John’s post on light-induced sonic booms has set a bad precedent of actually answering questions. (And it’s been a big hit around the internets, so our server keeps overheating.) Sensing an opportunity, commenters hungry for knowledge have chimed in to ask all sorts of perfectly good questions about cosmology. To keep things on track, let’s divert those questions to this separate thread. So this is the chance to ask all of those questions about the universe you’ve always wondered about. For example:
Q: If I plug in Hubble’s law for the velocity of a galaxy in terms of its distance (v = Hd, where H is the Hubble constant), at large enough distances the velocity will be greater than the speed of light! Doesn’t that violate relativity?
A: Yes, it would be greater than the speed of light, but no, it doesn’t violate relativity. What relativity actually says is that two objects can’t pass by each other at a relative velocity greater than the speed of light. The relative velocity of two distant objects can be whatever it wants. In fact, to be more of a stickler, the relative velocity of two distant objects is completely ill-defined in general relativity; you can only compare velocity vectors of objects at the same point. The notion of “velocity” almost makes sense in cosmology, but you have to keep in mind that it’s only an approximate concept. What’s really going on is that the space between you and the distant galaxy is expanding, which redshifts the photons traveling from there to here, and that reminds you of the Doppler shift, so you (and Professor Hubble, so you’re in good company) interpret it as a velocity. But it’s not a Doppler shift; both you and the galaxy are essentially “stationary” (although that concept is also not precisely defined), it’s just that the space between you is expanding.
In fact I already have a Cosmology FAQ that you’re encouraged to check out, and Ned Wright also has one. But feel free to ask questions here; I’m sure Mark will be happy to answer them.
February 20th, 2007 at 1:30 pm
That sparked a funny idea. Perhaps the acceleration of the expansion of our local universe due to dark energy is actually the byproduct of some far more advanced civilization’s method of getting around the light speed ‘barrier.’ We can see with our own observations it is not impossible that expanding space time pushes distant objects to ‘velocities’ faster than light with respect to each other’s far-removed locations. Could a sufficiently advanced civilization gain control over such a process? Are we seeing the after-effects of such an effort gone amuck with the acceleration of expansion, an environmental disaster of cosmological scale? Impossible to know of course, but a fun sci-fi plot-line
February 20th, 2007 at 2:01 pm
Once again thanks for answering my question, even if it opened yp a who can of questioning worms.
As we all know, the electro-magenetic force, and the weak nuclear force are the saame forces in diffrent manfistations, called the Electro-Weak force. When we go to the high energy’s and they combine, they share the same messanger particle. What is that particle, W/Z boson, a photon, or something diffrent. And at that energy, if the messanger particle is massless, or lower in need for mass do to energy, does the weak force happen more often? And what caused this symmetry break, lower engery, or some reason we don’t know. And finally, what can we make technological use for ir when they combine (i.e. we use anti-matter for PET scans.).
I nkow its a load of questions and some answer might just be unknown to man at this time. Also, if its too much to answer in on post sitting, feel free to take it over several posts. Alternatively, feel free to not answer it as it’s a lot of questions and you all have busy lives.
Thanks for helping this cheerleader for you all and physics, understand these phenominon.
~Thomas Francis Ryan III
February 20th, 2007 at 2:22 pm
Thomas — maybe it’s time to admit that electroweak “unification” isn’t really all that unified. At high energies, before the symmetry breaking, there were still two different types of electroweak bosons — three gauge bosons for the SU(2) part, and one for the U(1) part. But they were all massless, and the weak force was indeed stronger than it is now.
After the symmetry breaking, three bosons got heavy, and became the W’s and Z we know and love. One remained massless, and is now the photon. But there was a mixing-up along the way; the photon isn’t really the same as the U(1) boson pre-symmetry breaking, it’s a combination of that one and one of the SU(2) bosons. Likewise the Z. That’s the sense in which things are “unified.”
As for what does the breaking, we don’t really know, although the Higgs boson is the leading contender. It’s either that, or something more dramatic. And technological applications are always possible, but very far away from what we’re imagining right now. It takes billions of dollars just to access this energy scale; we don’t know any way of using electroweak symmetry restoration to make a smaller iPod.
February 20th, 2007 at 2:49 pm
What’s up with that whole Weakless Universe thing, and are there similar “big but discrete” changes we could imagine making to the fundamental physical laws to investigate the anthropic/landscape problem? (Such as, I dunno, throwing out a generation of quarks and/or leptons?)
February 20th, 2007 at 3:10 pm
You mean a universe without the weak interactions? People have talked about all sorts of related things, but I’m not an expert. You might take a look at Robert Cahn’s article “The eighteen arbitrary parameters of the standard model in your everyday life”:
http://prola.aps.org/abstract/RMP/v68/i3/p951_1
Unfortunately I don’t know if it’s available if you don’t have a subscription to Reviews of Modern Physics.
February 20th, 2007 at 3:12 pm
One thing I’ve always wondered is, above the electro-weak symmetry breaking scale, should we still see Zs and photons or Bs and W0s? Can the symmetry be broken in most of the universe, but be restored momentarily locally during a high energy collision (for instance at the LHC)?
February 20th, 2007 at 3:35 pm
1. The CMB is left over from the era of recombination so it gives us a picture of the universe at that time. Since dark matter doesn’t seem to interact with other matter can we assume some of it has been unaltered since even before the era of recombination? Could there then be some theoretical parameters about dark matter which would then give us a picture of the universe before recombination?
2. I hear every once and a while that assuming chaotic inflation, there could be many universes with different fundamental constants. What about inflation changes these constants? Are there any good references on this?
February 20th, 2007 at 3:37 pm
What relativity actually says is that two objects can’t pass by each other at a relative velocity greater than the speed of light.
Or maybe, “No observer will ever measure the speed of an object moving past him to be greater than the speed of light.” Two photons passing each other would have a relative velocity of 2c in the lab frame, no?
