What is the problem with the Big Bang Theory and seeing the early universe?

[RyanXXVI]

Like many, I have just recently learned about the theory of inflation and, though learning about, noticed a problem with the Big Bang Theory. To gather information on the Big Bang, telescopes point their "cameras" into deep space so we can "see" the early universe as it was forming. However, this does not make sense to me. If all matter and energy started at approximately the same point and then spread, the light should have spread faster than the matter that would make up our planet. Therefore, all the light from the early universe should have already passed us. You can see why this is a problem. For a visual, imagine a standard model of our solar system with concentric orbits. Now, replace the sun with the epicenter of the big bang, Mercury with our planet and have Pluto be the light from the Big Bang. Can someone please explain this, or, if my explanation is unclear, tell me why my problem is confusing (I have never been good at articulation). Thanks

 

[phinds]

There is no "epicenter" to the big bang. There is no center to the universe. The big bang was not an explosion that happened at a single point.

I suggest you Google "surface of last scattering" to get a start on understanding what you are asking about, and then come back if you still have questions (as you likely will )

 

[mfb]

Like many, I have just recently learned about the theory of inflation and, though learning about, noticed a problem with the Big Bang Theory.

You did not notice a problem with the theory, you noticed a problem with your understanding of the theory. Did you really think thousands of physicists would make such an obvious error (if it would be an error), and you were the first to find it?[/size]
phinds pointed out where the problem is.

 

[Matterwave]

Like the two posters above said, the solution is that there is no one point in our current universe on which the big bang occurred. In other words, it's not like you can point to a direction in the sky and say "the big bang happened that way!". That one point from which all emerged IS our current universe (ALL the infinity of it!). The big bang happened everywhere, because back then, everywhere was only 1 point, that 1 point expanded to be everything that we see! (Actually, one should probably not take the collapse back to the point of the big bang, as the singularity itself is indescribable with our current physics). Admittedly, that is a very weird notion, so it's not your fault that you made this mistake. The light that we see all around is light that came after the big bang, the farther we look (in any direction!), the farther back in time we see.

As it turns out; however, we can only see to the "surface of last scattering" (this is the CMBR). This is the radiation from the time when the electrons and protons cooled enough to combine into atoms (this is called recombination for some reason...even though it was the first time this happened) and let all the light out (previously, the light was trapped). This surface corresponds to a time of ~400,000 years after the big bang happened. So, currently, we can't see anything that happened before ~400,000 years after the big bang because the light couldn't move around before then.

Now, if we could get real neutrino observatories set up and watch the neutrinos produced from the big bang, we would be able to see much farther into our past (I don't know off the top of my head the exact number estimated for a neutrino's "surface of last scattering"). But neutrinos are notoriously difficult to detect, and the signal would be very very faint.

 

[phinds]

That one point from which all emerged IS our current universe (ALL the infinity of it!).

Stating that the universe is infinite in extent is personal speculation on your part. It might well be true or it might not. The universe could be finite but unbounded.

 

[RyanXXVI]

There is no "epicenter" to the big bang. There is no center to the universe. The big bang was not an explosion that happened at a single point.

I suggest you Google "surface of last scattering" to get a start on understanding what you are asking about, and then come back if you still have questions (as you likely will )

Thank you, phinds. Your balloon analogy helped me to understand and then an article that came up when I googled "surface of last scattering" as you told me to helped me to understand completely. However, the article has a completely separate problem I hope you can help me understand. The essay says "this scattering kept the Universe in a state of thermal equilibrium. Eventually the Universe cooled to a temperature at which electrons could begin to recombine into atoms". The problem with this is that the cooling of a closed system (which I assume the Universe is) in thermal equilibrium goes against the first law of thermal dynamics. I must be making another mistake, so could you please point it out? Thanks in advance.

 

[RyanXXVI]

Also, here is the link to the essay on the surface of last scattering (forgot to post it in the earlier post).

http://ned.ipac.caltech.edu/level5/Glossary/Essay_lss.html

 

[phinds]

Thank you, phinds. Your balloon analogy helped me to understand and then an article that came up when I googled "surface of last scattering" as you told me to helped me to understand completely. However, the article has a completely separate problem I hope you can help me understand. The essay says "this scattering kept the Universe in a state of thermal equilibrium. Eventually the Universe cooled to a temperature at which electrons could begin to recombine into atoms". The problem with this is that the cooling of a closed system (which I assume the Universe is) in thermal equilibrium goes against the first law of thermal dynamics. I must be making another mistake, so could you please point it out? Thanks in advance.

