<p>We don't really know at what energy scale general relativity actually breaks, but according to simple dimensional analysis arguments, the Planck scale is actually a plausible candidate.</p>
<p>Quantities at the Planck scale are actually defined by combining the three dimensional constants c (speed of light), h (Planck constant) and G (Newton's constant). At that scale, relativistic effects, gravity and quantum mechanics are all relevant, thus it is reasonable to assume that a new theory is necessary to describe physics at that scale.</p>
<p>Does time dilation work in a similar way in this new theory as it does in general relativity? We don't know, but I would bet it doesn't.</p>
<hr />
<p>Edit:</p>
<p>Now the question is more interesting in my opinion, because it can be answered with tools that we understand.</p>
<p>According to a <a href="https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric" rel="nofollow noreferrer">FRW cosmology</a> (neglecting curvature), the universe is described by the metric</p>
<p><span class="math-container">$$ds^2 = -cdt^2 + a(t)^2 (dr^2 + r^2 d\Omega^2)$$</span></p>
<p>in a special frame of reference called <em>comoving</em>. For an observer in the comoving frame, <span class="math-container">$t$</span> is the proper time elapsed since the Big Bang, and today it corresponds to <span class="math-container">$t_0 \approx 14 \text{Gyr}$</span>. <span class="math-container">$a(t)$</span> is called scale factor. Is a function of time that can be set to 1 today (<span class="math-container">$a(t_0)=1$</span>). In the past, a was less than 1. We can interpret <span class="math-container">$a(t)$</span> as the amount by which the universe is expanding. At Big Bang, assuming GR still applies, <span class="math-container">$a(t=0) = 0$</span> and we have a singularity.</p>
<p>As per the question, consider two observers (clocks) O1 and O2 at rest with respect to the comoving frame. At time <span class="math-container">$t_1$</span>, O1 sends a signal with frequency <span class="math-container">$\nu_1$</span> that is received at time <span class="math-container">$t_2$</span> by O2. If O2 measures the frequency of the signal, they will find</p>
<p><span class="math-container">$$\nu_2 = {a(t_1) \over a(t_2)} \nu_1 = {1 \over 1+z} \nu_1$$</span></p>
<p>where <span class="math-container">$z = {a(t_2) \over a(t_1)} -1$</span> is called <em>cosmological redshift</em>.</p>
<p>So, when O2 looks at O1's clock, they will see it going slower by a factor <span class="math-container">$1+z$</span>. This is usually interpreted as the consequence of the expansion of the universe: the distances increase and thus the propagating electromagnetic waves are stretched, their wavelength increasing, which decreases their frequency. But it could also be interpreted as some kind of time dilation. In a sense, O1's clock <em>was</em> running slower when it emitted the signal.</p>
<p>The earlier the signal is sent by O1, the smaller is <span class="math-container">$a(t_1)$</span> and the larger is the redshift, approaching infinity as <span class="math-container">$t_1 \rightarrow 0$</span>. Yet this does not mean that the universe is infinitely old. For each observer, the universe as a finite time. It can be shown that the comoving observers are the ones experiencing the longest time since the Big Bang. No one experiences an infinitely old universe.</p>
<p>In some way, this is similar to the situation of looking at an astronaut falling into a black hole. For a far away observer, the astronaut seem to take forever to cross the event horizon, but this isn't true: from the perspective of the astronaut, they traverse the horizon in a finite time. This analogy is wrong in many respects, but I hope it gives the idea of why the universe isn't infinitely old.</p>