February 20th, 2007 at 4:14 pm
Adam– Roughly speaking, the symmetry can be restored during the collision, but by the time you “see” them (interacting with the detectors), what we detect are ordinary W’s and Z’s and photons (or their decay products).
Chaz– I don’t think you should just go around adding velocities linearly, you should use the formula for the relativistic addition of velocities. Which would make your statement the same as mine.
February 20th, 2007 at 4:18 pm
Joseph– The dark matter only interacts via gravity, as far as we can measure. But the time-dependent gravitational fields definitely do affect (and are affected by) the dark matter. Yes, we can extrapolate backwards to describe what the universe should have been like during recombination.
It’s not inflation that changes the constants; the role of inflation is to provide a way to take regions where the constants are different, if such exist, and blow them up to universe-sized scales. Whether or not such regions can exist will depend on your theory. In the string-theory landscape picture, there are a bunch of different ways to curl up the extra dimensions, each of which gives rise to different low-energy physics. It’s as if spacetime itself comes in different “phases,” analogous to liquid/solid/gas phases, except that there are 10^500 of them (or whatever). Just like the speed of sound etc. is different between liquid water and ice, the parameters of low-energy particle physics are different in each phase.
February 20th, 2007 at 4:56 pm
I don’t think you should just go around adding velocities linearly
That’s probably best, but now there goes my whole weekend.
February 20th, 2007 at 5:08 pm
Ack, I knew there was another Adam. I knew the answer to that one, too.
February 20th, 2007 at 5:08 pm
Ok, here’s one. The fourth question in the cosmology faq claims
How can this be? If the universe is expanding in the sense that the spatial distance between any two points is increasing, without any local acceleration occurring at those points, doesn’t that apply to bodies in the solar system as well as to distant galaxies?
Why doesn’t the stretching of scales perturb the the orbits of the planets, even if the effect is unmeasureably small? What happens to conservation of energy when the gravitational potential moves underneath the bodies?
February 20th, 2007 at 5:57 pm
rillian,
That’s actually a very good point and as far as I know the question is not well-understood, both in terms of wht you should ask and what the answer is.
Richard Price actually worked on this a little bit: see gr-qc/0508052. The discussion is pretty low-level so somebody with a modest physics background can probably understand it.
-Sam
February 20th, 2007 at 6:18 pm
Would anybody be able to tell if the local cluster of galaxies, had been move to another position in time by a super advanced civilization before 2003? I am not saying this has happened, I would just like to know if anyone would know and if yes, how would you know?
February 20th, 2007 at 6:30 pm
In GR we always assumed our spacetime was torsion free. Is there any experiment which can detect whether or not our spacetime is purely torsion free or not?
February 20th, 2007 at 6:30 pm
Couple of things that always puzzled me (and not answered in the FAQ):
1) Is there a universally agreed upon mechanism that explains Cosmic Inflation i.e. the question of exactly what caused Inflation? Is it a “one-shot” deal happening only once just after the begining? Could the universe experience Inflation over and over at some cyclic rate?
2) String theory proposes More than 3(spatial) dimensions with the remaining dimensions curled up in some way (10^500 ways). Could Inflation have impacted why only 3 dimensions grew “bigger” and the rest curled up? Is it possible that at some future epoch, another inflationary event could “inflate” more than 3? How would humans perceive a universe with 4 big dimensions of space and 1 of time (I know I am mixing up two paradigms a bit, but a really fun Sci-fi Idea)?
Could one of the experts kindly elaborate…
February 20th, 2007 at 7:04 pm
How does a gravitationally bound system behave when put into an expanding background?
February 20th, 2007 at 7:10 pm
rillian and Sam and Arun– Actually the answer to that one is very well understood! It’s not true that the distance between any two points is increasing; it’s only true that the distance between any two widely-separated points is increasing. Here in the Solar System (or in the galaxy), the expansion rate is strictly zero (on average), not just very small.
In fact there are exact solutions to Einstein’s equation that model this situation. You can start with a perfectly homogeneous and isotropic universe filled with matter (dust), and take a spherical region therein. Imagine taking all of the matter in that spherical region and placing it at the center of the region, leaving empty space in the rest of the region and an otherwise smooth distribution outside. Then the exact solution to Einstein’s equation describing this situation — inside the sphere the geometry is just the conventional static Schwarzschild solution (indeed it must be, from Birkhoff’s theorem, while outside the universe expands in exactly the same way it would have if the matter had remained smooth everywhere.
The spherically-symmetric expanding universe outside has precisely no effect, in the same way that the electric field inside a sphere with charge on the boundary will be precisely zero.
February 20th, 2007 at 7:13 pm
Qubit, I have no way of proving it, but I’m pretty sure that didn’t happen.
Joseph, it depends on what the dynamics of the torsion field is. I argued here:
http://arxiv.org/abs/gr-qc/9403058
that the torsion should be a Planck-mass field that quickly decays away, so there is no way to detect it. (Unlike the metric, there is no symmetry protecting the torsion from getting a big mass.)
February 20th, 2007 at 7:17 pm
UniversalVM– Those are not in the FAQ just because we don’t know the answers. There is no agreed-upon model of inflation; it may be a one-shot deal, or it may be a many-shot deal. It might have something to do with the number of macroscopic dimensions, or it might not. Those are all active research questions; see e.g. this paper by Karch and Randall:
http://arxiv.org/abs/hep-th/0506053
As to whether we could live in higher-dimensional universes, I don’t know. Lower-dimensional ones, probably not.
February 20th, 2007 at 7:40 pm
Well, let’s be precise. The difference between any two points in an expanding FRW metric is increasing. As you point out, our universe is not described by by an FRW metric on short distance scales, so the distance between nearby points is not necessarily increasing. But who says it averages to zero? There’s intuition and your suggestive exact solution, and then there’s Price’s result, showing that a simple electromagnetically bound system expands with the universe for sufficiently weak binding forces (but it does remain bound as it expands). Does this result generalize to general electromagnetically bound systems? Gravitationally bound systems? I don’t know, nor would I know how to start asking. Are there definitions of “gravitationally bound” in the literature? I don’t know of any.