I'm not much on thermodynamics (MAN I hated that course in undergraduate school) but I think "closed system" doesn't apply to a system that is expanding, which the universe has been doing ever since the singularity.

I hope someone here with a better understanding of thermodynamics can give you a more definitive answer.

 

[craigi]

The essay says "this scattering kept the Universe in a state of thermal equilibrium. Eventually the Universe cooled to a temperature at which electrons could begin to recombine into atoms". The problem with this is that the cooling of a closed system (which I assume the Universe is) in thermal equilibrium goes against the first law of thermal dynamics.

I'm not much on thermodynamics (MAN I hated that course in undergraduate school) but I think "closed system" doesn't apply to a system that is expanding, which the universe has been doing ever since the singularity.

I hope someone here with a better understanding of thermodynamics can give you a more definitive answer.

The cooling is a reduction in the energy density due to the expansion, so it isn't an issue for the first law of thermodynamics.

That isn't to say that the expansion of the universe doesn't present problems for the first law of thermodynamics though. The vacuum energy is an issue, but then general relativity doesn't get on too well with it anyway.

 

[Mordred]

Thank you, phinds. Your balloon analogy helped me to understand and then an article that came up when I googled "surface of last scattering" as you told me to helped me to understand completely. However, the article has a completely separate problem I hope you can help me understand. The essay says "this scattering kept the Universe in a state of thermal equilibrium. Eventually the Universe cooled to a temperature at which electrons could begin to recombine into atoms". The problem with this is that the cooling of a closed system (which I assume the Universe is) in thermal equilibrium goes against the first law of thermal dynamics. I must be making another mistake, so could you please point it out? Thanks in advance.

The universe is treated as a close system as their is no outside influence. Just prior to last scattering their was a tremendous reheating phase due to the end of inflation. This high energy state allows thermal equilibrium. Different particle species will remain in thermal. equilibrium, only if they interact with each other often enough .Since the Universe expands, particle densities become smaller and smaller, and ultimately the various particle species decouple from each other

First law of thermodynamics: Because energy is conserved, the internal energy of a system changes as heat flows in or out of it. Equivalently, machines that violate the first law (perpetual motion machines) are impossible. Heat is the flow of thermal energy from one object to another.

if this is the law your referring to this law doesn't apply to cosmology as vacuum energy and quantum tunneling. Also the Heisenberg uncertainty principle is involved in quantum virtual particle production processes. Essentially the process is originally described by Allen Guth's false vacuum inflationary model. Which later included the inflaton for chaotic eternal inflation.
In essence a higher energy potential region (true vacuum) can quantum tunnel to a lower vacuum potential (false vacuum)(hopefully I got the sequence correct lol if not I'm positive Bapowell will politely correct me )

Through the above process and the Heisenberg uncertainty principle, its quite possible to have a universe develop from nothing. Lawrence R Krauss has written and supported this process

edit I did get the false vacuum true vacuum sequence wrong lol. the false vacuum is the local minimum but has a higher energy potential than the ground state (lowest energy potential true vacuum.) So tunneling will go from false vacuum to true vacuum

http://en.wikipedia.org/wiki/False_vacuum

 

[Matterwave]

Stating that the universe is infinite in extent is personal speculation on your part. It might well be true or it might not. The universe could be finite but unbounded.

Can't a guy get some artistic license in writing a response on here? lol. The Universe is spatially flat to a very good approximation, so even if it were closed and bounded, it would be unimaginably huge compared even to our currently unimaginably huge observable universe! Ok I revise my statement to "All the possibly infinite, or less likely, but still possibly closed and bounded, but without boundary, volume of the universe."

[STRIKE]As for the first law of thermodynamics and the expansion of the universe, I don't see any violation there. Consider the adiabatic free expansion of an ideal gas. In that case T goes down even without any heat transfer or the performance of any pdV work. [/STRIKE]

The below points are more complicated and might require some knowledge of general relativity:

The energy lost by physical particles and light due to the expansion of the universe is more problematic as that potentially violates conservation of energy as a whole. But one finds that since the FLRW metric is NOT time independent (unlike for static solutions), there is no Killing field associated with the coordinate time, and therefore free particle energies are not conserved. Energy conservation in General Relativity is a very touchy subject since the potential energy of the gravitational field, for non perturbative solutions of GR itself is very ill defined.

Edit: Actually for an ideal gas adiabatic free expansion does not lead to temperature decrease. I have redacted that part of my statement. I'll think about it a bit more.

 

[Mordred]

The cooling is a reduction in the energy density due to the expansion, so it isn't an issue for the first law of thermodynamics.

