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DanishDynamite
2007-Sep-11, 07:57 PM
I've just realized a very strange coincidence after reading a few threads here. The coincidence is so strange that I'm quite certain it is no coincidence and that I just haven't understood how certain concepts depend on each other.

Here's the coincidence:

The Hubble constant is a measure of the expansion rate of our Universe. It assumes that the further away something is from something else (cosmologically speaking), the faster they will move apart from each other and do so in a linear fashion. I.e if the Hubble constant was around 70 km/s/megaparsec (which it is) this would mean that something 1 megaparsec away from us would be moving away from us at about 70 km/s. And something 2 megaparsecs away from us would be moving away from us at about 140 km/s. Etc.

Fine.

Now, it would seem to me that any estimates of the value of this constant would not necessarily make use of the age of the Universe as part of the calculation of this value nor as part of the method of obtaining this value. Perhaps this is wrong, but I don't see how.

This is observation no. 1.

The age of the Universe is another interesting bit of knowledge. I'm not sure what evidence exists for this age, but I presume at least some of it is not dependent on the value of the Hubble constant. Is this correct?

This is observation no. 2.

If this is correct, then there is the very odd coincidence which I mentioned at the beginning. And the coincidence is this:

If the age of the Universe is around 14 billion years, then any photon we detect today could at most have traveled for 14 billion years, and hence at most have traveled 14 billion light-years or around 4,300 megaparsecs. Assuming a Hubble constant of 70 km/s/megaparsec, how fast would something be traveling away from us (according to Hubble) at this distance of 4,300 megaparsecs? Well, it would be traveling away from us at around 70 km/s/megaparsec X 4,300 megaparsecs = 301,000 km/s.

Anyone recognize that number?

That's the speed of light!

Surely this is not a coincidence?

antoniseb
2007-Sep-12, 12:48 PM
Surely this is not a coincidence?
It is not a coincidence. While there are ways to calculate the age of the universe, the fact of the implied age of the universe from the observed Hubble expansion is part of all the equations. Some years ago we thought we had modeled stars so that some globular clusters were 18 billion years old. We have since reworked stellar models.

It should be noted that the Hubble 'constant' has been growing in the last eight billion years or so (I'm not sure when the inflection point was). This is modest growth which we call the acceleration of expansion, and is currently attributed to 'dark energy'.

Ken G
2007-Sep-12, 02:21 PM
Yes, or put differently, in a universe with no gravitational sources, the Hubble constant would always be the same thing as the inverse of the age of the universe, in v/d units (note that also has the units of 1/t, you don't need light in there anywhere). The reason our Hubble constant also nearly obeys that rule, even though we do have gravitational sources, might be that dark energy has by now pretty nearly counteracted the attractive gravity that dominated the early universe.

Good for you for noticing that "coincidence", in effect you have stumbled on the real significance of the Hubble law-- it says that if you run time backward, the whole business comes together at the same time, a time controlled by the Hubble constant and gravity, a time of about 13.7 billion years.

DanishDynamite
2007-Sep-14, 06:44 PM
It is not a coincidence. While there are ways to calculate the age of the universe, the fact of the implied age of the universe from the observed Hubble expansion is part of all the equations. Some years ago we thought we had modeled stars so that some globular clusters were 18 billion years old. We have since reworked stellar models.
So the concept of the Hubble constant is directly or indirectly part of the equations which are currently used to estimate the age of the Universe?

Bummer.

Still, there are independent ways of at least determining a lower bound. The age of the oldest rocks on our planet have been determined using knowledge of the decay rate of radioactive particles, as far as I know. Couldn't something similar be used to determine lower bounds on the age of the Universe? One might have to use some assumptions about the way stars work, but it is my understanding that very small stars could potentially have life-times of at least 14 billion years.

In any case, I still don't quite understand why the connectivity of the age of our Universe and Hubble's constant must mean that things at the edge of our observable Universe must be moving away from us at lightspeed. Hubble's Law and our estimates of Hubble's constant let's us calculate at what point all of space was located at one point. Cool. But why is it that this time period is such that it exactly allows a photon of light to have traveled sufficiently far that, had it travelled in a "straight line", the place from which it started its journey would now, by Hubble's law, be traveling away from us at precisely lightspeed?

Can someone explain the obvious bit I'm missing?

