How did the big bang create space and time?

Question

Does the big bang theory state that space and time originated after the bang? So, was the singularity was converted into the vast space plus time?

Answer 1

"The Big Bang" is NOT a well defined concept, or perhaps I should say that it is NOT something which two researchers, active in the area, will necessarily agree. The "singularity" you write about is not contained in any main-stream Big Bang theory I am aware of. You need to be very careful when discussing any singularity.

The first thing you should know, before you toss the term around, is whether you are using the term in a physical (real) way, or whether you are using the term to describe our mathematics. In math, 1÷0 can be considered a "singularity" (but it need not be). When we encounter something in the real world for which our mathematical description of it has one or more singularities, that isn't evidence that a real world singularity exists, rather it is evidence that our math isn't up to the task of correctly describing the world.

The current "best" model is the lambda-CDM model, with inflation. That model allows predictions to go back (or forward) to (from) a time of about 1E-44 seconds. Further back and our physics breaks down (and gives us nonsense). At that time (so near to time zero, which might not even have ever have existed, that the difference is immeasurably small) spacetime was confined to a small hypervolume. The distances (as we measure things) between any two events (call them points, if you want; that is almost correct) would be very very very small. How small? I've read the size of a grapefruit or of a beach ball or a meter in diameter or...

Incidentally, when someone begins to speak/write about events outside our event horizon(s), s/he is babbling rubbish. Physics SHOULD confine itself to things which have meaning, there is nothing beyond any of our event horizons which can have any influence on our (Observable) Universe, hence it is religion, philosophy, or mumbo-jumbo to speak about it...but I digress.

The Λ-CDM model starts with a small bit of space time and from that everything we see, or sense (if you want to include neutrinos, gravity waves, dark energy, dark matter, ...) came. It does NOT deal with the singularity, so your question is ill-posed. That small bit of spacetime contained an enormous amount of energy (gravitational and otherwise) and it was the energy, not the spacetime which gave us the stuff that populates our Universe. It was that energy which also caused the creation of MORE spacetime, and it continues to do so today.

Hope that helps.

Answer 2

I first steer you to an SE post I did that illustrates a relationship between a quantum measure called the Tsirelson bound and the metric of spacetime. I will not go into great detail on this here, but it does define metric geometry according to something called magma, or with monoids and groupoids. This categorical equivalency is a formalism for how spacetime is built up from quantum states and entanglements.

Now let us look at the complementary relationship between black holes and $AdS$ spacetime. The condition for an accelerated observer near the horizon is given by a constant radial distance. We then considerable $$ \rho~=~\int dr \sqrt{g_{rr}}~=~\int \frac{dr}{\sqrt{1~-~2m/r~+~Q^2/r^2}} $$ with low and upper limits on integration $r_+~=~m~+~\sqrt{m^2~-~Q^2}$ and $r$. The result is $$ \rho~=~m log[\sqrt{r^2~-~2mr~+~Q^2}~+~r~-~m]~+~\sqrt{r^2~-~2mr~+~Q^2} $$ $$ = m log[\sqrt{r^2~-~2mr~+~Q^2}~+~r~-~m]~+~r \sqrt{g_{tt}}~-~Λ. $$ Here $\Lambda$ is a large number evaluated within an infinitesimal distance from the horizon We write the metric at this position $$ ds^2 ~=~ \left(1 ~-~ \frac{2m}{r(\rho)} ~+~ \frac{Q^2}{r(\rho)^2}\right)dt^2 ~-~ d\rho^2~-~r(\rho)^2dΩ^2. $$ With the near horizon condition we may set $r^2~-~2mr~+~Q^2 \simeq 0$ in the log so that $$ \rho~ \simeq~ m log(r ~-~ m) ~+~ r \sqrt{g_{tt}} ~-~ \Lambda. $$ The divergence of the log cancels the arbitrarily large $\Lambda$ $$ \frac{\rho}{r_+} ~=~ \sqrt{g_{tt}}. $$ We now write the metric as $$ ds^2~ =~ \frac{\rho^2}{r_+^2}dt^2~-~d\rho^2~-~m^2dΩ^2 $$ We may now observe that $d\rho^2~=~dr^2/g_{tt}^2$ and substitute in $\rho/m$ for $g_{tt}$ for $r_+~=~m$ and obtain $$ ds^2~ =~ \left(\frac{\rho}{m}\right)^2dt^2~-~\left(\frac{m}{\rho}\right)^2dr^2~-~m^2dΩ^2. $$ Or $$ ds^2~=~\left(\frac{\rho}{m}\right)^2dt^2~-~\left(\frac{m}{\rho}\right)^2 d\rho^2~-~m^2dΩ^2~ for~ \rho \simeq r. $$ This is the metric for $AdS_2$ in the $(t, r)$ variables and a sphere $S^2$ of constant radius $= m$ in the angular variables.

This is considerably easier to see than the approach taken by Carroll Johnson and Randall, which admittedly is a more exact derivation. I mention this because is should not escape one's attention that in $10$ dimensions this is $AdS_5\times S^5$ in the $AdS/CFT$ correspondence. This connects with the AdS black hole which reduces by a dimension and the $CFT$ information in the anti-de Sitter spacetime is also on the horizon of the black hole.

Suppose we have a black hole in $10$ dimensions that is in a near extremal condition. The condition for extremality for the ordinary spacetime black hole is $r^2~-~2mr~+~Q^2~=~0$. Then for $r^2~-~2mr~+~Q^2~>~0$ and suppose the black hole mass is $m~\rightarrow~m~+~\Delta m$ so the extremal condition is reached. This fluctuation in the mass is such that $\Delta m\Delta t~\sim~\hbar/c^2$, which is due to quantum mechanics. This process merges the inner and outer horizons of the black hole $r_{\pm}~=~m~\pm~\sqrt{m^2~-~Q^2}$. In addition the entropy of this black hole is $$ S~=~k\frac{(r_+^2~-~r_-^2)c^4}{4G\hbar c}, $$ which is zero in the extremal condition. Hence for a near extremal black hole in that fluctuates into the extremal condition projects this information into the $AdS_2$ spacetime. In effect the region between the two horizons is not demolished, but rather becomes a new type of spacetime. We then in this case have a sense that the structure of event horizons is associated with the emergence of spacetime.

Finally, let us consider Hawking radiation from a Schwarzschild black hole. I include the diagram below which is the Penrose conformal diagram for a black hole. In the regions I and II are hyperbolas that represent the constant radial position of an observer. The red circle is the virtual fluctuation of a particle which an observer on a constant radial path would observe to emerge from the past or white hole horizon and then approach the black hole horizon. The circle determines the $e^{2\pi iH/g}$ for the quantum field with $g~=~c^2/\rho$ on a constant radial path with $\rho$. The black hole with the split horizon represents two entangled blackholes in the region I and II. The emission of Hawking radiation, here diagrammed as the two dots connected by a red segment, transfers some of this entanglement to the two regions. The new event horizon is seen as the two hyperbolic paths in blue. The two black holes are then no longer completely entangled.

This is another illustration of how spacetime is built up from entanglements. Raamsdonk illustrated this in a paper. This presentation does not give a dynamics for how the big bang produces spacetime, but it does illustrate how spacetime is an emergent epiphenomenology of quantum mechanics. I am using the black hole as a sort of theoretical laboratory, which might in some way become more of an experimental object.