I hope cavediver doesn't mind me answering some of this for him; he is welcome to clarify my statements if needed.
quote:
Could you give an example of the "right context" where (m) would increase with (v)?
The problem is that the terms are somewhat vague and are used in different ways. In many fields (e.g. particle physics), the term "mass" is understood to mean a particle's invariant "rest mass," and relativistic particles are not described in terms of their increasing mass, but in terms of their increasing
kinetic energy. But it is also OK to think of the particle's effective mass as increasing.
Perhaps this is a clearer way to express the original statement:
The effective or equivalent mass of an object increases with the velocity of that object relative to an observer who is measuring its mass.
quote:
SR tells us that in the frame of reference of the photon the Earth is traveling at (c), and thus it's (m) should increase, if I'm not mistaken, eventually causing the Earth to collapes into a blackhole, which is obviously not the case. So, in relativity, how would (m) increase with (v)?
Interesting scenario. But remember that in addition to
mass,
length and
time are also relative. From the perspective of a photon, the earth has infinite mass, is an infinitely thin flat disc, and has its time frozen. So the "eventual" collapse will never come. (But I'm somewhat nervous about mixing gravity and SR as your scenario does; this is probably a better question for GR.)
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