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.
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 🙂
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
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.
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?)
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.
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)?
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?
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?
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.
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.
I don’t think you should just go around adding velocities linearly
That’s probably best, but now there goes my whole weekend.
Ack, I knew there was another Adam. I knew the answer to that one, too.
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?
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
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?
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?
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…
How does a gravitationally bound system behave when put into an expanding background?
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.
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.)
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.
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.
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?
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
(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.