February 20th, 2007 at 8:04 pm
Sean, thanks for the response. Unfortunately, I remain confused. Perhaps it would help if you explained how to determine if two points are widely-separated.
I believe you that the expansion continues as before outside your spherical region, but what about moving the mass to the centre stopped space inside that region from expanding? It’s it the empty space itself that’s supposed to be expanding?
February 20th, 2007 at 8:50 pm
Sean,
Re: #19. In a universe expanding due to a positive consmological constant, Birkhoff theorem doesn’t quite apply. It’s assumption that spacetime is empty (in the region that you cleared of dust) is no longer true due the Lambda-related stress energy.
The spherically symetric solution (which I believe is unique) in this case is the generalization of the Schwarzschild solution to de Sitter space. The associated Newtonian graviational potential phi is given by
February 20th, 2007 at 8:55 pm
(continuing from accidentally submitted post #24)
phi = -GM/r – (Lambda/6)r^2.
The gravitational repulsion from the r^2 term would indeed cause gravitationally bound systems to expand. The expansion is negligibly small, however, because Lambda (the cosmological constant) is tiny.
February 20th, 2007 at 9:16 pm
After Lambda turns on, and the gravitationally bound system adjusts to this, there is, of course, no additional expansion of it.
February 20th, 2007 at 9:52 pm
One can implement a Universal Turing Machine using 2D cellular automata. While I don’t know of anyone trying to formulate this in the context of string theory and D2-branes, it seems plausible that enough complexity can live on a 2D surface that matter could come together, evolve and one day wonder where it came from.
On the other hand, the string gas cosmology people have ideas on the blackboard about why six dimensions of space curled up and the other three didn’t. (The following is my attempt to explain something I admittedly don’t understand very well myself.) String interactions involve the intersection of strings, and because p-dimensional objects can intersect in at most 2p + 1 dimensions, a gas of 1D strings wiggling and winding through 10D spacetime can only maintain an equilibrium in at most three dimensions. Those three dimensions are free to expand, while the windings of the strings keep the other six dimensions curled up at the string-length scale (one umpteenth the diameter of a proton).
This is connected, I think, with the fact that one can construct knots in three dimensions but not two (the knot can’t pass over itself) or four (too much room for the knot to slip loose).
February 20th, 2007 at 10:11 pm
This is slightly off topic I think. I was just looking at my book shelf and pulled out a peculiar book that I’ve had for about 30 years, and never really got around to reading seriously: “Foundations of Special Relativity: Kinematic Axioms for Minkowski Space-Time” (John Schutz). Apparently it was an attempt at axiomatizing Special Relativity, and reads much like a math book with definitions, lemmas, and theorems. Can anyone tell me if any of this material is relevant anymore? Did this or other approaches lead anywhere? Should I toss it?
February 20th, 2007 at 10:30 pm
Richard, axiomatizing special relativity isn’t especially difficult. It’s nice to prove theorems and so forth, and it’s not wrong, but I don’t know if it’s especially helpful.
On the expansion stuff: after the Big Bang, all matter is moving away from all other matter (space is expanding everywhere). But gravitational attraction acts to pull matter together in overdense regions. At some point, which will depend on the physical size as well as the amplitude of the overdensity, the matter begins contracting rather than expanding. That’s the point at which it’s no longer correct to say that space is expanding in that region. More formally, two test particles initially at rest will not (on average) begin moving apart. You have to say “on average,” because local perturbations in the density will generally push and pull test particles all over the place.
That last bit is worth emphasizing: the real world is not perfectly homogeneous and isotropic, nor is the Solar System described by the Schwarzschild metric. These are only approximate notions. Ten billion years from now, however, when distant galaxies are twice as far away from us as they are now, the distance between the Earth and the Sun will be pretty much the same — and the influence of Jupiter will be much more important than the influence of other galaxies.
February 20th, 2007 at 10:39 pm
OK, here’s a new one: we know that an accelerated charge radiates. It would then appear that the equivalence principle would imply that a stationary charge in a gravitational field will radiate, but it doesn’t. What’s going on here? One would expect that the answer will depend on the frame of reference of the radiation detector, e.g., a detector accelerating along with the charge will see a static electric field. But does this mean that a detector accelerating relative to a stationary charge in a gravitational field will detect radiation?
February 20th, 2007 at 11:08 pm
Sean – “the space between you and a distant galaxy is expanding…”
As James Bjorken pointed out when the same claim was recently made in Scientific American, isn’t that really just a gauge choice? Other coordinate systems than FRW exist and have different interpretations.
Corresponding to any observable red shift of a distant galaxy, a nearby object with the same (Doppler) red shift would be moving away at less than the speed of light. Right?
February 20th, 2007 at 11:22 pm
CIP, it’s not really a gauge choice. The coordinate-invariant way of saying it is: two test particles, placed initially at rest with respect to each other, will begin to move apart. More formally, the expansion of timelike geodesics is positive.
sjn, that’s an old chestnut (but a good one). And the answer depends on the definition of “radiation.” If you mean an oscillating electromagnetic field in the far-field regime, a charged particle stationary on earth certainly doesn’t radiate, but neither does one with constant acceleration.
But it’s important to realize that the question is internally inconsistent; “radiation” is a phenomenon observable far from the particle, while “the equivalence principle” is a statement about what can be observed in small regions of spacetime. The correct thing to do is simply to solve Maxwell’s equations in the appropriate background with the appropriate boundary conditions. The answer will be unique, and that’s what will happen. Everything else is just words.
February 20th, 2007 at 11:26 pm
sjn’s question is one our theory group has debated-we are still not completely sure of the resolution either and I would love to hear Sean’s answer
February 20th, 2007 at 11:38 pm
SJN’s question is a classic. The standard answer is that whether or not something is radiating depends on your frame of reference. There is some dissent on this point, though.