That isn't to say that the expansion of the universe doesn't present problems for the first law of thermodynamics though. The vacuum energy is an issue, but then general relativity doesn't get on too well with it anyway.

if you want to get deep into the thermodyamics I recommend this article

http://arxiv.org/pdf/hep-ph/0004188v1.pdf

 

[timmdeeg]

Actually for an ideal gas adiabatic free expansion does not lead to temperature decrease.

Right, but I doubt that this plasma consisting of electrons and protons in thermal equilibrium with radiation behaves like an ideal gas. At least the temperature of the radiation is inversely proportional to the expansion.

 

[phinds]

Can't a guy get some artistic license in writing a response on here? lol.

Nah, they hired me to be the resident nit-picker

 

[Mordred]

Right, but I doubt that this plasma consisting of electrons and protons in thermal equilibrium with radiation behaves like an ideal gas. At least the temperature of the radiation is inversely proportional to the expansion.

why not? if they are in thermal equilibrium, their reaction rates is higher than the expansion rate then it can be described as a Bose-Einstein and fermi-dirac distributions.

see this article chapter 4

http://www.wiese.itp.unibe.ch/lectures/universe.pdf

of course you also have to account for entropy density, chemical potential and spin of each particle species however at high enough temperatures all degrees of freedom become relativistic

section 4.1

also doesn't the equations of state also show the relations between relativistic and non relativistic particles of an ideal gas. in cosmology?

http://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

this article defines the thermodynamic behavior to Gibb's law (ideal gas form)

http://arxiv.org/pdf/0708.2962v3.pdf

 

[timmdeeg]

why not?

also doesn't the equations of state also show the relations between relativistic and non relativistic particles of an ideal gas. in cosmology?

http://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

Why do you think that the perfect fluid (part of the FRW model) coincides with the plasma of the last scattering? Represents the latter part of said model too?

 

[ebos]

Well, I have a couple of questions/observations (what's really the difference?)
First, what would have been the diameter of the universe at recombination? Obviously some parts of the universe were already separated by this amount at this time and depending on the rate of expansion, I doubt we will EVER see those guys, could we?
Second, if space began at one point then we wouldn't be able to look in every direction to see the beginning or as close as we can get to the beginning? Or perhaps at some point in the future, when we have extremely detailed detection capabilities, we can look in every direction and see exactly the same event. So the question is, wouldn't space then have to include at least one other dimension in order to see a single item in every direction that you look?
And lastly, have the Hubble guys ever considered taking a Deep Field at the exact same spot and exactly the same exposure etc. several years apart to see if any "new" galaxies appeared or disappeared?
Thanks.

 

[phinds]

Well, I have a couple of questions/observations (what's really the difference?)
First, what would have been the diameter of the universe at recombination? Obviously some parts of the universe were already separated by this amount at this time and depending on the rate of expansion, I doubt we will EVER see those guys, could we?
Second, if space began at one point then we wouldn't be able to look in every direction to see the beginning or as close as we can get to the beginning? Or perhaps at some point in the future, when we have extremely detailed detection capabilities, we can look in every direction and see exactly the same event. So the question is, wouldn't space then have to include at least one other dimension in order to see a single item in every direction that you look?
And lastly, have the Hubble guys ever considered taking a Deep Field at the exact same spot and exactly the same exposure etc. several years apart to see if any "new" galaxies appeared or disappeared?
Thanks.

Your whole post is predicated on the totally erroneous assumption that the big bang singularity happened at a point. It did not. It happened everywhere and the universe at that time might have been infinite or it might have been finite but unbounded.

Also, galaxies do not appear or disappear in a matter of years. Hundreds of thousands of years is likely closer to reality.

 

[Mordred]

Why do you think that the perfect fluid (part of the FRW model) coincides with the plasma of the last scattering? Represents the latter part of said model too?

http://arxiv.org/pdf/0708.2962v3.pdf

look at equations 4 and 5 then read further down, he isn't specifying the reheating phase, he applies Gibb's law to the current cosmology conditions as well as covering the radiation dominant era. via an effective EoS. This is also done in the other link I provided as well as Dodelson's Modern Cosmology 2nd edition. If you want further proof look at the references in the first article. Interacting cosmic fluids in power–law Friedmann-Robertson-Walker cosmological
models

http://arxiv.org/pdf/0803.1086v1.pdf

"Usually the universe is modeled with perfect fluids and with mixtures of non-interacting perfect fluids" however in this case he has interactions. The articles I posted previously show the perfect fluid forms for fermions and baryons. So its essentially two perfect fluids however they didn't go into interaction between the two.

perfect fluid solutions are used extensively in cosmology, even to modelling spcific regions of stars, black-hole accretion disks etc. Yes they serve at best as approximations however they are used in nearly every application of cosmology.

further examples

"The Fluid Nature of Quark-Gluon Plasma"
http://arxiv.org/abs/0802.3552

"The Dynamical Behavior of a Star with Perfect Fluid"
http://arxiv.org/abs/0801.0294

"As is well known, static spherically symmetric perfect fluid distributions in general relativity, are described by a system of three independent Einstein equations for four variables (two metric functions, the ene
rgy density and the isotropic pressure" quote from this paper.

