New answers tagged

1

As stated in the answer you linked, the density of a black hole is defined by the ratio of its mass over the volume spanned by its Schwarzschild radius. That does not mean that there is actually uniformly distributed matter inside the Schwarzschild radius. All of the matter is packed very densely (in something with the characteristic length of the Planck ...


0

The term Big Bang does not have rigorous physical definition. And if you mean specifically inflation, then the modern inflationary models (chaotic inflation with various scalar field potentials) predict that inflation is always present at certain regions of space. Inflation is driven by a scalar field, the value of which lowers with time. When it drops ...


0

Roughly, in the integrands you have something like $$J^{(3)}+\alpha^2J^{(1)}\sim (x^2-\alpha^2)^{3/2}+\alpha^2(x^2-\alpha^2)^{1/2}=(x^2-\alpha^2)^{1/2}(x^2-\alpha^2+\alpha^2)=(x^2-\alpha^2)^{1/2}x^2$$


3

You understand that $\mathcal C$ violation is required, as if it weren't, processes related by $\mathcal C$ that violated baryon number conservation would balance, i.e. $$ P \to Q B \qquad \mathcal C:\qquad \overline P \to \overline Q \, \overline B $$ would result in no net baryon number violation. In these expressions, $B$ is a fermion carrying baryon ...


2

Actually there is a geometry that describes something like the naive idea of the Big Bang. But it's a bit of a cheat because it's really just a piece of the usual expanding universe metric. The first metric suggested to describe a collapsing star was the Oppenheimer-Snyder metric, which describes a spherical ball of dust collapsing under its own gravity. ...


1

What would happen if you were to release the energies of the big bang in our universe a second time? Have a look at this standard history of the universe, History of the Universe - gravitational waves are hypothesized to arise from cosmic inflation, an expansion just after the Big Bang Our universe is now at the far right. Note the beginning ...


6

Short answer: The ratios have changed over time... drastically. This is a consequence of the expansion of our universe. Initially (and by that I mean after the conjectured inflationary epoch, which I will not consider here), radiation dominated all other forms of energy by far. However, as the universe expands---as measured by the increase of the ''scale ...


3

Gravity acts on all matter, not just water (it just so happens that water flows with less resistance than rock) which is why we get noticeable water tides but not very noticeable earth tides. However, if you were to bring a very large gravitating body too close to earth, you would find that the earth isn't quite as solid as it feels. The answer to your ...


3

I think there are two ways to approach the question. If you are coming from the point of view of a theoretician trying to come up with a working model of the universe, you would definitely like to make the assumption of isotropy and homogeneity. This is usually what we do, as least to first order approximation. One of the reasons for that is that the ...


1

You have$\frac E{m_0}$, the energy divided by the rest mass is $\gamma=\sqrt{1-\frac{v^2}{c^2}}$. The proper time is lab time divided by $\gamma$. Since you have a fixed $E$, as $m_0 \to 0, \gamma \to \infty$ and the proper time goes to $0$. For the last part, you are supposed to assume that an $11$ MeV neutrino arrived $7$ seconds before a $7$ MeV ...


0

No, it hasn't. Lawrence M. Krauss when you look at CMB map, you also see that the structure that is observed, is in fact, in a weird way, correlated with the plane of the earth around the sun. Is this Copernicus coming back to haunt us? That's crazy. We're looking out at the whole universe. There's no way there should be a correlation of ...


0

In short: The particle horizon is the extent of our current past light cone, and the event horizon is the extent of our future light cone at $t=\infty$. It is important to be clear that these horizons are horizons only to an observer at this place in Space and Time. They do not mark physical boundaries between different regions in Space; rather, they ...


2

the cutting by universes is a way : to introduce possible new physics for each of these universes without leaving the homogeneity and isotropy cosmological principles, the known constants and the known physics of "our" universe to defer the infinity issue from our universe to a parent structure : the multiverse Homogeneity and isotropy are the main ...


0

This is a somewhat odd question since average is a somewhat vague term. Are you referring to temperature averaged by total mass? Or average temperature by volume? As mentioned in the comment above, the most important "Universal temperature" is the temperature of the Cosmic Microwave Background which is basically the light that was released when the ...


1

Pulling together what's been said in various comments: 1) General relativity admits models where spacetime is foliated by spacelike leaves, all of which are indexed by a global time coordinate. The simplest of these models is Minkowski space. All of your observations about models with comoving observers apply equally well to Minkowski space, so if you ...


2

Suppose two observers, Alice and Bob, are moving relative to each other since the beginning of the universe. While they do it, they construct the chronologies of all the events of the universe, as they record them in their frame of reference. They will construct different chronologies. However, and this is key, each can reconstruct the other's chronology. ...


2

A comoving observer and an observer that has been moving at $0.866c$ since Big Bang will disagree on their measured age of the Universe by a factor of 2. While both measurements are correct, we can say that the comoving observer measures a more "natural" age of the Universe. For instance, the comoving observer is the only observer who will measure the ...


