<p>If I remember Stephen Hawking alludes to some sort of "quickening of time" near the big bang in his book <em>A Brief History of Time</em> (though I read it 20 years ago, so don't hold me to the exact details). He makes an argument that if time is measured by the number of collisions in a given volume then the number of collisions should go to infinity as you approach the big bang, thus meaning the big bang was infinitely far in the past. Note this isn't really time dilation (though maybe it could be reframed as such) which the comparison of time like coordinates between different spacetime coordinate systems that are set up to represent different observers' points of view.</p>

<p>In fact I was thinking about this the other day and I think this argument doesn't hold water. It is more sensible to talk about the number collisions in a given comoving volume and use the conformal time as the coordinates, because the number of collisions in a unit comoving volume per unit conformal time should be constant throughout the life of the Universe. As @Stan Liou alludes to though, in the models of the Universe best thought to represent our reality the big bang happens at some finite past value of conformal time.</p>

CC BY-SA 3.0
2014-10-10T16:59:39.787Z
2014-10-10T16:59:39.787Z
John Davis
<blockquote>
  <p>there are certain laws that established by experiment (e.g. time diliation in presence of high density).</p>
</blockquote>

<p>There is no such law.</p>

<blockquote>
  <p>So what the basis for claiming this did not happen in early universe as well?</p>
</blockquote>

<p>The fact there is no such law, for one.</p>

<p>Ok, let's step back a bit and take the simpler examples of time dilation. In special relativity, the ur-example of time dilation is between inertial frames, which correspond to a family of comoving intertial observers. So in making a statement involving the time dilation factor $\gamma$ such as
$$\frac{\mathrm{d}t}{\mathrm{d}\tau} = \frac{1}{\sqrt{1-v^2}} = \gamma\text{,}$$
we're comparing one inertial observer (with time $t$) with some other, not necessarily inertial, observer with time $\tau$. This is also generalizable to comparing arbitrarily-moving observers.</p>

<p>For gravitational time dilation, the ur-example is a comparison of the passage of time for two different observers stationary at two different elevations in a gravitational field. The moral is just the same: any talk of time dilation is at least indirectly referring to a comparison between different clocks, and thus different observers.</p>

<p>It basically boils down to: time dilation of <em>what</em> relative to <em>what</em>? Once you understand this, you will see how your question is actually reducible to the previously linked one.</p>

<blockquote>
  <p>It seems to me that after performing this the Big Bang will be at infinite past (am I wrong?) or in other words, there would be no big bang at all. I understand that this amounts to "interpretation" by I still do not see why this time scale is worse than the stand one</p>
</blockquote>

<p>You can always formally define a time $t'$ such that the big bang occurs at $t'\to-\infty$, or some such thing, e.g., by $t' = t_0\log(t/t_0)$, where $t$ is the usual cosmological time and $t_0$ is some arbitrary time scale. But doing this is merely a relabeling of coordinates, and has no physical significance. In particular, it doesn't change the length of the worldline of any observer, which is the duration measured by a clock along that worldline, aka <em>proper time</em>.</p>

<p>And in the usual Big Bang cosmology (though not all FLRW solutions), the proper time of any observer, however idealized, is finite in the past. Relabeling to infinite time is no different then taking the usual Euclidean space in Cartesian coordinates, $(x,y,z)$, defining a new coordinate $\xi = \log x$, and then saying that the origin is now infinitely far away, being at $\xi\to-\infty$. You can define the coordinate, but it doesn't change actual distances.</p>

CC BY-SA 3.0
2014-10-10T16:33:12.360Z
Do u claim that in GR there is no dependency between density and time diliation? I distrust you. What I am speaking about is measure time diliation of a body immersed in massive medium of certain density regarding observer at infinity and then apply those derived formulas to the whole universe. Is it impossible or what?
Anixx
CC BY-SA 3.0
2014-10-10T16:43:34.987Z
@Anixx you can distrust all you like, but it doesn't change the facts. Density does affect local geometry, but your entire conception of time dilation is wrong. This is should become more obvious if you realize that time dilation is perfectly possible in a vacuum, e.g., at different radii in the Schwarzschild spacetime.
Stan Liou
CC BY-SA 3.0
2014-10-10T16:44:58.517Z
I never claimed it is impossible in vacuum. It happens in proximity to all massive bodies.
Anixx
CC BY-SA 3.0
2014-10-10T18:56:07.430Z
@Anixx You claimed it depends on density, and I provided a clear counter-example: for any isolated spherically symmetric gravitating body is exernally Schwarzschild, regardless of density. Density can affect the local geometry, and so can matter indirectly, as I've already said (in this case, how far down the geometry is actually Schwarzschild). But more importantly, the conceptual issue of time dilation is completely different from what you're supposing.
Stan Liou
CC BY-SA 3.0
2014-10-10T16:12:32.237Z
2014-10-10T16:12:32.237Z
Stan Liou
<p>At the time the Big Bang happened the matter had enormous density. According the GR (I may be wrong here) such density dilates time.</p>

