Big Bang Theory Primer

[DavidFirth]

This post was the mathematical derivation. I provided it to show that the equations of the Big Bang theory are not just made up. Thus the first equation in big red fonts, called the Friedmann equation, is an expression giving us the relation between the curvature of space and the rate of expansion of space. It was derived based on how an observer would calculate the gravitational and kinetic energy of a region of the universe with a certain mass 'm' and a certain distance away from her as the space expands between her and the object whose energy she is calculating.this is exactly the kind of thing you would do if you want to find the energy of, say, a flying projectile in the sky... but now the object is a distant galaxy millions of light years away.


The last equation, also in big red fonts, is called the fluid equation. It relates the mass density and pressure in a region of expanding space with its rate of expansion. This relation comes from using thermodynamic energy conservation principle on a region of expanding space. It is very similar to how an engineer calculates the amount of work that could be done by hot expanding steam in, say a steam engine or a steam based coal power plant. In a steam engine, what happens is that the heat from coal vaporizes the water to hot steam. Steam wants to expand in volume and exerts pressure on the piston which is displaced outwards resulting in mechanical movement of the piston which is the available work that is converted into motion of the wheels of the steam locomotive. In such cases, the energy conservation law relates the change in internal energy of the steam as it pushes outwards and converts this energy into work. The situation for an expanding spatial region of space with a uniform mass density is also similar. As it expands, the change in the internal energy of the region is balanced by the pressure force driven work due to this expansion. This relationship provides us with the fluid equation.

In a later post, I will discuss the physical consequences of these equations on the behavior of the universe. So stay tuned.

Okay, I think I'm following you. It seems to me that there are other possibilities that might explain all this other than Big Bang theory, though.

 

[SalixIncendium]

Okay, I think I'm following you. It seems to me that there are other possibilities that might explain all this other than Big Bang theory, though.

What other possibilities do you think might explain this?

 

[Polymath257]

Can you kind of "dumb this down" for us folk who never got past college algebra?

OK, a(t) is an expansion factor that describes how large a local 'piece' of the universe is. This varies with time, so we get a function a(t) of time, t. This is usually set up so that a(now)=1 for convenience.

So, while a(t) represents the amount of expansion, a'(t) represents how fast the expansion factor is changing. So, for example, a'(t)>0 for actual expansion and we would have a'(t)<0 for contraction.

The fraction (a'/a) tells us how fast expansion is happening *as a fraction of the expansion factor*. This is related to the percentage change.

So, in the equation

(a'/a) ^2 = ( 8π/3)ρG - k*(c/a) ^2

the left hand side tells us how fast the expansion is happening as a percentage per unit time.

The other side has two terms. The first, ( 8π/3)ρG , is mostly a constant. In fact, everything but the ρ is a constant. So, G is the gravitational constant known to Newton. The ρ however, represents the density of mass and energy. We expect this to go down as the universe expands since density usually goes down on expansion.

The second term on the right, k*(c/a) ^2 involves the 'spatial curvature' which gets into 4 dimensional geometry. There are three main possibilities: One is that the spatial part of the universe is 'positively' curved. The two dimensional analogy is the surface of a sphere. In this whatever direction on the sphere you choose, you eventually come back around to the starting point. The same happens for a three dimensional space that is positively curved. A zero curvature for two dimensions is like a plane, and for three dimensions it is like what most people just assume space must be like: going on forever with no 'wrapping around'. Negative curvature is trickier to explain, but the two dimensional analog is more like a trumpet horn.

So, the second term says something about how the curvature of space affects the rate of expansion of space. For 'flat' space, k=0 and there is no effect. For 'sphere-like' space, the expansion is *less* than what would be expected from just the density of mass and energy (the second term is subtracted) and for negative curvature it is *larger* than would be expected.

Now, there are actually a few pieces to even the ρ term. Ordinary matter loses density on expansion ρ=(mass)/(volume) and volume increases as a^3 (the cube of the expansion factor). BTW: dark *matter* decreases in density by this same formula.

For *radiation* (i..e, light), the energy density goes down faster that this, like 1/a^4. What this means is that in the very early universe, the energy from light is more relevant for expansion than the energy from mass.

Finally, for dark *energy*, the density stays constant for increased expansion. This is very unusual and is why we think of dark energy as the 'energy density of space itself'. Since the other terms decrease with time, dark energy was less relevant in the past and increases its effect on the expansion over time. It is always a term that serves to increase the expansion rate and when the matter and radiation densities get small enough, it becomes dominant. This leads to exponential grown (a rate proportional to the amount gives exponential growth or decay mathematically). it is this terms that leads to *accelerating* expansion as we see today.

 

[sayak83]

Okay, I think I'm following you. It seems to me that there are other possibilities that might explain all this other than Big Bang theory, though.

I would encourage you to create a thread explaining such alternatives in some detail. Then one can have a constructive discussion. Please remember that physics requires precision in observable predictions of its theories and evidence based justifications for the principles used to construct them.

 

[DavidFirth]

What other possibilities do you think might explain this?

I don't know. But I figure there must be other possibilities.

 

[DavidFirth]

I would encourage you to create a thread explaining such alternatives in some detail. Then one can have a constructive discussion. Please remember that physics requires precision in observable predictions of its theories and evidence based justifications for the principles used to construct them.

I don't know any other alternatives. I just figure there are. Sorry, I didn't mean to derail your thread.

 

[sayak83]

I don't know any other alternatives. I just figure there are. Sorry, I didn't mean to derail your thread.

Cool. No problem.

Happy Birthday.