February 20th, 2007 at 11:41 pm
(My answer is embedded in 32. Feel free to take issue with it.)
February 21st, 2007 at 12:05 am
Alright here is a “landscape” question
Let’s assume for the sake of argument that the landscape exists. What laws of physics are expected to hold in each every universe? Or are there no such laws? For example would thermodynamics be “true” in every universe? Assuming no such law is guaranteed in all members what laws would be most probable?
Elliot
(perhaps this thread should be considered opening a can of wormholes
)
February 21st, 2007 at 12:18 am
All right, so the statement that “structures formed from gravitational collapse of initially unbound material generically do not expand” is presumably supported by a wealth of numerical evidence and I definitely believe it. But I do have to add the modifier “generically”, because, for example, it a structure formed from gravitational collapse like a human being might decide to create a gravitationally bound system that does expand, like the “electromagnetic atom” Price constructed. Or maybe such a system can be formed during collapse , but it happens very rarely and therefore simulations don’t show it.
In any case, I think we have clarified the disagreement. It is possible in principle to have a bound system that expands with the universe (as shown by Price), but it is extremely unlikely that one would have formed in ours.
February 21st, 2007 at 1:19 am
Elliot,
Questions like yours tend to be asked about the Landscape, and this indicates the degree to which the whole idea flirts with incoherence. Sean previously referred to effective laws in our universe (and other universes) within the so-called multiverse. These effective laws are presumably a manifestation of the underlying fundamental law (laws?) which gives (give) rise to the Landscape in the first place, combined with relatively local features of the background spacetime.
The problem of course is that it is extremely hard, and perhaps* impossible, to test this putative fundamental law; the laws we know, and know how to test, are only indirect manifestations of it. The water is severely muddied by the role of the background.
That said, it is not at all clear that it makes any sense to talk about the laws of thermodynamics being different or inoperative in some parts of the multiverse. The idea of varying laws tends to suffer from scope creep; the original concern was with a relative small number of parameters derivable from observations and not fixed by known laws, in particular the cosmological constant. Of course, the idea of the Landscape has opened the floodgates; now we don’t really know where the hell we stand. See the discussion here.
[Speaking of thermodynamics and the cosmological constant, see the new paper Predicting the Cosmological Constant from the Causal Entropic Principle (hep-th/0702115 - Bousso, Harnik, Kribs, Perez).]
(* I’m being generous here.)
February 21st, 2007 at 1:37 am
Questions:
Why is the “initial” (post big bang, pre-stars) H/He ratio so high?
Why do galaxies collide instead of simply orbiting each other?
Does the universe have angular momentum?
February 21st, 2007 at 1:52 am
Elliot– Although we don’t know what kinds of conditions actually hold outside our observable patch of universe, in the landscape picture expected in string theory the range of possibilities is not all that dramatic. We’re really talking about different choices of low-energy effective field theories — particle contents, interactions, coupling constants. The basic frameworks of quantum field theory, relativity, and thermodynamics are expected to be pretty much the same throughout.
February 21st, 2007 at 1:58 am
Lab Lemming– The primordial He/H ratio is governed by Big-Bang Nucleosynthesis. Given the number of photons, neutrinos, and baryons in the universe, we can figure out that neutron-proton interconversion stops when there were about six protons for every neutron, just a second or two after the Bang. Nothing much happens for a while, except that neutrons decay. When it gets down to about one neutron for every seven protons, the temperature is low enough that Helium can form; we end up with about one Helium nucleus for every twelve free protons. Thus, about 25% Helium by mass.
Galaxies collide sometimes because they aim right at each other. Galaxies are pretty big; they are much closer to other galaxies, in units of their own size, than (for example) stars are within the solar neigborhood. (Many galaxies, of course, do orbit each other.)
The universe probably doesn’t have any appreciable angular momentum. There’s no evidence that it does, and if it did it would probably show up in CMB anisotropy. See also the story of the screwy universe.
February 21st, 2007 at 4:01 am
Sorry if this exposes my scientific naiveté (I do software not astrophysics), but I have a hypothetical:
I get in a spaceship and accelerate to half the speed of light to visit a distant star. During the trip, I give birth to a child (it’s my hypothetical, so I can do what I want). A problem develops in our spaceship, so we have to return to earth, and do so at half the speed of light.
To my child’s perspective, we’ve accelerated to the speed of light (i.e. the speed difference from his birth will seem to have been from 0 to the speed of light).
Have I violated any laws (besides good taste in hypotheticals)?
Thanks…
February 21st, 2007 at 4:27 am
Regarding Sean’s claim in 19, here’s the counter-argument I have heard: the perturbed FRW metric has g_{00}=-1-2\Phi and g_{ij}=\delta_{ij}a^2(1+2\Phi) where \Phi is the gravitational metric and is very small. As, e.g. a halo forms, the metric can maintain this form since \Phi remains small even as overdensities grow. Indeed, this form is consistent with the metric in the solar system since GM/r is very small everywhere in the solar system. Of course, the effect of \Phi on the motion of particles is much larger than the effect of \dot a, but Sean is claiming I think that there is no “a” in the solar system metric, so there is literally zero effect from \dot a. There is a large class of people who disagree.
I am not a relativist so may be missing something. I get the sense though that this is an open question.
February 21st, 2007 at 6:29 am
By “radiation” I meant something that could be detected and register in a detector such as a photomultiplier tube. I assume this would detect Unruh radiation if it is at rest in a gravitational field just as it would if constantly accelerating. But is a phototube which is at rest in the gravitational field of the earth able to register any photons emitted from a charged particle which is freely falling past it? Since the detection of a photon is a definite event this is not an observer dependent question.
February 21st, 2007 at 8:12 am
Ann,
Have you looked at chapter 8 of “Surprises in Theoretical Physics” by Rudolf Peierls?
