Is there a time paradox in Big Bang cosmology?

[glengarry]

In this post, I am going to assume the truth of the standard model of cosmology, which says that the universe is expanding as time progresses from some infinitely compressed state.

The paradox[/size]​

At every point in time, the universe has an average mass-energy density, which is equivalent to saying that it has an average gravitational potential.

By General Relativity, we know that clocks move slower in fields of higher gravitational potential.

If we go backwards in time, the universe gets progressively smaller, thereby consisting of a progressively higher average gravitational potential. It follows that the average clock in the universe will get progressively slower.

As we approach the moment of the singularity, we can see that the rate of the average clock will approach zero.

As we finally hit the singularity, clock rates become infinitely slow, meaning that the universe has truly existed forever, and the universe could not have had a beginning.

The universe is therefore eternal, and the concept of the big bang is null and void.

Has anybody heard anything like this? Any thoughts on how to "solve" it?

 

[marcus]

In this post, I am going to assume the truth of the standard model of cosmology, which says that the universe is expanding as time progresses from some infinitely compressed state...
Has anybody heard anything like this? Any thoughts on how to "solve" it?

You get gravitational time dilation only when you have a non-uniform gravitational field, so that one clock can be deeper down in the potential than the other clock.
But in standard model of cosmology the early universe was remarkably UNIFORM. Matter was remarkably evenly distributed, according to usual model.

So no time dilation effect. Nobody was deep down in a potential well compared with anybody else. So one could not compare relative rates of time passage.

It seems what you are talking about has no operational meaning.
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BTW most professional cosmologists would be surprised to learn U began with a state of "infinite compression". The singularity is in the classical Friedman equation model and is generally seen as a symptom that something is missing. The classical model simply does not apply at extreme density. By classical is meant non-quantum. Friedman equation was 1922 pre-quantum. It works very well until you get back to extreme density in very early time.

So considerable research currently goes into what is called Quantum Cosmology--where the singularity (i.e. failure of theory) is avoided and time-evolution continues uninterrupted. A singularity just represents something for theorists to fix. It limits the applicability of whatever theory has the singularity.

For a popular account you could google "tale two big bangs".
An essay about the "singularity" confusion put online by one of the world's top research institutes, the Einstein Institute near Berlin.

For a window on the professional research in cosmology without the "singularity" here are 500 papers or so:
http://inspirehep.net/search?ln=en&...2y=2013&sf=&so=a&rm=citation&rg=50&sc=0&of=hb
This is quantum cosmology research since 2009.

 

[glengarry]

It seems what you are talking about has no operational meaning.

The "operational meaning" of the paradox is completely wrapped up in the assumption that we are capable of logically comparing differences in average mass-energy densities between different moments in the evolution of the universe. It is meant to shine a light on possible inconsistencies in terms of the age of the universe, depending on which clocks we are using. I'm saying that the clocks of ca. 21st century Earth necessarily tick at different rates than those of ca. 10^-30 seconds after BB. According to our current reckoning of time, our current nanosecond might have to be adjusted to something like one trillion years, relative to the reckoning at that early moment.

But if it is not permissible to make that underlying assumption, then I want to know why. It seems to make logical sense to me.

 

[WannabeNewton]

The concept of a gravitational potential doesn't even make sense in GR for non stationary space-times.

 

[glengarry]

The concept of a gravitational potential doesn't even make sense in GR for non stationary space-times.

So, my concern is understanding the logical difference between these two cases:

1) Differences in gravitational potential between distinct points in the universe at a given moment

2) Differences in average gravitational potential between distinct moments in the evolution of the universe

I understand that the mathematical formalism of GR might not be capable of dealing with the logic of case #2. But this does not mean that case #2 is not itself a logically meaningful question with serious implications in terms of how we can truthfully speak about the universe.

If anyone is saying that the question is itself logically meaningless, I am very interested in knowing why.

 

[WannabeNewton]

If you want to use the idea of a gravitational potential when talking about non-stationary cosmological solutions to GR, you have to first make mathematical sense of what a gravitational potential in such a solution is. Cosmological solutions that are non-stationary (like the Friedman solution) don't have a natural notion of gravitational potential, which requires a time-like killing vector field to define. The Einstein static universe can be given a notion of gravitational potential but your argument deals with expanding universes which are necessarily non-stationary. If you can't codify gravitational potential mathematically for non-stationary cosmologies then why do you think making an argument that uses them has any meaning in such a case? It's like saying I'm going to make a logical argument in classical mechanics that uses a potential function obtained from friction when I can't even define a potential function for friction in general.