Ken G
2007-Sep-15, 01:08 AM
What you're missing is that it's not at all obvious. Imagine a picnic in the park, on top of a rubber sheet. There are ants crawling all over the sheet, which starts out very small. The ants crawl at a fixed speed, and would seem to be able to cross the tiny sheet very quickly, except the sheet is being stretched. Imagine the edges of the sheet are pulled at the speed the ants crawl (it's not quite right but will give you the basic idea of how the observable universe roughly works). Then the ones at the edge are barely making headway, and so you can stretch for a long time and they are just starting to reach the center. You won't get correct numbers that way, it's not obvious at all how to do that-- but it is the basic picture.

Jerry
2007-Sep-15, 11:13 PM
The 'coincidence' is actually a constraint: The way the parametrics are currently assembled, both the value of the Hubble constant and the age of the universe are tightly constrained. Any evidence that we find that indicates matter is more than 13.7byrs old, or the value of Ho is different, requires some other parametrics to be altered. Antoniseb mentioned that dark energy enters the equation with a lot of variability, so even though the cosmos are 'tightly constrained', there are still a few parameters that allow flexiblility. Check out the Ho and 'tweaking' q&a threads.

DanishDynamite
2007-Sep-16, 01:22 AM
What you're missing is that it's not at all obvious. Imagine a picnic in the park, on top of a rubber sheet. There are ants crawling all over the sheet, which starts out very small. The ants crawl at a fixed speed, and would seem to be able to cross the tiny sheet very quickly, except the sheet is being stretched. Imagine the edges of the sheet are pulled at the speed the ants crawl (it's not quite right but will give you the basic idea of how the observable universe roughly works). Then the ones at the edge are barely making headway, and so you can stretch for a long time and they are just starting to reach the center. You won't get correct numbers that way, it's not obvious at all how to do that-- but it is the basic picture.
Yes, I think I understand the concept of space expanding. And I understand that this expansion follows a linear law, i.e. the farther away, the faster the expansion. And I can see how that would allow one to calculate at what point in time everything was in one place.

An example:

Hubble's constant is currently around 70km/s/megaparsec. Let us look at a place now 1 megaparsec removed from us. This place is now moving away from us at 70 km/s. For the sake of simplicity, let us assume that it has always moved away from us at 70 km/s. How long would it then have been underway in order for it to be 1 megaparsec away from us now?

Well, 1 megaparsec is around 3.1 E19 kilometers. Divide this by 70 km/s and by the number of seconds in a year, and you get around 14 billion years. Halleluyah!

What I don't understand is the following:

The age of the Universe has been derived (see above). Suppose a photon had been traveling more or less unhindered for this amount of time and then hit a sensor here on Earth. It would then have been traveling for some 14 billion years and would have covered some 14 billion light-years. Using Hubble's Law, how fast would space be expanding at a distance of 14 billion light-years from us? Well, that would be 14 billion light-years (= 4,300 megaparsecs) divided by 1 megaparsec times 70 km/s = 301,000 km/s = speed of light.

Why is it that the age of the Universe derived from the expansion rate exactly allows a photon to in principle have traveled precisely far enough that Hubble's Law says that a place that far away would now be traveling away from us at light-speed?

I don't understand why these two things should be related.

DanishDynamite
2007-Sep-16, 01:27 AM
The 'coincidence' is actually a constraint: The way the parametrics are currently assembled, both the value of the Hubble constant and the age of the universe are tightly constrained.
I accept that. I just don't get the coincidence I've once again explained above.

Any evidence that we find that indicates matter is more than 13.7byrs old, or the value of Ho is different, requires some other parametrics to be altered. Antoniseb mentioned that dark energy enters the equation with a lot of variability, so even though the cosmos are 'tightly constrained', there are still a few parameters that allow flexiblility. Check out the Ho and 'tweaking' q&a threads.
Okay, thanks.

astromark
2007-Sep-16, 02:22 AM
and if i may... its not speeding away from us. Its just that the space it occupies and the void between us is expanding at such a rate as to give that perception. From our point of view.
Its not so much a coincidence as a rule of this universes very structure.

DanishDynamite
2007-Sep-16, 02:24 AM
and if i may... its not speeding away from us. Its just that the space it occupies and the void between us is expanding at such a rate as to give that perception. From our point of view.
Its not so much a coincidence as a rule of this universes very structure.
Please explain the coincidence.

astromark
2007-Sep-16, 09:21 AM
This is getting confussing... this thread was started by you.
You have detected a coincidence.
Post number 9 you ask me to explain... Well at the risk of repeating what has already been said. In my own words... Its the same answer to the same question. Just this time you have seen a link that is there because of the fact that the same rules apply to all. Nothing can exceed C. The speed of light in a vacuum. Objects at the edge of the visible universe appear to be receding away faster than is possible. Scroll up to read the Ants on the expanding sheet analogy. It may not be the maths you are looking for but it paints a clear image for me. I except that as the right solution to this question.
To explain this coincidence is to point out that yes these numbers tell the same story no matter how you tell it because the same rule of physics applies. It is no accident that the speed of light would be the number arrived at. Because that is the velocity of light.
Well there you are... all explained and now I am as confused as you. Ask Ken.

