It from Bit, QI Style.

Added: 2026-05-11

[00:00:05]Hello, I'm Mike McCullik. So today I want to talk to you about the simplest way to derive quantized inertia which is incredibly uh simple and elegant from from information.

[00:00:18]So we we first start from Landau's principle that says that every time you delete erase a bit of information you release a certain amount of energy which is given by well E is K T* log to the base 2 of two.

[00:00:37]So K being BM's constant and temperature being the the temperature uh T being the temperature.

[00:00:44]Turns out that if you do a little bit of maths that the energy you get from deleting n bits of information is KT* N KTN.

[00:00:55]So that's nice and simple. So now I'm going to consider a an object which is shown here as the vertical dashed black line shown on this this diagram which should be up here somewhere.

[00:01:13]So this is an object. So it's imagine it as a long rod if you like split up into a plank lengths shown by the dashed dashed lines.

[00:01:26]Now before it accelerates this object can see all the way out to the cosmic diameter which is shown by the blue sorry red vertical line on the right.

[00:01:38]So it can see a certain amount of length. So I've I've shown that with the dots extending from the left to the right. And each of those dots represents a plank length. And what I'm assuming is that each plank length has uh contains one bit of information. And that makes sense because a plank length is the smallest distance you can store information in.

[00:02:00]Okay. So now the object on the left accelerates to the left.

[00:02:07]So it will now see a reindler horizon.

[00:02:11]So an acceleration horizon which is shown by the the blue vertical line in the center.

[00:02:18]So now it won't see as many bits. A lot of bits will have been erased. It'll be behind the horizon. So this means that the it looks like the uh the entropy has gone down. But that can't be right because nature doesn't allow that. So we have to allow some energy to come out.

[00:02:37]So what is that energy? Well, the energy is going to be the difference between the KT times number of plank lengths we had minus KT times number of plank lengths we we now have. So it's it's a difference in those two things. And you can write this down. So the the number of bits that we had is the distance to the cosmic horizon which is theta /2 divided by the plank length. And the the number of bits we have after acceleration is given by the distance to the rim horizon which is c^ 2 over a divided by the plank length again.

[00:03:14]And if you take the difference of those you get a certain formula which is shown here.

[00:03:19]And then if you use= mc^² to replace the energy with the mass you assume also that the energy is thermalized. So E= KT.

[00:03:29]And if you do that uh then you get an equation which starts to look like the quant quantized inertial equation.

[00:03:40]So and that's shown here. So the only thing we need to do now is accept the fact that we had a vertical extended rod and we just need the inertial mass for one bit of it. So we divide by the length of the rod which is the um theta / 2 LP uh the cosmic radius divided by the plank length. And you get uh this formula which is the formula for quantized inertial which gives us the energy available for inertial mass.

[00:04:19]And you see it's it's not quite it's not not quite a simple simple formula and the difference. So the the second term in the equation is the term that enables us to predict galaxy rotation and all these different anomalies with quantized inertia without the use of dark matter or anything like that.

[00:04:43]So this is a very nice derivation that I published in 2020 in a paper. I made a bit of a mathematical error in that one but the answer was still the result was still valid and I published it in correct form in my my book uh which is shown here. So feel free to to read that and after this this video is over I'll put a a screenshot of the the full calculation so you can have a look at it.

[00:05:12]Okay. So, I hope you've enjoyed this this short and I look forward to seeing you next time. Goodbye.