What does SR say about the expanding universe?

[NWH]

So from my understanding SR loosely tells us that time is not constant and that depending on our motion relative to another observer will dictate our differences in rate of time. I was wondering what SR tells us about the expanding universe. In cosmology we're taught that the universe is expanding and that massive objects move away from us at an accelerated rate, moving faster and faster the further away they are from us. If we're to imagine the universe as a soup of individual systems and different perspectives of relativity, how do we imagine the overal essence of time?

As the furthest objects away from us move faster and faster, time must tick differently for those massive objects than it does here on earth. If we were to imagine Earth as system 1 and we were to observe the furthest galaxy away from us in the observable universe as system 2, system 2 is moving away from us at an accelerated rate and thus is altering its passage through time at a faster rate than we are. If we were to imagine the destruction of the universe from Earth's perspective, wouldn't system 2 experience the destruction of the universe before system 1 since it is accelerating away from us and altering its passage of time relative to us? However on the flip side, if I was positioned in system 2 wouldn't Earth experience the destruction of the universe before system 2 since it too is accelerating away at a faster rate? Couldn't we then conclude that I am indeed the center of the universe no matter where abouts in the universe I am?

It seems a paradox to me and I assume is an oversight in my thinking, I'd be curious to hear what SR actually says about the universe and where my logic is going wrong. Perhaps I'm making assumptions about the age of the universe and what the destruction of the universe actually is, giving it a finite moment in time that must be the same for all systems and something which is reached via time travel. I'm very puzzled by this, I've never thought about this before and it is beyond my basic knowledge of physics.

 

[PeterDonis]

Special Relativity does not deal with situations where gravity is present; the expansion of the universe is one such situation. You need General Relativity to deal with these situations.

According to GR, the time since the Big Bang, the beginning of the universe, is the same for all "comoving" observers, which are, roughly speaking, all observers that see the Cosmic Microwave Background Radiation (CMBR) as isotropic. We on Earth do *not* see the CMBR as isotropic, indicating that we are moving relative to a "comoving" observer passing through Earth's position now. That means we on Earth would see that slightly less proper time has passed for us since the Big Bang than for the "comoving" observer. But Earth's velocity relative to the "comoving" observer is very small compared to the velocity of light, so the difference is very small compared to the age of the universe.

 

[NWH]

Special Relativity does not deal with situations where gravity is present; the expansion of the universe is one such situation. You need General Relativity to deal with these situations.

According to GR, the time since the Big Bang, the beginning of the universe, is the same for all "comoving" observers, which are, roughly speaking, all observers that see the Cosmic Microwave Background Radiation (CMBR) as isotropic. We on Earth do *not* see the CMBR as isotropic, indicating that we are moving relative to a "comoving" observer passing through Earth's position now. That means we on Earth would see that slightly less proper time has passed for us since the Big Bang than for the "comoving" observer. But Earth's velocity relative to the "comoving" observer is very small compared to the velocity of light, so the difference is very small compared to the age of the universe.

This is probably more of a cosmology question, but what happens at 'the end of the universe?' Is that event finite? Is it instantaneous for all observers no matter where they are in space or time? If we observed the end of the universe from opposite ends of what is visible would we agree that it happened at the same moment in time, or would we disagree?

Let's rephrase the question. Like we imagine a clock on a rocket ship, flying away from Earth at almost the speed of light, ticking away at a slower rate than ours, will a clock ticking on another planet which is flying away from us as part of a galaxy located at the edge of the universe follow the same principles of time travel?

Time here on Earth is different to time in space, which is different to time next to our sun, which is different to time outside our solar system, which is different to time outside our galaxy, which is different to time inside a black hole etc. Clocks tick differently everywhere, experiments have shown this is the case, if one person travels through time fast enough won't they reach 'the end of the universe' before everyone else? Does a galaxies motion through space and gravity exhibit the same fluctuations in time as a rocket ship does?

Sorry for all the questions, some of them are rhetorical and serve only to give you an idea of what questions I'm asking my self. Right now I'm thinking that A) motion through space really does send you into the future or B) motion through space simply slows down mechanical and biological processes, causing things to decay at slower rates and only appear as if we're traveling into the future.

big bang >>>>>>> acceleration/time travel >>>>>>> big crunch

The idea that I'm the center of the universe no matter where I am because of everything accelerating away from me into the future is a spine chilling thought...

