If some kind of source was able to supply an infinite amount of energy, does that imply that it also must have an infinite mass? Is the contrary also true?

Aleseelomnl 2022-08-11 Answered
If some kind of source was able to supply an infinite amount of energy, does that imply that it also must have an infinite mass? Is the contrary also true?
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Answers (2)

kidoceanoe
Answered 2022-08-12 Author has 15 answers
It is very dangerous to talk about infinity in physics, especially when talking special relativity.
To your question: Yes the object would need an infinite amount of mass. E.G. Take a battery that would have an finite amount of energy inside.
Then you would have
M Total mass of the battery = M 0 , ( the usual Mass of an uncharged battery ) + E Amount of Energy the Battery can supply c 2
Now If you set lim E of course M Total mass of the battery also diverges

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Meossi91
Answered 2022-08-13 Author has 3 answers
For a photon E = | p | c. When p its energy E but its mass continues being zero.

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consider a particle, A receiving energy from a second one,particle B in a one dimensional collision.
E 2 = p 2 + m 0 2
E d E = p d p
For particle A:
E A d E A = p A d p A ( 1 )
For Particle B:
E B d E B = p B d p B ( 2 )
Now
d E A ∣=∣ d E B ( 3 )
From Conservation of linear momentum we have:
p A + p B = K
where k is a constant vector. Now,
d p A + d p B = 0
Or,
d p B = d p A
Or,
d p B ∣=∣ d p A ( 4 )
Applying relations ( 3 ) and ( 4 ) to ( 1 ) and ( 2 ) we have:
E A E B = p A p B ( 5 )
A pair of particles cannot interact unless relation ( 5 ) is satisfied. Can we conclude that that relation ( 5 ) to be a restriction for 1 D collisions?
Now let's move to the general type of 3d collisions between a pair of particles A and B.
A frame is chosen where the particle B is initially at rest in it.
E B d E B = p B d p B ( 6 )
If the particle B is initially at rest the RHS of ( 6 ) is zero. But the LHS cannot be zero unless d E B = 0.
How does one get round this problem?

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