# Why do we assume that the big bang implies a begining of time?

## Main Question or Discussion Point

If the universe expands by a percentage per unit time then it really would have no beginning. X number of years in the past it would have been half it's current size, 2X years in the past it would have been 1/4 it's current size, etc... At no time would it's size have been zero unless it's rate of expansion were, at that instant, infinite. Why do we think that happened?

BillSaltLake
Gold Member
The expansion has not been exponential up to now. Instead it is now proportional to ~t. At earlier times it was ~ t2/3 and even earlier it was ~ t1/2. The behavior you're talking about would require ~ebt where b is some constant.

How do we know that?

BillSaltLake
Gold Member
Looking back at the redshift vs. brightness of "standard candles", the conclusion is that the expansion parameter has been growing at between t2/3 and t1 as least as far back as 1/3 the present age. I've never seen any theory or evidence that the parameter has been growing exponentially during that time, but your assertion would require exponential growth. (However, LCDM hypothesizes that the parameter now grows as the sinh of t, which will eventually be dominated by an exponential.)

Last edited:
marcus
Gold Member
Dearly Missed
If the universe expands by a percentage per unit time then it...
Bill S.L. has given you a good picture of the past growth of the scale factor over time. The scale factor a(t) in the friedmann model is a handle on the size of the universe or average distance between galaxies.

The standard cosmology model does not assume a fixed rate of expansion.
The present percentage rate, right now, is about 1/140 of a percent per million years. This percentage used to be much larger, in the early universe. It has been declining steadily.

The usual way you see the Hubble rate written is in conventional units like 71 km/s per megaparsec. You can convert that to an approximate percentage rate easily. Just divide by 1000. That gives the fraction of a percent per million years. 71/1000 = 1/140, approximately. However neither the 71 nor the percentage should be thought of as staying constant over long periods of time.

btw if you are curious and want to know what the Hubble rate has been in past times, one easy way is to use the calculator called "cosmos calculator". Just google the name.

If you put in a redshift (of some light we are receiving today) it will tell you when that light was emitted and what the Hubble rate was when it was emitted.....and other things like how far etc. etc.

You will see that the Hubble rates in the early universe were huge compared with at present.

Last edited:
Fredrik
Staff Emeritus
Gold Member
mrspeedybob said:
Why do we assume that the big bang implies a begining of time?
We don't. The assumptions are

1. The assumptions that define general relativity:
a) Spacetime is a smooth 4-dimensional Lorentizan manifold with a metric.
b) The properties of matter are represented by a stress-energy tensor.
c) The relationship between the metric and the stress-energy tensor is described by Einstein's equation.

2. That spacetime can be "sliced" into 3-dimensional hypersurfaces that we can think of as representing space at different times, and that
a) each slice is homogeneous (in a specific mathematical sense).
b) each slice is isotropic (in a specific mathematical sense).

The first assumption says very roughly that Einstein's equation describes the relationship between the properties of matter (the stress-energy tensor) and how particles must move (the metric). The second assumption tells us to look for a specific kind of solution to Einstein's equation. A solution that's consistent with these assumptions is called a FLRW solution. I'll just quote myself for the next part.
The original big bang theory is the claim that the large-scale behavior of the universe is described approximately by a FLRW solution. In this context, the "big bang" is just a property of those solutions that can be characterized in many different ways, one of them being that the coordinate distance (in the "default" coordinate system used with these solutions) between any two timelike geodesics goes to zero as t (the time time coordinate of the same coordinate system) goes to zero.

Every event in these spacetimes has t>0, so there is no t=0, and therefore no specific event that we can call "the big bang".

In other big bang theories, such as theories involving inflation, the "big bang" is something different, something that happened everywhere in space at some specific time. I haven't studied such theories myself, so I won't try to elaborate. The reason I mention these theories is that they actually describe the big bang as something that "happened" in spacetime, but still not as an explosion, because it happened "everywhere" at roughly the same time. (Probably not at every point of the entire universe, but at least at every point of a much larger region of the universe than the part we can see).
I emphasize again that there's no t=0 in the theory. You seem to be asking how stuff at t=0 implies the stuff at t>0, but there isn't even a t=0 in the theory.

If the universe expands by a percentage per unit time then it really would have no beginning. X number of years in the past it would have been half it's current size, 2X years in the past it would have been 1/4 it's current size, etc... At no time would it's size have been zero unless it's rate of expansion were, at that instant, infinite.
This isn't the rate of expansion that's predicted by the theory, but you're right about what seems to be the main idea: If it's finite now, it was finite (zero doesn't count as "finite") at all times, i.e. for all t>0. If it's infinite now, it was infinite at all times.

The above (especially the last sentence) might seem to contradict the big bang theory, but it doesn't. I'll quote myself again:
Think e.g. of an infinite line with distance markings on it, and imagine the distance between the markings growing with time. The scale is changing, but the total size isn't.
The homogeneous and isotropic solutions can be divided into three classes: positive curvature, zero curvature, and negative curvature. The zero curvature case is a lot like that infinite line with a time-dependent scale. The only difference is that a line is 1-dimensional and space is 3-dimensional. The positive curvature case is a lot like a sphere with a time-dependent radius. The only difference is that a sphere is 2-dimensional and space is 3-dimensional.
If my comments about how t>0 for all events in spacetime makes you think "oh, this theory simply fails to tell us something about events with t=0 and t<0", you're making a naive mistake (that everyone makes until they've understood what I'm about to say). We all have an intuition about what sort of properties "time" has, which is based on our experiences, but the theory that actually describes time in a way that's consistent with our intuition (non-relativistic classical mechanics) has been thoroughly disproved by experiments that show us that special relativity makes better predictions about results of experiments than that theory. This means that our intuition is wrong. There are also experiments that show us that general relativity makes better predictions than special relativity. This proves that our intuition is even more wrong than we thought at first. If you're assuming that there must have been a time before the events with t>0, you're relying on your intuition, which has been proven wrong over and over again, instead of relying on of the best theories of science, one that has stood up to some amazingly accurate tests, and has never been disproved. (Not about the properties of time anyway. The behavior of matter on small scales is another...uh...matter).

