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Old Sep 22nd 2016, 02:35 PM   #11
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Originally Posted by Woody View Post
Going back to your original post on this thread,
You indicated that the state entered after symmetry-breaking is essentially random,
which then leads you on to your further thought about different states in neighbouring domains.
However if the state entered after the electro-week symmetry breaking were actually completely random,
then we could end up with adjacent particles having different states.
That way lies chaos.
However;
If one can apply a crystallisation style analogy
such that a seed of symmetry-breaking would encourage the surrounding region to adopt the same broken symmetry state,
then one could envision separate seeds setting off separate symmetry-breaking episodes,
leading to the scenario you first thought of.
Thanks for the article. It was interesting.

What you are saying is pretty much as I am conceiving of it. The problem with finding a good analogy for it is kind of like trying to find a solid melting into two possible liquid states at the same time...a situation that, to my knowledge, doesn't happen.

That's one reason I'm posting this in Thermodynamics. The other is that if we can have particle flow from one domain to another then we can set up a chemical potential. I have no idea how to apply that to this problem, however.

So let me set up a preliminary set of questions to be answered.
1) We have to have two domains of space-time separated from each other, but "touching." How can we set up the details for one of the domains in terms of the weak mixing angle such that we have a massless photon. I can probably set this question up now without too much trouble. So this isn't as much of a question but a set of initial conditions.

2) Assuming we have particle flow from one domain to the other we need to have at least continuity in space but possible discontinuities in weak isospin space. How do we set up equations of motion across the boundary?

3) With particle flow from one domain to another is it possible for the two domains to "mix" with each other, eventually creating a single superdomain covering all space?

4) And finally an obvious one. How could we detect such a pair of domains? I am assuming (without proof) that the boundary between two domains is observable in some sense.

Does that sound like a reasonable program to work with? Did I miss any crucial questions that anyone can think of?

-Dan
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Old Sep 22nd 2016, 04:50 PM   #12
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One normally thinks of the weak force as a very localized effect,
not even reaching beyond the bounds of the nucleus.
However when talking about the symmetry-breaking differently in different regions of space we seem to be talking about some kind of innate property of the fabric of reality which applies regardless of the presence of any particles.
Even regardless of the presence of any W or Z bosons.
W&Z bosons in one domain would be different from the W&Z bosons in the other.
What would happen to these bosons if they tried to cross the boundary?
I would suggest there are two options:
1) they can't
2) they have to convert to the type of the other domain.
If they are converting as they cross the boundary, might there be an energy or stability advantage of one domain over the other?
If one domain has the advantage over the other, then we can imagine that domain expanding at the expense of the other.

If you want an analogy, try Polymorphism
Here a substance can take on different crystalline forms,
But often these forms are mutually incompatible, if even a speck of the dominant crystal form is present, then the entire crystal will spontaneously adopt that form.
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Old Sep 27th 2016, 06:05 PM   #13
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Still pondering this one...

An idea I seem to be reading about quite frequently is that there is not just one way to make a coherent self-consistent universe.
The idea of different weak forces being just one example of this.
However once a particular parameter has been "set" (via symmetry breaking etc) then apparently it becomes the fixed state for the universe.
Particles (for example) will only be formed with specific, quite narrowly prescribed, characteristics.

What is the underlying feature of reality that defines these limits?
Are virtual particles similarly limited in the forms they can take?
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Old Oct 11th 2016, 07:51 PM   #14
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I did some review from start of QFT to Electroweak theory and found I had forgotten something really basic: When applying the Higgs method to the broken electroweak theory, from SU(2) x U(1) to the broken SU(2) and U(1) symmetries, we have to have a massless boson coming out in the U(1) sector. There is no way for me to get the massive photon because it would break the U(1) symmetry.

Grrrrrrrr..... I hate it when I forget the simple stuff.

Ah well, back to the drawing board.

-Dan
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Old Oct 14th 2016, 06:32 AM   #15
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The Usefulness of Mistakes

In computing, there are various methods used for exploring a solution space to find the optimum solution.
A useful analogy in this process is that of finding the lowest point in a landscape.
One of the most obvious methods is to follow the locally steepest gradient (i.e. the solution gets better quicker in that direction.
However it was found that adding some random "noise" to the direction could actually give better final solutions.
Using the landscape analogy this is equivalent to climbing out of the valley you are currently following, to find a "better" valley over the ridge.

I believe a similar model applies more widely, and is particularly pertinent in scientific research.
If you just follow the current valley you will never find the better solution that lies over the ridge.
Mistakes are a fine source of noise to send us wandering across the landscape.

Besides which, when you try to make an impossible scenario work you get a good insight into why it is actually impossible.
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