February 21st, 2007 at 10:27 am
A small addendum to Sean’s answer (#41) to Lab Lemming’s second question (#39):
Galaxies can also collide even if they start out orbiting each other, because their orbits can decay due to what’s called dynamical friction. Consider a small, “satellite” galaxy orbiting close to a larger one, so that it’s within the outer part of the big galaxy’s dark-matter halo. As it orbits, the gravity of the satellite attracts nearby DM particles from the halo. Because the satellite is moving, more DM particles will tend to accumulate behind the satellite than in front of it, and the satellite will fell a net backwards pull from the gravity of the extra DM behind it. This removes energy from the satellite’s orbit, causing it to spiral in towards the big galaxy.
(Energy and angular mometum are still conserved; the energy and angular momentum lost by the satellite galaxy are gained by the DM particles of the halo.)
February 21st, 2007 at 11:15 am
dave– You have to ask yourself, “the speed of light relative to what?” Nowhere on your journey would you be passing by any objects with a relative velocity faster than the speed of light, so you’re fine.
February 21st, 2007 at 11:18 am
Not a Relativist– The metric you describe is certainly not a solution to Einstein’s equation in the Solar System; it’s approximately good on length scales over which you can average the density, but most of the space in the Solar System is really empty, and such averaging doesn’t make sense.
February 21st, 2007 at 11:22 am
Ann– I think that your set-up is “local” enough that the equivalence principle does tell you the answer. And that answer should be the same as the answer to “If I have a stationary particle in empty space and my detector accelerates past it, does it detect photons?” To which I presume the answer is “yes,” since it sees a time-dependent field. But really my point is that you just solve Maxwell’s equations, specify the coupling of the detector to electromagnetism, and read out the answer. (We can think perfectly classically for this problem, right?)
February 21st, 2007 at 2:08 pm
Sean #21 – Thank you for the link. However on following up with that link, I am now begining to have some serious doubts. To me it seemed that Inflation was universally accepted and all/most of the mechanics of it completely described. However looking at the open questions that still remain, it is looking more and more like a “device” to explain the large scale uniforminty that we observe…Are we on solid ground when we take cosmic inflation as a “given”. Is there an undeniable single observation that forces us to accept Inflation ?
Blake Stacey #27: So life in 2D is possible, in 3D is certain, we exist (I think..) how about 4D – four large dimensions of space (and one of time). Is there any reason that organisms of equal or greater complexity than humans can not exist in 4D?
Also, thanks for the links to String Gas cosmology. Interesting reading… but sounds like a lot of work needs to be done before they could start laying out interesting results.
February 21st, 2007 at 2:36 pm
A friend of mine posed this question the other day. Since time runs slower in a gravitational field, just how slow would things have been going at the time of the Big Bang? Of course, since the entire universe runs slow, it’s not like anyone would have noticed. But if there was an outside observer in some higher dimensional space, maybe everything took place quite leisurely. So, starting at some epsilon of time from the beginning, how long would the first second take to happen (to an outside observer)?
February 21st, 2007 at 2:44 pm
UniversalVM, inflation is a very promising idea, and it’s made some predictions that have turned out right. But it’s certainly not established beyond reasonable doubt. That’s okay; it’s just how science works. We’ll try to keep testing the idea, and coming up with better models.
General Electron– Time only runs slower in a gravitational field compared to some region far away (and even then it’s a very imprecise notion, which a careful general relativist would never use). What really matters is how signals propagate from one event to another. If there were such an extra-dimensional observer, what they would see would depend sensitively on the geometry of spacetime between them and us. So there’s no unique answer, I’m afraid.
February 21st, 2007 at 2:57 pm
One of the quantum numbers of a particle is called spin, meaning angular momentum. Is this a mneumatic device, (i.e. Like quarks having “color” just to create a new quantum property of the particle, thus having nothing to do with the colour), or do they really spin?
The universe started with a big bang. In theory, it must have been a uniform distrubtion of all the sub atomic particles. As we all know, something changed this uniformity, then came inflation, so even a really small thing become huge after that multiplier. I know we don’t know why it they started clumping, but know that it did thanks to COBE’s fine details. In your expert opinions, was it quantum flucuations that “mixed up” the uniformity, thus letting gravity do its thing, or dark matter popping out, causing the uniformity to stop. But if that were the case, shouldn’t the dark matter be unifrom in theory from what little we know of its nature now.
Finally, the main goal of physics is to quantisize gravity. As of yet, we haven’t found this massless, spin 2 particle, which should be really easy to find/create since its all around us and like photons, they can dump off of the source in large quanties due to the maslessness. So, my question is this. It seems really easy in theory to create said particle or even detect it since it so ubiqutious. What are the odds that Einstien was right and its really warpage of space time on this one force. It’s seems the most strange, has the heircharical delimea, GR’s been vary well tested, and we can’t find a particle that should be as easy to find as a proton. Obviously, with the singularities it predicts and the whole using it for the black hole research, it needs fine tuning, no one doubts that. But how probable is it that it really is warped space-time without quanta, and the other three do. Ball park average from what you’ve seen and experienced It seems like the obvious answer to me, but you guys are experts on these things and thay’ve been kicking in my head as well.
Anyone care to take a crack at these? I know the answer to some parts is we don’t know, but in that case, give me what you suspect likely, or failing you having a suscipition of another expert if you know of one.
February 21st, 2007 at 5:34 pm
Thomas– Spin really is part of the angular momentum of a system.
According to inflation, the density perturbations arise from quantum fluctuations. In the simplest models, the fluctuations of dark matter are correlated with those of radiation and ordinary matter; but there are plenty of non-simple models.
As far as gravitons go, it’s really hard to make individual gravitons, because gravity is very weak. It’s easy to make coherent superpositions of many gravitons — that’s just a classical gravitational field, such as the one holding you to the Earth. And there is no inconsistency between thinking of gravity as the curvature of spacetime and believing in massless spin-2 gravitons; the latter is just the quantized weak-field description of the former. We don’t have a complete theory of how quantum gravity works beyond the weak field, but it still makes sense to believe in gravitons.
