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.
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)?
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.
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.
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.
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 ???
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?
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.
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?
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…
Thanks, Prof. Baez!
I keep thinking of and hearing about wonderful ideas for books. . . Had I only world enough and time. . . .
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.
… 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)?
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
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.
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.
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.
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!
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
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.
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.
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?
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.
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.
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.
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?