 

[PeterDonis]

This is probably more of a cosmology question, but what happens at 'the end of the universe?' Is that event finite? Is it instantaneous for all observers no matter where they are in space or time? If we observed the end of the universe from opposite ends of what is visible would we agree that it happened at the same moment in time, or would we disagree?

The universe may not have an "end"; it depends on how much matter there is compared to its current rate of expansion. The best estimates at present indicate that the universe will continue to expand forever, so it will not have an end.

In models where the universe does have an end, the end works much like a "time reversed" version of the beginning. The "Big Crunch", like the Big Bang, is a single event, and it lies at the future endpoint of all worldlines in the spacetime, just as the Big Bang lies at the past endpoint of all worldlines. So the Big Crunch is "instantaneous" in the sense that it is a single event that every observer's worldline ends in. Since it is a single event, and all worldlines end in it, it does happen "at the same time" to all observers in one sense; but different observers in relative motion may disagree on how much time elapses along their worldlines from a given event to the Big Crunch (or from the Big Bang to a given event).

Let's rephrase the question. Like we imagine a clock on a rocket ship, flying away from Earth at almost the speed of light, ticking away at a slower rate than ours, will a clock ticking on another planet which is flying away from us as part of a galaxy located at the edge of the universe follow the same principles of time travel?

Probably not. Strictly speaking, it depends on the velocities of both the rocket and the distant galaxy relative to "comoving" observers (observers who see the CMBR as isotropic) in their local vicinity. But all galaxies we have observed have very small velocities relative to "comoving" observers, as the Earth does; whereas a rocket moving at nearly the speed of light relative to the Earth would also be moving at nearly the speed of light relative to "comoving" observers. So I would expect its clock to tick slower than that of the distant galaxy.

Time here on Earth is different to time in space, which is different to time next to our sun, which is different to time outside our solar system, which is different to time outside our galaxy, which is different to time inside a black hole etc. Clocks tick differently everywhere, experiments have shown this is the case, if one person travels through time fast enough won't they reach 'the end of the universe' before everyone else?

The time differences you are talking about now are not due to relative motion, but to being at different depths in various gravitational potential wells (at least that's how I'm interpreting your references to Earth vs. in space, next to the sun, in a black hole, etc.). This does affect rates of time flow, but it's distinct from relative motion so I would advise leaving it out of the discussion until we are clear about the effects of relative motion.

Does a galaxies motion through space and gravity exhibit the same fluctuations in time as a rocket ship does?

See my comments above on the rocket ship vs. the galaxy.

Sorry for all the questions, some of them are rhetorical and serve only to give you an idea of what questions I'm asking my self.

No problem, these are all good questions.

Right now I'm thinking that A) motion through space really does send you into the future or B) motion through space simply slows down mechanical and biological processes, causing things to decay at slower rates and only appear as if we're traveling into the future.

Are these really distinct possibilities, or just different ways of saying the same thing? Put another way, how would you design an experiment to distinguish the two? After all, we are all "traveling into the future" regardless of our individual velocity, so that term isn't really very helpful as it stands.

Let me illustrate by considering a specific scenario, suggested by what you say next:

big bang >>>>>>> acceleration/time travel >>>>>>> big crunch

Consider two possible observers who travel through the entire history of a closed universe (remember that, as I said above, we don't know if our actual universe is closed, currently our best estimate is that it isn't so there will be no big crunch, but we'll assume there is one for this scenario). One is a "comoving" observer; he travels along a "comoving" worldline from big bang to big crunch, and all the way he sees the CMBR (or the equivalent) as isotropic. The other starts out with a very large relative velocity to the "comoving" observer, one that is a large fraction of the speed of light--to be concrete, we'll say 0.866c, so that the relativistic gamma factor is 2--and travels from big bang to big crunch that way. The second observer will of course see the CMBR (or the equivalent) as highly non-isotropic all the way.

Suppose that the first observer experiences 50 billion years of proper time from big bang to big crunch. Then the second observer will experience (to a first approximation, at least) only 25 billion years of proper time from big bang to big crunch (because of the gamma factor of 2 due to his velocity). So in one sense, the second observer reaches the big crunch "twice as fast", since he only experiences half the proper time; so he "travels into the future" faster. However, both observers will meet at the big bang and big crunch events; that is, they both start out together at the big bang, and they both end up together at the big crunch. So in that sense, they both experience both events "at the same time"; they just disagree on how much time elapsed between them, so they both "travel into the future" at the same "speed", but the rates of their mechanical and biological processes are different relative to this "speed".