February 21st, 2007 at 8:42 pm
The Dark Energy could be the result of some higher order symmetry breaking exercise, is it possible? or to say it in different way could we think of dark energy as some new (5th) force which separates out at largest cosmological scales ???
February 21st, 2007 at 8:46 pm
Re: 32 I think you demolished a strawman, Sean. Nobody is arguing that spacetime curvature is a gauge choice. The question is whether you view the resulting relative motion as ordinary velocity or as “expansion of space.” FRW coordinates seem to be very convenient for our local Cosmos, but in GR they are just a coordinate choice. Or am I missing something?
February 21st, 2007 at 9:22 pm
There is a big difference between ordinary velocity and expansion of space (in principle, at least). In fact, I would argue that the previous answer reveals that. If I put two non-interacting test particles in the midst of a set of non-interacting dust particles, all of which are moving away from each other, the test particles just sit there; they don’t pick up any velocity. Whereas, if it’s really space that is expanding, they do start moving along with it.
Another example, which I use in my book: consider light emitted from one galaxy to another, where the galaxies are initially stationary with respect to each other. While the light is en route, the galaxies are moved apart, and then brought to rest again before it is absorbed. Is there a redshift? If the “moving apart” means that we move the galaxies through a non-expanding space, the answer is “no”; if it means that we expanded space, the answer is “yes.” So there are physical differences between ordinary velocity and expansion of space.
February 21st, 2007 at 11:30 pm
Here’s a basic one that’s bothered me for a while: If the universe began in a singularity, then aren’t all regions in causal contact with one another? So why is there a horizon problem?
February 22nd, 2007 at 12:33 am
Blake Stacey writes:
I find the whole anthropic/landscape problem terminally dull. To me, the good thing about studying “big but discrete” changes in the laws of physics is that it’s a fun excuse for imagining weird universes while getting practice doing physics.
You could write a very fun textbook where you took the Standard Model, deleted various particles or interactions, and described the resulting universes.
Start with something simple: U(1) gauge fields and nothing else. A universe of pure light — Maxwell’s equations!
Then try SU(2) gauge fields and nothing else. What would that be like? I guess you get glueballs if the coupling constant is big enough!
Then try SU(2) × U(1). Then throw in a Higgs! Etcetera…
In a bunch of the fancier versions you’d get some kind of “chemistry” going on…
February 22nd, 2007 at 9:26 am
Thanks, Prof. Baez!
I keep thinking of and hearing about wonderful ideas for books. . . Had I only world enough and time. . . .
February 22nd, 2007 at 10:23 am
The fact that no radiation from before the recombination epoch can reach us today is well understood, and appears to be validated by the CMB. However, one aspect which I haven’t seen discussed is that before recombination, radiation is effectively moving in a highly dispersive medium, so the phase velocity of light is reduced dramatically. Yet the hot big-bang theory is extrapolated back beyond this time as if nothing significant occurs.
In the standard model, assuming a flat universe, the speed of light enters the Friedmann eqation in two places: explicitly in the term involving the cosmological constant (although this is often hidden as a scaling factor); and impicitly in the term involving the energy density. At times before recombinaton only the latter term should be important, and assuming a black body radiation spectrum for the energy density one obtains the usual expression for the temperature of the universe at time t:
T^4 = A/( t^2 c^5)
where I’ve absorbed most constants in A, but I’ve left explicit the dependence on the speed of light c (which comes from the photon dispersion relation). If c is constant one obtains the usual relation: log(T)=-1/2 log(t) + const
However, if c is actually varying with the size (age) of the universe this relation would be modified. I don’t know how c might vary between the time of the big bang and the recombination era, but presumably it was smaller for smaller values of t, when the universe was denser, and approached the speed in vacuum at the time of recombination. So just for fun let’s suppose it has a power law behaviour, c=c0*t^β Then the relation between temperature and the age of the universe becomes
T^4 = B t^(5β-2)
So depending on the value of β, the temperature could decrease more slowly (than for c=const), not at all, or actually increase with time depending on whether β is smaller, equal to or greater than 2/5.
The last paragraph was just meant to indicate that if c does indeed vary with time before recombination, due to the fact that radiation scattering is increasingly strong as one moves back through time, then the standard relation for the temperature of the universe as a function of time could be modified, affecting the usual view of the history of the universe.
February 22nd, 2007 at 10:24 am
… At high energies, before the symmetry breaking, there were still two different types of electroweak bosons — three gauge bosons for the SU(2) part, and one for the U(1) part. But they were all massless, and the weak force was indeed stronger than it is now.
After the symmetry breaking, three bosons got heavy, and became the W’s and Z we know and love. One remained massless, and is now the photon. But there was a mixing-up along the way; the photon isn’t really the same as the U(1) boson pre-symmetry breaking, it’s a combination of that one and one of the SU(2) bosons. Likewise the Z. That’s the sense in which things are “unified.”
As for what does the breaking, we don’t really know, although the Higgs boson is the leading contender. … – Sean, comment #3
You’re saying that the weak gauge bosons, or their equivalents above electroweak symmetry breaking energy, are massless? Wouldn’t they have infinite range at high energy (massless), then?
The photon has infinite range at all energies. The weak 80-90 GeV Z and W+/- gauge bosons have a range of about 10^{-16} m. At distances beyond this range, there will only be photons (so the symmetry will be broken due to the masses of the Z and W+/- bosons) but at distances well within the 10^{-16} m range, the property of mass will cease to attenuate the massive bosons, so they will be present along with photons, hence unification.
At higher energy, there is a smaller distance between interacting particles, so there is less intervening vacuum. If the vacuum contains a Higgs field which gives rise to mass by “miring” the particles to give them inertia (like treacle), you’d expect to require some distance before mass is acquired.
