If physics involves so many assumptions and simplification in the process of calculating, how does the math actually check out?

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For example, I’ve seen that an electron is assumed to be a point-particle, i.e, occupies negligible space.

But it obviously has mass, so it’s gotta occupy *some* space!

However, the math seems to add up (pun intended), and the behaviour of the electron can be explained.

How?

(This was inspired by the *assume a spherical cow* thing)

In: Physics

6 Answers

Anonymous 0 Comments

Margins of error.

I don’t want to talk about electrons as I’m aware there are lots of theories that I’m not fully versed on. However, I can talk about some basic engineering.

Say you’re making a bridge across a river. You measure the river to be 10m wide. Your bridge has a bit of an arch, so you’ll need 12m of material to make it. Great.

But what if your measurements were slightly off and it’s actually 10.1m?
What about when it gets warm, since your bridge is made of metal it will expand. Or contract when it’s cold.

We build in margins of error that are perfectly acceptable to account for these issues. On a bridge if it wasa few mm too big for the holds you built either side you could probably just squeeze it in, compressing it slightly. Same with basic wooden furniture: IKEA don’t have precision measuring, but we know wood is a little bit flexible so whatever it’s fine.
For larger bridges heat expansion can be an issue, so they often have expansion joints or even roller wheels built in to allow for small changes.

Basically we can do maths close enough that our assumptions don’t matter, it’s close enough that noone will notice the difference.

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