 

[NWH]

Thanks for the answers! It's starting to make more sense now! The way I'm thinking about it is that if a big crunch ever did occur, the big crunch would start happening before we actually observed it. if we imagine the universe expanding, we observe the expansion of the universe because of light traveling towards us from distant galaxies. If the universe was to start contracting again, we wouldn't observe the light from those contracting galaxies until it actually reached us. Unless of course contraction would occur at speeds faster than the speed of light, in which case we'd experience contraction before we saw it coming. That would mean that the contraction of the universe is always relative to my position in the universe as is the expansion.

Couldn't we then conclude that just because we observe an expanding universe doesn't mean that it's actually expanding in a uniform and ever accelerating fashion? Surely it would be impossible for the universe to accelerate forever. If the universe is expanding at an accelerated rate then eventually mass would reach maximum velocity as it approached closer to the speed of light, wouldn't it? That would bring about the end of a uniform accelerating universe as we observe it and would give birth to a universe that's more of a jumbled mess where only the lightest objects reach the farthest depths of the universe. Am I thinking about it right?

Sorry but my technical knowledge is seriously lacking, I can only really conduct thought experiments in my head, it's fun to think about but eventually you have to ask questions. Sometimes you just have to understand what it is you're thinking about, and cosmology/relativity aren't the easiest things to think about lol.

It's like, if it were possible for us to have faster than light communications we would receive messages from the future telling us about the demise of the universe before we our selves experienced it, however we would be able to know roughly which regions of space those messages came from by looking at the farthest edges of the universe. Do you understand where I'm coming from? I think I'm probably confusing my self as well as you now lol.

 

[Ich]

If the universe was to start contracting again, we wouldn't observe the light from those contracting galaxies until it actually reached us. Unless of course contraction would occur at speeds faster than the speed of light, in which case we'd experience contraction before we saw it coming.

The turning pont from expansion to contraction is supposed to happen everywhere at the same cosmological time. This means that you see it first in your neighbourhood, while the rest of the universe still seems to be expanding. You don't need a signal from somewhere to start the contraction, it happens everywhere independently .

 

[NWH]

The turning pont from expansion to contraction is supposed to happen everywhere at the same cosmological time. This means that you see it first in your neighbourhood, while the rest of the universe still seems to be expanding. You don't need a signal from somewhere to start the contraction, it happens everywhere independently .

But don't objects that accelerate away from our frame of reference reach the end of time faster than we do? We will eventually meet at the end of time, as stated by the poster above, but time will elapse quicker for them. If we could communicate faster than the speed of light wouldn't they tell us about the end of the universe before we experience it? After all time elapsed quicker for them than it did for us, it's only because communications are limited to the speed of light that it appears as if everything happens at the same moment in time.

 

[Ich]

But don't objects that accelerate away from our frame of reference reach the end of time faster than we do?

They could just spiral around us at near lightspeed to reach "the end of time faster". You have to understand what that phrase means, it has already been pointed out to you: those observers simply "age slower", they don't travel into the future to send us signals from there.

That said, with superluminal communication you can create all sorts of funny things. It simply isn't consistent with relativity.

 

[NWH]

They could just spiral around us at near lightspeed to reach "the end of time faster". You have to understand what that phrase means, it has already been pointed out to you: those observers simply "age slower", they don't travel into the future to send us signals from there.

That said, with superluminal communication you can create all sorts of funny things. It simply isn't consistent with relativity.

I still don't feel like I fully grasp it despite understanding what you are saying. If your passage through time is reduced to 100 years instead of 1000 years that IS time travel, your clocks ticked slower, you aged slower, everything else around you moved on in time at a faster rate than you did. If we had one clock on Earth and a clock on a planet somewhere in a far away galaxy at the edge of the universe, then we must be able to make comparisons between those frames of reference. Does SR simply have nothing to say about that?

I'm probably overlooking something which has already been said and if so I apologise for that. But as I understand it, our frame of reference in and around the Earth is different to the frame of reference from someone all the way across the universe, especially if the universe continues to expand at an accelerated rate. We observe their galaxy in a state of motion where as we observe our selves to be rather stationary (not including forces of gravity such as orbits etc). If time was the same for both of us then we must be in the same frame of reference and neither of us are in a state of motion. One of us must experience an event different to the other if one of us is in a state of motion relative to another frame of reference, that is how simultaneity works, right? Doesn't that mean the 'end of the universe' can't be the experienced the same for all observers?

