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26

We need to be precise about the phrase the size of the universe. Specifically I'm going to take it to mean the maximum possible separation between any two points. In an infinite universe two points can be separated by an arbitrarily large distance, so if the maximum distance between two points is finite this means the universe must not be infinite. The ...


11

This claim is simply wrong. The flat hyperplane is of course infinite, but non trivial topologies can be flat and still finite. The simplest example is the 3-torus, but there are even the Klein bottle and the Hantzsche-Wendt manifold. See for example page 27 of Janna Levin - Topology and the Cosmic Microwave Background, which show you ten different closed ...


9

I'm not going to provide a full answer here, because I don't know the answer, but I want to give some statements that illustrate quite nicely the kind of problems one would face when determining topology of anything: We know spacetime is a manifold. That means, locally, it looks just like $\mathbb{R}^4$. That's already a bummer. We can't do jack at one ...


9

Measuring $w$ is actually what I do for a living. The current best measurements put $w$ at $-1$ but with an uncertainty of $5\%$, so there's a little room for $w \ne -1$ models, but it's not big and getting smaller all the time. Indeed, we'd all be thrilled if, as measurements got more precise, $w \ne -1$ turns out to be the case because the $\Lambda$CDM ...


8

The cosmic microwave background has a redshift of about $1100$, see here for instance. Keep in mind that the "surface of last scattering" that gives rise to the CMB in fact existed everywhere in space, it's just that the photons currently reaching us have $z\sim1100$.


8

I think the key conceptual hurdle is that the vacuum state is not nothing. Quantum field theory describes matter as excitations in quantum fields. These quantum fields are very strange things, and I don't know of any easy way to explain to a non-physicist what a quantum field is. The key thing is that the quantum fields fill all of spacetime. So a vacuum is ...


6

Yes, there have been suggestions that such particles exist, and an example is the sterile neutrino. But your question is a little more involved than you might think at first sight. For example if the sterile neutrino only interacts through gravity what interaction caused it to be created in the first place? There is nothing in the Standard Model that could ...


6

Actually the "last scattering surface" of the CMB corresponds to the transition of the interstellar/intergalactic medium from an ionized plasma to cooler neutral atoms, about 300 000 years after the big bang. Most atoms have excitation and ionization energies in the visible, so the CMB was probably visible when it formed. We can be a little more precise ...


6

Is it because the acceleration is too weak? It is too weak with respect to the four forces we measure. The fact that the four known forces are so much stronger means that agglomerates of particles, up to the scale of galaxies are not internally affected, they keep their structure intact, like the famous raisins in the rising bread. It is only at the ...


4

Nice question. First off, there's a definitional problem because we can't apply a Lorentz boost to the universe as a whole. Lorentz symmetry is a local thing. So when we talk about "Lorentz symmetry" for the universe as a whole, I think we have to keep in mind that we mean something a little different. Basically if the "Lorentz symmetry" has already been ...


4

You're actually pretty close to the correct method for estimating the age of the Universe, but $H$ is not constant with time, it is $H=H(t)$. One of the many ways of writing the equation to solve is: $$t(z) = \frac{1}{H_0}\int_z^\infty \frac{dz}{(1+z)E(z)}$$ Here $z$ is redshift; $z\rightarrow\infty$ at the Big Bang, and $z=0$ now, so if you integrate ...


3

There aren't E and B fields in the entire universe. For example, there are no electric fields inside a conductor. I'm sure there are quite a few other such examples. If you mean "why are there electromagnetic waves throughout the entire universe?", one answer is because the radiation field drops like $1/r$, so the field from a single source never ...


3

The centre of mass of a system is simply the weighted average position of the mass distribution in that system. Since the universe is thought to be homogeneous and isotropic, any observer should roughly observe themselves as being at the centre of mass for their observable universe. However, I do not think that is quite the answer you were looking for. From ...


3

I think that it is important to note that (almost) everyone doing cosmology works within the framework of the FLRW universe. This implies that we assume that the universe is spatially homogeneous and isotropic, i.e. 'every place is the same (at least on large scales)'. Now, think of a flat, finite universe: Is it possible to maintain that all places are ...


3

In Minkowski spacetime the one way light travel time to a galaxy at proper distance $\chi$ is just: $$ t = \frac{\chi}{c} $$ so: $$ \chi = ct $$ As you say. However in an FRW universe the travel time is given by a different equation so the proper distance is not simply $ct$. Let's assume all motion is in the $x$ direction, so the metric simplifies to: ...


