A few short items:
Guth started his physics career in this sunny scientific world. Now sixty-four years old and a professor at MIT, he was in his early thirties when he proposed a major revision to the Big Bang theory, something called inflation…
He wears aviator-style eyeglasses, keeps his hair long, and chain-drinks Diet Cokes. “The reason I went into theoretical physics,” Guth tells me, “is that I liked the idea that we could understand everything—i.e., the universe—in terms of mathematics and logic.” He gives a bitter laugh. We have been talking about the multiverse…
“We had a lot more confidence in our intuition before the discovery of dark energy and the multiverse idea,” says Guth. “There will still be a lot for us to understand, but we will miss out on the fun of figuring everything out from first principles.”
One wonders whether a young Alan Guth, considering a career in science today, would choose theoretical physics.
The only hint anywhere in article that some physicists might feel that there is something wrong with this picture is the passing remark that some [unnamed] physicists “remain skeptical of the anthropic principle and the reliance on multiple universes to explain the values of the fundamental parameters of physics.”
A theoretical Higgs prize would likely take much longer, since it will take a while to be sure that whatever is found behaves the way a Higgs should. Guralnik continues his campaign for the prize here.
For those who wonder: the fact that the Higgs has (perhaps) been found has no influence on my ideas on gravity. These ideas remain correct.
- A First Course in Loop Quantum Gravity, by Rodolfo Gambini and Jorge Pullin. This book explains the ideas behind loop quantum gravity at an introductory level, suitable for undergraduates, or anyone wanting as non-technical as possible of an introduction to the subject. Maybe it can be sold in a package with Barton Zwiebach’s A First Course in String Theory.
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Fascinating Mathematical People edited by Albers and Alexanderson. This contains a wonderful interview with my colleague Dusa McDuff. There’s also this exchange in the interview with Ahlfors:
Mathematical People: How about physicists?
Ahlfors: Well, I don’t believe in physics!
Mathematical People: You don’t believe in physics? Why not?
Ahlfors: Physicists are so close to physics, but they don’t know mathematics.
Mathematical People: … There’s also a great deal of mathematics used by string theorists.
Ahlfors: But it’s the wrong theory. I like the knot theory aspects, especially the knot theory applied to string theory. The strings are knots now, and there are these ready-made knot theorems that can be applied. That appeals to me.
Probably physicists are important for mathematics, but they cannot be important for me in any sense. I don’t think that mathematicians should take their inspiration from physics.
- Magical Mathematics: The Mathematical Ideas That Animate Great Magic, by Ron Graham and Persi Diaconis.
- Division Algebras, Lattices, Physics, Windmill Tilting, by Geoffrey Dixon. Dixon tells his personal story about pursuing research in particle physics, trying to connect it to the mathematics of the division algebras over the reals. I’m sympathetic to the idea that this kind of algebra has something to do with the patterns we see in the SM symmetries and quantum numbers. Unfortunately I still think no one yet knows the right way to understand this.
Update: One more. See here for an explanation of why string theory is useful:
Dr. Kaku explains that time machines do not violate Einstein’s laws of physics, and that – difficult though it might be – future humans would be wise to build one and slip through a wormhole to one of the alternate dimensions proposed by string theory before the cooling universe extinguishes all known life.
Update: The Times has an article and series of letters about the Higgs/Nobel issue, see here.
Suppose there will be a Nobel Prize for the theory of Higgs particle and everything, I really don’t see how Guralnik and his company can win over H, E, or B. They beat the GHK team in print. If no more than 3 people can share the prize, the HEB are the obvious choice.
Besides, none of them proposed the final theory for how electroweak symmetry breaking works in reality. They only provided a mechanism. It doesn’t matter who did a better job (Guralnik thinks the GHK team had a more complete and rigorous paper).
I think the best Guralnik can achieve is that no one will win it for the theoretical part unless the number of candidate is reduced to 3. We’ll see.
JC,
Brout is no longer alive, so that’s one less. If those goes on long enough, mortality will reduce the number of contending candidates to 3.
I should also point out that Philip Anderson actually has a better case than any of these people for a piece of such a prize, see
http://www.math.columbia.edu/~woit/wordpress/?p=3282
I bought Magical Mathematics a little while ago. It is a beautiful book, also with many beautiful pictures of Graham juggling, as well as explanations of card tricks. But I am pretty sure my copy that I ordered from Amazon did not contain a deck of cards.
If the Nobel prize is disputed between 5 in theory, between how many is in experiment? I think a Nobel prize for the Higgs definitely should go to at least two theorists, or even 3 and leave the experimental Nobel prize for something that was not predicted that the experiments happen to find (if). And even in this case the most neutral thing to do is to give the prize to CERN (therefore to Rolf Heuer as its representative) , also because people forget there is a not so easy accelerator effort called LHC involved in this whole process and we would not a a Higgs without it. Tough call, but doable if the Nobel committee wants to be less unfair as possible (to some degree a Higgs Nobel prize is doomed to be unfair).
A last comment is that I am not so sure I agree that it should take that long to give the prize for a Higgs. As I understand the prize should be given to those who conceived the idea of a Higgs field, not to some random model builder who happened to use the idea and hit the jackpot. So even without knowing its exact properties, we will know if it is some kind of Higgs or not and this should be enough.