CC BY-SA 4.0
2022-07-09T06:04:03.077Z
Thank you, please see edit for a reformulation of the question that can potentially use GR to a greater certainty.
seamux
CC BY-SA 4.0
2022-07-10T16:31:40.020Z
Thank you! The analogy at the end is exactly what I was trying to arrive at (see my reply to comment in the original question). Imprecise it may be, it provides an intuition for constructing thought experiments. The reason why I emphasize on time perceived by a later observer than time experienced by a comoving observer is because of the practical implications. For example, in an inflating universe that came from a singularity, this conjecture would imply that any local observer at any $t>0$ would not be able to intercept useful information transmitted at the moment of the Big Bang, as ...
seamux
CC BY-SA 4.0
2022-07-10T17:03:31.657Z
... as the information would be effectively flattened (if of finite wavelength) or take an infinite amount of time to arrive. This in turn would mean that the state of a singular universe at the moment of the Big Bang cannot exert a casaulity on any later state of the universe at a local scale, as if it happened infinitely long ago. This is an apparent paradox. In all likelihood the conjecture is flawed, and a different kind of physics did govern in the very early universe, or the universe didn't come from a singularity, or there's something else concerning the nature of time and space.
seamux
CC BY-SA 4.0
2022-07-08T17:39:02.720Z
2022-07-09T09:46:31.933Z
2022-07-09T09:46:31.933Z
Prallax
<p>I guess this question can be broken down into three consecutive parts:</p>
<ol>
<li>Does general relativity apply during the Planck Epoch?</li>
<li>If yes, does the gravitational time dilation prediction apply during the Planck Epoch before the fundamental forces are separated?</li>
<li>If yes, albeit without matter, would the mass energy equivalent packed into such a compact universe severely dilate time, such that to an observer from a later stage of the universe, the epoch would appear to last forever, and therefore (huge conjecture here) making the universe effectively infinitely old and without a beginning?</li>
</ol>
<p>Edit: if I may, I would like to relax the assumptions and reformulate the question to help extrapolate the hypothesis in the original question as a possible scenario:</p>
<p>Suppose we place a clock in the very early universe after the Planck epoch at a point where general relativity applies and the universe is still dense and smooth enough for gravitational time dilation to occur uniformly at a universal scale relative to a later stage of the universe. The universe rapidly expands then expansion slows, allowing a later observer to receive the signal transmitted by this clock during the denser state (let’s make the signals transmitted via gravitational waves, or a hypothetical type of radiation to which the early universe is transparent, since the early universe is likely opaque to electromagnetic radiation at that point in time). Relative to an identical clock adjacent to the observer, does the earlier clock appear to tick slowlier? If so, is it reasonable to conjecture by extrapolation that the earlier the universe being observed by a present observer, the slowlier time appears to pass, coming to a halt at gravitational singularity, thereby stretching the backward playback time of information received from beginning of the universe infinitely long, giving the appearance that the universe is infinitely old? This extrapolation, of course, is contingent upon a similar mechanism of time dilation during the Planck Epoch, GR or not.</p>

CC BY-SA 4.0
2022-07-08T13:28:07.257Z
Does this answer your question? [Age of the universe and time dilation](https://astronomy.stackexchange.com/questions/6525/age-of-the-universe-and-time-dilation)
antlersoft
CC BY-SA 4.0
2022-07-08T18:59:23.703Z
@antlersoft thank you, not quite, though. I’m more interested in whether the universe would appear to be infinitely old to an observer looking at information coming from the very early universe (or actually infinitely old relative to such an observer), analogous to how an object falling through an event horizon would appear to be frozen in time to an outside observer, than the actual time elapsed or experienced by a comoving observer.
seamux
CC BY-SA 4.0
2022-07-09T09:31:52.823Z
On a related note, a quantum gravity theory *might* say that the arrow of time isn't well-defined around the Planck epoch, due to Heisenberg uncertainty. That is, it might not be possible for *any* "observer" to assign an unambiguous order to the very earliest events. I'm pretty sure there's some info on Physics.SE about this, but I can't find it, maybe it's hiding in comments, or The h Bar archives.
PM 2Ring
<cosmology><general-relativity><time-dilation>
Planck epoch and time dilation
seamux
# Planck epoch and time dilation

(Asked by: username_0 on 2022-07-08)

I guess this question can be broken down into three consecutive parts:

1. Does general relativity apply during the Planck Epoch?
2. If yes, does the gravitational time dilation prediction apply during the Planck Epoch before the fundamental forces are separated?
3. If yes, albeit without matter, would the mass energy equivalent packed into such a compact universe severely dilate time, such that to an observer from a later stage of the universe, the epoch would appear to last forever, and therefore (huge conjecture here) making the universe effectively infinitely old and without a beginning?

Edit: if I may, I would like to relax the assumptions and reformulate the question to help extrapolate the hypothesis in the original question as a possible scenario:

Suppose we place a clock in the very early universe after the Planck epoch at a point where general relativity applies and the universe is still dense and smooth enough for gravitational time dilation to occur uniformly at a universal scale relative to a later stage of the universe. The universe rapidly expands then expansion slows, allowing a later observer to receive the signal transmitted by this clock during the denser state (let’s make the signals transmitted via gravitational waves, or a hypothetical type of radiation to which the early universe is transparent, since the early universe is likely opaque to electromagnetic radiation at that point in time). Relative to an identical clock adjacent to the observer, does the earlier clock appear to tick slowlier? If so, is it reasonable to conjecture by extrapolation that the earlier the universe being observed by a present observer, the slowlier time appears to pass, coming to a halt at gravitational singularity, thereby stretching the backward playback time of information received from beginning of the universe infinitely long, giving the appearance that the universe is infinitely old? This extrapolation, of course, is contingent upon a similar mechanism of time dilation during the Planck Epoch, GR or not.