I know it was pointed out that GR must be used instead of SR where gravity is involved, so sorry for repeating the same question, I just don't understand it...

 

[Ich]

I've got the impression that you're still struggling a little bit with the concept of time dilation in SR. So my following answer may be even more confusing for you. If so, let me know.

If we had one clock on Earth and a clock on a planet somewhere in a far away galaxy at the edge of the universe, then we must be able to make comparisons between those frames of reference. Does SR simply have nothing to say about that?

SR is valid only in the absence of gravity. However, you still can use SR-like Einstein synchonisation in an open universe to establish a notion of simultaneity. (Note: there is no big crunch in an open universe!)
Conceptually, this means that you have the universe filled with infinitely many clocks, each at rest and synchronized wrt its neighbours. Of all these clocks only one is free falling, which marks the center of this coordinate system.
With this notion of simultanteity, you see indeed other galaxies increasingly time dilated, the further away they are. So they are still younger now, and some finite distance away even the Big Bang is still happening now.
If something was to happen at a specific cosmological time thoughout the universe, according to SR synchronization, it would happen here e.g. now, and in the outer universe in the distant future, because of time dilation. It would take even longer for us to see the light of this event.
In an accelerating universe, there are regions that are hidden behind an event horizon, where we can observe nothing of such an event, and where we even can't assign a time coordinate to these events by the outlined method.

 

[galaxion1]

That means we on Earth would see that slightly less proper time has passed for us since the Big Bang than for the "comoving" observer. But Earth's velocity relative to the "comoving" observer is very small compared to the velocity of light, so the difference is very small compared to the age of the universe.

Is there any relation to measure this slight difference of time rate on Earth in terms of gravitational time dilation due to expansion of the universe? thanks

 

[PeterDonis]

Is there any relation to measure this slight difference of time rate on Earth in terms of gravitational time dilation due to expansion of the universe? thanks

The expansion of the universe doesn't cause any "gravitational time dilation"; that's a term that only applies in specific types of scenarios, like objects at different altitudes above a static gravitating body.

 

[marcus]

... Surely it would be impossible for the universe to accelerate forever. If the universe is expanding at an accelerated rate then eventually mass would reach maximum velocity as it approached closer to the speed of light, wouldn't it? That would bring about the end of a uniform accelerating universe as we observe it and would give birth to a universe that's more of a jumbled mess where only the lightest objects reach the farthest depths of the universe. Am I thinking about it right?
... I think I'm probably confusing my self as well as you now lol.

To answer your question "Am I thinking about it right?", no you aren't thinking about it right.
There is no reason that the acceleration of distance growth cannot continue forever. Distance growth is not like ordinary motion and is not governed by SR and is not limited by c.

It is governed by GR in a way that is summarized by Hubble law. Hubble law describes the increase in the distance between two objects or observers who are at rest with respect to Background (so-called proper distance at a particular moment of Universe Time.) It says that the rate of increase is proportional to the distance. So for very large distances the rate can easily be larger than c. The distances to most of the galaxies we observe are, in fact, increasing faster than c. SR has nothing to say about this.

Is there any relation to measure this slight difference of time rate on Earth in terms of gravitational time dilation due to expansion of the universe? thanks

We can estimate the slight difference (but forget the red stuff for the time being.) The slight differerence the other poster was talking about is that due to solar system motion relative to Background. Our motion is roughly 1/1000 of the speed of light so the effect is ridiculously small. Our clocks are slower than standard Universe time by less than one ten thousandth of one percent.

That tiny fraction of percent slowing is an ordinary SR effect. It is not due to gravity or to the expansion of distances. One can calculate it but it is to small to worry about. Our time here on Earth is essentially the same as Standard Universe Time as would be measured by an observer out in intergalactic space who is at rest relative to the Background.

Expansion does not affect time. Expansion is not like ordinary motion because nobody gets anywhere by it, everything just becomes farther apart from everything else as distances grow. Since it is not like ordinary motion, special relativity time slowing and mass change do not apply, and the SR speed limit does not apply. Distances can easily increase faster than c. Indeed the distances to most galaxies that we observe ARE increasing faster than c.
Observers in those galaxies are not experiencing SR mass or time effects due to the fact that the distance from them to us is increasing say at twice the speed of light.

But don't objects that accelerate away from our frame of reference reach the end of time faster than we do? We will eventually meet at the end of time, as stated by the poster above, but time will elapse quicker for them. If we could communicate faster than the speed of light wouldn't they tell us about the end of the universe before we experience it? After all time elapsed quicker for them than it did for us, it's only because communications are limited to the speed of light that it appears as if everything happens at the same moment in time.