Shannon Starr,
Thanks for letting us know. It’s entirely possible the deck of cards was just a promotional bribe included in the package from my friends at PUP to get me to mention the book. Anyway, it’s a fun book, even if you don’t get an extra pack of cards with it…
IMO any Nobel prize for the Higgs should go to theorists alone. Experimentalists already obtained Nobel prize for discovering W and Z particles in the electroweak sector using hadron colliders. I don’t think they deserve another prize for discovering the Higgs simply by using a more powerful hadron collider, without revolutionary change in experimental method. If they discovered something groundbreaking using a future muon collider, that might be more Nobel-worthy.
One more comment before Christmas.
Kaku multiverse and string theory. It´s incredible how these guys simply manage to sell the same story every week and still get attention. Kaku is the kind of author I like to read to relax because he has some fascinating stories (the lecture is almost certainly based on his “Physics of the impossible”) that has nothing much to do with real physics problems that real physicists have like calculating parton density functions, so it´s really a relaxing “not thinking about my job” thing. Kind of read that is nice to tell my little kid about and that has the same value of us seeing Star Trek.
Guth´s comments on the multiverse by the way gives me just yet another hint that they all already completely departed to a different reality that is not really connected with physics anymore. It´s hilarious to say “we will miss out on the fun of figuring everything out from first principles”. Who is going to miss it? I think physicist will keep trying, also because most experimentalists (the only ones capable of making the real decisions where the filed will head to) are not even aware of the level of madness things went in string theory. The only thing that is unfortunately missing is to acknowledge that the multiverse thing is not theoretical physics and start an independent field with an independent name, maybe connected to the philosophy departments (I hope not to offend any philosopher here).
Peter, isn’t the claim for Anderson rendered moot by his already having won in 1977?
On the main point discussed in this thread (so far), I like the idea of distinct awards for the theorists & experimentalists, partly because in this case justice seems to demand it; but also because it allows for the possibility of the sort of ‘politicized’ award given in the case of the Peace prize involving Gore. An award specifically identified with CERN, such as to Heuer, maybe coupling it with Oddone (since Robert Wilson is long dead & Lederman’s got one), might make for an effective slap at Congress for having cancelled the Supercollider, thereby exporting discoveries that link so strongly to the history of physics in this country.
Avattoir,
The Nobel is for specific discoveries, you can get it more than once (John Bardeen is an example, I don’t know if there are others). What Anderson got the Nobel for in 1977 was a completely different topic, work on disordered materials.
Has there been any update in SUSY @ LHC? Has SUSY been excluded to higher energies from the summer’s previous announcement?
Don’t you get tired of bashing popular hype? I mean, what’s the point? No one takes Kaku seriously, if they ever did. It’s almost like going after Fritjof Capra…
Regarding Guth: the thing is, inflation seems to be a compelling explanation for a number of observations – in particular, it’s at least consistent with the concordance Lambda-CDM model and WMAP data. And there’s really nothing else around to do the job. But once you take inflation seriously, you’ve got eternal inflation, and then you’ve got multiple universes. So even though they’re unobservable (like “parallel earth” 10^20 light years away in this universe), this model that seems likely to be true also entails them. So why complain when smart & informed people draw out that extrapolation?
FB,
Who’s bashing Kaku or taking him seriously?
And, it’s hard to believe, but it looks like I haven’t written enough blog postings explaining why evidence for inflation doesn’t imply the string theory multiverse, with different low energy physics in every universe.
re Kaku: OK, if I say “mock” instead of “bash” does that help? I just mean why waste the pixels?
On inflation & the multiverse, I suppose you are referring to a post like this one: http://www.math.columbia.edu/~woit/wordpress/?p=4043. I understand that inflation by itself doesn’t imply the landscape. But eternal inflation is a pretty straightforward inference, and that gives multiple “pocket universes” as the lingo has it. Whether they’re the ones implied by the landscape is another matter. Maybe they all look like this one. Why complain about this kind of speculation? Is it really that different from talking about the likely existence of parallel Woit all those many light years away?
I’m not a physicist, but I wonder if the prize to Nambu could be considered a prize for the Higgs mechanism. Perhaps they could justify awarding the prize before the experimental confirmation of the Higgs boson because Nambu’s work was general enough. (And perhaps they didn’t want to wait too long – another prominent Japanese physicist (Yoji Totsuka) had passed away without winning the Nobel Prize earlier that year (2008).) But isn’t Nambu’s work important in large part because it lead to the Higgs mechanism and the Standard Model?
I won’t be too surprised if no Nobel Prize is awarded for the theory of the Higgs boson. A Nobel Prize can be shared by only up to three people. There is no posthumous prize. It is too difficult to choose when there are six or seven contributors of which one is already dead (Brout) and one have already won a Nobel Prize albeit for a different topic (Anderson). And prizes have been awarded for related topics (Weinberg and Salam, ‘t Hooft and Veltman, and Nambu) already.
There is one person who will most definitely get the nobel for Higgs and that is Peter Higgs.
Could you just imagine the public ridicule the Nobel Committee would face if they didn’t honour the man after whom the particle is named?
