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my question is that if the mass of an object increases, wouldn't it collapse into a black hole before we had to worry about requiring infinite energy to accelerate it?

clearly i am wrong cuz thats not it so what am i missing?

- Thread starter Routaran
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my question is that if the mass of an object increases, wouldn't it collapse into a black hole before we had to worry about requiring infinite energy to accelerate it?

clearly i am wrong cuz thats not it so what am i missing?

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By inputting energy in getting the particle to move up to some critical fraction of the speed of light, at some point you might not tell the difference in an inertial frame between a sufficiently large collection of particles with finite rest mass that can locally collapse spacetime on itself vs. a particle with large relativistic mass that can do the same. The only difference between the two cases would be the role that quantum uncertainty would play, which plays a big role in whether a black hole can form.

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jtbell

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A dollar bill is equivalent to a dollar in gold, but the bill is not gold.

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Here's the simple answer:

The equation:

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

describes the relationship between the total energy of an object, its speed, and its invariant (rest) mass, where [itex]\gamma=1/\sqrt{1-v^2/c^2}[/itex].

Similarly:

[tex]\mathbf{p}=\gamma m\boldsymbol{v}[/tex]

gives the momentum of an object.

Back when Special Relativity was new, physicists (I'm not sure whether or not Einstein came up with the idea) invented something called the "relativistic mass" which is given by [itex]m_r=\gamma m[/itex] so that the energy and momentum equations simplify to:

[tex]E=m_rc^2[/tex]

[tex]\mathbf{p}=m_r \boldsymbol{v}[/tex]

The relativistic mass increases with increasing velocity. The invariant (some would say "real") mass does not. Almost all physicists have abandoned the idea of relativistic mass nowadays because it has proven to be pretty much useless. The only people who haven't done away with it are authors of science books directed at people with little to no physics background because they think it makes things more intuitive. In my opinion, it only serves to confuse people who want to go deeper into the subject.

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[itex]m_r[/itex] was invented by Newton (see definition II) but it was invariant in classical mechanics and it was simply called mass. When Einstein replaced Galilei transformation by Lorentz transformation [itex]m_r[/itex] became velocity dependent.Back when Special Relativity was new, physicists (I'm not sure whether or not Einstein came up with the idea) invented something called the "relativistic mass" which is given by [itex]m_r=\gamma m[/itex] so that the energy and momentum equations simplify to:

[tex]E=m_rc^2[/tex]

[tex]\mathbf{p}=m_r \boldsymbol{v}[/tex]

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Exactly. The question raised in the original post is proof of just that. Routaran, relativistic mass doesn't gravitate. It is better to think of invariant mass as the cause.The relativistic mass increases with increasing velocity. The invariant (some would say "real") mass does not. Almost all physicists have abandoned the idea of relativistic mass nowadays because it has proven to be pretty much useless. The only people who haven't done away with it are authors of science books directed at people with little to no physics background because they think it makes things more intuitive.In my opinion, it only serves to confuse people who want to go deeper into the subject.

As far as why "almost all physicists have abandoned the idea of relativistic mass nowadays": Look at the equation for relativistic mass: [itex]E=m_rc^2[/itex]. Relativistic mass is just a synonym for energy. Energy is a useful concept; relativistic mass, much less so.

That is too much historical revisionism. Newton knew nothing about special relativity; it was a couple of hundred years after his time. To say that Newton invented the concept of relativistic mass is worse than wrong; it is wronger than wrong. Newton didn't invent the concept of mass, either. Newton himself attributes his first two laws and his first several definitions to his predecessors.[itex]m_r[/itex] was invented by Newton (see definition II) but it was invariant in classical mechanics and it was simply called mass.

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<irony>Really?</irony>Newton knew nothing about special relativity; it was a couple of hundred years after his time.

Please carefully read what I wrote. I never claimed that Newton invented the concept of relativistic mass. In fact I mentioned that the mass as used Newton's definition II was invariant in classical mechanic and became relativistic in SR.To say that Newton invented the concept of relativistic mass is worse than wrong; it is wronger than wrong.

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