**Tags:** cosmology, general-relativity, time-dilation

> **Comments:**
> **username_1**: Does this answer your question? [Age of the universe and time dilation](https://astronomy.stackexchange.com/questions/6525/age-of-the-universe-and-time-dilation)  
> **username_0**: @username_1 thank you, not quite, though. I’m more interested in whether the universe would appear to be infinitely old to an observer looking at information coming from the very early universe (or actually infinitely old relative to such an observer), analogous to how an object falling through an event horizon would appear to be frozen in time to an outside observer, than the actual time elapsed or experienced by a comoving observer.  
> **username_2**: On a related note, a quantum gravity theory *might* say that the arrow of time isn't well-defined around the Planck epoch, due to Heisenberg uncertainty. That is, it might not be possible for *any* "observer" to assign an unambiguous order to the very earliest events. I'm pretty sure there's some info on Physics.SE about this, but I can't find it, maybe it's hiding in comments, or The h Bar archives.  

---

## 1 answers

### Answer by username_3 on 2022-07-08. Score: 5

We don't really know at what energy scale general relativity actually breaks, but according to simple dimensional analysis arguments, the Planck scale is actually a plausible candidate.

Quantities at the Planck scale are actually defined by combining the three dimensional constants c (speed of light), h (Planck constant) and G (Newton's constant). At that scale, relativistic effects, gravity and quantum mechanics are all relevant, thus it is reasonable to assume that a new theory is necessary to describe physics at that scale.

Does time dilation work in a similar way in this new theory as it does in general relativity? We don't know, but I would bet it doesn't.

---

Edit:

Now the question is more interesting in my opinion, because it can be answered with tools that we understand.

According to a [FRW cosmology](https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson%E2%80%93Walker_metric) (neglecting curvature), the universe is described by the metric

$$ds^2 = -cdt^2 + a(t)^2 (dr^2 + r^2 d\Omega^2)$$

in a special frame of reference called *comoving*. For an observer in the comoving frame, $t$ is the proper time elapsed since the Big Bang, and today it corresponds to $t\_0 \approx 14 \text{Gyr}$. $a(t)$ is called scale factor. Is a function of time that can be set to 1 today ($a(t\_0)=1$). In the past, a was less than 1. We can interpret $a(t)$ as the amount by which the universe is expanding. At Big Bang, assuming GR still applies, $a(t=0) = 0$ and we have a singularity.

As per the question, consider two observers (clocks) O1 and O2 at rest with respect to the comoving frame. At time $t\_1$, O1 sends a signal with frequency $\nu\_1$ that is received at time $t\_2$ by O2. If O2 measures the frequency of the signal, they will find

$$\nu\_2 = {a(t\_1) \over a(t\_2)} \nu\_1 = {1 \over 1+z} \nu\_1$$

where $z = {a(t\_2) \over a(t\_1)} -1$ is called *cosmological redshift*.

So, when O2 looks at O1's clock, they will see it going slower by a factor $1+z$. This is usually interpreted as the consequence of the expansion of the universe: the distances increase and thus the propagating electromagnetic waves are stretched, their wavelength increasing, which decreases their frequency. But it could also be interpreted as some kind of time dilation. In a sense, O1's clock *was* running slower when it emitted the signal.

The earlier the signal is sent by O1, the smaller is $a(t\_1)$ and the larger is the redshift, approaching infinity as $t\_1 \rightarrow 0$. Yet this does not mean that the universe is infinitely old. For each observer, the universe as a finite time. It can be shown that the comoving observers are the ones experiencing the longest time since the Big Bang. No one experiences an infinitely old universe.

In some way, this is similar to the situation of looking at an astronaut falling into a black hole. For a far away observer, the astronaut seem to take forever to cross the event horizon, but this isn't true: from the perspective of the astronaut, they traverse the horizon in a finite time. This analogy is wrong in many respects, but I hope it gives the idea of why the universe isn't infinitely old.

> **Comments:**
> **username_0**: Thank you, please see edit for a reformulation of the question that can potentially use GR to a greater certainty.  
> **username_0**: Thank you! The analogy at the end is exactly what I was trying to arrive at (see my reply to comment in the original question). Imprecise it may be, it provides an intuition for constructing thought experiments. The reason why I emphasize on time perceived by a later observer than time experienced by a comoving observer is because of the practical implications. For example, in an inflating universe that came from a singularity, this conjecture would imply that any local observer at any $t>0$ would not be able to intercept useful information transmitted at the moment of the Big Bang, as ...  
> **username_0**: ... as the information would be effectively flattened (if of finite wavelength) or take an infinite amount of time to arrive. This in turn would mean that the state of a singular universe at the moment of the Big Bang cannot exert a casaulity on any later state of the universe at a local scale, as if it happened infinitely long ago. This is an apparent paradox. In all likelihood the conjecture is flawed, and a different kind of physics did govern in the very early universe, or the universe didn't come from a singularity, or there's something else concerning the nature of time and space.  

---