Here's another quote that might help:
You might enjoy these two articles
Lineweaver SciAm article "Misconceptions about the Big Bang"
http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf

And "A Tale of Two Big Bangs" at Einstein Online (a research institute's outreach website)
http://www.einstein-online.info/en/spotlights/cosmology/index.html [Broken]

I have edited the post to fix the broken link to the first article. Edit: This quote seems unnecessary now that the man himself has shown up. (These links are included in marcus's signature).

Last edited by a moderator:
Chalnoth
If the universe expands by a percentage per unit time then it really would have no beginning. X number of years in the past it would have been half it's current size, 2X years in the past it would have been 1/4 it's current size, etc... At no time would it's size have been zero unless it's rate of expansion were, at that instant, infinite. Why do we think that happened?
Well, the expansion is only exponential when you are dominated by some sort of vacuum energy density, or something that acts very much like it. In other words, it only happens when the universe is completely empty of everything but a smooth, unchanging energy density.

When you have this sort of situation, the expansion is exponential as you mention, but it also has the property that it makes the universe more dilute, with whatever small amount of other stuff is in it getting more and more spread out.

So if we wind the clock back in time, if we have anything in the universe, anything at all besides this smooth, uniformly dense stuff, it will get more and more dense going backward in time, until it comes to dominate the energy density, and causes it to collapse into a singularity.

This means that given what we know, our region of space-time had to have a beginning somewhere. Nobody seriously thinks that that beginning was an actual singularity, but smooth time-evolution simply doesn't work.

zonde
Gold Member
If my comments about how t>0 for all events in spacetime makes you think "oh, this theory simply fails to tell us something about events with t=0 and t<0", you're making a naive mistake (that everyone makes until they've understood what I'm about to say).
I would say that if "t>0 for all events" then t is not time dimension.
Intuitively dimension is linear scale that extends from infinity to infinity. So if you say that "t" is not defined for t=0 and t<0 then I assume it's a nonlinear scale of time.

We all have an intuition about what sort of properties "time" has, which is based on our experiences, but the theory that actually describes time in a way that's consistent with our intuition (non-relativistic classical mechanics) has been thoroughly disproved by experiments that show us that special relativity makes better predictions about results of experiments than that theory.
Classical mechanics has been thoroughly disproved by experiments?
Does not seem right.

Besides intuitive understanding of time requires preferred reference frame and not really that Galilean transformation preserves all laws of physics.
And special relativity is not in conflict with idea of preferred reference frame.

This means that our intuition is wrong. There are also experiments that show us that general relativity makes better predictions than special relativity. This proves that our intuition is even more wrong than we thought at first.
There isn't developed up to date interpretation of gravity from perspective of preferred frame (not counting Newtonian gravity). So you can not know how adequate is general relativity compared to hypothetical intuitive version of gravity.

Fredrik
Staff Emeritus
Gold Member
I would say that if "t>0 for all events" then t is not time dimension.
Why?

So if you say that "t" is not defined for t=0 and t<0 then I assume it's a nonlinear scale of time.
What does "non-linear" mean in this context? t is defined so that it agrees with the number displayed by an ideal clock moving as described by a timelike geodesic. That sounds like a good reason to call it "time".

Classical mechanics has been thoroughly disproved by experiments?
Does not seem right.
Non-relativistic classical mechanics makes some predictions that aren't even close to agreeing with experiments. That makes the theory wrong, but that doesn't make it a bad theory. All theories are wrong. Some are just less wrong than others. The ones that make good predictions are considered "good" theories. Non-relativistic classical mechanics is a very good theory because it makes very accurate predictions about a wide range of experiments.

Theories appear to be like tools, as my Dad always used to say, "you have to use the right tool for the right job!"

zonde
Gold Member
Why?
There is always "before" when we talk about time i.e. it's infinite.
Your scale stops at 0. So at some point I go back one unit of time and I am out of defined range. That could happen if unit of time is not fixed and becomes infinite too. But that picture deviates too much from intuitive understanding of time so I wouldn't call it time. Use some other name for it, for example "hyperbolic time".

What does "non-linear" mean in this context? t is defined so that it agrees with the number displayed by an ideal clock moving as described by a timelike geodesic. That sounds like a good reason to call it "time".
In BigBang model size of the clock is not fixed relative to the size (scale) of the universe. If we still hold on to idea about constant speed of light that makes unit of time variable too.
If unit of time is variable then scale constructed using this unit is "non-linear".
At least that's how I see it.

Non-relativistic classical mechanics makes some predictions that aren't even close to agreeing with experiments. That makes the theory wrong, but that doesn't make it a bad theory. All theories are wrong. Some are just less wrong than others. The ones that make good predictions are considered "good" theories. Non-relativistic classical mechanics is a very good theory because it makes very accurate predictions about a wide range of experiments.
Yes, all theories are wrong if we suppose they are universal. But I don't see much point in categorizing all theories as wrong.
So if we know conditions under which theory works well we usually will say that it's right under given conditions.
And I can only agree with Tanelorn. You can break any tool if you use it in a wrong way.