3

Just to add to John Rennie's answer, the objects where we expect to see the largest frame dragging effects are spinning black holes. There, there is actually a surface called the ergosphere (outside of the event horizon), where it is impossible for observers to stay stationary with respect to observers far from the black hole. In a sense, their reference ...


3

The spacetime outside a spinning mass is described by the Kerr metric. To explain how the Kerr metric produces frame dragging is hard, because it's not something for which there's an easy intuitive model. Frame dragging arises because the spacetime geometry links the angle measured around the spinning object to time, and this means the angle changes with ...


3

The point is that during the ordinary phase of the Big Bang expansion, the difference $|\Omega-1|$ was rather dramatically increasing with time. Today, we know that $|\Omega-1|\lt 0.01$ or so. If we use the cosmological equations to reconstruct what $|\Omega-1|$ had to be when the Universe was a second old, or very young, we find out that the following ...


3

This is too long for a comment so I'll post it as an answer, even though this question is years old. If Alcubierre warp bubbles are physically possible, which is exceedingly unlikely, and if the equivalence principle is correct, you could definitely escape from a black hole in one, because there's nothing locally special about the event horizon. In a large ...


2

This answer is within the current physics and theoretical understanding, which has developed a successful formalism that includes all the experimentally seen particles in the Standard Model. The model has been very successful in predicting several new particles using its symmetry and mathematics, the experimental observation of the Higgs boson serving as ...


2

As has been discussed in many questions around here (e.g. here), relativity tells us only about local properties and behavior of a space-time. There are some exceptions when we make global assumptions - if we have a space of globally and strictly constant positive curvature, non-trivial topology is imminent because the space has to be the 3-sphere ...


2

The cosmological constant is a constant energy density per unit volume of space, so as the universe expands this does indeed create energy as it creates new space. In this sense conservation of energy is violated. Actually this is less surprising than you might think. Conservation of energy is linked to a symmery called time shift symmetry by Noether's ...


2

Your question can't be answered because the qualifier when it was only the size of our solar system is meaningless. The size of the universe is a rather vague concept. The universe may well be infinite (it's unlikely we'll ever know for sure) in which case it was always infinite and it doesn't have a size. You could ask about the size of the observable ...


2

The special state of motion you're talking about is often called the Hubble flow. (edit: oops, Ben Crowell already mentioned this.) I think that in modern slow-roll inflation the source of this asymmetry is an asymmetry in the tiny (Planck-scale?) seed of inflation, whatever it was, inflated by a factor of $e^{60}$ or more. The inflaton potential has to be ...


1

The structure of general relativity does not allow the theory itself to be classified in terms of global, discrete symmetries such as time-reversal. The Einstein field equations don't refer to a time coordinate; they're expressed tensorially, which means that they are completely independent of what coordinates you choose. Since there is no guarantee that you ...


1

Actually, energy is often not Conserved in general Relativity. For are more in deep explanation see: http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html But just notice that Dark Energy might not necessarily end up being the cosmological constant, but a new force field, so its behavior might differ from that of an actual cosmological ...


1

The CMB was emitted at an energy of $E_{em}=13.6\text{ eV}$, which is the binding energy of hydrogen. This corresponds to a wavelength of $$ \lambda_{em} = \frac{hc}{E_{em}} \approx 9.12\times 10^{-8}\text{ m}$$ Redshift can be calculated by $$ 1+z = \frac{\lambda_{obs}}{\lambda_{em}} $$ If we observe blue light at 400 nm, we get a corresponding redshift ...


1

Just to add what the other questions say, if the sizes of the atoms were changing, there would have to be some corresponding change in at least one of the fundamental constants. For instance, if the size of the Hydrogen atom changed, then the ground state of the hydrogen atom would no longer be governed by the Bohr radius: $$a_{0} = ...


1

The strictly true equation for $\epsilon$ is $\epsilon=\frac{|\dot H|}{H^2}$, which is never negative. This is often written as $\epsilon=-\frac{\dot H}{H^2}$ because $\dot H$ is usually a very small and negative number. As for $\eta$, if $\dot\epsilon$ is negative, $\eta$ will be as well. However, a negative $\dot\epsilon$ would tend to indicate that ...


1

As I understand it, the solar system evolved from a massive molecular cloud. To me, this seems to break the second law of thermodynamics, as I think it suggests order from disorder. There are two problems here. One is the concept of entropy as disorder. A number of thermodynamics texts have now discarded this old concept. For one thing, it doesn't help ...



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