I have a conceptual question about relative mass

[DrStupid]

I don't know, why anybody is insisting on this confusing idea of relativistic masses (in fact when you introduce a relativistic mass it were even direction dependent, which has been said already above or recently in another thread in this forum).

If a "relativistic mass" depends on direction is a matter of its definition. E/c² for example is independent from direction. There is no reason to start such discussions over and over again. It is sufficient to advice against the use of relativistic mass. That has been done in this thread.

 

[vanhees71]

Why don't you just use $E/c^2$ without naming it (in my opinion errorneously) "mass"? There is no need for renaming well-established quantities such that the language confuses the facts. An energy is an energy and mass is invariant mass! Obviously it's not sufficient to give the said advice, because you still insist on using "relativistic mass" in addition to the physically one and only mass, which is the invariant mass.

 

[PeterDonis]

How can we see that if we don't even know what "amount of material" means?

Because whatever it means, it can't be frame dependent, and relativistic mass is frame dependent.

And invariant mass can't be "amount of material" either, because "amount of material" should be additive, and invariant mass is not.

Please do not post in this thread again about "amount of material"; it is a thread hijack and will get you a warning and a thread ban. As I said before, if you want to discuss possible relativistic (or non-relativistic, for that matter) definitions for "amount of material", please start a separate thread on that topic.

 

[PeterDonis]

I don't know, why anybody is insisting on this confusing idea of relativistic masses

Because that is the topic of this thread. If you don't want to discuss relativistic masses, don't post in this thread. If you want to discuss what "amount of material" means, whether in relativity or Newtonian mechanics, then please, as I said to @DrStupid, start a separate thread. Don't hijack this one.

 

[DrStupid]

Why don't you just use $E/c^2$ without naming it (in my opinion errorneously) "mass"?

Because we are talking about relativistic mass.

 

[PeterDonis]

Why don't you just use $E/c^2$ without naming it (in my opinion errorneously) "mass"?

Because this thread is about relativistic mass. Pointing out that it is the same thing as $E / c^2$ is fine, although even that was not always true in historical usages of the term "relativistic mass" (I referred to longitudinal vs. transverse mass in an earlier post).

 

[anuttarasammyak]

If mass increases with velocity(v), can I say velocity is a quantity dependent on (v)?

I would rather say
If mass does not increase with velocity(v), we say velocity is a quantity dependent on v.
Such a velocity is called 4-velocity. 4-velocity explains that we cannot go beyond c.

If mass increase with velocity, we can keep using traditional velocity(v). Here mass=mass(v) explains that we cannot go beyond c.

Using the factor $\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$
One attribute it to velocity $u(v)=v\gamma$. The other attribute it to mass $m(v)=m\gamma$ in the momentum
$$p=\gamma \cdot m \cdot v=(\gamma \cdot v)\cdot m=(\gamma \cdot m )\cdot v$$
Two ways do not contradict but the modern way is the former, 4-velocity method, which you observe variable v is enclosed in one variable leaving the other a constant.