<p>If so, could it be that the time periods just after Big Bang which are usually considered happening in small part of a second (such as the Planck epoch), in reaity took billons of year (or may be, infinity) but due to time dilation appear to us as spanning only microscopic parts of a second? Could it be that the age of the universe is dramatically underestimated?</p>

CC BY-SA 3.0
2014-10-10T15:10:11.733Z
If this was true, time would be dilated for the entire universe, and so there really wouldn't be any point.
HDE 226868
CC BY-SA 3.0
2014-10-10T15:16:27.980Z
@Stan Liou I do not ask about different observers. I already saw that question. It is not a duplicate.
Anixx
CC BY-SA 3.0
2014-10-10T15:18:31.730Z
@Anixx time dilation only ever makes sense when comparing different observers (or frames, which generalize families of observers), so indeed it is.
Stan Liou
CC BY-SA 3.0
2014-10-10T15:23:56.833Z
@Stan Liou there are certain laws that established by experiment (e.g. time diliation in presence of high density). So what the basis for claiming this did not happen in early universe as well? Can we assuming this diliation derive a "real" time scale of the universe and put each early-Universe event on this scale? It seems to me that after performing this the Big Bang will be at infinite past (am I wrong?) or in other words, there would be no big bang at all. I understand that this amounts to "interpretation" by I still do not see why this time scale is worse than the stand one
Anixx
CC BY-SA 3.0
2014-10-10T15:46:58.240Z
@Anixx The problem here is that closer you get to the Big Bang, the more unreliable GR becomes. At the singularity it doesn't matter what GR predicts, because without a quantum theory of gravity we have no way of trusting those predictions.
David H
CC BY-SA 3.0
2014-10-13T01:55:13.567Z
I think you're confusing time dilation with propagation (speed) of light through a medium, which was indeed too dense for light to even propagate during the dark ages. There was no time dilation on the universal scale and in its true meaning simply because there's no wider frame of reference to observe it in than the one you'd like to apply it to. But if you're asking if time run faster or slower at differently dense parts of it, then sure, it does that still. But that's nothing special to early universe, it's "just" gravity. Not that we really know what it is, but  that's what it does. Q.E.D.
TildalWave
CC BY-SA 3.0
2014-10-13T02:00:20.090Z
BTW I voted to close as "unclear what you're asking" because I could use a clarification to better understand the question and am not exactly sure my previous comment hits the spot. I kinda hate how the system displays like I marked it as a duplicate too, just because others did so before me. I mean, how can I be sure that it is a duplicate if I'm not even exactly sure what the question is? :O
TildalWave
CC BY-SA 3.0
2014-10-14T00:01:01.900Z
Are you perchance alluding to the recently published book by Louise Riofrio titled “The Speed of Light” in which she presents her $GM=tc^3$ theory? It was also discussed by its author in [September 7 edition of The Space Show](http://www.thespaceshow.com/detail.asp?q=2310), if that helps. Show is archived and you can listen to it [via this link](http://archive.thespaceshow.com/shows/2310-BWB-2014-09-07.mp3) (MP3). Some of what you wrote in your question reminded me of that so perhaps you'll find it relevant / interesting. Cheers!
TildalWave
<cosmology><big-bang-theory>
Time dilation at the Big Bang
Anixx
# Time dilation at the Big Bang

(Asked by: username_0 on 2014-10-10)

At the time the Big Bang happened the matter had enormous density. According the GR (I may be wrong here) such density dilates time.

If so, could it be that the time periods just after Big Bang which are usually considered happening in small part of a second (such as the Planck epoch), in reaity took billons of year (or may be, infinity) but due to time dilation appear to us as spanning only microscopic parts of a second? Could it be that the age of the universe is dramatically underestimated?

**Tags:** cosmology, big-bang-theory

> **Comments:**
> **username_1**: If this was true, time would be dilated for the entire universe, and so there really wouldn't be any point.  
> **username_0**: @username_2 I do not ask about different observers. I already saw that question. It is not a duplicate.  
> **username_2**: @username_0 time dilation only ever makes sense when comparing different observers (or frames, which generalize families of observers), so indeed it is.  
> **username_0**: @username_2 there are certain laws that established by experiment (e.g. time diliation in presence of high density). So what the basis for claiming this did not happen in early universe as well? Can we assuming this diliation derive a "real" time scale of the universe and put each early-Universe event on this scale? It seems to me that after performing this the Big Bang will be at infinite past (am I wrong?) or in other words, there would be no big bang at all. I understand that this amounts to "interpretation" by I still do not see why this time scale is worse than the stand one  
> **username_3**: @username_0 The problem here is that closer you get to the Big Bang, the more unreliable GR becomes. At the singularity it doesn't matter what GR predicts, because without a quantum theory of gravity we have no way of trusting those predictions.  
> **username_4**: I think you're confusing time dilation with propagation (speed) of light through a medium, which was indeed too dense for light to even propagate during the dark ages. There was no time dilation on the universal scale and in its true meaning simply because there's no wider frame of reference to observe it in than the one you'd like to apply it to. But if you're asking if time run faster or slower at differently dense parts of it, then sure, it does that still. But that's nothing special to early universe, it's "just" gravity. Not that we really know what it is, but  that's what it does. Q.E.D.  
> **username_4**: BTW I voted to close as "unclear what you're asking" because I could use a clarification to better understand the question and am not exactly sure my previous comment hits the spot. I kinda hate how the system displays like I marked it as a duplicate too, just because others did so before me. I mean, how can I be sure that it is a duplicate if I'm not even exactly sure what the question is? :O  
> **username_4**: Are you perchance alluding to the recently published book by Louise Riofrio titled “The Speed of Light” in which she presents her $GM=tc^3$ theory? It was also discussed by its author in [September 7 edition of The Space Show](http://www.thespaceshow.com/detail.asp?q=2310), if that helps. Show is archived and you can listen to it [via this link](http://archive.thespaceshow.com/shows/2310-BWB-2014-09-07.mp3) (MP3). Some of what you wrote in your question reminded me of that so perhaps you'll find it relevant / interesting. Cheers!  