 

[Polymath257]

I don't know any other alternatives. I just figure there are. Sorry, I didn't mean to derail your thread.

At this point, for times after about a millisecond into the expansion, alternatives to the BB have been eliminated by observational evidence. Before that, it is still anybody's game.

 

[Thief]

so God needed a chalkboard to plan the event

yeah right

 

[David T]

I said it is

You claim it is dead on arrival, but fail to explain why you at is the case. I think you are wrong in this evaluation, but am willing to consider any actual argument you can make (especially if it is based on evidence).

In the OP, it is noted that we actually know that galaxies are moving away from each other. This is known through the red-shifts and how those red-shifts change with increasing distance (the red-shift is related to speed away from us).

What, precisely, is your issue with this?

Then, the proposal is made that this is actually an expansion of space itself and NOT simply the galaxies moving through space. This may be harder to grasp, but it isn't a particularly difficult thing if you ponder it a but. The analogy with a rising cake is helpful, perhaps.

Anyway, this is the basic idea that can be put into general relativity and derive equations describing how fast the universe will expand based on the amount of matter and energy in it.​

I was extremely clear it was DOA before it was articulated. Everyone seems to be hung up on this. Cosmology in articulation is always a reflection. it reveals not what is but how we perceive. So if there was some self correcting thinking going on and honesty then I would have no problem. If you look at the model it's self contained self referential. So to treat recursion as the cosmos is confused. That's like saying I believe x to be true therefore x is true because I believe x to be true. There is actually a reason the multiverse has come about. This model ignores that totally. That model as well has flaws its a mathematical model nothing more than that be honest. Mathematical modelling is not reality at all not even remotely closd or every movie with cg effects are real. Omg Pandora and avatar are really I take it all back.this model requires does not exist to literally exist. How is that not teleological fantasy? Ya all need to learn how to breathe and get outdoors more. Ya all might try camping, spending G a lotore time actually engaging in nature rather than watching it in your head.​

 

[sayak83]

I said it is

I was extremely clear it was DOA before it was articulated. Everyone seems to be hung up on this. Cosmology in articulation is always a reflection. it reveals not what is but how we perceive. So if there was some self correcting thinking going on and honesty then I would have no problem. If you look at the model it's self contained self referential. So to treat recursion as the cosmos is confused. That's like saying I believe x to be true therefore x is true because I believe x to be true. There is actually a reason the multiverse has come about. This model ignores that totally. That model as well has flaws its a mathematical model nothing more than that be honest. Mathematical modelling is not reality at all not even remotely closd or every movie with cg effects are real. Omg Pandora and avatar are really I take it all back.​

The Big Bang model made multiple predictions that were later validated by astronomers. This shows that the Big Bang theory is the correct description of the universe within its domain of applicability. It also refutes your claim that it is self referential.

 

[DavidFirth]

The Big Bang model made multiple predictions that were later validated by astronomers. This shows that the Big Bang theory is the correct description of the universe within its domain of applicability. It also refutes your claim that it is self referential.

Lets not forget all the problems that exist in Big Bang theory. Dark matter and dark energy, two things we cannot prove exist, must exist for the Big Bang theory to work. As a matter of fact most of the universe must be made up of dark energy/dark matter for the theory to work. The Big Bang theory is hardly the end all be all theory of everything.

 

[sayak83]

Lets not forget all the problems that exist in Big Bang theory. Dark matter and dark energy, two things we cannot prove exist, must exist for the Big Bang theory to work. As a matter of fact most of the universe must be made up of dark energy/dark matter for the theory to work. The Big Bang theory is hardly the end all be all theory of everything.

That is true. You should consider Big Bang more like a macroscopic theory, like theory of thermodynamics in the 19 th century. Much of the laws of thermodynamics and behavior of gases were predictable by those (still true and very useful) laws without anybody understanding what made those gases behave as they do... till Boltzmann came along and explained them through collisions between atoms of gas molecules.

 

[SalixIncendium]

**MOD POST**

This thread has been moved to a non-debate forum, therefore the material presented in this thread is not subject to debate.​

 

[DavidFirth]

Sorry if I was debating. I didn't realize I was.

 

[sayak83]

Questions and discussions still warmly welcomed.

 

[SalixIncendium]

Sorry if I was debating. I didn't realize I was.

Just to be clear, the mod post wasn't directed at you, specifically. I just wanted to make everyone aware that it was not the OP's intent to have the material presented debated.

 

[sayak83]

Sorry if I was debating. I didn't realize I was.

Nothing to do with you David. Salix asked me if I would like to move it to the Material world discussion section so that the thread does not get derailed by off topic debates in future. I assented, as it looked a good idea.

 

[DavidFirth]

Just to be clear, the mod post wasn't directed at you, specifically. I just wanted to make everyone aware that it was not the OP's intent to have the material presented debated.

Nothing to do with you David. Salix asked me if I would like to move it to the Material world discussion section so that the thread does not get derailed by off topic debates in future. I assented, as it looked a good idea.

Oh, okay. I do want to learn about the Big Bang theory even though I don't believe it. It is rather interesting whether it is real or not.

 

[YmirGF]

That is true. You should consider Big Bang more like a macroscopic theory, like theory of thermodynamics in the 19 th century. Much of the laws of thermodynamics and behavior of gases were predictable by those (still true and very useful) laws without anybody understanding what made those gases behave as they do... till Boltzmann came along and explained them through collisions between atoms of gas molecules.

Thank you for an enlightening and highly readable thread. Though I haven't learned anything new it is awesome to see it all put so succinctly. Bravo.