New answers tagged

1

There are a few problems I can think of with this idea - Gravity has to, at some distance turn from positive, to zero, to negative. It would be interesting to know that distance. Will the repulsion increase, or decrease with increasing distance? Dark energy hypothesis indicates repulsion would go up with increasing distance. Which does not make sense - ...


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Gravity, per general relativity (GR), is normally attractive. Normally means that the sources of the gravity, and thus the sources that determine the geometry and curvature of spacetime, have positive energy density, and obey other positive energy conditions. The pressure and other factors that enter into the stress energy tensor that is the source of the ...


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Like it was said before, there is no a priori reason why nature should treat everything symmetrically. Much to the contrary, we know several examples of P- and CP-violating processes. And in other cases we do not even know the reason why a process is "symmetric", when in principle it would be allowed to violate CP (see: the strong CP problem). I guess you ...


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There's not reason to assume nature should treat everything symmetrically. There are many phenomena in nature that we actually know are asymmetric. For example the weak force violates parity symmetry (meaning the weak force has a preference for right or left handedness).


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How can we look into the past? Light has a fixed velocity of almost 300.000 meters per second. Sunlight takes about 8 minutes to reach us. So we see the sun always 8 minutes ago. As the other answer says, stars are much further away and it takes light that much longer to reach us. How do we know how far away the stars are? There are various methods that ...


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Stars are very far away. So light takes a while to get from stars to you. The light arriving now shows you what the stars looked like when the light left. It is like getting a letter from a far away friend. The letter took a few days to arrive. It has news from a few days ago.


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You go outside at night and you look at the sky. That's the universe and that's the past streaming in on you. With your own eyes, of course, you can't see much farther than approx. 2.5 million years back - the Andromeda galaxy is easily seen, even though it's not as pretty as in astrophotographs: https://en.wikipedia.org/wiki/Andromeda_Galaxy. What you will ...


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I don't think this is a bad question, nor am I sure it is completely unscientific --- not that I am certain it is. If we follow Raamsdonk and others we have reason to think that spacetime is built up from entanglement. This is an entanglement of states or within some sort of fundamental vacuum. This might mean there are different vacua that are in ...


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Energy loss by photons occurs in a dielectric medium when the photons interact with the atoms of which the dielectric is made. This interaction does not normally result in a red-shift of the photons, but rather an attenuation of a beam of photons due to photons being absorbed. Depending on the nature of the material and the energy of the photons, the ...


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Given a few plausible assumptions about the universe its spacetime geometry is described by a solution to the Einstein equations called the FLRW metric. If we know the densities of various types of matter/energy present, e.g. photons/matter/dark energy/anything else, then we can calculate how the expansion of the universe varies with time. Generally ...


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I don't know if negative pressure (but see my added edit below) , more importantly there is a theory of inflation, and some good evidence for it. It was caused by a yet unknown inflation field, with its parameters somewhat matching what the cosmic microwave background (CMB) measurements show. [edit added: The field is a quantum field that rolled from a high ...


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Pocket universes have arisen in different theories. Just to name you two, one is alan Gut's inflationary theory idea that Eternal inflation produces pocket universes with all physically allowed vacua and histories. Another is that from sean carroll, who claims that inside every black hole there is an entirely new universe.


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I'm not sure if this is exactly what you want, but there's a book called Practical Statistics for Astronomers by J.V. Wall and C.R. Jenkins that might fit the bill. According to the Cambridge University Press website (the book is a part of Cambridge Observing Handbooks for Research Astronomers): Astronomy needs statistical methods to interpret data, but ...


3

The heat death of the universe is the idea you are describing (this idea is also known as the Big Freeze). The problem with this idea is for it to work the cosmological constant has to be zero...and it isn't zero. It's very tiny, but it isn't zero. The other problem with your idea is the belief that because it all "freezes", so to speak, it'll all collapse ...


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You must not really have looked hard enough. They are the same phenomenon The Big Freeze, which is also known as the Heat Death, is one of the possible scenarios predicted by scientists in which the Universe may end. It is a direct consequence of an ever expanding universe. The most telling evidences, such as those that indicate an increasing rate of ...


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A 2013 paper by Shtanov and Sahni (already mentioned by Ben Crowell in the comments) says that the modes grow exponentially in conformal coordinates, and Barrow et al overlooked the fact that the conformal time changes very little during and after inflation. A 2014 preprint by Tsagas, one of the authors of the original paper, cites Shtanov and Sahni and ...


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Absolute location, absolute direction, and absolute time are in-explainable with current physics. Therefore absolute speed/velocity does not make sense either. The absolute point where all the expanded matter was concentrated at/before the big bang, may pertain to some location within universe. Even if the point itself expanded, the original reference still ...


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There are other shapes of galaxies. In particular, look at ellipticals.