---

## 2 answers

### Answer by username_5 on 2014-10-10. Score: 2

If I remember Stephen Hawking alludes to some sort of "quickening of time" near the big bang in his book *A Brief History of Time* (though I read it 20 years ago, so don't hold me to the exact details). He makes an argument that if time is measured by the number of collisions in a given volume then the number of collisions should go to infinity as you approach the big bang, thus meaning the big bang was infinitely far in the past. Note this isn't really time dilation (though maybe it could be reframed as such) which the comparison of time like coordinates between different spacetime coordinate systems that are set up to represent different observers' points of view.

In fact I was thinking about this the other day and I think this argument doesn't hold water. It is more sensible to talk about the number collisions in a given comoving volume and use the conformal time as the coordinates, because the number of collisions in a unit comoving volume per unit conformal time should be constant throughout the life of the Universe. As @username_2 alludes to though, in the models of the Universe best thought to represent our reality the big bang happens at some finite past value of conformal time.


---

### Answer by username_2 on 2014-10-10. Score: 2

> there are certain laws that established by experiment (e.g. time diliation in presence of high density).

There is no such law.

> So what the basis for claiming this did not happen in early universe as well?

The fact there is no such law, for one.

Ok, let's step back a bit and take the simpler examples of time dilation. In special relativity, the ur-example of time dilation is between inertial frames, which correspond to a family of comoving intertial observers. So in making a statement involving the time dilation factor $\gamma$ such as
$$\frac{\mathrm{d}t}{\mathrm{d}\tau} = \frac{1}{\sqrt{1-v^2}} = \gamma\text{,}$$
we're comparing one inertial observer (with time $t$) with some other, not necessarily inertial, observer with time $\tau$. This is also generalizable to comparing arbitrarily-moving observers.

For gravitational time dilation, the ur-example is a comparison of the passage of time for two different observers stationary at two different elevations in a gravitational field. The moral is just the same: any talk of time dilation is at least indirectly referring to a comparison between different clocks, and thus different observers.

It basically boils down to: time dilation of *what* relative to *what*? Once you understand this, you will see how your question is actually reducible to the previously linked one.

> It seems to me that after performing this the Big Bang will be at infinite past (am I wrong?) or in other words, there would be no big bang at all. I understand that this amounts to "interpretation" by I still do not see why this time scale is worse than the stand one

You can always formally define a time $t'$ such that the big bang occurs at $t'\to-\infty$, or some such thing, e.g., by $t' = t\_0\log(t/t\_0)$, where $t$ is the usual cosmological time and $t\_0$ is some arbitrary time scale. But doing this is merely a relabeling of coordinates, and has no physical significance. In particular, it doesn't change the length of the worldline of any observer, which is the duration measured by a clock along that worldline, aka *proper time*.

And in the usual Big Bang cosmology (though not all FLRW solutions), the proper time of any observer, however idealized, is finite in the past. Relabeling to infinite time is no different then taking the usual Euclidean space in Cartesian coordinates, $(x,y,z)$, defining a new coordinate $\xi = \log x$, and then saying that the origin is now infinitely far away, being at $\xi\to-\infty$. You can define the coordinate, but it doesn't change actual distances.

> **Comments:**
> **username_0**: Do u claim that in GR there is no dependency between density and time diliation? I distrust you. What I am speaking about is measure time diliation of a body immersed in massive medium of certain density regarding observer at infinity and then apply those derived formulas to the whole universe. Is it impossible or what?  
> **username_2**: @username_0 you can distrust all you like, but it doesn't change the facts. Density does affect local geometry, but your entire conception of time dilation is wrong. This is should become more obvious if you realize that time dilation is perfectly possible in a vacuum, e.g., at different radii in the Schwarzschild spacetime.  
> **username_0**: I never claimed it is impossible in vacuum. It happens in proximity to all massive bodies.  
> **username_2**: @username_0 You claimed it depends on density, and I provided a clear counter-example: for any isolated spherically symmetric gravitating body is exernally Schwarzschild, regardless of density. Density can affect the local geometry, and so can matter indirectly, as I've already said (in this case, how far down the geometry is actually Schwarzschild). But more importantly, the conceptual issue of time dilation is completely different from what you're supposing.  

---

