BSc (Hons) in Theoretical Physics and working on his masters) (SSLR).<b/>
His answer is below:<br/>
Philosophical answer: Every theory we have in physics is only correct
up to a certain point. For example, Newtonian mechanics works ok at
macroscopic scales and low energies. If you go down to the nano scale,
Newtonian mechanics doesn't work anymore and you have to use quantum
mechanics. If you go to the high energy scale, you have to use general
relativity. (If you want high energies and small scale, you need a
theory of quantum gravity which nobody has worked out yet.) Of course,
in the future there will be better theories that work at higher
energies and smaller scales but there will always be a cutoff when the
theory breaks down and you have to discover something new. So if
you're talking about infinite energy (= infinite momentum) and
infinite forces, this situation is not described accurately by any
theory we know today. So the answer is: I don't know and maybe we will
never know.
Mathematical answer: Let's choose to work using the Newtonian
mechanics theory. This is based on real numbers and differential
calculus (functions and their derivatives and so on). Now "infinity"
isn't a real number and you can't treat it like one. You can only have
things that become infinite in certain ways. For example, f(x) = 1/x
-> infinity as x -> 0. To solve problems involving infinities you have
to know how fast the different quantities go to infinity to do the
calculations. For example, 1/x^2 goes to infinity faster than 1/x as
x->0. Depending on the relative growths, the answer could be that the
unstoppable force wins, the immovable object wins or there is a tie.
So the answer is: It depends which one is more infinite than the
other.
While the situation you describe obviously could never happen, we do
actually consider these kinds of limits quite often for real problems.
This is because it is often easier to solve equations when you pretend
that something has infinite mass and is immovable. This often turns
out to be a good approximation even though the mass is of course
finite. Of course, to actually do the calculations, you always have to
know or decide which quantities are more infinite than others.
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