What does When the Universe was one minute old mean?

[John Bleau]

What does "When the Universe was one minute old" mean?

I understand time in terms of references such as how long the second hand takes to travel around a clock, or the definition in terms of the cesium atom, or other references such as planetary motion and heartbeats, but without such references for the early universe, what exactly does a one minute old, or a one second old universe mean? What does the age of the universe mean at a time t when none of our present references (AFAIK) make sense?

 

[chroot]

Welcome to PF, John Bleau. It's an excellent question. I don't think it's particularly troubling to not have references -- time still exists even if you have no clock. I am more troubled by the fact that GR eliminates the concept of a universal time coordinate.

If GR dictates that it makes no sense to define an 'instant' in time (the same instant everywhere in the universe, like the Newtonian model of time) then it surely makes no sense to define a 'minute' after the big bang, either. The same argument applies -- does that declaration of time apply everywhere in the nascent universe?

Perhaps someone with more experience with models of the early universe can answer.

- Warren

 

[DevilsAvocado]

I understand time in terms of references such as how long the second hand takes to travel around a clock, or the definition in terms of the cesium atom ...

Everything is relative, as good old Albert told us, and so is the second hand and the cesium atom (e.g. GPS satellites are corrected for relativistic effects). The only constant is the speed of light 299.792.458 m/s.

Good question though, and I can't really tell you how they for example measure the Planck epoch (10^–43 seconds).

 

[marcus]

... the concept of a universal time coordinate.
...

Cosmology is based on GR, but is a separate discipline. In cosmo there is a widely used universal time coordinate variously known as universe time or Friedmann etc model time.

The vast majority of cosmo papers use the Friedmann equations as their basic model of the universe. These have a 3+1 split, a time coordinate, and a scale factor a(t) which is an increasing function of time. The Friedmann equations govern the increase in a(t).

They are simple differential equations which are derived from GR. Cosmologists do not use the full GR eqn as a rule. Almost everything is done with the simplified model. So universe time has a meaning.

The meaning of universe time is observationally linked to the CMB. Light from the ancient matter while still a hot cloud of gas. Observers are at rest relative to CMB if they see no doppler dipole. Two observers, both at rest, are synchronous if they both measure the same CMB temperature. This is only an idealized approximation but you get the idea.

Universe time is the time experienced by all the observers who are at rest relative to Background.

======================

When one studies the early universe, basically what one is talking about is the Friedmann model of the early universe.

This comes equipped with universe time. Using the model we can tell how the temperature and density rise as we crank back in time, because they depend on the scalefactor a(t).
And we know what particle reactions occur at high temperature and density so we can talk about the matter and radiation that would prevail at one hour, one minute, one second, of universe time.

But as they approach the start of expansion, using the Friedmann model, people become dissatisfied and mistrustful of the model. So they modify it.

 

[bapowell]

As Warren mentions, there is no universal time in GR. When we talk about the history of the universe, for example, when we say that the CMB formed 300K years after the big bang, we implicitly mean that this is the time as measured by an observer that is comoving with the expansion of the universe -- an observer locally at rest but moving along with the expansion. This is typically the cosmological time that people refer to.

NOTE: Looks like marcus beat me to it. To connect our replies, comoving observers are at rest relative to the CMB.

 

[marcus]

Sorry Powell, if I'd known you were answering I wouldn't have. Over and out to you. I've been seeing you giving the straight dope on all this stuff. Hopefully the OP will ask more questions and you will respond.

 

[DaveC426913]

The only constant is the speed of light 299.792.458 m/s.

I am not sure we can take for granted that the speed of light in the early moments of the BB was the same as what it is now. 'twas in those few moments that those very laws of the universe were being writ.

 

[Chronos]

We can safely say it was probably very different from what we now see.

 

[DevilsAvocado]

I am not sure we can take for granted that the speed of light in the early moments of the BB was the same as what it is now.

You’re absolutely right. Matter and the laws of physics was of course created during the early moments of the BB, and furthermore – the photons/light was 'trapped' until the last scattering (~400,000 after BB).

So when would it be accurate to talk about a constant speed of light? Dark ages, Recombination, Photon epoch...?

 

[John Bleau]

I'll be studying your answers, everyone, thanks. I'll post later in the coming week.

chroot, thanks for your welcome.

