Does Time Expand? Universe Expansion Explained

[ShadowKnight]

I'm sorry if this has been asked before here - having some trouble with the search engine through our company proxy. The universe is expanding, which means that space is expanding between objects in the universe. To me this means that a journey between here and a red shifted galaxy (if possible) would actually take longer because the distance between us and the other galaxy is increasing, kind of like catching up to the back of a moving train. So if I have this view wrong then my next question may not matter (but if I have it wrong someone please correct me).

Space is spacetime. So to me if space (distance) is expanding, doesn't that mean that time is somehow expanding with it? Distance can be measured spatially but how could we measure the increase in time due to expanding spacetime?

Also, IF (notice the capital IF) one were able to stand outside of spacetime, what is the speed of the expansion of the universe from that vantage point?

 

[Crosson]

The standard model of cosmology, which currently agrees with many (independent) experiments, does not involve expansion in time.

It is unclear how expansion in time would do anything but confuse the issue (although it is a valid and interesting question) because most cosmological models are interested in how the universe evolves in time.

 

[SpaceTiger]

Space is spacetime. So to me if space (distance) is expanding, doesn't that mean that time is somehow expanding with it?

The word "expansion" already implies the passage of time, so that's like asking, "how does time depend on time?". The answer to that is that time equals itself. It doesn't make sense to say time is "stretching" with time.

If you're going to think about things in terms of "spacetime", you should think of the universe as one giant static object embedded in a coordinate system (spacetime).

Also, IF (notice the capital IF) one were able to stand outside of spacetime, what is the speed of the expansion of the universe from that vantage point?

It doesn't make sense to stand outside of spacetime, but you can stand outside of the universe. Since you can only see the universe if you're inside of it, the answer is that you couldn't say anything about its expansion.

 

[marlon]

If you're going to think about things in terms of "spacetime", you should think of the universe as one giant static object embedded in a coordinate system (spacetime).

But the universe IS the actual spacetime, isn't it ? So how do i need to 'interprete' this embedding of the universe in space time.

I mean, apart from the universe, what is there to say ? The universe is space time and space time is the universe...

regards
marlon

 

[SpaceTiger]

But the universe IS the actual spacetime, isn't it ? So how do i need to 'interprete' this embedding of the universe in space time.

I mean, apart from the universe, what is there to say ? The universe is space time and space time is the universe...

It depends on how you define the "universe", of course, but you can always mark events outside of our horizon. Technically, a coordinate-free representation of spacetime is probably better, but not as easy to conceptualize for a novice. As long as you don't associate any physical reality with the parts of the coordinate system outside of the universe, it should work just as well.

 

[eNathan]

I think he means this.

We travel through time at 1 sec / sec
If time expands, we travel at 2 sec / 2 sec

We cannot notice any difference even if time did expand, they are mathematicly the same.

 

[A_I_]

the equation of time dilation is t' = (factor of lorentz)t

factor of lorentz = 1/ squared root(1- u^2/c^2)

 

[JesseM]

Also, IF (notice the capital IF) one were able to stand outside of spacetime, what is the speed of the expansion of the universe from that vantage point?

If you could stand outside spacetime, it would just be a static curved 4D manifold, it wouldn't be changing in any way. The "expansion rate" could be thought of in terms of looking at successive 3D cross-sections of this 4D manifold and seeing how fast things move apart from one cross-section to another. I can't think of what the "expansion of time" would even mean, I can only think of changes in terms of one quantity varying as you vary another quantity, like the distance between galaxies increasing as you vary the time variable.

 

[ShadowKnight]

Also, IF (notice the capital IF) one were able to stand outside of spacetime, what is the speed of the expansion of the universe from that vantage point?

Let me re-phrase this question a bit. I'm trying to figure out at what speed the universe itself is expanding. Observing the speed that another galaxy is receding from ours isn't going to provide that answer because that is its motion relative to our galaxy and our galaxy is moving in relation to others. So what I'm wondering is does anyone have any theories (or do we know?) how fast the universe is expanding. So IF (there's that capital IF again) one could physically stand at the exact center of the universe where the BB happened, what speed realative to this absolute position is the rest of the universe expanding?

 

[JesseM]

So IF (there's that capital IF again) one could physically stand at the exact center of the universe where the BB happened, what speed realative to this absolute position is the rest of the universe expanding?