Foster, inflation has a whole bunch of conceptual problems. See talks by Brandenberger,Steinhardt, Turok, Penrose (many of which you can find online
at KITP or PI). Plus I think a Harrison-Zeldovich spectrum + lambda cdm model is consistent with observations.
My copy of the Diaconis/Graham book did not come with a deck of cards.
It’s a nice book anyway.
Good timing of this blog Peter.
Last week an interesting article ran over here in the Times by John Richardson on the topic Nobel issues and options. It was followed by two letters from 1) Frank Close (of course) and 2) Guralnik, Hagen, and Kibble (ditto).
GHK must be feeling the heat due to last week’s results and Frank’s comments. Close seems to be positioning himself as referee on all things “Higgs” – of course I thought we had John Ellis for that.
__________________
The Times
British physicist could be in line for Nobel Prize
John Richardson
December 14 2011
If the LHC experiments find the Higgs boson, the theoretical physicists who first suggested it are expected to win a Nobel Prize. There is a hitch, however: each Prize has a strict limit of three recipients each year, but six people suggested the particle’s existence at almost exactly the same time.
Peter Higgs proposed the particle that came to bear his name in 1964, to explain why matter has mass. But a pair of Belgians, François Englert and Robert Brout, and three Imperial College London physicists, Gerald Guralnik, Carl Hagen and Tom Kibble, published papers containing the same idea within a few months of Higgs, in the same journal.
It is now accepted that all six conceived the Higgs simultaneously and independently, and all were awarded the prestigious J. J. Sakurai Prize for Theoretical Particle Physics in 2010.
The Nobel Prize’s rules were laid down by Alfred Nobel a hundred years ago, when science was a much smaller and less international enterprise than today, and Erik Huss, of the Nobel Foundation, thinks they are unlikely to be changed. “You can’t just rewrite something that’s over a hundred years old,” he said.
However, a compromise may be possible. Last year’s Nobel Prize for Physics was awarded to three physicists, but at the announcement, the committee honoured the teams of which each was a member — though their colleagues did not receive any of the prize money.
There may be pressure on the committee to make an award sooner rather than later, to ensure all the potential recipients – aged between 74 and 82 years old — receive any recognition they deserve. The Nobel Prize cannot be awarded posthumously.
__________________
The Times
Letters to the Editor
December 16 2011
The problems faced by the administrators of the Nobel Prizes, and the huge possibilities opened up by the Higgs boson
Sir, You said (report, Dec 14) that six people suggested the Higgs boson’s existence at the same time and that this is a problem for Nobel Prizes, which can be shared by at most three. As this assertion was adjacent to a commentary by me and is false, it needs expunging.
Peter Higgs uniquely drew attention to the boson, which now bears his name. While it is true that Higgs is but one of six (at least) who independently discovered how to give mass to fundamental particles, it is by studying the properties of the eponymous boson that the whole idea can be tested, as my book The Infinity Puzzle explains.
If the mass mechanism is regarded as key, then there is indeed an overabundance of candidates. However, if the boson is key to a Nobel Prize, there is no problem with the limit of three winners.
Professor Frank Close
Professor of Theoretical Physics, University of Oxford
__________________
The Times
Letters to the Editor
December 21 2011
Boson issue
Sir, while we are enjoying Professor Frank Close’s recent book The Infinity Puzzle, we take issue with his letter (Dec 16) on some significant points. In this letter he implies that our paper “GHK” did not have the “eponymous boson”. Our 1964 Physical Review Letters paper, written while all three of us were at Imperial College London, has the boson and describes it with what amounts to the same equation as that derived by Peter Higgs.
Additionally, the GHK paper was unique in that it explained in detail how the mass mechanism is consistent with the laws of causality and charge conservation along with other essential insights not presented elsewhere.
Gerald Guralnik, Brown University
C. R. Hagen, University of Rochester
Tom Kibble, Imperial College London
Oliver,
Thanks a lot for pointing this out. Someone else should join in the fun and write to The Times about Anderson.
Since number of Nobels have come up, here is from the web:
“…the International Committee of the Red Cross has won the most Nobel Prizes. The Red Cross received the Nobel Peace Prize in 1917, 1944, and 1963.
The only other people or organizations that have received more than one Nobel Prize are Marie Sklodowska Curie (for physics in 1903 and chemistry in 1911), Linus Pauling (for chemistry in 1954 and peace in 1962), John Bardeen (for physics in 1956 and 1972), Frederick Sanger (for chemistry in 1958 and 1980), and the Office of the United Nations High Commissioner for Refugees (for peace in 1954 and 1981).”
I second Neo’s question. When will LHC publish new SUSY results based on this year’s data?
anon and neo,
Maybe you should try the question at Matt Strassler’s blog and see what he has to say about it. For the first ATLAS/CMS SUSY searches, the ones that were widely advertised before LHC turn-on as the best bet for finding SUSY, nothing showed up in the first 2 inverse fb or so. The reach of these searches won’t go up very much with the analysis of the full 5 inverse fb of this year, so no one expects anything there.