JB

 

[John Bleau]

Sorry about the time between my posts, life intervenes...

If I understand correctly, there is disagreement and uncertainty as to how to quantify time in the very early stages of the universe (say, the Plank epoch).

Re the "simplified model" marcus refers to (thanks, marcus): could someone post the differential equations or refer me to a website that has them?

Re two observers at rest: not sure what that means. Could someone explain how two observers might not observe the same CMB temperature? Would it be by one of them accelerating to an extremely high velocity as compared with the other?

===============

I'd like to describe how I've had to vulgarize the Big Bang for myself so that more knowledgeable posters here might tell me where my conception clashes with current theory. Then I might be able to incorporate the notion of time into it.

Is it reasonable for me to conceive of the Big Bang as a singularity like a black hole (a white hole, actually)? To picture the history of the universe, I use the balloon analogy, in which a balloon expands from a singularity. I imagine myself as a two-dimensional creature on top of the balloon (its North Pole) and all my lines of sight (through 360°, which is why the CMB is observed all around us) go back in time, curving around a smaller and smaller balloon, back to the singularity. I believe this analogy is very commonly used. The measurement of time here would seem quite straightforward, as it would be the length of the curve divided by the speed of light. Except that as we approach the singularity, its density affects time and space. When we reverse the arrow of time, this is similar to falling into a black hole, isn't it? Maybe I read wrong, but I read somewhere that falling into a black hole actually takes forever. If that is the case, wouldn't the age of the universe be infinite?

 

[bapowell]

Re two observers at rest: not sure what that means. Could someone explain how two observers might not observe the same CMB temperature? Would it be by one of them accelerating to an extremely high velocity as compared with the other?

Sure, or even just moving at constant velocity. If you are locally at rest with respect to the CMB (comoving with the expansion) you will measure a uniform temperature (modulo intrinsic anisotropies on the order of 1/100000). Now, if you are moving relative to the CMB, then the CMB photons in front of you will be blue shifted relative to those in the back, leading to a temperature profile like this:

This "dipole" anisotropy is still small relative to the average temperature of the CMB. For the Earth, moving at around 625 km/s relative to the CMB, it gives an effect on the order of 1/1000.

 

[DevilsAvocado]

http://en.wikipedia.org/wiki/Friedmann_equations"

 

[John Bleau]

Thanks both.

bapowell, it seems that this gives meaning to "absolute motion." Intuitively, I would have thought that the apparent source of the CMB would have shifted slightly for the "moving" observer, making it appear as homogeneous as for the "at rest" observer. Has the "dipole anisotropy" been observed experimentally and reliably? If so, then this is a pretty major revelation for me.

 

[bapowell]

Has the "dipole anisotropy" been observed reliably and experimentally?

Sure. The picture I included above is the actual dipole as seen by NASA's COBE satellite. However, we're still not talking about 'absolute motion' -- the CMB merely serves as a convenient frame of reference. Research "CMB dipole" or any of the CMB experiments (COBE, WMAP, etc) for more information.

 

[DevilsAvocado]

... the CMB merely serves as a convenient frame of reference.

Very interesting, does this in any way 'neutralize' the SR Inertial frame of reference?

http://en.wikipedia.org/wiki/Inertial_frame_of_reference#Background"

In practical terms, the equivalence of inertial reference frames means that scientists within a box moving uniformly cannot determine their absolute velocity by any experiment (otherwise the differences would set up an absolute standard reference frame).[16][17] According to this definition, supplemented with the constancy of the speed of light, inertial frames of reference transform among themselves according to the Poincaré group of symmetry transformations, of which the Lorentz transformations are a subgroup.

If the "CMB frame of reference" is available and the same everywhere in the universe, why can’t we use this as the "absolute standard reference frame"?

 

[bapowell]

Very interesting, does this in any way 'neutralize' the SR Inertial frame of reference?

Well, the SR inertial frame is not applicable in cosmology, due to the presence of gravity. In a homogeneous universe, however, observers comoving with the expansion are inertial observers in that their worldlines follow geodesics.

If the "CMB frame of reference" is available and the same everywhere in the universe, why can’t we use this as the "absolute standard reference frame"?

It sort of has become the standard reference frame, since, as we have mentioned above in this post, it has become a common frame to use when talking about the age of the universe and other observer-dependent quantities. However, I still would avoid the word 'absolute', because, although convenient, the rest frame of the CMB is by no means physically preferred over an other frame.

