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.
After Lambda turns on, and the gravitationally bound system adjusts to this, there is, of course, no additional expansion of it.
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).
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?
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.
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?
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?
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.
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
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.
(My answer is embedded in 32. Feel free to take issue with it.)
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 ;))
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.
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.)
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?
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.
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.
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…
Regarding Sean’s claim in 19, here’s the counter-argument I have heard: the perturbed FRW metric has g_{00}=-1-2Phi and g_{ij}=delta_{ij}a^2(1+2Phi) 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.
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.
Ann,
Have you looked at chapter 8 of “Surprises in Theoretical Physics” by Rudolf Peierls?
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.)
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.
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.
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?)
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.