And also get mad at it because it came in their equation so it must hat some sort of mistake.
In: Physics
Infinities are okay in math and physics, so long as you know how to handle them. When used right, they cancel each other out so that you get an answer that makes sense. But, sometimes, the math is just not able to escape those infinities, such as in the centre of a black hole. There’s obviously something happening there that physicists don’t understand, and a lot of research and theory goes into trying to figure out what that is. They’ll know it’s figured out when the infinity in the black hole’s singularity is elegantly cancelled out.
Reverse the idea. If a charge is moved from you to be infinitely far away, its electical field, asymptotically approaching zero, becomes zero. That’s a handy property to have for your next equation.
in science there is often the concept of thought experiments where you think of the absolute edge case that can’t ever actually have in real life and try to relate that to how things react in the real world, and ideally your model should explain both accurately.
Even though you can’t actually bring a charge from infinity, it’s helpful to think of what would happen if and when the charge had zero potential energy. from that you can then say the formula for potential energy is this, it’s never zero and that’s why we almost always measure it relative to something else
its a misnomer. they don’t actually mean infinity, they just mean counting until you can’t count any more
It tests that the maths is reasonable. In the limit the formula generally blows up or tends to zero as one parameter tends to infinity, and this should make sense. If it blows up when you would expect it to tend to zero then something in your formula is upside-down.
Infinity and zero are useful tools to think about cases where some factors are incredibly large/small (in comparison to each other or others). For example, it can make equations easier or let you work around situations with multiple unknowns if you can manipulate the situation so that some of these unknowns go to zero, and can be dropped from the equation entirely.
A cat is both alive in the box and dead in the box. A useful hypothesis for testing what the outcomes could be.
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