Dan Does Physics

Otis

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… I don't get much chance to do my Physics-ing here.
You asked for this? :wink:

I was reading an article about a new model in which our universe has an anti-matter partner on the "other side of the Big Bang", where time runs backwards and antimatter dominates.

I have a question concerning the highlighted text in the excerpt below.

… the entity that respects the [CPT] symmetry is a universe–antiuniverse pair. The antiuniverse would stretch back in time from the Big Bang, getting bigger as it does so, and would be dominated by antimatter as well as having its spatial properties inverted compared to those in our universe – a situation analogous to the creation of electron–positron pairs in a vacuum …

What is meant by inversion of spatial properties? To begin, I had tried googling "spatial properties universe", but, being unable to glean a clear definition after checking six sites, I gave up.

The author's analogy doesn't help me because I know nothing about the creation of electron-positron pairs in a vacuum. (I do know that the positron is the antimatter counterpart to the electron.)
 
That's a neat article. Thanks for sharing.

Much of what I'm going to talk about here comes from Weinberg's "The Quantum Theory of Fields". If you like you can look up the references there.

We really don't need to invoke an extra "anti-Universe" in order to talk about CPT. Any (relativistic) Quantum Field Theory contains CPT symmetry. If we find that CPT is not a symmetry of nature most of our theories aren't worth as much as garbage. Let's talk some.

Why do we even care about CPT invariance? Well, it is basically the principle that if we can make a physical process go "backward" then we are doing a CPT transformation. It would make a great deal of sense that the Universe should be able to go backward or forward under the same laws. (I'm ignoring things like entropy, which sets a "forward" direction for time. I read once that it was possible to reverse time and still be able to do the entropy thing but I don't recall how.)

CPT is an invariance that is broken into several pieces. First of all, parity is such an obvious symmetry of nature that it took a very long time to find out that it is not always a symmetry. A parity transformation takes a vector x into a new vector -x. Until somewhere in the early 60s it was assumed that all the laws of nature were invariant under a partity transformation. I mean, really, it shouldn't be that complicated, but it actually is. There was an experiment being done on a lump of cobalt and it was noticed that electrons were being preferentially emitted in a specific direction, which is pretty weird. Now-a-days we say that the weak nuclear force, the mechanism for radioactive decay, does not require parity invariance. So P (the parity operator) is not conserved.

To save a long conversation (I'll give more details if you request) "charge conjugation" is also not an invariant operator. (That's where you replace your particle with its anti-particle.) The decay of a neutral kaon has two pion decay channels, \(\displaystyle \pi ^0 ~ + ~ \pi ^0\) and \(\displaystyle \pi ^+ ~ + ~ \pi ^0 ~ + \pi ^- \). For a long time it was thought that there were two particles, each with its own decay channel, but it was eventually proven that there is only one of the things. Some other heavy mesons have similar decays. So charge conjugation as an invariance is down, too.

To make things even worse, if we combine P and C we find that even the CP operator (switch the parity and do charge conjugation) is also not an invariance.

That leave us with time invariance (make everything move "backward" in time), T. We don't know if this one is conserved but since we are speculating that CPT is invariant and that CP isn't then we are left with the conclusion that T is also not invariant.

These are small, but detectable, variances. All but T and CPT have been directly measured.

I can go into more detail if anyone wants.

-Dan
 
I appreciate your time in posting that information, Dan, but I can't recognize an answer to my question. I think I need to back up a step.

Instead of asking for the meaning of spatial-properties inversion, I ought to have asked for a definition of spatial properties.

What are the spatial properties of our universe? Is there a list that you can point me to?

Cheers :cool:
 
I've look at it again and I'll give it another shot.

What the article seems to talk about when it says "inversion of spatial properties" is to apply the CPT operation (change the particle into an anti-particle, switch the parity from x to -x, and run time backward) to our matter dominated Universe and you will get what is happening in the anti-matter dominated part. So if we have an electron moving in the +x direction with a momentum p then the anti-matter side has a positron moving along the -x direction with a momentum p. (The momentum gets a - from the parity operation as well as one from the time reversal so they cancel out.)

At least that's what I think they are talking about.

I'll think it over tonight and look at the article again in the morning.

-Dan
 
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