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The answer is the same reason why a glass of water left out at room temperature will evaporate. Even though most of the particles will be below the boiling point, the equilibrium one expects is not entirely in the liquid phase. The occasional particularly energetic water molecule will vaporize, just as the occasional neutral hydrogen atom will be struck by a ...


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You are right that the universe formed atoms much earlier (at the temperature when photons can no longer ionize the atoms, i.e. at around $T = 150,000 K$ as you point out with your order of magnitude calculation). However, photons could still scatter off these atoms. Indeed this was quite likely considering the high density of matter in the universe. The ...


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I have communicated with both of these fellows. The mathematics is based on Donaldson's theorem that in four dimensions there exists an infinite number of atlases of charts on a manifold that are homeomorphic but not diffeomorphic. I am not able to go into the mathematics, for it is pretty deep. It centers around the moduli space of self-dual connections $SD/...


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The derivation by Pols is correct. Ryden makes the strange decision to plug the relativistic rest energy $\varepsilon = \rho c^2$ into the classical ideal gas law. Surely it makes more sense to define a classical kinetic energy $$ u = \frac{1}{2}\rho\langle v^2\rangle $$ so that $$ P = \frac{2kTu}{\mu\langle v^2\rangle} = \frac{2}{3}u. $$


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The key statement is that the $a_{\ell,m}$ are independent Gaussian random variables. For each $\ell$, there are $2\ell+1$ of them. So their sum is, essentially by definition, a chi-squared distribution with $2\ell+1$ degrees of freedom. Now, it is a known fact that the variance of a chi-squared distribution with $k$ degrees of freedom is just $2k$, so ...


3

I would like to answer with the words of L.D. Landau, from his book Statistical Physics (first edition $1958$):


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Thermodynamics says that entropy increases in a closed system. The Steady State Theory claimed that the universe was not closed. In 1929 Hubble showed that the universe is expanding. To explain how an expanding universe can be Steady State, they claimed that new matter was created continuously to keep the density constant. This new matter would have very ...


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I wonder of you are overthinking this. Wald says: If the universe had always expanded at its present rate that is, $\dot{a}$ is a constant and independent of time. In that case the value of $a$ at time $t$ after the Big Bang is simply: $$ a = \dot{a} t $$ So if you define $T$ by $T = a/\dot{a}$ then $T$ is necessarily the age of the universe.


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Whatever you're supposed to do on this, you first need to understand quantum theory in curved spacetimes, and the ADM method in general relativity (which is basically the Hamiltonian approach to general relativity), and there are always issues as to what is the time coordinate you choose, and since it is not invariant what does it mean. In FRW the time is ...


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So, there are several possible ways the universe could be baryon symmetric: A region of the universe where antimatter dominates. There is a problem with this theory, though - 30 years' worth of scientific research has calculated just how far away this type of region would have to be, and from these calculations it is considered very unlikely that any part ...


1

For the case $\Omega_M + \Omega_\Lambda = 1 = \Omega_\text{total}$, which is a good approximation for $t \gtrsim 10^8 \; \text{yr}$, an explicit formula for a(t) is $$a(t) = \left[ \frac{\Omega_{M,0}}{\Omega_{\Lambda,0}} \sinh^2 \left( \frac32 \sqrt{\Omega_{\Lambda,0}} \, H_0 \, t \right) \right]^{\frac13}$$ or, plugging in numbers from Pulsar's answer, $$...


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I've answered the questions I can below. @John Rennie already gave a link to Lemaitre's paper. Here's a summary from John Gribbin's The Scientists, on page 596-597: ...the Belgian astronomer Georges Lemaitre (1894-1966), who was also an ordained priest, independently published similar solutions [to those of Aleksandr Friedmann's] to Einstein's ...


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The idea of a "Zero-Energy Universe" is a theory held by a limited number of scientists. There are several stackexchange question that expand on the theory and may help you. Zero energy universe Total energy of the Universe


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Whether the dark energy is constant or not will ultimately be determined by experiment. At the moment there is no evidence that the dark energy is changing, but the experimental errors are still quite large so a change is not ruled out. There are lots of papers on this subject, but as yet no firm conclusions. It is important to be clear that dark energy ...


2

I'd put this as a comment, but don't have enough rep...anyway, as this answer and the comments within state, the equation of state isn't necessarily linear. One thing I'd add is that one can define $w$ to be the ratio $\frac{P}{\rho}$ (as it's dimensionless), and since in general both pressure and density depend on time (no $\vec x$ dependence is allowed in ...


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The energy $h\nu$ of a photon is simply the contraction $$ h\nu = g_{\alpha\beta} k^\alpha u^\beta $$ of its momentum $k^\mu$ with the frame's velocity $u^\mu$. The frequency shift is then given by $$ 1 + z = \frac{\nu_S}{\nu_O} = \frac{(g_{\alpha\beta} k^\alpha u^\beta)_S}{(g_{\sigma\rho} k^\sigma u^\rho)_O} $$ where we denote the velocities of both source ...