There wouldn't be a center. According to the Big Bang theory, the Big Bang was not an explosion in a preexisting 3-dimensional space, with matter and light expanding out into empty space from some central point--instead, matter and energy are understood to fill all of 3D space, and what's expanding is space itself. The key is to understand that the Big Bang theory is based on Einstein's theory of general relativity, which explains gravity in terms of matter/energy causing spacetime to become curved--depending on the average density of matter/energy throughout the universe, a consequence of this is that the universe as a whole can be curved, with either positive curvature, zero curvature, or negative curvature. For a closed universe with positive curvature, you can visualize it if you drop the dimensions by one--instead of curved 3-dimensional space, which is impossible for us to visualize, picture a 2D universe a la Flatland in which 2D space is actually curved into a sphere, and "expanding space" means that the sphere is blowing up like a balloon while the bits of 2D matter on the surface do not change in size. You can see that if you pasted a bunch of bits of paper on a balloon and then blew it up, each bit would see the other bits receding from it, just like what we see with other galaxies. If you play the movie backwards so that the size of the sphere approaches zero, you can seen that all the bits of matter throughout the universe get more and more squished together, approaching infinite density as the size approaches zero--this is what the big bang is supposed to be. Of course, this analogy forces you to picture the 2-dimensional surface of the sphere expanding in a higher 3rd dimension, and while it is possible that our curved 3D space is expanding in some kind of higher 4D space, mathematically there is no need for such a thing--instead of describing the curvature of a surface with reference to a higher-dimensional "embedding space", it is possible to describe curvature using purely intrinsic features that could be observed by a being confined to the surface (like whether the sum of angles of a triangle drawn on the surface is more, less, or equal to 180 degrees), and general relativity uses only such intrinsic features to describe what it means for space to be curved (see this page on differential geometry, the mathematical basis for general relativity, which talks about the difference between intrinsic and extrinsic descriptions of curvature).

For a universe with zero curvature, picture an infinite chessboard in which all the squares are growing at the same rate, while the pieces at the center of each square remain unchanged in size. If you play the movie backwards, the distance between any two squares approaches zero as you approach the moment of the big bang, which means the density of the matter on the squares (represented by the chess pieces) approaches infinity as it gets smushed together more and more tightly. A universe with negative curvature would be something like an infinite saddle-shape which is a little harder to picture expanding, but if you can picture the other two you get the basic idea. From Ned Wright's Cosmology Tutorial, a graphic showing the 2D analogues of the three types of spatial curvature, negative, zero, and positive:

 

[DrChinese]

Let me re-phrase this question a bit. I'm trying to figure out at what speed the universe itself is expanding. Observing the speed that another galaxy is receding from ours isn't going to provide that answer because that is its motion relative to our galaxy and our galaxy is moving in relation to others. So what I'm wondering is does anyone have any theories (or do we know?) how fast the universe is expanding. So IF (there's that capital IF again) one could physically stand at the exact center of the universe where the BB happened, what speed realative to this absolute position is the rest of the universe expanding?

Not sure if this will help you or not: Our 13.7 billion year old universe currently has an estimated radius of 78 billion light years, i.e. a diameter of 156 billion LY. There are known objects moving more than 3c relative to us. Thus most of that velocity is due to the expansion of space itself (certainly anything over c).

 

[ShadowKnight]

Thanks DRChinese and JesseM, very helpful. If something is moving 3c relative to us, how can we know it is there?

 

[moving finger]

The word "expansion" already implies the passage of time, so that's like asking, "how does time depend on time?". The answer to that is that time equals itself. It doesn't make sense to say time is "stretching" with time.

Now this is interesting. The word expansion also already implies a space in which to expand, so one could say that it's also like asking "how does space depend on space"... and yet we DO quite happily talk about the expansion of space...

If as you say "time equals itself", then why is it not the case that space also "equals itself"?

If we can talk about the expansion of space, why can't we also talk about the expansion of time?
MF

 

[moving finger]

If you could stand outside spacetime, it would just be a static curved 4D manifold, it wouldn't be changing in any way. The "expansion rate" could be thought of in terms of looking at successive 3D cross-sections of this 4D manifold and seeing how fast things move apart from one cross-section to another. I can't think of what the "expansion of time" would even mean, I can only think of changes in terms of one quantity varying as you vary another quantity, like the distance between galaxies increasing as you vary the time variable.