 

[marcus]

The "operational meaning" of the paradox is completely wrapped up in the assumption that we are capable of logically comparing differences in average mass-energy densities between different moments in the evolution of the universe...

W. B. Newton answered already but in case anyone finds it interesting or amusing I'll continue comment.
You should know that when we look back at ancient galaxies they ARE in an on average denser environment but there is no sign that atoms are vibrating differently or stuff is orbiting at different speeds or hot stuff is radiating on a different timetable. All the evidence is consistent with natural processes going the same rate. Even tho they were in a known higher uniform average density.

There is no theoretical reason, no trapeze of equations that would allow you to conclude they shouldn't be going the same rate. There is no "gravitational potential" that the ancient galaxies were DEEPER in than we are, so no physicist could work out an equation to say that their clox and atoms SHOULD be going slower.

Sorry there's really no "paradox" (or much of a leg to stand on :biggrin).

A. We do not observe natural processes going overall slower back in those denser days.
B. There is no theoretical reason they should. (Higher overall density does not translate naively into depth in some "potential well".)

If your aim is to learn something then how about this? Here's an example to think about:
The most ancient light we can see is the CMB and comes from hot gas that was around 3000K (like the surface of an orangish star somewhat cooler than Sol).

It comes from a time when average density was about 1 billion times what it is today.

That ancient glowing hot gas is one of the most intensely studied environments in cosmology. We know the speed of sound in it, and the approximate chemical composition, and the sizes of the very slight fluctuations in temperature (one part in 100 thousand) and the size-range of fluctuations in density. The details of the picture all fit together consistently: that gas, which was back around year 380,000, was physics-as-usual. The natural processes that we would consider clocks were running the same then as they do today.

And yet the universe was a BILLION times denser.

 

[glengarry]

Cosmological solutions that are non-stationary (like the Friedman solution) don't have a natural notion of gravitational potential, which requires a time-like killing vector field to define. The Einstein static universe can be given a notion of gravitational potential but your argument deals with expanding universes which are necessarily non-stationary.

So... unless I can decipher what "time-like killing vector fields in cosmological solutions to GR" has to do with developing an idea of average gravitational potential, then I'll never know why the logic of the paradox doesn't make sense?

Hmm... that's unsatisfying, to say the least!

It's just weird that you can have a static universe that includes the idea of average gravitational potential, but once the universe expands even one millimeter, the whole concept goes up in smoke.

 

[glengarry]

I'm sure everything you are saying makes perfect intuitive sense.

But I just want to understand why the essence of the paradox doesn't make any logical sense.

 

[marcus]

Look back at the statement of the bogus "paradox". It begins with a false statement:

"At every point in time, the universe has an average mass-energy density, which is equivalent to saying that it has an average gravitational potential."

The two statements are simply not equivalent!

Try to remember where you got this wrong idea. Did someone tell you this? Did you read it in a book by a popular author? Something to be learned here could be to stop trusting what that person says about physics stuff, or that author, if you can remember who it was who gave you the idea.

There are lots of things you could be learning at this site. It's too bad to waste time obsessing over a simple mistaken idea.

Here's a T or F question for you to answer on the basis of standard mainstream cosmic model:

Analyzing the light from a certain galaxy, received today, we see the wavelengths are three times what they were when the light was emitted and started its journey towards us.
When the light was emitted the distance to that galaxy was increasing faster than c, yet the light still got here. Possible or not possible?

BTW one of your two inequivalent statements certainly is true! At every time there is an average density. At the time the galaxy's light I mentioned was emitted the overall average density was over 20 times what it is today. True or false?

How about giving these a shot?

 

[glengarry]

Look back at the statement of the bogus "paradox". It begins with a false statement:

"At every point in time, the universe has an average mass-energy density, which is equivalent to saying that it has an average gravitational potential."

The two statements are simply not equivalent!

...and I want to know the theoretical reasoning behind this non equivalence. Everything I know of GR says that all I need to know is the total energy contained within a given space in order to know how much the resulting curvature will be. And the value of this curvature is what we call the stress-energy tensor, aka "gravitational potential".

