frequently seen gamma, no?

Same reason as momentum, I also explained that to you in the other thread.Another question on the side: I've seen two different versions of the equation for the mass-energy equivalence, one with and one without the gamma factor. What's the difference?

- #5

- 392

- 0

You mean the reason for the gamma is because of the use of relativistic mass? And yet in the other thread you tell me to base relativistic mass on relativistic momentum. That's circular. Are you saying that relativistic mass is a definition and thus relativistic momentum is as well? That would still leave the question of "why the gamma?".The whole darned thing was introduced in order to reconcile the relativistic momentum/energy:

[tex]p=\gamma m(0)v[/tex] (1)

[tex]E=\gamma m(0)c^2[/tex]

with the Newtonian counterpart:

[tex]p=mv[/tex] (2)

So the best thing is to tell your teacher that your proof is you grouped together [tex]\gamma[/tex] and proper massm(0)into [tex]\gamma m(0)[/tex] and you assigned that quantity tom

- #6

- 329

- 0

"Relativistic mass" is just a misnomer, ok? Try to learn to forget about it, it has no meaning. Tolman's derivation from the other thread has no "relativistic momentum" in it, ok?You mentioned the following:

You mean the reason for the gamma is because of the use of relativistic mass? And yet in the other thread you tell me to base relativistic mass on relativistic momentum. That's circular.

Can't you read ? Relativistic momentum is a definition.Are you saying that relativistic mass is a definition and thus relativistic momentum is as well? That would still leave the question of "why the gamma?".

"Relativistic mass" is an unfortunate misnomer that corresponds to the result of multiplying [tex]\gamma[/tex] by proper mass. It has no physical meaning.

- #7

- 5,697

- 981

an inertial observer (with unit 4-velocity [tex]\tilde t[/tex]

can write that vector as the sum of two vectors, a "temporal" one parallel to [tex]\tilde t[/tex] and a "spatial" one perpendicular to [tex]\tilde t[/tex].

[tex]\gamma[/tex] is [tex]\cosh{\theta}[/tex], the analogue of cosine(angle) , and [tex]\gamma\beta[/tex] is [tex]\sinh{\theta}[/tex], the analogue of sine(angle), where the [Minkowski-]angle [tex]\theta[/tex] (called the rapidity) is between [tex]\tilde P [/tex] and [tex]\tilde t [/tex].

- #8

jtbell

Mentor

- 15,657

- 3,728

There are some leads in this thread from last year:I can't seem to dig up any derivation for the equation for relativistic momentum:

[tex]p=\gamma mv[/tex]

https://www.physicsforums.com/showthread.php?t=107361

(which I should have thought of looking for when I posted in your other thread about relativistic mass)

- #9

- 329

- 0

There is an even better one here.There are some leads in this thread from last year:

https://www.physicsforums.com/showthread.php?t=107361

(which I should have thought of looking for when I posted in your other thread about relativistic mass)

- Replies
- 78

- Views
- 55K

- Last Post

- Replies
- 5

- Views
- 3K

- Last Post

- Replies
- 6

- Views
- 8K

- Last Post

- Replies
- 5

- Views
- 3K

- Replies
- 13

- Views
- 15K

- Replies
- 11

- Views
- 9K

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 6

- Views
- 2K

- Replies
- 8

- Views
- 4K

- Last Post

- Replies
- 1

- Views
- 823