But why can't one think of this? After all, in the 4D manifold "Block Universe" picture there is no intrinsic difference between the time axis and the 3 space axes... all four axes are orthogonal and define the 4D manifold.

The "expansion rate" you refer to is simply taking the change in 3 of the (space) axes as a function of the 4th (time) axis. There is no reason why we should not also measure a change in the 4th (time) axis as a function of one or more of the other 3 (space) axes.

If it makes sense to talk of space (the 3 space axes) expanding along the time axis, then (by symmetry) why does it not make sense to also talk of time expanding along the space axes? There is no intrinsic reason why the axes should be treated differently in this respect.
MF

 

[DrChinese]

Thanks DRChinese and JesseM, very helpful. If something is moving 3c relative to us, how can we know it is there?

That's a great question!

The answer is that it was not moving so fast away from us when the light was emitted. As space expands, the red shift occurs. During its journey to Earth, it moved from one region of space to another, almost like climbing a ladder. The object that emitted it was being carried away from us faster and faster during this time. But the light was getting closer and closer, and was eventually able to bridge the gap. Light emitted from that same galaxy today will in fact never reach us.

This has implications for the look of the universe in the *far* distant future. As time passes, more and more of the universe will be outside viewing range. Eventually, only light from the Milky Way will be visible to us!

 

[SpaceTiger]

Now this is interesting. The word expansion also already implies a space in which to expand, so one could say that it's also like asking "how does space depend on space"... and yet we DO quite happily talk about the expansion of space...

We talk about the expansion of space with time. If space was all there was (no time), it wouldn't make sense to talk about expansion.

 

[ShadowKnight]

DrChinese; so based on this ALL galaxies are actually retreating from each other due to the expansion of space - even if they are moving toward us? Meaning that even if a galaxy behind ours (I use behind descriptively only) is heading toward us at equal or greater velocity than ours is traveling in the same direction - not only will it never approach us but eventually it will fall so far behind at such a rate of speed that its light will no longer reach us either? Even though it is on the same trajectory as ours?

Kind of makes you feel really lonely, knowing that not only is the space between galaxies tremendously vast now but it is only growing larger.

 

[moving finger]

That's a great question!

The answer is that it was not moving so fast away from us when the light was emitted.

And that is a wrong answer (based on a common misconception).
It is a common fallacy that we cannot see light from objects which are apparently moving away from us at superluminal speeds.

What your "answer" is saying is that objects which are now apparently moving away from us at 3 times the speed of light, were moving away from us at sub-light speeds in the past when the light was emitted (and this is what allows the light to reach us). But such distant objects have always been traveling away from us at superluminal speeds.

In the standard lambda-CDM concordnace model ALL objects with redshifts greater than 1.46 are "receding" at superluminal speeds, and yet we see them.

Suggest you check the excellent papers by Davis & Lineweaver for a full explanation of what happens.

eg
http://www.astro.columbia.edu/~dave/papers/lineweaver.pdf

MF

 

[moving finger]

We talk about the expansion of space with time. If space was all there was (no time), it wouldn't make sense to talk about expansion.

As I said in my reply to JesseM's post :

If we think of spacetime as a 4D manifold, then what we are effectively doing when we say that space (3 dimensions) is expanding is that we are tracking the variation of those 3 dimensions with respect to te 4th dimension. Hence (this is where I agree with you) it follows that we "need" the 4th dimension in order to track the changes in the other 3.

But geometrically we are just as entitled to talk about tracking changes in the 4th dimension with respect to one or more of the other 3 dimensions. In the 4D spacetime manifold all 4 dimensions are orthogonal.

Yet by convention we always talk of space expanding/contracting with time, and never consider that it is just as correct to think of time expanding/contracting with space.

MF

 

[SpaceTiger]

But geometrically we are just as entitled to talk about tracking changes in the 4th dimension with respect to one or more of the other 3 dimensions. In the 4D spacetime manifold all 4 dimensions are orthogonal.

Now you're just talking about inverting the description of the same expansion that we now describe wrt to time. It's no different from talking about dx/dy instead of dy/dx. The function will be different, but it won't be saying anything mathematically new (nor anything intuitively useful). It also wouldn't be what we normally call "expansion", because that implies that time is the independent variable.