We know that every point in a universe will necessarily have to consist of a specific value for the stress-energy tensor. And given the validity of GR, every specific value of the stress-energy tensor is equated with a specific clock rate.

At every instant of the evolution of the universe, we should be able to average all of the clock rates in order to come up with an average rate. I'm thinking that the average rates will seem to get slower as we move backward in time.

So, if we decide to set our current notions of average clock rate as a standard -- set it to 1 -- then this will seem to cause the age of the universe to appear to approach infinity. But, if we set the average clock rate at the smallest instant after the Big Bang as a standard, then this should cause the age of the universe to appear to approach zero.

Try to remember where you got this wrong idea. Did someone tell you this? Did you read it in a book by a popular author? Something to be learned here could be to stop trusting what that person says about physics stuff, or that author, if you can remember who it was who gave you the idea.

Believe it or not, I am quite capable of independent thought.

There are lots of things you could be learning at this site. It's too bad to waste time obsessing over a simple mistaken idea.

I'm sure you are speaking the truth, which is why I'm trying to understand the fundamental logic at play in terms of how we can speak of some kind of objective standard of time when it comes to a dynamically evolving system such as an expanding universe.

The only way we can speak of time is by way of regularly occurring phenomena, such as cosmic rotations/revolutions and atomic clocks. We obviously cannot directly relate these current phenomena to the earliest moments of the universe, because there simply weren't any regularly occurring phenomena back then.

Therefore, we need to come up with some kind of idea of objective time in order to obtain an objectively valid timespan for the age of the universe.

My point is that the duration that we currently call the age of the universe does not seem to rest upon firm theoretical ground in terms of its correlation to some kind of objective standard of temporality.

Here's a T or F question for you to answer on the basis of standard mainstream cosmic model:

Analyzing the light from a certain galaxy, received today, we see the wavelengths are three times what they were when the light was emitted and started its journey towards us.
When the light was emitted the distance to that galaxy was increasing faster than c, yet the light still got here. Possible or not possible?

BTW one of your two inequivalent statements certainly is true! At every time there is an average density. At the time the galaxy's light I mentioned was emitted the overall average density was over 20 times what it is today. True or false?

How about giving these a shot?

Are you saying that the only way to get around the logic of the paradox is through experimental data? That is, the brute, empirical fact that we see light at a certain frequency means that the logic behind the paradox is invalid?

First of all, the light that we see from a specific galaxy is transmitted from a location with a specific density. The idea of the average density of the universe doesn't apply to specific instances of EM emission and reception.

The whole point behind the paradox concerns what kinds of statements we can make about the universe as a whole, and not about phenomena that occur within specific spacetime slices of the universe.

I am not convinced that all of the "big picture" statements that cosmologists make about the universe are entirely logically founded.

 

[marcus]

... the value of this curvature is what we call the stress-energy tensor, aka "gravitational potential"...

But this is not true! The stress energy tensor is not the same as gravitational potential.

...and I want to know the theoretical reasoning behind this non equivalence.

I don't have to give you reasoning behind NON-equivalence You have no reasoning to support the claimed equivalence. Two mathematically different things that nobody in history of science ever said were the same AFAIK. If there is no mathematical reason to support something...

...We know that every point in a universe will necessarily have to consist of a specific value for the stress-energy tensor. And given the validity of GR, every specific value of the stress-energy tensor is equated with a specific clock rate.

That's not true! Where did you get that idea? It is not what GR says at all! That's why I ask who told you that. If you MADE THAT IDEA UP YOURSELF then you are going against Einstein and GR on your own. If somebody told you that, then you should be skeptical of what they say in future (sometimes people get misinformed by bad websites.)

Believe it or not, I am quite capable of independent thought.

Exactly! I was guessing that you are capable of independent thought and that you arrived at this wrong assumption by yourself. But I asked if you got it from somewhere else just to be sure. I don't know any scientific basis, no equations that say that. The red highlight thing sounds completely unfamiliar and made up. But there must have been something you heard or read that gave you this idea, perhaps you misunderstood.

 

[Chalnoth]

I would point out two things:
1. To get time dilation, you first need some sort of density contrast. You don't get any time dilation at all from just having a constant density that changes over time.
2. The early universe was incredibly smooth. At the time the CMB was emitted, when our universe was approximately 300,000 years old, the density contrast was only one part in one hundred thousand or so. Earlier, the density contrast was much smaller.

So no, there's no paradox, because there's no time dilation.