SUSY proponents have been claiming that these first searches weren’t the right ones, that it’s only later, more difficult ones where they now think SUSY will show up. I’m also curious exactly which searches they’re willing to claim as decisive ones, and what the state of those searches is. Maybe Matt or someone else can be encouraged to write about this. In general, I thought that the experiments weren’t planning much in the way of release of new data until the winter conferences (e.g. Aspen in February).
True, the Nobel is for specific achievements, but even those who have multiple Nobel worthy accomplishments have historically not won two Nobels. (Einstein never won for either version of the theory of relativity, for example.) John Bardeen is the only exception (as far as winning two physics prizes is concerned). I assume this is because he worked in collaboration; the Nobel committee couldn’t very well award Cooper and Schrieffer and ignore their co-author. But given that they already have too many possible winners for the Higgs mechanism, it seems especially unlikely that they’d take the essentially unprecedented step of giving a share of the award to a past laureate.
Peter,
As a somewhat informed layman trying to explain the fanciful idea of the multiverse to a bunch of smart humanities professors who know little about science, I found myself unable to answer a few of their basic questions, and I wondered if you could chime in. It goes without saying that like you, these professors and I think the multiverse idea is far-fetched. Still, we recognize that you and other readers of this forum, while not supporting the multiverse hypothesis, are likely knowledgeable enough about it to answer our questions.
1) If there are multiple expanding universes, do they collide? For instance, could a different universe’s expansion collide with ours and, presumably, lead to all manner of destruction as stars from different universes run into each other? Wouldn’t these events be observable in principle? If so, wouldn’t that make the multiverse a testable idea, and assuming a lack of evidence for it, one that conflicts with, or lacks, experimental evidence?
2) I was asked whether space extends forever, and answered (hopefully correctly) that it does NOT — that the frontier of space in our universe is the outer reaches of expanding space caused by the big bang. This then lead to 2 questions:
(a) What is “beyond” that frontier (e.g., what if you’re on the most distant object of the universe and throw a baseball outward…Does that act create new space?) Relatedly,
(b) What is the “stuff” that supposedly separates different universes of the multiverse? “Space,” or something else? Given (by definition) that this “stuff” isn’t part of any of the different universes, what is it? If the concepts of distance and location apply to such a substance (e.g., the notion of “between” different universes), then it seems unsatisfying to me to simply say that nothing exists there.
3) Are any/all of the different universes of the multiverse supposed to have originated from the same Big Bang as our universe’s (and if so, why would they constitute a different universe than ours)?
4) One hears from the same writers who promote the multiverse that, in light of the accelerating expansion of our universe due to dark energy, one day our universe will be essentially “empty.” Yet if there are 10^500 other universes that could potentially be expanding into ours, wouldn’t the “stuff” from those universes potentially make our universe much more interesting than the barren wasteland depicted by the aforementioned writers?
I recognize you and many of your readers are not proponents of the multiverse (neither am I), but I think that discussing issues like these has value for either discrediting the multiverse or for finding ways to learn more about it. Thanks.
Brathmore,
The key to understanding many of these issues is to recognize that space does not need a meta-space (and then meta-meta-space, and then…) in which to exist.
In particular, expansion of space need not be expansion into anything else. Not also that the metric curvature of space is measured inside space itself; there’s no notion of curving “up” or “down” in another dimension.
Brathmore,
I’m not Peter, but I can try to answer some of your questions. I’ll break it up into two comments — this one will try to paint a general picture of inflation and the multiverse, and with that context I’ll talk about your specific questions in a second comment.
The general topic you are talking about is the creation of “bubble” (“pocket”) universes within a total Universe, in the context of something called eternal inflation. Eternal inflation seems to be a generic prediction of most models of inflation. What I’ll discuss assumes “false vacuum” eternal inflation, but the general issues that arise should be there for other ways currently considered for modeling inflation.
The inflation idea is that there is a “scalar field” that permeates all space, and it is in a state of high, essentially constant potential energy. (The origin of the potential energy, or more accurately potential energy density, is a “potential” which is a property of the scalar field itself.) According to Einstein’s general relativity, under this circumstance of constant positive energy density space will expand exponentially fast. Obviously you won’t get anything interesting if space expands exponentially forever, so inflation needs to end somehow. That is where quantum mechanics (and hence probability) comes in. The scalar field quantum mechanically “tunnels” out of the “false vacuum” (elevated potential energy) state in which it is trapped, then slowly decreases in potential energy until it reaches the minimum of the potential (the “true vacuum” state). But the tunneling event that leads to an end of inflation doesn’t occur everywhere at once; it is localized to a region of space, i.e., it follows a probability distribution in each (exponentially expanding) region of space. It would be great if it ended everywhere at once, but that isn’t the way quantum mechanics works.
When inflation ends locally this way, the event corresponds to formation of a “bubble” (“pocket”) universe. Because tunneling follows a probability distribution, bubble universes form at a characteristic average rate. This is analogous to the decay of radioactive atoms — a given radioactive isotope has a characteristic decay rate, but the decay process itself is random so you never know when or where the next decay will occur.