Heh heh. What is this "end of time" thing? It sounds like something out of Wagnerian opera or some culture's mythology

In normal mainstream cosmology we do not expect an "end of time". We have a standard expanding geometric Background and a standard Universe time as measured by observers at rest relative to Background. And other observers typically measure time within a tiny fraction of a percent of standard (because they aren't moving very fast relative to background). So we have an idea of approximate simultaneity.

If you twiddled with the parameters of the model, making the Universe a lot denser than it really is, you could get the model to predict a slowing expansion and eventual collapse, but this would be experienced at approximately the same moment of Universe time by all observers. they wouldn't be able to communicate it about it immediately, communication takes time. But they would all see it beginning to happen at about the same historical era.

But that would be a different case, that does not fit the observational data. GR is the best law of geometry we have so far. It has been tested repeatedly. Maybe it is not perfect but it sure has proven reliable so far. And if you fit the GR model to what we see you get a best fit model Universe that is the best most reliable we have so far. And it does not collapse.
Of course it could be wrong! People are always trying to improve the model and get more data and get a better fit---constant struggle. But this is the best we have so far.

Also a lot of current work on geometry is in the direction of so-called "nonsingular" models of geometry, in which a collapse would cause rebound. It would have observational consequences. If our expansion is the result of a rebound it would leave traces in the ancient light that can be looked for, according to a bunch of papers about this. So even if our U's geometry were eventually destined to collapse it is NOT a done deal that this would lead to an "end of time". Our own cosmic microwave background has to be studied in finer detail in order to learn more about this.

Cosmology is an exciting subject. Keep asking questions and have fun!

 

[Chronos]

Keep in mind that time is relative for all observers. Processes in distant galaxies appear to occur at a slower rate than processes appear to occur in our galaxy due to relativistic time dilatiom [GR, to be specific]. This is why astrophysicists adjust the light curves of distant supernova - they are time dilated commensurate with their redshift. An observer in a distant galaxy would notice no time dilation effects within their galaxy, but, upon observing our galaxy would conclude that processes in our galaxy are time dilated. So if they observed a supernova in the milky way its light curve would be time dilated by the same amount as a supernova in their galaxy would appear time dilated to us.

 

[twofish-quant]

I was wondering what SR tells us about the expanding universe.

Nothing really. SR fails miserably once you take into account gravity.

One interesting thing is that you end up with a better understanding of what is happening with the universe if you ditch relativity altogether and do everything in Newtonian mechanics. With Newtonian mechanics, you are assuming the speed of light is infinite, and for a lot of cosmology, that works quite well.

If I were teaching a cosmology class to undergraduates, I'd start with the Newtonian model, and then add in general relativity as a "correction".

 

[twofish-quant]

If we had one clock on Earth and a clock on a planet somewhere in a far away galaxy at the edge of the universe, then we must be able to make comparisons between those frames of reference.

No we don't. If the galaxies is outside of the cosmic horizon or inside a black hole, then you *can't* make comparisons between the frames of reference.

I know it was pointed out that GR must be used instead of SR where gravity is involved, so sorry for repeating the same question, I just don't understand it...

It helps if you ditch relativity and think of it in the Newtonian world.

 

[galaxion1]

Expansion does not affect time. Expansion is not like ordinary motion because nobody gets anywhere by it, everything just becomes farther apart from everything else as distances grow. Since it is not like ordinary motion, special relativity time slowing and mass change do not apply, and the SR speed limit does not apply

Ok... let me rephrase the question ...Does the expansion of universe result in experiencing a different gravitational potential on Earth than that experienced 4.5 billion years ago when Earth was formed (as it is farther apart now from the sun, the center of the galaxy, etc)?
If yes...then as "the gravitational time dilation" says "Clocks at higher gravitational potentials run faster, and clocks at lower gravitational potentials run slower"...and that means that the time rate at certain point in the universe did change since the big bang till present...

 

[Chronos]

You have it backwards, time slows in higher gravity field relative to lower gravity fields.

 

[galaxion1]

You have it backwards, time slows in higher gravity field relative to lower gravity fields.

actually the phrase I used is the same on wikipedia
http://en.wikipedia.org/wiki/Gravitational_time_dilation

I wish I could find any relation demonstrating this difference in time rate on earth
in different eras (if exists)

 

[PAllen]

There is no reason that the acceleration of distance growth cannot continue forever. Distance growth is not like ordinary motion and is not governed by SR and is not limited by c.

