QI Doesn't Violate the Equivalence Principle

[00:00:05]Hello. I'm Mike McCulloch.

[00:00:08]Today I'd like to talk to you about the the equivalence principle, which is a common criticism of quantize inertia.

[00:00:14]The the criticism is that quantize inertia violates the the equivalence principle, specifically the weak equivalence principle that has been tested.

[00:00:26]So, the usual way this is tested is very similar to to Galileo's experiment, actually, of many many hundreds of years ago where he dropped two balls off the the Tower of Pisa, and these two balls had different masses, and he found that they fell fell together, which violated what Aristotle had said.

[00:00:49]Aristotle said that larger objects fall more rapidly than than smaller ones.

[00:00:55]And so, the equivalence principle was was established, and this was taken in much more seriously by by Einstein when he was developing general relativity.

[00:01:08]And the equivalence principle is actually the basis for general relativity, hence the the criticism of QI that it violates it.

[00:01:17]But I'm going to show you very simply that QI does not violate the equivalence principle, or at least the weak equivalence principle.

[00:01:24]So, we could start by looking at an object which is accelerating, so the force on it F equals MA, but let's say the force on it is also gravitational, so we have GMM over R squared here.

[00:01:39]So, this could be the the motion of a body falling in a gravitational field.

[00:01:44]In quantize inertia, little M in the F equals MA, the M in in that equation, is slightly modified into M times a factor which is 1 minus 2 C squared over a theta where a is the acceleration theta is the cosmic diameter.

[00:02:03]So, we can write this like this.

[00:02:06]And then if you multiply out the terms, you get you get this.

[00:02:10]At the third line here.

[00:02:12]And then you can uh you can get this.

[00:02:15]So, that this shows that the the acceleration of the object of the the falling ball if you like is given by a GM over r squared which is uh simply the the the same as we had before.

[00:02:30]Plus a a term which is 2c squared over theta.

[00:02:36]And the interesting thing here is that the the the second extra term due to quantized inertia is independent of the mass. There's no mass in there.

[00:02:45]So, that means that although quantized inertia makes objects accelerate downwards in a gravitational field slightly more quickly. So, Galileo's two balls will fall slightly faster.

[00:02:58]It it treats them all the same no matter what their mass is.

[00:03:01]So, the Galileo's two balls would still fall together to the ground.

[00:03:07]And so, the weak equivalence principle is not not contradicted at all by by quantized inertia.

[00:03:17]Okay. So, I hope you've enjoyed this short.

[00:03:21]And I look forward to speaking to you tomorrow.

[00:03:24]Bye.