 

[moving finger]

Now you're just talking about inverting the description of the same expansion that we now describe wrt to time. It's no different from talking about dx/dy instead of dy/dx. The function will be different, but it won't be saying anything mathematically new (nor anything intuitively useful). It also wouldn't be what we normally call "expansion", because that implies that time is the independent variable.

I'm not talking about mathematically. I am talking about conceptually.

Often new insights and understanding are gained by opening one's mind to new concepts, new ways of looking at things.

We could be blinkered and say "it makes sense to talk of space varying with time, but it makes no sense to talk of time varying with space" (your position?) or we could be open-minded and accept that it is just as legitimate to talk of time varying with space as it is of space varying with time (which is mathematically the correct position).

MF

 

[SpaceTiger]

Often new insights and understanding are gained by opening one's mind to new concepts, new ways of looking at things.

Alright, that's cool. I think there are some cases in GR where that would be quite helpful, actually, but I'm not so sure about cosmology. It certainly would help if the general public could incorporate the spacetime concept as a more unified whole. I dont' mean that to be condescending or bitter or anything, but the cosmology questions I get are really frustrating, cause they can't get beyond traditional definitions of space and time.

 

[JesseM]

The "expansion rate" you refer to is simply taking the change in 3 of the (space) axes as a function of the 4th (time) axis. There is no reason why we should not also measure a change in the 4th (time) axis as a function of one or more of the other 3 (space) axes.

If it makes sense to talk of space (the 3 space axes) expanding along the time axis, then (by symmetry) why does it not make sense to also talk of time expanding along the space axes? There is no intrinsic reason why the axes should be treated differently in this respect.
MF

OK, but expansion of what? If you take the 4D manifold and slice it into a bunch of spacelike 3D cross-sections (I believe the technical name for this is a 'foliation'), then the cross section of each worldline will be a point, and you can observe that these points get further apart in successive cross-sections. Maybe there's another way to make sense of the notion of expansion aside from tracking the motion of test particles, I don't know. But if not, then this won't work if you take cross-sections along a spatial axis. So if it doesn't work, then I guess the reason there is not a "symmetry" here as you suggest is that worldlines are always timelike, never spacelike (maybe the idea could still make sense if you allow tachyons? Would GR make a definite prediction about how tachyons should move through curved spacetime?)

 

[DrChinese]

And that is a wrong answer (based on a common misconception).
It is a common fallacy that we cannot see light from objects which are apparently moving away from us at superluminal speeds.

What your "answer" is saying is that objects which are now apparently moving away from us at 3 times the speed of light, were moving away from us at sub-light speeds in the past when the light was emitted (and this is what allows the light to reach us). But such distant objects have always been traveling away from us at superluminal speeds.

In the standard lambda-CDM concordnace model ALL objects with redshifts greater than 1.46 are "receding" at superluminal speeds, and yet we see them.

Suggest you check the excellent papers by Davis & Lineweaver for a full explanation of what happens.

eg
http://www.astro.columbia.edu/~dave/papers/lineweaver.pdf

MF

Yes, that is my reference on the subject too. Their papers are great, very eye-opening.

You are correct that objects can be receding from us >c and the light can still reach us. Lineweaver and Davis explain in some basic terms how light from an object receding at greater than c can eventually reach us. It does this by moving into a region of space that is receding a bit less, and then into another region that recedes a bit less, and so on. Eventually it got here.

But that will not always be true for most stellar objects. There is effectively some "horizon" for lack of a better word. Once this horizon is reached, that object disappears forever from our perspective.

Essentially all objects are being accelerated away from us by the expansion of space. That expansion does not have a limit of c.

 

[DrChinese]

DrChinese; so based on this ALL galaxies are actually retreating from each other due to the expansion of space - even if they are moving toward us? Meaning that even if a galaxy behind ours (I use behind descriptively only) is heading toward us at equal or greater velocity than ours is traveling in the same direction - not only will it never approach us but eventually it will fall so far behind at such a rate of speed that its light will no longer reach us either? Even though it is on the same trajectory as ours?

Kind of makes you feel really lonely, knowing that not only is the space between galaxies tremendously vast now but it is only growing larger.