Maybe you can now see how eternal inflation comes about in this picture. Bubbles form at a particular rate, and as a consequence of the “equation of motion” for the scalar field they continue to expand afterward. Meanwhile space outside the bubble continues to expand exponentially at a faster rate than the bubble, so the total volume of empty space (i.e., not contained inside bubble universes) within the total Universe increases exponentially faster than the fraction of the total Universe that is occupied by bubble universes. This will continue to be true forever — because the probability of a tunneling event occurring within a given “box” is proportional to the volume of the box, and the volume of such boxes is increasing exponentially fast, there can never be enough tunneling events to end this runaway effect. Hence if inflation starts it is eternal to the future.
You can also see where the so-called multiverse comes about in this picture. Just as the volume of inflating space grows exponentially, so does the number of bubble universes in them.
I’ll make a couple of general comments about this picture. First, it should be clear that the inflation idea doesn’t depend at all on string theory — it comes from mixing scalar fields, quantum mechanics and general relativity. What string theory does in an inflation picture is vastly complicate what form the potential takes, so that it is possible for tunneling plus field evolution to occur in a huge number of different ways. You’ve probably heard of the string theory landscape of perhaps 10^500 different vacua — inflation gives a way to “populate” all those different vacua, at least in principle.
Second, since eternal inflation appears to be a generic feature of inflation models that are “up to the job” of accomplishing what inflation is “designed” to do, it is a very small step to conclude that the multiverse is a prediction of inflation. Except perhaps for string theory landscape enthusiasts, this proliferation of bubble universes is not desirable from a theory standpoint because it likely compromises the predictivity of the theory, at least somewhat. There doesn’t appear to be an easy way to escape the prediction that with inflation you get a vast number of bubble universes, i.e., a multiverse.
On the other hand, according to the most “natural” way of computing probabilities, i.e., the volume measure, we almost certainly don’t live in the universe we observe (!). The volume measure is a weighting by relative volume; for example, the probability of finding ourselves in a universe at least 13.7 billion years old is the total volume of all bubble universe aged 13.7 billion years or more, divided by the total volume occupied by all bubble universes. As you might be able to see from the discussion above, the volume fraction of universes much younger than ours is exponentially greater than the volume fraction of universes our age or older. This means that the natural probability measure predicts that with near certainty our universe should be much younger than we observe. This is a dramatic failure of an important prediction of (eternal) inflation. There are some very smart people actively trying to find a different way of computing probabilities that is also “natural” but that doesn’t predict our observable universe doesn’t exist. We’ll see, there certainly is good justification for skepticism…
Marty,
Thanks for the thoughtful reply. I admit that these issues are way over my head, so some of the questions I still have may not make sense, or may have been answered by your previous response…but here goes nothing:
If I understood your post correctly, bubble universes are contained within the larger universe (which began expanding about 14 billion years ago), and the bubble universes are expanding at a slower rate than the larger universe. If so, won’t there be objects in the bubble universe that will collide with objects in the larger universe? Wouldn’t we be able to observe this?
For instance, I imagine the larger universe like an ever-expanding solid balloon, and a bubble universe to be a small bubble within that balloon that itself begins to expand outward in all directions. But if so, won’t there be situations where the bubble universe is expanding in the opposing direction of the larger universe? (e.g., In a cartesian coordinate system, suppose the center of the larger universe is located at (0,0,0), the left-most edge of the larger universe is located at (-100,0,0), and the center of a bubble universe is at (-50,0,0) and has currently has radius 10. I would expect that the point (-40,0,0), the bubble universe is traveling in the positive X-direction, whereas at that same point the larger universe is traveling in the negative X-direction).
Shouldn’t we be able to observe these bubble universes? Wouldn’t some of them be expanding towards us and be observable as such (e.g., we see a pocket of stuff corresponding to the bubble universe that is blue-shifted compared to its surroundings?). Couldn’t there be collisions between the bubble universe and larger universe that are observable?
Brathmore,
Now, on to your specific questions…
Yes, with an emphasis on “in principle.” If two bubbles formed closely enough to each other, their expansion could “outrun” the exponential expansion of space between them and the bubble walls would collide. This should create a big mess with lots of energy dissipated in the collision. However, almost all such events would occur so far away from Earth that the huge disturbances in the CMB or matter distribution would essentially be point-like, making them unobservable for all practical purposes. There is a very small but still finite probability that the aftermath of such a collision would be detectable by us. See this post by Matt Johnson on Cosmic Variance for more information:
Observing the Multiverse.
You are touching on what I think is one of the most non-intuitive aspects of the Big Bang model. A “bang” conjures up an image of an initial explosion somewhere in a larger space, and the debris flies outward into the larger space (otherwise, what would it fly into?). That isn’t the “real deal” in the Big Bang model. One of the central tenets of cosmology is that on large enough scales (say, several hundred megaparsecs), the universe is homogeneous and isotropic. (Obviously a lump of matter like a star or galaxy is an inhomogeneity; that’s why it’s important to average over much larger volumes.) Our observable universe started out homogeneous and isotropic, and it has remained homogeneous and isotropic since then.
There is a unique kinematical description of an expanding homogeneous universe — it is the Hubble law. It says no matter where you are in the observable universe, when looking outward at sufficiently large distance scales everything is moving away from you as though you were at the center of an expanding sphere. (To understand this better, read about the Hubble law.) But again, that’s only a consequence of a homogeneous and isotropic expanding universe. This situation of uniformly expanding space can be modeled as space expanding according to a time-dependent scale factor a(t), which governs how the volume of the universe increases with time. Roughly, think of V * a(t – t_0) as the the volume of the universe after a time t – t_0 has elapsed, assuming you measured its volume as V at the time t_0.