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Here are some references: Time and chance by david Albert Time's arrow by huw price From eternity to here by sean carroll The direction of time by H. D. Zeh Physical basis of time Asymmetry by paul davies There are many other excellent books or articles about the subject. Especially, in relation to the foundation of statistical mechanics I saw Two ...


0

All these statements are meant to be understood in terms of large populations of particles. For example, if the mean energy per particle in the Universe is smaller than the mass of electron, it is impossible to produce many of them and they in general will annihilate or transform into other species. In thermal equilibrium this can be understood just by ...


0

We have to be careful what we mean when we say "moving away". Imagine a grid in which we are at the origin and there are light sources located at each of the grid intersections. If the grid stays as it is while the light sources accelerate away from us, their light will appear to be redshifted. If you set up the accelerations such that everything moves ...


0

That is not quite that simple. There is theory and measurements, and it places some constraints. There is more. First, if the universe is infinite now it was infinite at the Big Bang. You can have an infinite universe and have it all in the spacetime at the Big Bang. It does not grow to be infinite, it either is or is not. (Ignoring multiple dimensional ...


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As you and others have said, it looks like Boltzmann could plausibly be credited with the idea that the universe had a low-entropy past: The second law will be explained mechanically by means of assumption A (which is of course unprovable) that the universe, considered as a mechanical system—or at least a very large part of it which surrounds us—...


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The question is a bit weird because from that distance, the photons would take so long to come back, I am not even sure a whole species could survive long enough to see one photon come back. You have to realize that even for the Sun, as relatively close as it is, photons take on average 8min 20sec to arrive. So you're always seeing the Sun as it was over ...


1

Infinity is a mathematical concept, as well as the concept of variables describing dimensions. Physics is about observations, either in the laboratory or of the cosmos, which are fitted with mathematical models. It started with the geocentric system, became the heliocentric system and then the realization that the galaxy is composed out of sun like stars, ...


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If "open" means nonpositive spatial curvature (which is the usual meaning), then no. The experimentally measured spatial curvature is consistent with zero, but the error margin includes values on both sides of zero. There's no conflict in the Friedmann equations between accelerating expansion and positive spatial curvature. If "open" means "never ...


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"If inertia is a property of the matter form of mass-energy, and it is a property that allows for the transfer of energy, then why doesn't the energy dissipated in a vacuum, as does applied radiant/free energy" The problem with your logic is that is flawed. It is equivalent to "some fruits are apples; oranges are fruits: why do not oranges taste like ...


1

So that narrows it down to some time between 1896 and 1979 The second law was known to Clausius, and trivially implies the knowledge that the entropy in the far past was much less than now. (That is, if one is permitted to apply the notion to the universe as a whole; cf. below.) It seems that Clausius stated explicitly (in 1856) only the extrapolation to ...


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The raisin bread analogy can be used to help in understanding this too: Dough is much more expandable than the raisin material. Raisins will expand a bit due to the heat and the pull from the dough stuck on their surface, but it is the dough that is moving. The forces that are holding the raisin together are much stronger than the force expanding the ...


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You are correct, the recession velocity predicted by the hubble law is negligible at the local group, even if gravity among them could be absent. Their gravitational attraction though, is hard enough to keep them bound together.


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Bob Bee's answer already covers a lot of extra detail, so I just want to give the very concise answer to your specific question. One form of one of the Friedmann equations is: $$H(t) = \sqrt{\frac{8\pi G}{3}\rho(t) - \frac{kc^2}{(a(t))^2}}$$ In a universe with zero global spatial curvature ($k=0$), like ours is thought to be, then the expansion rate $H(t)$ ...


0

Translations and rotations are not different. A rotation is a general state of motion, and a pure translation is a degenerate form of rotation. In fact a translation is just an indication that rotation occurs at a distance, just as a torque is an indication that a force is acting on a distance and angular momentum is an indication that something at a ...


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The comment by Walter is on the right track: The "acceleration" does not refer to the fact that recession speed increases with distance, because this is just a consequence of space expanding everywhere. This is why we measure the expansion in km/s per megaparsec. Today, the expansion rate (the Hubble constant) is $H_0 \simeq 70\,\mathrm{km}\,\mathrm{s}^{-1}\,...


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The FLRW energy equation for the motion of test masses in the universe is $$ \left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G\rho}{3}. $$ the scale factor for space is $a$ and its time derivative is $\dot a$. I derived this from Newtonian dynamics. The density of mass $\rho$ for the case of a quantum vacuum energy level is constant. I now replace this with ...



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