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The Uncertainty Principle

Here is a brief explanation of why the "Heisenberg uncertainty principle" is implied by quantum theory. It's not nearly as mysterious as people think. Yes, if you don't have any matrix math background you won't be able to follow this. But you still might see it's just a little bit of math, there isn't a lot of stuff to it. The Uncertainty Principle is not a Principle, it's not a law of physics, it's just one of many results you can work out about quantum theory with a small amount of math:

-- In quantum theory observables can be represented by Hermitian matrices.

-- If an observable of a system can be represented by a particular matrix at a particular instant, then all matrices of the same dimension represent observables of that system.

-- In a state specified by the vector |psi>, an observable X is sharp if and only if X|psi> = x|psi> for some real number x. In which case x is an eigenvalue of X and |psi> is an eigenvector of X.

Now let Y be any matrix that does not have |psi> among its eigenvectors. (For any vector, there exists an infinity of such matrices.)

If the actual state is |psi>, the observable Y cannot be sharp. (Because of the 'if and only if' above.)

Elliot Temple on March 5, 2015

Messages (4)

In other words, not all observables of a system are sharp at any given point in time. (Sharp means the same in all universes.)

curi at 5:58 PM on September 4, 2017 | #8982 | reply | quote

> (Sharp means the same in all universes.)

Clarification: Sharp is the same in all *relevant* universes. Like for an experiment, it only includes the universes in which the experiment is done. We're basically just looking at the universes which could be the same, ignoring the ones that are permanently different.

curi at 11:35 PM on May 2, 2019 | #12268 | reply | quote

The physics argument after the first paragraph was written by David Deutsch, not me. He gave me permission to post it, but only under my own name. I first posted it to the *Fabric of Reality* discussion group in 2011, and after sharing it several times I posted it here so that I could link people to it. I never wanted to take credit for it, but I did anyway because I wanted to share it with people in order to help them understand physics, and DD wouldn't provide other options. I think the argument is important and should be shared with the world.

I understood the math and the argument myself, and I don't think anyone got the mistaken idea that I'd invented the argument myself as original physics research (I am not a physicist). I think that I did mislead some people into believing that I'd written this particular version of the argument myself. I apologize for that.

I forgot how the argument worked, and then went through it and figured it out again by myself without DD's help, at least once (my best guess, from memory, is that I did that three times). That demonstrates that I wasn't just fooling myself by thinking I understood it right after DD explained it to me. I'm actually able to follow and understand it myself without his help.

curi at 4:23 PM on June 26, 2021 | #20640 | reply | quote

#20640 DD refusing to let me post that anonymously is from memory. I haven't found the relevant IMs. (I did an email search and only found me sharing it publicly five times.) My recollection is that I always preferred to attribute things to DD to to anonymous, and did that when he let me. I've recently reread chat logs where that came up – where DD didn't want to share something under his name but I pushed him to let me share it and attribute it to anonymous. In one case I reread recently, DD at first said OK share and attribute it to [one of his pseudonyms]. But then before I posted it he remembered that he'd said the same thing to someone else who didn't know about that pseudonym, and he didn't want to out the pseudonym to them, so then he came up with a different plan. I'd often prompt him repeatedly to get things like a way to share something he wrote that I thought was good.

curi at 4:37 PM on June 26, 2021 | #20642 | reply | quote

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