Ken G
2007-Sep-16, 01:49 PM
Why is it that the age of the Universe derived from the expansion rate exactly allows a photon to in principle have traveled precisely far enough that Hubble's Law says that a place that far away would now be traveling away from us at light-speed?
I don't understand why these two things should be related.
There are really two questions here, connected to your two words "exactly" and "related". The reason they are related comes from the fact that the earliest light we can see comes from material that is expanding away from us at something like (not necessarily exactly) the speed of light. If that material was moving much slower than that, it could not have come from close to us originally and still have its early light just getting to us now, and it if were expanding away faster than that, the expansion would inhibit the light arrival (think of the rubber sheet). So they have to be related: if the Hubble constant had come out larger, all the scales are shortened-- the distance at which you reach c is closer, and the time it takes the material to get to that distance is less.

But when you ask must this work exactly, then it is indeed just a coincidence. What must come out exactly is the distance you plug into the Hubble law to get to c must always equal the distance light can cross in the time 1/H, you can see that just from v = Hd. Your question is, why does the light that takes 1/H to cross d=c/H have to come from the same stuff that is at d=c/H right now? It doesn't, that only happens for an expansion that is neither accelerating or decelating, or one where the early deceleration by dark matter is nearly compensated by late acceleration from dark energy, as ours seems to obey.

DanishDynamite
2007-Sep-17, 08:01 PM
There are really two questions here, connected to your two words "exactly" and "related". The reason they are related comes from the fact that the earliest light we can see comes from material that is expanding away from us at something like (not necessarily exactly) the speed of light.
Why would this be the case?

If that material was moving much slower than that, it could not have come from close to us originally and still have its early light just getting to us now,...
Why not?

... and it if were expanding away faster than that, the expansion would inhibit the light arrival (think of the rubber sheet).
Not understood.

Sorry, I'm not trying to be stubbornly contradictory, I just can't see the conclusion you draw.

So they have to be related: if the Hubble constant had come out larger, all the scales are shortened-- the distance at which you reach c is closer, and the time it takes the material to get to that distance is less.
Yes, I understand how the Hubble constant would automatically set a value for a distance at which things must move away from us at lightspeed. In that sense, it does provide an ultimate lower bound for a distance beyond which can know nothing.

But when you ask must this work exactly, then it is indeed just a coincidence. What must come out exactly is the distance you plug into the Hubble law to get to c must always equal the distance light can cross in the time 1/H, you can see that just from v = Hd. Your question is, why does the light that takes 1/H to cross d=c/H have to come from the same stuff that is at d=c/H right now? It doesn't, that only happens for an expansion that is neither accelerating or decelating, or one where the early deceleration by dark matter is nearly compensated by late acceleration from dark energy, as ours seems to obey.
Wow, you totally lost me there, Ken G. Could you explain it again, please? In small bits. :)

Please.

DanishDynamite
2007-Sep-20, 12:27 AM
Still looking forward to a reply by Ken G.

Ken G
2007-Sep-20, 01:52 AM
Still looking forward to a reply by Ken G.

The problem is I'm not quite sure what to do but to repeat the rubber sheet analogy. Are you saying that you don't see why the farthest parts of the rubber sheet from which we can receive ants in that model is controlled (though not necessarily equal to) the distance the part of the sheet that is moving at "ant speed" has been stretched? Or that you don't see the connection with the expanding universe? Note that the argument for when it will come out exactly is far more difficult than simply an argument that shows they are related.

DanishDynamite
2007-Sep-22, 12:51 AM
The problem is I'm not quite sure what to do but to repeat the rubber sheet analogy. Are you saying that you don't see why the farthest parts of the rubber sheet from which we can receive ants in that model is controlled (though not necessarily equal to) the distance the part of the sheet that is moving at "ant speed" has been stretched? Or that you don't see the connection with the expanding universe? Note that the argument for when it will come out exactly is far more difficult than simply an argument that shows they are related.
As I've already said, I understand how the Hubble constant would automatically set a value for a distance at which things must move away from us at lightspeed. In that sense, it does provide an ultimate lower bound for a distance beyond which can know nothing.

But I don't understand why the Hubble constant, which describes how fast the universe is expanding, and hence how long time has passed since the universe was at one point, should at the same time require that an object at the distance a photon coulk have traveled during this age of the universe, must be moving away from us at light-speed.