A natural follow-on question is, “Then why does a(t) increase? What makes space expand if we aren’t adding new energy/matter to the universe?” That one is harder and there is disagreement about the best way to answer that question. I don’t think there is any consensus even among the most accomplished cosmologists. Some will argue that space really is expanding, whereas others will say the idea of “expanding space” is nonsense and a source of confusion.
Am not sure if I answered that satisfactorily in my previous comment. In the eternal inflation picture, you can think of the space between bubbles as space filled with a scalar field which is trapped in a “false vacuum” state.
The Big Bang cosmology describes the evolution of the interior of “our bubble” universe, whereas the multiverse corresponds to the evolution of an eternally inflating Universe.
It seems you are referring to collisions between bubble universes. If the (eternal) inflation picture is correct, then presumably there have been a huge number of collisions of our bubble with other bubbles that “nucleated” nearby. However, according to the same picture even just our own bubble universe should be incredibly huge, far far larger than what we observe. Most such collisions (unless they occurred very early in our universe) would affect only an extremely tiny fraction of our bubble, so the amount of potentially interesting (i.e., probably catastrophic) mixing is very limited. Moreover, there would be a very limited region surrounding our bubble in which other bubbles could nucleate and eventually collide with ours. The thickness of that region depends on how rapidly the walls of our bubble and nearby bubbles accelerate toward each other after nucleation (this acceleration need not be the same for every bubble). But still, it is clear that if no bubble wall can move faster than the speed of light within the exponentially expanding “outside” space there is going to be a limit to how far away a bubble can nucleate and eventually collide with ours. This means that almost all bubble universes would never collide with ours.
If our universe were a bubble universe, by now the wall of our bubble would be far far beyond our Hubble horizon, and any collisions happening “now” would never affect us nor ever become visible. The accelerated expansion within our own universe would insulate us even more, since any effects of a collision would need to outrun the accelerated expansion. So you’re almost certainly safe…
Hi Brathmore,
Sorry I didn’t see your follow-up comment before posting my second comment. Anyway, if I understand your follow-up questions I think I may have answered them in that second comment. As far as things being over your head, that’s fine and expected if you haven’t studied this stuff before. It just means you will probably have to think about the answers and do a bit of follow-up study to get the main ideas. (Wikipedia might be a start, but in my opinion it’s a mixed bag because some articles can feel a bit technical if all you’re looking for is a conceptual picture.)
I just want to make one clarification. You said
The 14 billion years ago would apply to our bubble and not the total Universe (or multiverse). We would have no way of knowing when eternal inflation started; all such information would lie well beyond our horizon, outside our “protective” bubble.
Marty,
Thanks so much for your extensive posts. I think a key source of my questions in my second post was thinking, incorrectly, that our universe was the “total universe” and that the other “bubble” universes were contained in ours. Now its clear to me that what is meant is that our universe is just one bubble in an ever-expanding total universe that we don’t observe. Thanks for the clarifications.
Marty, the volume measure is in no way natural. It’s terrible – if you use a volume measure on an infinite volume you get nonsense results – the most likely place to be, for example, is inside a black hole. Gibbons and Turok wrote a paper on this, using the Liouville measure which in a sense is the only ‘natural’ measure available to the theory. Again, they found bad news for inflation, but using a much more mathematically rigorous way of defining measure.
Of course, all this discussion has been about eternal, vacuum tunnelling inflation instead of the now normal slow-roll paradigm which seems to answer a lot of these questions quite easily. It’s still got bad probability results, but I think some people have been looking at this in other contexts (Ashtekar and Corichi?) to show it becomes probable in modified gravity.
Correct me if I’m wrong, but in eternal inflation without string theory, the bubble universes all have the same laws of physics (e.g., the same values of parameters in the standard model), but the string landscape problem is that each of the bubble universes is in principle different, one could have two species of light fermions, and another could have six. ?? Thanks in advance.
Anonyrat,
Yes, that’s the problem with the inflation implies unpredictive multiverse argument. Inflationary theory just uses a single scalar field, one that has nothing to do with particle physics. If the eternal inflation universe exists, it’s a rather boring one, endless similar universes with the same physics.
To ruin predictivity, you need string theory, where the single inflaton field is replaced by some huge number of moduli fields governing the size, shape, and other aspects of the complicated “string vacuum” configuration. These are required to have scalar fields that give different low energy physics. Whatever you think of the eternal inflation multiverse, there’s no argument from it that gives the kind of multiverse promoted as an excuse for string theory’s failure.