Yes, eventually it will just be us and Andromeda... then Andromeda will disappear too. I do not know if the Milky Way will get pulled apart by the expansion. Not to be morbid, but the sun will have long since died anyway.

 

[moving finger]

OK, but expansion of what? If you take the 4D manifold and slice it into a bunch of spacelike 3D cross-sections (I believe the technical name for this is a 'foliation'), then the cross section of each worldline will be a point, and you can observe that these points get further apart in successive cross-sections.

Yep, and this is precisely the definition of "expansion of space with time" (ie the points defining the space axis dimensions move further apart as we progress along the time axis).

Maybe there's another way to make sense of the notion of expansion aside from tracking the motion of test particles, I don't know. But if not, then this won't work if you take cross-sections along a spatial axis.

I believe you are having trouble visualising it because you are still thinking of "objects moving in space" rather than the variation of one dimension with another. I don't see why you need to introduce "test particles" - after all we are not talking about the motion of objects "in space", we are talking about the expansion of space itself.
Let's make it simpler and imagine a 2D universe, one time axis and one space axis (we can visualise this on a piece of flat paper). Now, we can postulate that the space axis dimension is expanding with time; if we marked the dimension as points on the space axis then we see (as you pointed out already) that these points get further apart as we move along the time axis (take successive cross-sections in time). This is exactly the 2D counterpart of the expanding 4D universe (I hope you will agree).
We can, if we wish, swap the axes and now postulate that the time axis dimensions are expanding with space; if we marked these dimensions as points on the time axis then we see that these points get further apart as we move along the space axis (take successive cross-sections in space).
What I have described is clearly logically and rationally possible.
The problem is... what does this MEAN in reality?
And IF the conclusion is that it really is meaningless to talk about the expansion of time in space, then WHY does this not also mean that it is meaningless to talk about the expansion of space in time?
MF

 

[moving finger]

Yes, eventually it will just be us and Andromeda... then Andromeda will disappear too. I do not know if the Milky Way will get pulled apart by the expansion. Not to be morbid, but the sun will have long since died anyway.

but hopefully the Physics forum will still be here!
MF

 

[JesseM]

I believe you are having trouble visualising it because you are still thinking of "objects moving in space" rather than the variation of one dimension with another.

That's not really the reason--see below.

Let's make it simpler and imagine a 2D universe, one time axis and one space axis (we can visualise this on a piece of flat paper). Now, we can postulate that the space axis dimension is expanding with time; if we marked the dimension as points on the space axis then we see (as you pointed out already) that these points get further apart as we move along the time axis (take successive cross-sections in time). This is exactly the 2D counterpart of the expanding 4D universe (I hope you will agree).

But how do you "mark the dimension as points on the space axis" without introducing some notion like the path of test particles moving on geodesics? Space itself doesn't come labeled with any markings at all, if you just have a curved 2D manifold and look at successive unmarked cross-sections, I don't see how you can decide how much space has "expanded" from one cross-section to another just by looking at each cross-section's curvature.

 

[moving finger]

But how do you "mark the dimension as points on the space axis" without introducing some notion like the path of test particles moving on geodesics? Space itself doesn't come labeled with any markings at all, if you just have a curved 2D manifold and look at successive unmarked cross-sections, I don't see how you can decide how much space has "expanded" from one cross-section to another just by looking at each cross-section's curvature.

yes, and this is the root of the problem.
Cosmologists routinely talk about the expansion of space, but how can we claim it is "right" to talk about "the expansion of space with time" when (as you say) space doesn't come labelled with any markings, if at the same time we cannot talk of "the expansion of time with space" for precisely the same reason?
MF

 

[JesseM]

yes, and this is the root of the problem.
Cosmologists routinely talk about the expansion of space, but how can we claim it is "right" to talk about "the expansion of space with time" when (as you say) space doesn't come labelled with any markings, if at the same time we cannot talk of "the expansion of time with space" for precisely the same reason?

I'm not sure of the exact meaning of expansion of space, hopefully someone more well-versed in general relativity will...but I had always assumed it had to do with the way the distance between test particles following geodesics would increase over time.

 

[moving finger]

I'm not sure of the exact meaning of expansion of space... I had always assumed it had to do with the way the distance between test particles following geodesics would increase over time.

ok... and maybe the expansion of time has to do with the way the time between test particles following geodesics would increase over space...
MF

 

[JesseM]

ok... and maybe the expansion of time has to do with the way the time between test particles following geodesics would increase over space...

