The Big Bang time paradox

[Geronimo]

Originally posted by KrazyHorse
No. It's actually easy.

The "density of matter" is more properly "the energy density in matter". For non-relativistic matter, most of that energy density is in the mass itself (mc^2). For ultrarelativistic matter most of that energy density is in the kinetic energy (gamma-1)mc^2. Total energy is gamma*mc^2. Gamma is a quantity which depends on velocity. It's 1 at v = 0 and goes to infinity at v = c.

Kinetic terms in the energy density are hit by a redshifting factor. If the mass is nonrelativistic then this redshift has minimal effect on the energy density, since the largest chunk (mc^2) is unaffected, so we see a 1/a^3 dependence. If the mass is ultrarelativistic then we can basically ignore the mc^2 bit and concentrate solely on the (gamma-1)mc^2 part. This part scales as 1/a^4 (like radiation).

These are the simple cases. For matter with (gamma-1) of order 1 (i.e. the kinetic energy is roughly the same as the rest mass) the behaviour is slightly more complicated. It behaves somewhere in between the two extremes above.

ahhh now i see. "density" in this case had nothing to do with the distribution of mass through volume but was instead a description of how much energy is associated with a given mass of whatever component we are describing. As the universe expands photons and "hot" particles of matter will lose energy density faster than "cold" particles of matter then?

My next question would be, is the "physical density" (number of particles per unit volume I'm not sure what the term would be) going to decrease at about the same rate for all components of the universe as the universe expands?

[KrazyHorse]

The term you're looking for is "particle density" or "number density". We try to keep the terms as simple as possible. And yes, unless the particles annihilate or pop out of the vacuum then their number density goes as 1/a^3

[Geronimo]

Originally posted by KrazyHorse
The term you're looking for is "particle density" or "number density". We try to keep the terms as simple as possible. And yes, unless the particles annihilate or pop out of the vacuum then their number density goes as 1/a^3

Thanks, the the posts all seem perfectly clear now!

btw, are there or is there even a theoretical possibility of components of the universe that have mass that have no particles associated with them? I'm guessing black holes might be an example since not only might they not be particles (they aren't strictly speaking right?) but they aren't even points if they are rotating right? Is there anything else?

[KrazyHorse]

In other words, if you have 8 protons/m^3 and 4 electrons/m^3 and you expand space, then if there isn't enough energy around to start creating new particles you will still see twice as many protons per m^3 as you do electrons per meter^3

But if the electrons were really fast while the protons were slow then the energy density in electrons will drop quicker.

[Ned]

I don't think anyone addressed my last two questions.

1) Do we know anything about the spacial density of DM?

2) Can the close proximity of two singularities disrupt the event horizon of one or both essentially causing a release or "inflation' of the matter of the disrupted singularity?

[KrazyHorse]

The reason we're more interested in energy densities here is that it's the energy density which curves space and thus directs the expansion of the universe.

[KrazyHorse]

Originally posted by Ned
I don't think anyone addressed my last two questions.

1) Do we know anything about the spacial density of DM?

No, what you asked was:

Have we any information on the spacial density of dark energy? If it has mass, wouldn't int interact with light matter and dark matter in the same gravitational way as light matter?

and I answered

The spatial density of DE is generally assumed to be uniform. This is not necessary (except if it's simply a cosmo constant), but it's a good approx on cosmo scales.

We know much less about DE than we do about DM. Since its presence was unimportant until very recently (like redshifts of order one) we have limited information about its history. What we basically have is a brief clip that tells us it's there and what overall density it has currently/in the recent past, but not much about anything else.

As for

Second, could the close proximity of two singularities break down one or both event horizons thus allowing the release of the mass within?

I'm going to give a tentative "no" here, but I'm not sure. As I said, I'm not a general relativist, and this is not an easy question. Finally,

Could this explain the big bang if possible?

I don't see why, but I might not understand what you're proposing.

[KrazyHorse]

As for the spatial density of DM, we have some very good ideas. As I said, because its not buoyed upward by radiation pressure, it tends to collapse faster into clumps. Therefore you expect to see more of it in clusters of galaxies and less between clusters. This differentition will be stronger than that for regular matter. In other words, if the regular mass overdensity is 100% in the densest clumps then it might be 200% when talking about dark matter. Note that these numbers are completely made up since I'm not a large scale structure guy and it's been a year since I've seen anything having to do with n-body simulations.

Even within galaxies you will see a denser concentration of DM at the center than you see of regular matter. There's nothing to stop it collapsing other than its own kinetic energy. Regular matter gets blown away from overdense regions due to radiation pressure (plus some other effects). Dark matter just sees the gravity pulling it in.

And the fact that dark matter clumps up faster is one of the best reasons to say that it's there. For instance, galaxies wouldn't look like they do without clumps of dark matter at the center.

[Geronimo]

Originally posted by KrazyHorse
The reason we're more interested in energy densities here is that it's the energy density which curves space and thus directs the expansion of the universe.

now I'm confused again.

maybe it's because I have some basic concepts wrong.

The gravitation of an object is a reflection of its curving of spacetime right?

I could have sworn that relativistic mass doesn't contribute to the gravitational field of an object. IE if a small object like a baseball were acclerated so close to the speed of light that it's apparent inertia was like that of a stellar black hole at rest it still would have only the gravitational field of a baseball.

Now it sounds as if when moving so close to the speed of light the baseball would curve spacetime far more than it did at rest. I already know time for an observer in the baseball would slow tremendously and I know the baseball would shorten considerably but I didn't know those were considered aspects of bending spacetime.

How many ways can spacetime be bent?

I think there is something very very fundamental and probably quite simple that I'm misunderstanding here.

[KrazyHorse]

I could have sworn that relativistic mass doesn't contribute to the gravitational field of an object.

You are wrong.

[KrazyHorse]

http://en.wikipedia.org/wiki/Stress-energy_tensor

[Kuciwalker]

Originally posted by KrazyHorse

I could have sworn that relativistic mass doesn't contribute to the gravitational field of an object.

You are wrong.

Then couldn't a particle be a black hole from some frames of reference but not from others moving at a different speed relative to it? Or is this one of the problems with special relativity that general relativity fixes?

[KrazyHorse]

Then couldn't a particle be a black hole from some frames of reference but not from others moving at a different speed relative to it?

No. Your coordinates transform in addition to your forces.

[KrazyHorse]

This is the reason you have to be very careful when talking relativity.

Everything transforms.

[Geronimo]

Originally posted by KrazyHorse

I could have sworn that relativistic mass doesn't contribute to the gravitational field of an object.

You are wrong.

Lol, believe it or not it was either something you or intgrspin posted here in these very forums that led me to that belief.

So again for the record, if a small object is accelerated close enough to the speed of light can it eventually collapse into a black hole by virtue of curving spacetime more at those speeds?