 

[DevilsAvocado]

Okay, thanks for info bapowell.

 

[DevilsAvocado]

... I imagine myself as a two-dimensional creature on top of the balloon (its North Pole) and all my lines of sight (through 360°, which is why the CMB is observed all around us) ...

Don’t know if this is of any value to you (it’s not exactly the balloon analogy), but it definitely helped me to put my own little life in perspective to the CMB and the rest.

The Known Universe Scientifically Rendered For All to See
https://www.youtube.com/watch?v=<object width="640" height="505"><param name="movie" value="http://www.youtube.com/v/17jymDn0W6U&hl=en_US&fs=1&rel=0&color1=0x2b405b&color2=0x6b8ab6"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/17jymDn0W6U&hl=en_US&fs=1&rel=0&color1=0x2b405b&color2=0x6b8ab6" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="640" height="505"></embed></object>

Go to http://www.youtube.com/watch?v=17jymDn0W6U&hd=1", it’s amazing.

 

[DaveC426913]

The Known Universe Scientifically Rendered For All to See

It's cool but I am still a fan of "Cosmic Zoom", even though it's a good 30 years old by now and needs to be updated.

What was really cool about it was it went the other direction as well, down to the subatomic level.

(In case the name doesn't ring a bell, the start and end of the film was at a human scale - of a mosquito on the arm of a person at a picnic in a park.)

 

[Chronos]

We do, but, CMB photons were not 'released' until ~380,000 years after the BB. It's usefulness as a clock prior to that is undefined. We can wind the 'clock' back prior to that using nuclear interactions, but, this clock starts to fall apart as we approach the Planck temperature. It is not necessarily incorrect to suggest the BB itself may have taken an an eternity to unfold based on anything recognizable as a clock.

 

[DevilsAvocado]

It's cool but I am still a fan of "Cosmic Zoom", even though it's a good 30 years old by now and needs to be updated.

Found it! The mosquito->subatomic part is cool, but the rest definitely need some graphical 'rejuvenation'...

https://www.youtube.com/watch?v=<object width="480" height="385"><param name="movie" value="http://www.youtube.com/v/8oF18rk_H0Y&hl=en_US&fs=1&rel=0&color1=0x006699&color2=0x54abd6"></param><param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param><embed src="http://www.youtube.com/v/8oF18rk_H0Y&hl=en_US&fs=1&rel=0&color1=0x006699&color2=0x54abd6" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="480" height="385"></embed></object>

 

[John Bleau]

Thanks for the replies. I remember cosmic zoom - or the series of pictures it was based on. I appreciate the answer to "two observers at rest" part of my question.

I'm still curious about the other part, though, which I reproduce here:

Is it reasonable for me to conceive of the Big Bang as a singularity like a black hole (a white hole, actually)? To picture the history of the universe, I use the balloon analogy, in which a balloon expands from a singularity. I imagine myself as a two-dimensional creature on top of the balloon (its North Pole) and all my lines of sight (through 360°, which is why the CMB is observed all around us) go back in time, curving around a smaller and smaller balloon, back to the singularity. I believe this analogy is very commonly used. The measurement of time here would seem quite straightforward, as it would be the length of the curve divided by the speed of light. Except that as we approach the singularity, its density affects time and space. When we reverse the arrow of time, this is similar to falling into a black hole, isn't it? Maybe I read wrong, but I read somewhere that falling into a black hole actually takes forever. If that is the case, wouldn't the age of the universe be infinite?

 

[bapowell]

Maybe I read wrong, but I read somewhere that falling into a black hole actually takes forever. If that is the case, wouldn't the age of the universe be infinite?

For the observer that's falling into the black hole, he crosses the event horizon in finite time. However, to an observer that is at rest relative to this free fall, he sees the free falling observer's watch slow down, with the time dilation becoming maximal infinitesimally close too the horizon.

In general relativity, there are an infinite number of equivalent reference frames, each with their own time devices. The age of the universe only has meaning once we pick a reference frame within which to measure it. For an observer comoving with the expansion (at rest with respect to the balloon), the age of the universe is finite (just as it takes such an observer only a finite time to traverse the event horizon of a black hole). We are essentially comoving observers.