Presumably, is it a case that a proto- W+, W- or Z starts out mass-less close to particle (i.e., a distance corresponding to very high energy in a scattering experiment), and then acquires mass by the Higgs miring mechanism as it travels away (into regions at greater distance, corresponding to lower energy physics)?
February 22nd, 2007 at 12:25 pm
Chris W wrote:
[Speaking of thermodynamics and the cosmological constant, see the new paper Predicting the Cosmological Constant from the Causal Entropic Principle (hep-th/0702115 - Bousso, Harnik, Kribs, Perez).]
This looks very interesting and provocative.
Thanks
Elliot
February 22nd, 2007 at 12:29 pm
fred (58)– That one is hard to explain beyond “trust me, that’s what the math says.” Even though the Bang was a point in space, at any moment afterwards there were points which (in an ordinary matter/radiation-dominate universe) would still be out of causal contact today. And of course the Bang singularity itself doesn’t really count as part of the geometry; it’s just the place where our ignorance becomes complete.
February 22nd, 2007 at 12:35 pm
James (51)– You’re right that the pre-recombination universe is a highly ionized plasma. However, the factor “c” that enters into those formulas isn’t “the speed of light,” it’s “the speed of light in vacuum.” It doesn’t matter what speed photons are actually traveling.
What does matter is how the energy density scales with the expansion of the universe, and that will definitely be 1/a^4, even when you take the plasma effects into account. In fact, the success of primordial nucleosynthesis assures us that this isn’t just a guess; it’s empirically correct. Any other expansion history would give a very wrong set of light-element abundances.
February 22nd, 2007 at 12:38 pm
Z (62)– I’m not sure I understand what you are saying. Below the electroweak symmetry-breaking scale, the Higgs has a vacuum expectation value everywhere, and the W’s and Z’s are massive everywhere; their distance to other particles doesn’t matter. Above that scale, they are massless and in principle long-range, but in practice they are frequently interacting with other particles in the plasma. I hope that helps.
February 22nd, 2007 at 1:12 pm
Even though the Bang was a point in space, at any moment afterwards there were points which (in an ordinary matter/radiation-dominate universe) would still be out of causal contact today. [Sean (64)]
Can you address this more technically? (I took GR many years ago…) Thanks!
February 22nd, 2007 at 1:30 pm
Well… it’s just a matter of tracing back the light cones in a radiation-dominated universe. I don’t know how to be more technical and explict than that without actually doing the calculation; see e.g. here:
http://arxiv.org/abs/astro-ph/0401547
February 22nd, 2007 at 2:57 pm
Sean (65) thanks for your response. It seemed to me that the factors of “c” came from the black body radiation formula and hence from the photon dispersion relation. I don’t see why the latter should be the same in a dense plasma as in free space. The classical result is that k/ω = sqrt(εμ) and only in free space is this equal to the speed of light in vacuum.
February 22nd, 2007 at 5:28 pm
I forgot to mention that I wasn’t questioning the 1/a^4 dependence of the energy density, which leads to a Hubble constant H=1/(2t) This can be plugged back into the Friedmann equation to give
(1/2t)^2 = 8πGρ/3
(with curvature k=0 and ignoring the term involving the cosmological constant for small t)
Then for radiation the average energy density is ε=ρc^2 =αT^4 where α is the radiation constant which contains a factor 1/c^3. Substituting for ρ one gets the equation I gave above. This makes it clear that the factors of c are coming from the photon dispersion relation.
February 22nd, 2007 at 8:47 pm
Three Interesting Dark Matter Papers
I would like to bring to your attention three interesting papers which discuss the prospects for us being able to detect dark matter in the near future. Each paper focuses on the most popular dark matter candidate WIMPs (Weakly Interacting Massive Particles). The first paper (astro-ph/0609126) takes all that we know e.g. the constraints from collider experiments and cosmology and does a state of the art bayesian analysis of the detectability of neutralino dark matter. The main result of this paper is well summarized in a probability bar graph which shows that there is a 95% probability that the particle cross section is between 10^-8 pb and 10^-10 pb. For reference, the two most sensitive direct searches are the Xenon10 and CDMS II, and during 2007, as discussed in the second paper (astro-ph/0611124), will just begin to probe the 10^-8 pb cross section. It will take 1 ton detectors to reach 10^-10 pb.
The last paper (hep-ph/0611065) discusses how there is a relationship between the ability of the Tevatron and the LHC to produce the heavy Higgs and the ability of dark matter direct detection experiments to detect the WIMPs. According to the paper, if the heavy Higgs is found in the LHC collider, and many people think it will be, then dark matter will likely be found in the near future by direct detection experiments. Of course, this study makes some assumptions also known as “priors”, but the take home message, at least to me, is that it seems likely that we will solve the dark matter mystery soon.
What do Sean and company think? Is it likely that the dark matter will be found soon?
February 22nd, 2007 at 10:54 pm
I don’t know if it’s likely or not, but it’s certainly promising. Any such estimate depends very strongly on the nature of one’s favorite models, so placing odds is hard. I’m optimistic, but that might just be my naturally sunny disposition.
February 23rd, 2007 at 8:15 am
Thanks, Sean. Just two more quick questions about normal matter:
Is there a way to determine how much normal matter is now stuck in black holes, neutron stars and other highly dense entities?
On a related note, once a neutron star forms, can you ever get anything out of it again? (practically, not theoretically)?
Thanks for doing this, by the way.
February 23rd, 2007 at 12:31 pm
The best constraints on normal matter are really constraints on the baryon density, from primordial nucleosynthesis and the cosmic microwave background. (They’re consistent, implying that baryons make up about 4-5% of the critical density). If you’re talking about black holes etc. that were made after recombination, both constraints would still apply. If you’re talking about primordial black holes, they wouldn’t contribute to that 4-5%.
I have no idea what’s practical and what’s not. Is getting stuff out of the Sun practical? There’s no obstacle in principle to getting stuff out of a neutron star.
