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RECENT POSTS IN THIS TOPIC

Sergey Fedosin: on 10/4/12 at 5:45am UTC, wrote If you do not understand why your rating dropped down. As I found ratings...

Tommy Anderberg: on 10/3/12 at 13:24pm UTC, wrote Hello. I apologise again for a very late reply. I do not currently have...

Peter Jackson: on 9/22/12 at 16:55pm UTC, wrote Tommy I struggled to keep up with your essay but then every page had...

Hoang Hai: on 9/19/12 at 15:47pm UTC, wrote Dear Very interesting to see your essay. Perhaps all of us are convinced...

Tommy Anderberg: on 9/18/12 at 16:31pm UTC, wrote Hi, sorry about the late reply. I am busy trying to pay back the time debt...

Benjamin Dribus: on 9/15/12 at 3:43am UTC, wrote Dear Tommy, Very interesting and very educational. It is nice to see the...

Yuri Danoyan: on 9/6/12 at 14:11pm UTC, wrote Tommy, you wrote: "But by forcing us to consider the dynamics, this...

Tommy Anderberg: on 9/2/12 at 17:22pm UTC, wrote I try to avoid prejudices. ;) About inflation, it's been several years...

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FQXi FORUM
November 18, 2019

CATEGORY: Questioning the Foundations Essay Contest (2012) [back]
TOPIC: The Forgotten Landscape by Tommy Anderberg [refresh]

Author Tommy Anderberg wrote on Aug. 31, 2012 @ 11:02 GMT
Essay Abstract

Contrary to common lore, the standard model of particle physics has a “landscape” of physically inequivalent vacua, most of them quite different from ours. I discuss some cosmological consequences and related observational constraints, show how non-perturbative electroweak dynamics selects our special vacuum, and put an old idea to rest.

Author Bio

I am a guy who wonders how the world works.

Harlan Swyers wrote on Sep. 1, 2012 @ 01:17 GMT
This is a great paper, and makes a great point. There is a lot to digest on friday evening so I may have missed some point, but starting with this from paper:

"Fans of the unitary gauge sometimes do not seem to

realize that once the possibility of ⃗θ gradients is accepted,

the argument is over. Instead, they claim that imposing

the unitary gauge turns such gradients into collections

of short-lived, massive gauge bosons, which decay on the

time scale of weak interactions. This works only if you

give up locality – the residual O(3) symmetry must be

broken the same way across the whole universe – and

forget to quantize."

Is the time scale used for the selection mechanism largely at the electroweak scale? How fast does the dyanmic mechanism evolve before final selection? I may be naive on this still, but the impression is that sufficient time must ellapse to filter out the non viable vacuum states and once the more stable becomes apparent then some process must select one that is viable. Am I understanding correctly?

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Author Tommy Anderberg replied on Sep. 1, 2012 @ 16:56 GMT
Thanks. :)

The time scale depends on the initial conditions. There is a bunch of simulation results online which illustrate this. The link is the very last reference in the paper. Fair warning: I find the animations hypnotic, if you do too, you might end up staring at them for a long time.

If you set all fields except
${\vec\theta}$
to 0, all that's left is a non-linear sigma model. It's completely isotropic, so it never settles down. As you dial up electromagnetic radiation,
${\vec\theta}$
is driven toward the third axis. When the energy densities of the two fields are roughly the same, it takes only a few collisions between wave fronts to collapse an initial random distribution to a rough first approximation of the "cigar" in Fig. 7. After that, it settles down asymptotically, in a balance between radiation pressure toward the axis and thermal motion away from it. In Minkowski space, the equations are scale invariant, so the time is completely determined by the characteristic wavelength of the initial configuration.

I should perhaps have emphasized that this is good for plain vanilla big bang and bad for inflation ending below the Higgs scale. With the latter, you get a big patch of essentially constant
${\vec\theta}$
decoupled from electromagnetism (the couplings are all through derivative terms). If it is a few billion ly across, it could then take a few billion years to find its way home.

P.S. FQXi forum noob question: is there some way to make inline equations instead of having them appear on a spearate line?

Harlan Swyers replied on Sep. 2, 2012 @ 01:40 GMT
Tommy,

Unfortuntely I'm a noob to fxqi too, so the latex thing here is kind of weird, I'm used to the dollar sign approach to latex, so I'm not sure about the inline equations for these posts...that aside...

Holy cow! You definitely have given me an option for how to spend my labor day weekend, HaNLON looks pretty sweet.

Indeed, this is based on a complete crackpot theory, its amazing any of this ever gets on arxiv at all ;-)

Since you mentioned the big bang and inflation, do you mind if I ask if you have any prejudices regarding the latter. Slow roll vs Guth's original model seems to be a hot topic at the moment.