But that doesn't make any sense, unless the test particles are tachyons (and I don't think you can define the notion of a geodesic for tachyons)--if you slice spacetime into a series of non-spacelike-sections, you won't have the same collection of test particles in each slice, you'll just get particles randomly appearing and disappearing from one slice to the next. Try to visualize a spacetime filled with worldines, and what happens if you take a series of slices along the time axis vs. what happens if you take a series of slices along a spatial axis, hopefully you can see what I mean.

 

[moving finger]

But that doesn't make any sense, unless the test particles are tachyons (and I don't think you can define the notion of a geodesic for tachyons)--if you slice spacetime into a series of non-spacelike-sections, you won't have the same collection of test particles in each slice, you'll just get particles randomly appearing and disappearing from one slice to the next. Try to visualize a spacetime filled with worldines, and what happens if you take a series of slices along the time axis vs. what happens if you take a series of slices along a spatial axis, hopefully you can see what I mean.

It makes sense. I think the reason you cannot make sense of it is because you are stuck in thinking of test particles which have worldlines with a unique separation in their "space values" for each "time value".
Try to think of it instead as two spacetime events rather than as test particles or worldlines.
Let us define "time-simultaneous" as meaning the two events take place at the same time but at different points in space (I know, I know, simultaneity is relative! but let's assume a non-relativistic scenario), and let us define "space-simultaneous" as meaning the two events take place at the same location in space but at different points in time.

Now, what is being said is the following :
In the "space" case the "space interval" between two time-simultaneous events depends on their location in time - for expanding space the events are further apart in space if the events take place at later times - for contracting space the events are closer together in space if the events take place at later times.

In the "time" case the "time interval" between two space-simultaneous events depends on their location in space - the two events are either further apart or closer together in time depending on their location in space.

Now one might ask - how can the time-interval between two space-simultaneous events be different, depending upon their location in space?

Think of gravitational time-dilation. Near a massive body, this is exactly what happens - the time-interval between two space-simultaneous events near the massive body IS different (it is greater) compared to the time-interval between two space-simultaneous events in empty space.

MF

 

[JesseM]

It makes sense. I think the reason you cannot make sense of it is because you are stuck in thinking of test particles which have worldlines with a unique separation in their "space values" for each "time value".
Try to think of it instead as two spacetime events rather than as test particles or worldlines.
Let us define "time-simultaneous" as meaning the two events take place at the same time but at different points in space (I know, I know, simultaneity is relative! but let's assume a non-relativistic scenario), and let us define "space-simultaneous" as meaning the two events take place at the same location in space but at different points in time.

OK, but the point is that when you take spacelike slices along the time axis, you can say the two events are just the positions of the particles at that moment in time, so you can compare the distance of the two events in one spacelike slice to with the distance of the "corresponding" two events in a later slice (ie the position of the same two particles at the later time). But what correspondence is there between events in one slice taken along a space axis with events in another slice taken along the same space axis?

In the "space" case the "space interval" between two time-simultaneous events depends on their location in time - for expanding space the events are further apart in space if the events take place at later times

What events are further apart? Any two pairs of random events in different slices will be further apart, regardless of how you choose them? If in the first slice I choose the events "clock on Earth reads 2005" and "clock on Earth reads 3005", and in another slice I choose the events "clock on Alpha Centauri reads 2005" and "clock on Alpha Centauri reads 2008", does that mean time has shrunk? What if I had instead chosen the events "clock on Alpha Centauri reads 2005" and "clock on Alpha Centauri reads 4005"? Without some correspondence between the events on one slice and another, without some kind of rule saying "if you pick events A and B in your first slice, you must always pick events A' and B' in the second one", then your choice of which two events in each slice to pick will be totally arbitrary, so there will be no well-defined procedure to decide whether "time is expanding" or not. So, your argument still makes no sense to me.

 

[Chronos]

I haven't followed this whole thing in detail, but time and space are interchangeable. A lazy way to visualize an event is by imagining a four dimensional hypersphere whose virtual surface is:

X^3 + Y^3 + Z^3 + T^3 = 1 [or other arbitrary constant].

Note: cubing the factors is a lazy way of preserving CPT symmetry.