Andy,
I agree with you that the canonical measure worked out by Gibbons and Turok is more rigorous and deserving of being called the “natural” measure. I probably should have called the volume measure the “simplest” or “most straightforward” measure. I thought the volume measure conceptually easier to understand at the technical level of the rest of my response, since my goal was to make a simple point. (I probably shouldn’t have even brought the subject up…)
However, if you assume that eternal inflation began at some finite time in the past rather than being eternal to the past, then the present-day volume of the total Universe would not be infinite (unimaginably huge, yes; infinite, no). So if one bases a volume measure on these finite volumes and takes this imperfectly defined measure to be representative of the measure you would obtain for an ensemble of pocket universes, then I think what I wrote is reasonable, i.e., that it predicts our observable universe should almost certainly be somewhat younger than it is. This conclusion can be modified by changing how relative volumes are computed. Anyway, like I said, I probably shouldn’t have brought it up; the subject of measures on an eternally inflating Universe is complicated and controversial, and I am certainly no expert on it.
As you noted (and as I mentioned at the beginning of my initial comment), my discussion was in the context of false vacuum eternal inflation. You mentioned a “now normal slow-roll paradigm which seems to answer a lot of these questions quite easily,” but I’m not sure what you mean in particular. Are you referring to chaotic inflation? You need slow roll in any workable inflation model I’m aware of in order to get the right spectrum of CMB perturbations, i.e., [tex]\delta \varphi/\/\varphi \sim 10^{-5}[/tex]. For example, in the “open inflation” variant of false vacuum eternal inflation, right after a bubble nucleates the scalar field slowly rolls down the potential for a “long enough” period to give the desired number of e-folds of inflation inside the bubble; this is a second stage of inflation (the first stage being the metastable local minimum where eternal inflation occurs).
Marty,
First a seemingly technical but actually important point: the volume of the universe could still be infinite even if inflation is not eternal. It depends on the topology of the spatial slice on which you perform the calculation – if you pick your space-time manifold to be R^4 with spatial slices R^3 you will always have infinite total volume. You then define volume with respect to a fiducial cell volume at a given time, and test the evolution of this cell to show expansion etc. In a closed model, or a T^3 X R model, you certainly do have finite volume, so the volume measure could make sense, but in the R^4 case you don’t. Now at first this appears to be just splitting hairs, but in constructing a measure on an infinite space, the measure itself will depend crucially on how the limit of infinite volume is taken, and you can effectively sneak in any prejudices you like by taking the limits in different ways, something I think you’re hinting at when you talk about how the relative volumes are computed.
When talking about slow roll I’m really meaning an inflaton modelled as a scalar field with a pure quadratic potential, which is what G+T talk about (admittedly a lot of my understanding comes from their paper, so I’m probably biased). Here you do see that although relative volumes do depend heavily on initial conditions, every point in the phase space does come to an end of inflation (or rather crosses \phi=0 at which point inflation is by hand brought to a halt as the inflaton couples to other fields here – this part always seems hazy). Likewise, the space-time has a singularity in the infinite past – there is no eternal inflation. I never really understood why people seemed to add the vacuum tunnelling part to this – just set a scalar field with a quadratic potential and inflation occurs. Of course, here I must admit my ignorance as there may well be a good reason for it, but for all I can tell you can’t observationally distinguish between the models and the pure quadratic potential (ie just making the particle massive) seems the simplest to my mind.
Hi Andy,
I agree with you about obtaining an infinite volume spatial slice in [tex]\mathbb{R}^4[/tex]. In fact, the example I mentioned of open inflation inside a bubble does just that. Open inflation is somewhat non-intuitive in that you have a finite bubble when volume is computed with respect to the exponentially expanding space outside the bubble, (i.e., where you have a scale factor which goes as [tex]e^{Ht}[/tex] with t the “cosmic time”), but by appropriate choice of slicing inside the bubble (e.g., as [tex]\mathbb{R}^3[/tex]) you obtain an infinite volume inside the bubble. The slicing is chosen so that just after nucleation and the second era of inflation occurs inside the bubble, the spacelike surfaces are hypersurfaces of equal scalar potential (homogeneous and isotropic); the later time hypersurfaces are the time evolution of those early-time hypersurfaces. Thus, the cosmic time inside the bubble is different than the cosmic time outside the bubble.
Outside the bubble, when I mentioned finite (but huge) volume for the total Universe, I was thinking of a particular kind of slicing, i.e., slices of constant cosmic time where the bubble volumes and the eternally inflating region are both finite for finite cosmic time; t=0 marks the start of inflation. I admit this isn’t very general.
Slow roll inflation with the kinds of potentials that are usual in particle physics (e.g., [tex]V(\varphi) \propto \varphi^2[/tex] or [tex]V(\varphi) \propto \varphi^4[/tex]) don’t seem to work well, in that they don’t give the right amount and kind of inflation required for inflation to do the job it is designed to do — inflation typically ends too early and you don’t get the right spectrum of CMB perturbations. Potentials that work better apparently need to be of the “hand crafted” variety, containing a long, gentle slope. (You also need [tex]\dot \varphi[/tex] initially small, which requires some way of obtaining that condition. Tunneling from a false vacuum provides one such way, as in the instanton formalism.)
Take the case of a slow-roll inflation model with no false vacuum or tunneling, but just a long gentle slope of the potential. I think this is what you were envisioning. Since the inflaton is a quantum field by assumption, it can behave differently in different regions. As the inflaton slowly rolls down the gentle slope, vacuum fluctuations can act on it stochastically, nudging it back up the slope in some regions (increasing the energy density) and thereby causing that region to tarry in its descent toward the end of inflation there. Inflation lasts longer in such a region than in one where the inflaton continues to descend normally or is nudged down the slope. Since the regions where the inflaton tarries will inflate more, the total volume of the Universe becomes dominated by them rather than by regions where inflation ends. Thus, you still get eternal inflation in this picture even though there is no false vacuum with tunneling.
