# Relativistic Mass vs. Invariant Mass.

#### DNMock

Hey all, I'm quite confused on this and am curious to be put straight. Now I understand the basic principles of relativity, this one just bugs me.

Now I have always been taught that the famous E=MC^2 formula was proof that mass would reach toward infinity as it neared the speed of light. Stephen Hawking even says "Because of the equivalence of energy and mass, the energy which an object has due to its motion will add to its mass." in his book A Brief History of Time.

Now I was informed by some other members that this isn't really the case, and that the whole notion of a massive object approaching the speed of light would not collapse into a black hole, etc. etc. and I believe them to be correct in their assessment.

So what is going on here, and why am I reading two very different views on a similar subject, or are they both correct and it's just the Mr and Mo terminology that is off and screwing everything up

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#### atyy

The statement by Hawking presumably refers to the relativistic mass in special relativity, which does not include gravity, nor black holes.

In general relativity, there are several notions of mass. One notion is the stress-energy tensor, which determines the curvature of spacetime. A counterpart of the relativistic mass forms only one component of the stress-energy tensor, so "moving" fast does not necessarily lead to the formation of a black hole. The sorts of motion that lead to collapse can be studied beginning with the http://www.ias.ac.in/pramana/v69/p15/fulltext.pdf".

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#### PAllen

Also, note that the invariant mass of a system of particles does include a contribution from the relative motion of the particles. Thus the kinetic energy of gas contributes mass towards 'becoming a black hole', but overall motion of a ball of gas relative to something else does not.

#### Phrak

The statement by Hawking presumably refers to the relativistic mass in special relativity, which does not include gravity, nor black holes.

In general relativity, there are several notions of mass. One notion is the stress-energy tensor, which determines the curvature of spacetime. A counterpart of the relativistic mass forms only one component of the stress-energy tensor, so "moving" fast does not necessarily lead to the formation of a black hole. The sorts of motion that lead to collapse can be studied beginning with the http://www.ias.ac.in/pramana/v69/p15/fulltext.pdf".
Wait. Several? Are there more than two?

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#### PAllen

Wait. Several? Are there more than two?
See, for example: http://relativity.livingreviews.org/Articles/lrr-2009-4/ [Broken]

Among others: ADM, Komar, Bondi, Bartnik, Hawking

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#### ?????

Now I have always been taught that the famous E=MC^2 formula was proof that mass would reach toward infinity as it neared the speed of light. Stephen Hawking even says "Because of the equivalence of energy and mass, the energy which an object has due to its motion will add to its mass." in his book A Brief History of Time.

Now I was informed by some other members that this isn't really the case, and that the whole notion of a massive object approaching the speed of light would not collapse into a black hole, etc. etc. and I believe them to be correct in their assessment.
Your formula is wrong. I can't really type it as I want on this post but it looks like the following E=(MC^2)/(1-v^2/C^2)^.5. As velocity v gets larger, the total energy of mass M gets larger. But this is a relative mass - a guy riding on M will not see any change in the value of M no matter how big v is.

Think of it this way. Guy 1 is on mass M and guy 2 is on another mass stationary relative to mass M. Now Guy 2 and his mass accelerate to high v. Well, nothing has happened to guy 1 and mass m, but guy 2 still sees a relative velocity of v. So guy two can do experiments that will show that mass M is now larger by the formula I gave you above. But nothing has actually happened to guy 1 and mass M. That's why Einstein called it Relativity Theory.

#### Phrak

See, for example: http://relativity.livingreviews.org/Articles/lrr-2009-4/ [Broken]

Among others: ADM, Komar, Bondi, Bartnik, Hawking
Thanks. I'd forgotten.

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#### jtbell

Mentor
In the early days of relativity people sometimes used "transverse mass" and "longitudinal mass" in connection with the effects of forces perpendicular and parallel to an object's motion, in F = ma.

#### harrylin

Hey all, I'm quite confused on this and am curious to be put straight. Now I understand the basic principles of relativity, this one just bugs me.

Now I have always been taught that the famous E=MC^2 formula was proof that mass would reach toward infinity as it neared the speed of light. Stephen Hawking even says "Because of the equivalence of energy and mass, the energy which an object has due to its motion will add to its mass." in his book A Brief History of Time.

Now I was informed by some other members that this isn't really the case, and that the whole notion of a massive object approaching the speed of light would not collapse into a black hole, etc. etc. and I believe them to be correct in their assessment.

So what is going on here, and why am I reading two very different views on a similar subject, or are they both correct and it's just the Mr and Mo terminology that is off and screwing everything up
Indeed it's mainly a matter of terminology: nowadays it has become most popular to mean with "mass", "rest mass". And it should be clear from the principle of relativity that an object can only collapse into a black hole if it has a great rest mass.

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