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Author Tommy Anderberg replied on Sep. 2, 2012 @ 17:22 GMT
I try to avoid prejudices. ;) About inflation, it's been several years since I last looked at models in any detail. Linde's 0705.0164 is a comprehensive review which I remember liking at the time. This spring, March or April, I trawled the arXiv for limits on low scale inflation, but didn't find anything particulaly stringent. Unless I missed something, in which case I'd like to hear about it, there's no obvious observational limit down to the QCD scale (just pulling this out of memory; let's say quite a bit below the electroweak scale to stay on the safe side). So I don't have much to say on the subject, sorry.

Yuri Danoyan wrote on Sep. 6, 2012 @ 14:11 GMT
Tommy, you wrote:

"But by forcing us to consider the dynamics, this intransigence

eventually leads to a natural explanation."

My explanation are very natural

http://fqxi.org/community/forum/topic/1413

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Member Benjamin F. Dribus wrote on Sep. 15, 2012 @ 03:43 GMT
Dear Tommy,

Very interesting and very educational. It is nice to see the Hopf fibration appearing in the description of the Higgs vacuum manifold. I have played around with this in quantum information theory, but wasn't aware that it arises in this context. Also, your final sentence seems to imply that there may be a moral that applies to string theory. Do you mind sharing what that might be? Take care,

Ben Dribus

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Author Tommy Anderberg replied on Sep. 18, 2012 @ 16:31 GMT
Hi, sorry about the late reply. I am busy trying to pay back the time debt incurred to finish the essay in time. :/ I think the occurrence of the Hopf fibration in this context is not widely known. Apart from my own stuff, the only place I remember seeing it discussed is a very nice paper by Lepora and Kibble, hep-th/9904178. They only mention it in passing, and by the time I derived the eqs. A1-A4 I had long forgotten about it. I had to stare at the equations for quite a while before I realized what I was looking at. Even then it only seemed like a mathematical curiosity. Like everybody else, I was only looking at the boson sector and handwawing about the fermions. Only this summer was I finally riled up enough to work through the scarily messy fermion couplings and be reminded once more that (1) the math is smarter than us and (2) the devil is in the details.

The final sentence... oh well, with only two days left to the annual Ig Nobel ceremony and still no word from the committee, I guess I blew it again, and no longer risk anything by revealing that it was my shot at this year's award. In that vein, it's supposed to first make you laugh, then make you think. I have been trying to come up with an answer to your question which will not interfere excessively with that goal, but so far unsuccessfully. ;)

Hoang cao Hai wrote on Sep. 19, 2012 @ 15:47 GMT
Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close...

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Peter Jackson wrote on Sep. 22, 2012 @ 16:55 GMT
Tommy

I struggled to keep up with your essay but then every page had something that jumped out and took on reality for me. Thank you for a new view on the SM, not really my area, and the following;

In "the vacuum manifold ...'vacuum' is not synonymous with "empty." the apparent philosophical issues with which are the lead theme of my own essay, (which applies logical structures on the physical not just the abstractions).

Also; "The physical picture is of two large regions with constant but different θ, separated by an interpolating boundary smooth enough to make reﬂection negligible." Could this be a transition zone of n=1 with focussed re-emissions?

Perhaps see also the equivalence of your Fig 5 and Richard Kingsley-Nixeys Fig 2. (Cluster Shock crossing) interpretation providing such a boundary zone.

Your Fig 4 looks remarkably like the model of the big bounce recycling emergent from a discrete field model (DFM) of "physically inequivalent vaccua." or a (Hopf) em toroid with (quasar) jets of re-ionized matter. Have you seen the similarity?

Do give me your thoughts. And I hope you can read my essay, though it may be as dense and tricky for you as yours was for me. How many languages do you speak!?

Best wishes

Peter

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Author Tommy Anderberg replied on Oct. 3, 2012 @ 13:24 GMT
Hello. I apologise again for a very late reply. I do not currently have time to do the essays justice, so it will also be a brief one.

When I first set out to simulate the dynamics of the low energy effective theory, I was hoping to find sharp, essentially flat transition layers separating different domains. I did worry about possible deflection and focusing effects on light traversing them, especially along edges between domains, and spent some time doing raycasting through random cell structures to estimate the possibility of observational problems.

But that was all several years ago, before I got actual simulations working. What came out of those was very far from the neat geometric structures I had been envisioning, so that worry went out the window.

Based only on a cursory perusal of the essays you mention, I don't think there is much commonality, beyond the fairly common recurrence of similar mathematics

in different contexts. As to why that happens, I guess it might be a good topic for a future essay contest. :)

Sergey G Fedosin wrote on Oct. 4, 2012 @ 05:45 GMT
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [equation] and [equation] was the quantity of people which gave you ratings. Then you have [equation] of points. After it anyone give you [equation] of points so you have [equation] of points and [equation] is the common quantity of the people which gave...

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