2

Very often we don't. We just stick to $k=0$, because for most practical purposes, this is fine. But all measurements contain uncertainties. The latest Planck results (Parade et al. 2015) combined with observations of the baryonic acoustic oscillations yield$^\dagger$ $\Omega_k = 0.000\pm0.005$. We don't know whether the curvature on much larger scales than ...


0

I don't really have the background to understand such matters, but this presentation by Alan Guth gave me at least some idea of what it means to say the energy of a gravitational field is negative (which Guth calls a "miracle of physics"). Starting at 0:52:00 in that video clip, Guth presents this thought experiment... ...where it's taken as a given that ...


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SN 1987A is (was?) in the Large Magellanic Cloud, which is gravitationally bound to the Milky Way. This means that its motion relative to us is only minimally affected by cosmological expansion, and talking about it in terms of a $z$ parameter is misleading at best. The best estimates of the distance to SN 1987A are about 168,000 light-years. If you ...


1

Of course you won't find it anywhere - SN 1987A is in the Large Magellanic Cloud, just 168000 ly away. At this scales cosmological expansion is negligible compared to other processes so measuring its redshift is says little useful about its distance. $z=0.1$ corresponds roughly to 1 Gly. The universe is HUGE. Here's plot from wikipedia


3

The Magellanic clouds are satellite galaxies of the Milky Way. They are right next door. Google says 61 kPc to the LMC which means trivial cosmological redshift.


1

Philo's answer is spot on, and I'll basically be rephrasing it here into a form that makes more sense to me. Hopefully it will help some others as well. Rather than only dialing back the clock 1B years, let's go waaaay back and see what things look like: we go back 13.82B years and look out into space... And there's no space! The universe is very ...


2

We cannot see anything closer than 380,000 years after the big bang because that is when radiation and matter decoupled. The CMB is a picture of what the universe looked like at that point. All clumping of matter into stars, galaxies, etc has occurred since then. If we had looked 1 billion years ago, we would see the same except that the CMB temperature ...


3

In a static universe it would indeed be true that if you looked at an object, say, 10 billion light years away you would be looking at it as it had been 10 billion years ago. This isn't really an application of special relativity and is merely a consequence of a finite speed of light. Our universe, however, is expanding and so you can actually see across ...


2

From the theory of Thompson scattering (see http://farside.ph.utexas.edu/teaching/em/lectures/node96.html ) we know that a charged particle of mass m interacting with a plane wave electromagnetic field of Strength $E_0$ and frequency $\omega$ has an effective dipole moment of magnitude $$d=\frac{e^2E_0}{m\omega^2}$$ Note that the dipole moment scales ...


1

The effects of gravity are really only observable to us on a macroscopic (large) scale. When a large enough number of (perfectly neutral) Hydrogen atoms come together they will gravitate towards each other. That sets things in motion for the Hydrogen to heat up. Once they reach a high enough temperature and density, they will ionize and the protons can ...


3

It depends on the scales which you are interested in. During the deSitter evolution of the universe (let's assume exact deSitter and completely flat potential for simlicity) the fluctuations of the inflaton field exit the horizon and freeze in with a power spectrum of $H_*^2/(2\pi)^2$ where $*$ denotes that the value of the Hubble parameter is taken at the ...


0

It's hard to see how gravitational repulsion between matter and antimatter would do any of those things, (1) because gravity is weak, and (2) because matter and antimatter are intermixed in the early universe, so the matter-antimatter repulsion would be competing with matter-matter attraction and antimatter-antimatter attraction.


0

They are 2 different concepts. According to the inflationary paradigm, the primordial fluctuations , visible with a contrast scale of $10^5$, are supposed to be the seeds of the galaxies and of the parent structures. Not all is clear but , with the informations which are available, this idea is enough credible to be intensively studied. On another hand, ...


2

The main point to grasp is that the tiny inhomogeneities seen in the CMB are too small (by a factor of 100) to grow into the structures we see today without something like "cold dark matter". The CMB was formed at the epoch when normal (baryonic) matter and the radiation filling the universe decoupled. Only at this point was normal matter free to start ...


4

There is a limited sense in which this correct. When inflation ended there was a temperature rise known as reheating, and we believe it was at this stage that the standard model particles were first created, or at least the majority of them. If you are measuring temperature by the energies of the standard model particles then this would have been the hottest ...


0

Trying to answer my old question myself: The cited piece is talking about an infrared cutoff, which basically amounts to giving the propagating particle a mass which appears squared in a propagator. So I think, what is meant is considering $$\lim_{\Lambda\to 0}\int \frac{d^4p}{p^2+\Lambda}$$ and this $\Lambda$ of course has a mass dimension of 2.