Why is there this connection?

Ken G
2007-Sep-22, 03:16 AM
But I don't understand why the Hubble constant, which describes how fast the universe is expanding, and hence how long time has passed since the universe was at one point, should at the same time require that an object at the distance a photon coulk have traveled during this age of the universe, must be moving away from us at light-speed.

Why is there this connection?
The rubber analogy answers this question. Let's say you start out with a tiny rubber sheet that is being stretched, the right edge much faster than an ant can crawl, the left edge is anchored (that's where you are). After 1 hour, the stamp has reached a much larger size. Now imagine that an hour into the expansion, an ant is arriving at the left side (to be observed by you). We will backtrack to see where that ant came from, that is, we'll watch the movie backward. At t minus 1 minute, where t=1 hour, that ant was making very good headway walking backward against the shrinking rubber, pretty much at full ant speed, because the speed of the nearest parts of the shrinking rubber are very slow. But somewhere out there on that rubber sheet is a point that is coming back toward the left edge at the speed an ant can crawl, so when our backward crawling ant gets to the neighborhood of that point, it will appear to be virtually motionless. That means it will spend a very long time in the vicinity of that point. The details of the expansion don't matter as long as it is pretty smooth, it will always be true that the ant will spend a very long time somewhere around that "Hubble limit". It will take a very specific type of expansion to make it exactly that point, but it is roughly true, unavoidably. So whatever is the age of the expansion, that's pretty much where that ant will have come from initially. That's the connection.

DanishDynamite
2007-Sep-22, 03:35 AM
The rubber analogy answers this question. Let's say you start out with a tiny rubber sheet that is being stretched, the right edge much faster than an ant can crawl, the left edge is anchored (that's where you are). After 1 hour, the stamp has reached a much larger size. Now imagine that an hour into the expansion, an ant is arriving at the left side (to be observed by you). We will backtrack to see where that ant came from, that is, we'll watch the movie backward. At t minus 1 minute, where t=1 hour, that ant was making very good headway walking backward against the shrinking rubber, pretty much at full ant speed, because the speed of the nearest parts of the shrinking rubber are very slow. But somewhere out there on that rubber sheet is a point that is coming back toward the left edge at the speed an ant can crawl, so when our backward crawling ant gets to the neighborhood of that point, it will appear to be virtually motionless. That means it will spend a very long time in the vicinity of that point. The details of the expansion don't matter as long as it is pretty smooth, it will always be true that the ant will spend a very long time somewhere around that "Hubble limit". It will take a very specific type of expansion to make it exactly that point, but it is roughly true, unavoidably. So whatever is the age of the expansion, that's pretty much where that ant will have come from initially. That's the connection.

I've read this 4 times now, and I still don't understand. It's possible I'm hopelessly stupid but I personally don't think this is the case.

Could you explain again, using just photons, expansion and the Hubble constant?

Ken G
2007-Sep-22, 03:58 AM
If you want my explanation, you must take it at face value. The ants are identical to the photons, the Hubble law is identical to the behavior of stretching rubber. There is no difference at all, none-- I find the latter easier to picture because you could really do it. Pick any smooth rule you like for pulling on the edges of the rubber sheet, just make it expand very fast at its outer boundaries, and watch the movement of an ant with time running backward from the present (so the rubber is actually shrinking in this movie). I claim it is virtually inevitable that your ant will spend a very great deal of time at a distance from you that is in the general ballpark of the "Hubble limit", like a person walking backwards on a moving walkway, because that limit is roughly where the moving walkway is moving at the same speed as the backward-walker, so the backward-walker is at a nearly stationary distance there for a long time. Note that limit is a real distance, not a location on the sheet. It's much harder to get the location on the sheet even approximately right, you'd need calculus, and very good knowledge of the expansion law. But even if you know that law very roughly, you'll know the real distance, roughly, because of that "stationary" effect. If you know calculus, I can translate all of this into the appropriate equations, but even if you don't, you can just try it out with some rough numbers and you should be able to see how inevitable this is. Then, the final step is to note that for any age of the universe that is approximatable by a constant expansion, i.e., 1/H, the backward-walker must be in the general ballpark of that "stationary" point at that time. If the ant is much closer at that time, you get a contradiction because it would have been walking at pretty much full ant speed (c) all that while (because the stretching is slow nearer to us than the Hubble limit), so we reach a contradiction. We also reach a contradiction if we assert that the ant is much farther than the Hubble limit at a time 1/H, because how did it get across that "stationary zone" in so short a time? It won't have had time to do so.