 

[John Bleau]

For the observer that's falling into the black hole, he crosses the event horizon in finite time.

This is not my understanding. As I understand it, for him, there is no point at which he can say he's crossing the event horizon - it's always in front of him. So from his point of view, he never actually crosses it.

I would have thought that it is we who see, in finite time, the traveler fade away and disappear from view. Of course, we would not actually see him cross the event horizon, of course, due to the light from him tending toward zero as he approaches it.

 

[bapowell]

This is not my understanding. As I understand it, for him, there is no point at which he can say he's crossing the event horizon - it's always in front of him. So from his point of view, he never actually crosses it.

You are mistaken. Moving clocks run slow. He, like all observers, measures a proper time. See http://en.wikipedia.org/wiki/Black_hole#Event_horizon"

 

[John Bleau]

Here's the quote in Wikipedia (emphasis mine):

On the other hand, an observer falling into a black hole does not notice any of these effects as he crosses the event horizon. According to his own clock, he crosses the event horizon after a finite time, although he is unable to determine exactly when he crosses it, as it is impossible to determine the location of the event horizon from local observations.

As I interpret this, when he crosses the event horizon as we see it, there is a finite time according to his own clock. However, as he sees it, the event horizon remains in front of him.

 

[bapowell]

I'm confused. The quote is right in front of you. "...he crosses the event horizon after a finite time..."

Here's the quote from wikipedia just before that one:

"To a distant observer, clocks near a black hole appear to tick more slowly than those further away from the black hole.[32] Due to this effect, known as gravitational time dilation, an object falling into a black hole appears to slow down as it approaches the event horizon, taking an infinite time to reach it."

I don't see the confusion.

EDIT: You are confusing time dilation. Moving clocks run slow. That's the mantra. Everyone measures their own proper time. That's another one. It can't take the free falling observer a finite amount of time do something, according to his own watch, that takes him an infinite amount of time to do, according to his own experience.

 

[John Bleau]

It is confusing, as we have two frames of reference. Note that they say: "taking an infinite time to reach it" - is that from our "at rest" point of view?

 

[DaveC426913]

Found it! The mosquito->subatomic part is cool, but the rest definitely need some graphical 'rejuvenation'...

There's another much more sophisticated version of this. It is narrated and it has data showing what scale is being viewed and talks about the geometric expansion of the view by 10 times with every square box seen.

And
I hope the artwork is of more advanced quality...

 

[bapowell]

It is confusing, as we have two frames of reference. Note that they say: "taking an infinite time to reach it" - is that from our "at rest" point of view?

Yes, "to the distant observer" it "takes an infinite time to reach it". This means that, on the distant observer's watch, it takes an infinite amount of time for the free falling observer to cross the horizon.

The free falling observer is oblivious to this fact, and just goes right on falling into the black hole. Even though he can't say exactly when he crossed it, he does indeed cross it, and after a finite amount of time.

 

[John Bleau]

I'm wondering if the event horizon itself is observer-dependent. Say now that the observer is on Earth, which is revolving around the sun. When Earth is moving in the direction of the black hole, I doubt that makes the observer suddenly see the traveler cross the event horizon. I imagine this is the case regardless of the observer's velocity (as long, anyway. as we're not catching up to the traveler) - to us it takes an "infinite amount of time" for him to reach the event horizon.

Are we on the same page on this?

 

[John Bleau]

I'm wondering if the event horizon itself is observer-dependent. Say now that the observer is on Earth, which is revolving around the sun. When Earth is moving in the direction of the black hole, I doubt that makes the observer suddenly see the traveler cross the event horizon. I imagine this is the case regardless of the observer's velocity (as long, anyway, as we're not catching up to the traveler) - to us (observers) it takes an "infinite amount of time" for the traveler to reach the event horizon.

Are we on the same page on this?

 

[bapowell]

The event horizon of a black hole is observer independent. It is a property of the asymptotic structure of the spacetime, not on the worldline of any particular observer.

Also, it's not just a matter of relative motion. Are you suggesting that as long as the outside observer is moving then he no longer sees the free falling-into-the-black hole observer's time dilating? I probably started that by saying "to an observer at rest" in an earlier post. Since we are talking about gravitational time dilation here, what's relevant is the curvature of spacetime in the neighborhood of each observer. The intense gravity of the black hole is redshifting the free falling observer's time relative to the outside observer, regardless of the outside observer's state of motion.