All static spherically symmetric anisotropic solutions of Einstein's equations

http://arxiv.org/pdf/0712.0713v3.pdf

its even used in quantum applications

Perfect fluid quantum Universe in the presence of negative cosmological constant
http://arxiv.org/abs/0711.3833

Perfect fluid spheres with cosmological constant
http://arxiv.org/abs/0711.1450

Exact and Perturbed Friedmann-Lemaitre Cosmologies
http://arxiv.org/abs/0709.3863

The evolution of cosmological gravitational waves in f(R) gravity

http://arxiv.org/abs/0708.2258

as you can see perfect fluid calculations are involved in a wide variety of aspects

section 5.2 has the equation of the effective EoS for different species in regards to the CMB.

in this article

http://arxiv.org/pdf/1302.1887v1.pdf

so effectively you can calculate the EoS for each species and derive an effective EoS then apply that to a perfect fluid solution. Or you can also choose to treat each species as a separate perfect fluid. with or without interactions with each other as per the dark matter dark energy example above. In the last article he also shows a derivative of a curvature fluid.

 

[ebos]

Sorry but I was speaking timewise - a point in time - it makes more sense to me to think of the universe in time except in some circumstances where I would need distance as an example. And why wouldn't galaxies appear or disappear in a matter of years? If we can just barely detect a couple of photons of an early galaxy now we surely wouldn't see anymore in a few years. And, the reverse could also be true. Suddenly one year a few photons would appear, then more, etc. especially once our detection abilities become more sensitive.

 

[phinds]

Sorry but I was speaking timewise - a point in time - it makes more sense to me to think of the universe in time except in some circumstances where I would need distance as an example. And why wouldn't galaxies appear or disappear in a matter of years? If we can just barely detect a couple of photons of an early galaxy now we surely wouldn't see anymore in a few years. And, the reverse could also be true. Suddenly one year a few photons would appear, then more, etc. especially once our detection abilities become more sensitive.

You seem to think that the formation of galaxies is one thing and their becoming visible to us is a completely different thing. I don't get how that would work. They become visible to us as they are formed, just many billions of years after the fact.

 

[Mordred]

Well, I have a couple of questions/observations (what's really the difference?)
First, what would have been the diameter of the universe at recombination? Obviously some parts of the universe were already separated by this amount at this time and depending on the rate of expansion, I doubt we will EVER see those guys, could we?
Second, if space began at one point then we wouldn't be able to look in every direction to see the beginning or as close as we can get to the beginning? Or perhaps at some point in the future, when we have extremely detailed detection capabilities, we can look in every direction and see exactly the same event. So the question is, wouldn't space then have to include at least one other dimension in order to see a single item in every direction that you look?
And lastly, have the Hubble guys ever considered taking a Deep Field at the exact same spot and exactly the same exposure etc. several years apart to see if any "new" galaxies appeared or disappeared?
Thanks.

Sorry but I was speaking timewise - a point in time - it makes more sense to me to think of the universe in time except in some circumstances where I would need distance as an example. And why wouldn't galaxies appear or disappear in a matter of years? If we can just barely detect a couple of photons of an early galaxy now we surely wouldn't see anymore in a few years. And, the reverse could also be true. Suddenly one year a few photons would appear, then more, etc. especially once our detection abilities become more sensitive.

When cosmologists refer to the point-like start of the universe they are really referring to the beginning of the observable portion of our universe. Or more accurately our universes lightcone, or causality. As Phind's pointed out we do not know anything beyond the observable portion of our lightcone.

http://en.wikipedia.org/wiki/Observable_universe

http://en.wikipedia.org/wiki/Light_cone

a particle such as a photon follows its worldline in physics, the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime. The concept of "world line" is distinguished from the concept of "orbit" or "trajectory".

http://en.wikipedia.org/wiki/World_line

The speed of light, and rate of expansion determines our lightcone. Or our observable universe. So galaxies cannot pop in and out of our observable universe. As the speed of light is faster than matter can move. Once light from a region reaches us that region is now part of our observable universe. However at some far distance future the rate of expansion may prevent light from ever reaching us. Keep in mind the further you look the further back in time your looking. So eventually you can see as far back as the dark ages prior to the CMB. This is simply due to the amount of particle interferance to the mean free path of photons. Photons simply could not travel far without encountering other particles.