Frank Close responded to the GHK letter in the London Times posted above. Point is around a “massive” vs. massless boson. Frank says GHK was massless (which is correct). GHK has stated such but claims the boson gets mass through leading order approximations to the 4 physical degrees of freedom.
GHK has not responded but certainly it will look like that below from Guralnik over the past summer.
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The Times
Letters to the Editor
December 22 2011
Massive Boson
Sir, My letter specifically (Dec 16) referred to the “Massive” (sic) boson which bears Higgs’s name.
GHK, the work of Gerald Guralnik, C. R. Hagen and Tom Kibble (letter, Dec 21), contains an equation for a boson without mass. While mathematically this might “amount to the same equation [as Higgs]”, for physics the difference is … massive, in all senses of the word.
Only a massive boson can decay, and it is the decays that can prove the mass mechanism. Higgs first wrote the relevant equation for this decay in 1966. If GHK, or anyone else, made published mention of decays of the massive boson before that, I shall correct my book The Infinity Puzzle, where these arguments are outlined in greater detail.
In the meantime I hope they continue to enjoy it.
Frank Close
Professor of Theoretical Physics
University of Oxford
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Again, while we will have to wait to see if GHK responds, one can bet it will sound a bit like this below from Guralnik’s recent APS talk/notes this past summer. It will be based on the fact that fundamentally the difference between massive and massless at lowest order is insignificant.
The Beginnings of Spontaneous Symmetry Breaking in Particle Physics — Derived From My on the Spot “Intellectual Battlefield Impressions”
Authors: G. S. Guralnik
(Submitted on 11 Oct 2011)
http://arxiv.org/abs/1110.2253
p. 9
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Recently it has been claimed that the GHK paper does not have the “Higgs boson”. This claim astonishes us. We, far more than any of the other groups, keep very careful track of the degrees of freedom of our scalar electrodynamics model. On the bottom of the right column of page 586 of the GHK paper are the three equations for the leading order approximations to the 4 physical degrees of freedom. We observe that the two degrees of freedom of the vector field combine with one scalar boson to form the three degrees of freedom of a massive spin one vector field. There is one remaining scalar field, 2 in our notation, which in our approximation has zero mass. That this mass is zero has absolutely nothing to do with any dynamical constraint including the Goldstone theorem. The Goldstone theorem, if valid here, would only constrain the mass of 1. The zero mass is an artifact of how we pick the explicit action and the leading order approximation. This is different from the Higgs paper in that he puts in an explicit pure scalar interaction. In a 4 dimensional renormalizable theory that interaction is limited to being pure quartic. As was our practice mirroring that commonly used by Schwinger and associates, we did not put in this explicit quartic term in scalar electrodynamics but were fully aware that such a term is generated in higher approximations. Ultimately because, of renormalization, the GHK choice of the action is operationally identical to the one used by Higgs.
In summary, our purpose was to show that the Goldstone theorem did not constrain physical mass in scalar gauge theories. We demonstrated this generally and in a specific example. The mass of 2 happens to be zero in leading order, but as was obvious to us and every other experienced field theorist of that time, this would change order by order as the theory was iterated in a manner closely related to how it changes in unbroken scalar electromagnetism.
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Hagen also spoke about this briefly in the Sakurai lectures.
http://www.youtube.com/view_play_list?p=BDA16F52CA3C9B1D
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Finally, this was found on ABC Radio. An interview with Lord Bob May of Oxford – not sure if he and Close know each other as they are both at Oxford. He comments a bit on his time at Harvard and with GHK.
ABC Radio National
December 24, 2011
Australian scientific superstars No.1 – Interview with Lord Robert May of Oxford
Robert May has achieved the pinnacle of scientific success: President Of The Royal Society, Chief Scientist in the UK, Order of Merit, the equivalent of three Nobel Prizes – yet he could have been a lawyer in Sydney like his dad, instead of Member of the House of Lords. This is the first of a series of interviews with top Australian scientists.
http://www.abc.net.au/radionational/programs/scienceshow/australian-scientific-superstars-no1—robert-may/3745700
….
But secondly I had this group of graduate student friends because they were more my age than the faculty people, and in particular a chap called Gerald Guralnik who, interestingly, along with Tom Kibble here in the UK and Higgs of the Higgs Boson, two years ago the American Physical Society gave its award essentially for the ideas of the Higgs Boson which were simultaneously arrived at by three different groups, the first of whom was not Higgs but was Kibble, Guralnik and Hagen. The other two groups proved the result in a special gauge. Kibble, Guralnik and Hagen had done it two years earlier, but Kibble is a really modest, meticulous person. He said, ‘We’re not publishing it until we have proved it with gauged generality.’ So if you go to the website of people comparing this unusual…six people get the prize that it is thought may go to no more than three for a Nobel for the discussion, well, if it’s going to go to any three, which three?
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