 

[John Bleau]

Apart from your first sentence, we're on the same page.

Let's now take your last sentence. It will serve well to illustrate just why I'm confused.

The intense gravity of the black hole is redshifting the free falling observer's time relative to the outside observer, regardless of the outside observer's state of motion.

Let us now take a second traveler B, following the first traveler A toward the event horizon. Let us also say that traveler A's velocity is such that he remains in front of B (ie, between B and the event horizon, or heading toward the EH at greater velocity). From B's perspective, A takes forever to cross the event horizon, yet is between it and B. How can this be so while at the same time B, from his own perspective, crosses the event horizon in finite time?

 

[bapowell]

Good question, John. I'm not immediately sure what the answer is. I would suggest that once B reaches the event horizon, his clock is equally redshifted relative to A's clock. Perhaps they both fall in at the same time according to B, while A thinks that A falls in first. There's no paradox here, since simultaneity is observer dependent.

 

[John Bleau]

Thanks bapowell,

I consider the question still open, though it has strayed somewhat from the original post (though it's still related in a manner I was hoping to clarify). My own conception of the event horizon is similar to the speed of light in SR - we can accelerate as much as we please, the speed of light remains unattainable. Likewise for "approaching" the EH. But possibly this is a topic for another thread after which we could return to this one. Or maybe it's already been broached - I don't know, I'm new here.

Anyway, thanks, I learned quite a bit.

At any rate, I have to get back to work. I'll pop by tomorrow or next week.

 

[DevilsAvocado]

There's another much more sophisticated version of this.

Okay, that explains it.

 

[DevilsAvocado]

... My own conception of the event horizon is similar to the speed of light in SR - we can accelerate as much as we please, the speed of light remains unattainable. Likewise for "approaching" the EH.

I think the answer to your EH question is here:

http://en.wikipedia.org/wiki/Event_horizon#Interacting_with_an_event_horizon"
...
For the case of the horizon around a black hole, observers stationary with respect to a distant object will all agree on where the horizon is. While this seems to allow an observer lowered towards the hole on a rope to contact the horizon, in practice this cannot be done. If the observer is lowered very slowly, then, in the observer's frame of reference, the horizon appears to be very far away, and ever more rope needs to be paid out to reach the horizon. If the observer is quickly lowered by another observer, then indeed the first observer, and some of the rope can touch and even cross the (second observer's) event horizon. If the rope is pulled taut to fish the first observer back out, then the forces along the rope increase without bound as they approach the event horizon, and at some point the rope must break. Furthermore, the break must occur not at the event horizon, but at a point where the second observer can observe it.

Attempting to stick a rigid rod through the hole's horizon cannot be done: if the rod is lowered extremely slowly, then it is always too short to touch the event horizon, as the coordinate frames near the tip of the rod are extremely compressed. From the point of view of an observer at the end of the rod, the event horizon remains hopelessly out of reach. If the rod is lowered quickly, then the same problems as with the rope are encountered: the rod must break and the broken-off pieces inevitably fall in.

These peculiarities only occur because of the supposition that the observers be stationary with respect to some other distant observer. Observers who fall into the hole are moving with respect to the distant observer, and so perceive the horizon as being in a different location, seeming to recede in front of them so that they never contact it. Increasing tidal forces (and eventual impact with the hole's gravitational singularity) are the only locally noticeable effects. While this seems to allow an in-falling observer to relay information from objects outside their perceived horizon but inside the distant observer's perceived horizon, in practice the horizon recedes by an amount small enough that by the time the in-falling observer receives any signal from farther into the hole, they've already crossed what the distant observer perceived to be the horizon, and this reception event (and any retransmission) can't be seen by the distant observer.

Edit: http://en.wikipedia.org/wiki/Apparent_horizon" is observer-dependent.

 

[John Bleau]

Thanks for your reply, DA.

This suggests to me that if our universe is emerging from a white hole or falling into a black hole, then there is no reaching the singularity. It would mean that, in fact, we have been emerging from the Big Bang indefinitely.

I suspect that "when the Universe was one minute old" is a projection of our local geometry to the singularity. On the rubber sheet model, this would be akin to our extending a straight line and not having it curve along the rubber sheet.