 

[timmdeeg]

Mordred, thanks for presenting so many links, which must have been quite time consuming. I will have a look at them. However it seems we don't talk about the same thing, perhaps I didn't express myself correctly.

My question: Why does the last scattering plasma cool down due to the expansion of the universe?

The expansion of the universe is an adiabatic process (no heat transfer between system and surrounding). Therefore, if the plasma including radiation would behave like an ideal gas, its temperature wouldn't decrease, as Matterwave already stated. I assume that the cooling of the photons, which are in thermal equilibrium with the protons and electrons, is responsible. Needless to say that photons are no ideal gas.

 

[bapowell]

The plasma loses energy to the expansion.

 

[Mordred]

Right as Bapowell mentions the plasma cools, due to expansion. Any change in volume results in a decrease of energy-mass density. Which also results in a drop of temperature. Photons, baryons, fermions, dark matter included.

As the numerous articles will show, one can calculate the effective EoS of a multi-species plasma such as the last scattering by including the spin of each species, entropy density, rate of reactions, chemical potential, and its individual energy-density to pressure relations on both matter and energy.

This is valid in cosmology as the distribution is homogenous and isotropic, any uniform plasma, gas, energy or matter itself or as a multi-species, can be treated as an ideal gas. The ideal gas laws serve as an approximation only regardless of the application even in the classical container ie a tank filled with helium.

Photons is one the easiest examples to treat as an ideal gas as it is its own anti-particle with spin of 1, its entropy is s=2. This will have a Bose-Einstein and fermi-dirac distribution.

http://www.wiese.itp.unibe.ch/lectures/universe.pdf

chapter 4.0 of this article shows the fermi-dirac and Bose-Einstein distribution metrics as well as the photons treatment as a specific example to what I just wrote. My ability with the latex forms aren't up to writing the forms without struggling with it lol

 

[bapowell]

This will have a Bose-Einstein and fermi-dirac distribution.

You've said this multiple times in recent posts: how can it be described by both distributions? (recall Fermi-Dirac is appropriate to spin 1/2 particles -- the photon is a boson!)

 

[timmdeeg]

The plasma loses energy to the expansion.

Thanks for helping out.

The plasma consists of particles and photons. Do you say that the energy loss is given by
$$|{\bf u}_0| = |{\bf u}_i|\frac{a(t_i)}{a(t_0)}$$
as you explained in the other thread, whereby the proper velocity of the particles u has to be replaced by the momentum p in the case of the photons?
If I understand it correctly the kinetic energy of the particles goes asymptotically to zero as they are approaching the Hubble flow.

 

[bapowell]

Yes, that's right. The redshift corresponds to the energy loss.

 

[timmdeeg]

Photons is one the easiest examples to treat as an ideal gas as it is its own anti-particle with spin of 1, its entropy is s=2.

http://www.csupomona.edu/~hsleff/PhotonGasAJP.pdf

Just in case you are interested in the comparison of equations for ideal and photon gases.

 

[Mordred]

You've said this multiple times in recent posts: how can it be described by both distributions? (recall Fermi-Dirac is appropriate to spin 1/2 particles -- the photon is a boson!)

lol yeah thanks, went by the descriptive in one of my articles but when I looked back I see the article did break it down later on in the metrics for each case separately. For some reason I missed that lol.

Timmdeeg that article definitely paints a slightly different picture lol. An arbitrary number of bosons can occupy the same state its the grand canonical partition function takes the form.

Z(β,) = Trexp(−β(H−N))

where β= 1/kBT is the inverse temperature, and μ is the chemical potential. H and N
are the Hamiltonian and the particle number operator. The trace extends over all possible states.

where only one fermion can occupy the same quantum state.

Your article mentions the comparison between photon gas per number of particles in a container as compared to other types of gases. However he didn't touch on the distinction between bosons and fermions and the number that can occupy the same state. Unless I missed the metric comparison in the article you posted.

he mentions the fermi-dirac and Bose-Einstein distribution, however doesn't show the equations. I've also never heard of Sackur–Tetrode equation’s. I'll have to try and look that one up when I have time

edit turned out to be easily found

http://en.wikipedia.org/wiki/Sackur–Tetrode_equation
http://en.wikipedia.org/wiki/Gibbs_paradox

I can see where the author of your paper is coming from, in regards to the quantum uncertainties and the 2nd law of thermodynamics

we should start a new thread lol seems were hijacking this one lol