0

And if you still need an answer for your speed of expansion (of the universe, because the solar system isn't expanding just by itself), it is measured to be about 74.3 km/s per megaparsec (a megaparsec being about 3 million light-years)


0

Our solar system isn't expanding, because it's bound by gravity. Even though space is expanding, the positions of objects in the solar system stay the same because gravity pulls them back. This is true for all gravitationally bound objects, even galaxies and galaxy clusters.


1

Whenever you have mass you have energy too, lots of energy for a tiny bit of mass. And it is energy not mass, that is related to spacetime curvature. Your idea that mass curves spacetime and energy does not, is a lie, completely 100% baseless and simply untrue. It's just that the energy associated with mass is the largest energy you are used to seeing ...


0

According to Einstein's theory of general relativity, both matter and energy curve spacetime. The theory already makes an allowance for matter-energy equivalence. The Einstein field equations are: $$G_{\mu\nu} + \Lambda g_{\mu\nu} = k T_{\mu\nu}$$ The left hand side has the Einstein tensor G which encapsulates the curvature of spacetime, and the right side ...


0

The early Universe is largely in a state of thermal equilibrium, after inflation the Universe has a large temperature allowing for all degrees of freedom to obtain equilibrium. This can be seen from the Boltzmann equation, which describes how the number density changes in the expanding Universe. Equilibrium is obtained by a particle species if $\Gamma \gg ...


1

This is probably too late to be useful, however yes you should assume slow roll and that the inflaton's potential energy is dominating the energy density of the Universe. So solve: $3H\dot{\phi} + V'(\phi)=0$ with: $H^2 = 8\pi G V(\phi) /3$ This slow roll approximation is valid if the slow roll parameters are $\ll 1$ which requires $\alpha \ll 1/m_p$.


1

The scalar spectral index, like the above answer states, describes how the density fluctuations vary with scale. As the size of these fluctuations depends upon the inflaton's motion when these quantum fluctuations are becoming super-horizon sized, different inflationary potentials predict different spectral indices. These depend upon the slow roll ...


2

So the 'old' model of inflation was based on the idea that a scalar field (the inflaton) was trapped initially in some meta-stable vacuum. If it's energy density dominates the Universe at this time then the Universe inflates. This continues until the field tunnels out of this vacuum and inflation ends. This leads to bubble nucleation as different patches of ...


3

Cosmic microwave background radiation is very "cold", i.e. the average energy is very low. It started in the region of atomic levels, order of electron volts, but is now order of magnitude lower and the only interactions it can have with atoms in the atmosphere are elastic scatters. The origin of the CMB radiation at 380.000 years after the Big Bang is ...


2

In a static spacetime, there is (by definition) a timelike Killing vector field $\xi^\mu$, which implies that geodesics with four-velocity $u^\nu$ have a conserved quantity $\epsilon = -g_{\mu\nu}\xi^\mu u^\nu$. For example, in Schwarzschild spacetime, this is $$\epsilon = \left(1-\frac{2M}{r}\right)\frac{\mathrm{d}t}{\mathrm{d}\lambda}\text{,}$$ where ...


0

I send a blue photon up to my friend, who is x meters above me in some tower (we are both at rest relative to each other). He measures the photon and finds out it is red. We both conclude that a gravitational redshift occurred. However, where did the energy go? It didn't go anywhere. The ascending photon didn't lose any energy. There is no magical ...


2

The Christoffel symbols for your metric are $$ \begin{split} &\Gamma^0_{ij}=a\dot{a}\gamma_{ij}\\ &\Gamma^i_{0j}=\frac{\dot{a}}{a}\delta^i_j\\ &\Gamma_{jl}^{i}=\tilde\Gamma^i_{jl} \end{split} $$ then $$ ...


1

Semantics is wrong in more than one way. First of all, there is no "first" without time, and time only exists in the universe, so the question is not well posed. If there was something before the big bang, then both are a part of the same "universe/multiverse" for which common laws must hold (you can't just discretely switch laws all of the sudden - and if ...


0

The "laws" we have found allow to predict how the "universe" manifests itself (including a concrete concept of universe) are nowhere to be found other than our social interactions as agents. They are in no way in the same phenomenological level than, well, actual observable phenomena (what you call the universe). You can see this hierarchy in the fact that ...


6

This is a metaphysical/philosophical question, imo. There is the platonic ideals school, in this case read for ideals=mathematics, which postulated that ideals existed and nature fell into their form. I have seen a number of theoretically inclined people who are really of that school. One does not have to think of the beginning of the universe to start ...


0

Closely related to your question is that of whether mathematics is discovered or invented. If it is discovered, where does it "live"? Also relevant might be the view of Tegmark on the Mathematical Universe Hypothesis Where he posits that everything is "made of mathematics" and that the physical world is just one such instantiation out of a possible ...


8

I believe a great answer to your question is: We don't know We still can't resolve the time before electroweak interactions, so how can we even come close to answering this question? You might get answers from some theories (or I prefer to call them theorems because they're only math until today) like string theory or loop quantum gravity or M-theory or ...



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