February 23rd, 2007 at 1:25 pm
Relevant to cosmology I think:
Q. Are you physicists satisfied with current mathematical “state” of infinity (and 0 to a less degree)?
More generally, what kind of mathematical “discovery” would make you really excited?
February 24th, 2007 at 12:06 pm
Sean,
I found a good introductory reference for my above question about chaotic inflation and differing constants and your possible string landscape answer( You probably saw it on arXiv.org but if not):
“Eternal inflation and its implications”, by Alan Guth.
http://arxiv.org/abs/hep-th/0702178
It’s a great Introductory article.
February 25th, 2007 at 2:20 am
Sean,
You said: “I don’t know if it’s likely or not, but it’s certainly promising.” However, the dictionary.com definition of the word promising in the context you are using it is “giving favorable promise; LIKELY to turn out well.”
Talk of favorite models implies that we really don’t have any evidence guiding us toward a strong “suspect” for the dark matter. By analogy, if when a dectective is asked how likely is it that the murderer will be found and he responds by saying each detective has his favorite suspect, then we would rightly conclude that the police force really has no clue who committed the murder. So, are you saying that we really don’t have any clue what the dark matter is? and, if so, how can it be “certainly promising?”
February 27th, 2007 at 8:18 pm
There was an article in physorg today, with the lead… “A hidden twist in the black hole information paradox”.
It ends with, “Quantum information cannot be completely hidden in correlations: Implications for the black-hole information paradox” appears in the latest Physical Review Letters.
Sorry for being so dumb on this, but just what does ‘information’ mean in this context?
March 1st, 2007 at 3:11 pm
hi,
can we discuss about gravity wave background, why should there be one and how is it related to inflation ?
and can it be seen ?
March 1st, 2007 at 11:56 pm
Dark Matter and Dark Energy seem to be “in these days”. If there is interest in another possible candidate for Dark Matter, read comment 30, in Sean’s “find of Dark Matter and Sterile neutrinos” February 10, 2007 blog. If not turned-off by what is shown and interested in “the rest of the story” (even for Dark Energy) more can be said!
March 2nd, 2007 at 12:29 pm
hello guys, no I am disapppointed as no one has answered my ques. Come on, I want to know why should there should be a GWBR and how is that connected to inflation. Sean please! I will be looking forward to ur answer!
March 4th, 2007 at 11:07 am
Sean, I have brought this up before . maybe you and other readers of CV
can chime in again.
My queston is what exactly did
Kopeikin-Fomalant experiment measure?
Sergei insists that his measurement is a model-independent measurement of
speed of gravity and has provided (IMO) reasonable counterarguments
to his critics.
However even the papers which critiqued his measurement take completely
diffrenet point of view. See Samuel’s paper which says that this does not
even measure speed of gravity in GR.
What do readers of CV think?
March 4th, 2007 at 2:19 pm
zeenia– There are different possible sources for a gravity-wave background, and searching for it is an ongoing project. Any major ruckus in the early universe is a candidate to make gravitational waves; for example, a strong phase transition (analogous to bubbles in boiling water) could stir things up and leave gravitational waves behind. Even better, gravitational waves could be created during inflation, just as density perturbations are. People are trying to detect the influence of such waves in the cosmic microwave background, and perhaps someday via a dedicated satellite.
Shantanu– Measuring the “speed of gravity” is like measuring the “speed of blue”; the concept just doesn’t apply. You can talk about the speed of propagation of gravitational radiation — in that case, the prediction of GR is unambiguous that gravitational waves propagate at the speed of light. Arguing about whether some particular measurement is really probing the “speed of gravity” is a waste of time; the important thing is that no observation yet performed is inconsistent with the predictions of GR.
March 4th, 2007 at 6:40 pm
Sean,
I am not sure if the study of the CMBR is your area of cosmological expertise, but I was wondering, what is your opinion of the conclusions reached in a recent paper titled “On the apparent lack of power in the CMB anisotropy at large angular scales” by Amir Hajian of Princeton University? (astro-ph/0702723) When the COBE data was released one of the puzzling unexpected aspects of the full-sky CMB maps was the absence of long wavelength fluctuations; this odd feature, odd in the sense that it is at odds with inflationary theory, also exists in the WMAP data (or does it?). In other words, if the Universe is infinite and homogeneous, as inflation predicts, it is awfully improbable that we should not be seeing long wavelengths in our tiny portion of the cosmos.
But now, as reported in the above mentioned paper, it appears that there is no deficit in large scale power in the full sky maps, and the explanation for the apparent lack of large scale power is that masking the sky near the galactic plane creates this appearance.
March 12th, 2007 at 2:04 am
[...] All of which springs to mind because the Modern Mechanix blog has unearthed a Popular Science article from 1932 by Donald Menzel, an astronomer at Harvard, that explains Lemaître’s ideas. (The time between Hubble and Humason’s discovery and Menzel’s article is somewhat less than the time between the 1998 discovery of dark energy and yesterday’s New York Times article.) Menzel’s piece does a great job of explaining the basics of the Big Bang model, long before it was given that name by Fred Hoyle. Indeed, he touches on many of the questions that still arise in a good Cosmology FAQ! For example, he emphasizes that the redshift is due to the expansion of space, not to the Doppler effect. The case of the universe is analogous, except that the expansion, being of a three-dimensional volume, cannot be visualized. The phenomena are, however, comparable. The nebulae are not running away from us. Their recession is due to expansion of space. This may, perhaps, seem to be quibbling over terms, since it amounts to the same thing in the end. Nevertheless, the distinction is worth keeping. According to the relativity theory, there is a difference between the running away of the nebulae and expansion of the medium in which they are imbedded. [...]
March 13th, 2007 at 1:45 am
The good forum, has found answers to many questions.
Thanks:-))
March 16th, 2007 at 3:30 am
Is this thing still on?
If so, I have a question.
Why can’t physicists use the standard model to calculate exact decay constants for radionuclides, thus alleviating us geologists from having to measure them?