I would like to expand on this point because it is so often a source of confusion.

Even in SR, and using standard inertial coordinates, the distance between to bodies can grow by up to twice the speed of light if each is going near c in opposite directions relative to some observer (the distance being that measured by this observer). This does not contradict that an observer moving with either body will measure the other having a velocity relative to them of less than c.

Further, 'standard inertial coordinates' are not a physical observable, and are not required by SR. The only requirement for a simultaneity convention is that it connect events with spacelike separation. In terms of light cones, a simultaneity surface intersects the world line of body between its forward and backward pointing light cones. If the initial observer in the scenario above chooses to use a time dependent simultaneity convention, that starts out 'just outside' its backward light cone, changing over time to approach its forward light cone, then the proper distance between two separating bodies in this valid SR coordinate system can grow by any multiple of c at all! This can be exploited to model many features of an expanding universe in SR, without curvature.

 

[marcus]

Is there any relation to measure this slight difference of time rate on Earth in terms of gravitational time dilation due to expansion of the universe? thanks

Hmmm. I see I did not understand your question the first time round. I thought when you said "this slight difference" you were referring to something another poster had already mentioned which had to do with speed of motion, not with depth in a gravitational field.

So I responded that the time rate difference due to motion was very small.

But you are asking about gravitational time dilation. Has that changed since the formation of the solar system?

I don't think it has appreciably changed. Expansion of U would not cause Earth distance from Sun to increase appreciably. We might actually be closer now because of other effects, but all very tiny.

Ok... let me rephrase the question ...Does the expansion of universe result in experiencing a different gravitational potential on Earth than that experienced 4.5 billion years ago when Earth was formed (as it is farther apart now from the sun, the center of the galaxy, etc)?
If yes...then as "the gravitational time dilation" says "Clocks at higher gravitational potentials run faster, and clocks at lower gravitational potentials run slower"...and that means that the time rate at certain point in the universe did change since the big bang till present...

I don't think the Hubble law expansion of distances would make the solar system get farther from the center of the galaxy.

We're talking about miniscule effects which would have negligible effect on passage of time. Roughly speaking Hubble expansion DOES NOT CHANGE THE SIZE OF BOUND SYSTEMS. whether they are gravitationally bound or crystal lattice bound, like rock and metal, or whatever. Galaxies don't change size because of Hubble expansion.

But there are other effects which cause orbits to decay. So we may be slightly CLOSER to the center now than when the sun and planets formed.

If that is true then our clocks would now be running a wee bit slower than they were 4 billion years ago.

I would say these effects of time of changing orbit radius are so small, though, that one might as well ignore them. Just my two cents. Someone else may have a different opinion.

 

[twofish-quant]

Does the expansion of universe result in experiencing a different gravitational potential on Earth than that experienced 4.5 billion years ago when Earth was formed (as it is farther apart now from the sun, the center of the galaxy, etc)?

No.

One thing about the expansion of the universe is that it assumes that the universe is almost smooth. Once you get to a region of space in which this is not true, then the expansion calculations don't work any more.

One way of thinking about this is to imagine the universe to be a gas. You can take a gas and image it to be a continuous fluid. The gas expands and contracts. However, the expansion of the gas doesn't affect the atoms, because if you are looking at individual atoms, then the assumptions you are making about the gas being smooth are wrong.

If yes...then as "the gravitational time dilation" says "Clocks at higher gravitational potentials run faster, and clocks at lower gravitational potentials run slower"...

That may not be a good way of describe the situation. I've often found that talking about clocks running faster or slower leads to all sorts of confusion. Especially around black holes.

The problem is that if you think that gravity makes clocks run slow, then once you get close to the event horizon you start thinking that "time stops" which it doesn't.

 

[twofish-quant]

actually the phrase I used is the same on wikipedia
http://en.wikipedia.org/wiki/Gravitational_time_dilation

I wish I could find any relation demonstrating this difference in time rate on earth
in different eras (if exists)

I'll fix the article later. It's worded badly.

Gravitation potentials are negative so "lower" potentials (in the context of the article) means "stronger gravity" (or "higher potential" if you are looking at the absolute value of the thing).

 

[Chronos]

The Wiki article is clear, if taken in context. It is less clear if you omit the caveats. I admit I fell for that one.