Is the speed of expansion of the universe faster than light?

[GrayGhost]

A geodesic can not curve relative to itself, since it is analogous to a straight line in flat space.

Hmm, interesting. While I'd agree that a geodesic is the shortest path thru a non-euclidean space, it seems to me that spacetime is curved unto itself. And if it is, then so too should geodesics be. We don't have a 5th dimension to gaze down upon 4-space, yet we know it's curved. If not curved unto itself, then curved wrt what? A geodesic may be analogous to a straight line in euclidean space, but only in the sense that it is the shortest path. no?

But in the spirit of what you are saying, picture two geodesics traveling from within a supercluster into empty space. Within the supercluster, each geodesic would measure the other geodesic to be approaching it parabolically. As the geodesics leave the supercluster, each would measure the other to go through an inflection point, after which they would measure the other geodesic to be moving away parabolically.

Yes, agreed. However, I was considering tangents at 2 distantly separated points (of local segments) of a very long geodesic, whereby said points reside within vastly separated galaxies. I wasn't considering multiple geodesics.

Unless I'm misunderstanding, it sounds like you're talking about an unobservable prediction, which is avoided in science.

Maybe so. Kinda like string theory.

GrayGhost

 

[CJames]

We don't have a 5th dimension to gaze down upon 4-space, yet we know it's curved. If not curved unto itself, then curved wrt what?

You kind of answered your own question when you said we don't have a 5th dimension to gaze down on 4-space. The curvature of space is defined by the way that geodesics curve with respect to each other, not by comparison with a hypothetical flat 5th dimensional space.

Yes, agreed. However, I was considering tangents at 2 distantly separated points (of local segments) of a very long geodesic, whereby said points reside within vastly separated galaxies. I wasn't considering multiple geodesics.

Right, I was trying to answer the spirit of your question, instead of the question itself, since a geodesic can't diverge (or converge) with itself.

As I said later, it would probably help you understand what's happening if you realized that the space inside a gravity well is contracting, in the same sense that the space between superclusers is expanding.

In the same way that there is less and less space between two planets falling toward each other, there is more and more space between two galaxies "falling" away from each other. That's all that is meant by saying that space is expanding.

 

[GrayGhost]

GrayGhost, Perhaps it would be clearer what is meant by "expanding space" if you were to realize that, in the same sense, the space inside a gravity well is "contracting." From this perspective, it should be clear why the space inside a gravity well is not expanding.

Would it not be proper to say that space contracts in a gravity well only if you progress to deeper potential, not if you remain at one gravitational potential?

I do realize what you are saying. Yet, gravitation and spacetime expansion are 2 different things arising from 2 different sources. One is the suspected dark energy and the other is spacetime curviture from mass. How do we know that both activities do not occur in superposition within gravity wells? It seems reasonable that gravitation could overwhelm expansion within some reach, that spacetime expansion might be a negligable effect even though it exists in the well. EDIT: But then, as mentioned, there would likely be no way to prove it.

GrayGhost

 

[GrayGhost]

Quoting a bit more from the FAQ (I wonder how many have read it...)

For the technically minded, Cooperstock et al. computes that the influence of the cosmological expansion on the Earth's orbit around the Sun amounts to a growth by only one part in a septillion over the age of the Solar System. This effect is caused by the cosmological background density within the Solar System going down as the Universe expands, which may or may not happen depending on the nature of the dark matter. The mass loss of the Sun due to its luminosity and the Solar wind leads to a much larger [but still tiny] growth of the Earth's orbit which has nothing to do with the expansion of the Universe. Even on the much larger (million light year) scale of clusters of galaxies, the effect of the expansion of the Universe is 10 million times smaller than the gravitational binding of the cluster.

Then it is fair to say that spacetime expansion occurs even within gravity wells? That gravitation and expansion may be superpositional effects, and the effect of expansion negligible. Yes?

GrayGhost

 

[pervect]

I think you're missing my point, and Ned Wright's too. Look at the part that says:

This effect is caused by the cosmological background density within the Solar System going down as the Universe expands.

 

[CJames]

Would it not be proper to say that space contracts in a gravity well only if you progress to deeper potential, not if you remain at one gravitational potential?

What I'm getting at is that two objects which start out at rest with respect to one another will move toward one another. In that sense, the space between them is contracting. Universal expansion is just the opposite of this.

I do realize what you are saying. Yet, gravitation and spacetime expansion are 2 different things arising from 2 different sources. One is the suspected dark energy and the other is spacetime curviture from mass. How do we know that both activities do not occur in superposition within gravity wells? It seems reasonable that gravitation could overwhelm expansion within some reach, that spacetime expansion might be a negligable effect even though it exists in the well. EDIT: But then, as mentioned, there would likely be no way to prove it.

GrayGhost

While they come from two different sources, I wouldn't agree that they are two different things. They are both the effect of energy on spacetime. Mass causes geodesics to move toward each other, while negative pressure causes geodesics to move away from each other.

If you are saying that the negative pressure which causes space to expand is located at every point in space, I believe that this is the mainstream position. But this doesn't translate into saying that every point in space is expanding, because gravity overcomes this negative pressure several billion times over. It is only when this negative pressure wins out over gravity that space starts expanding.

 

[GrayGhost]

I think you're missing my point, and Ned Wright's too. Look at the part that says:

This effect is caused by the cosmological background density within the Solar System going down as the Universe expands.

Well, I'm aware of the cosmic microwave background radiation. Is he referring to the "energy density" of the CMBR there?

GrayGhost

 

[GrayGhost]

What I'm getting at is that two objects which start out at rest with respect to one another will move toward one another. In that sense, the space between them is contracting. Universal expansion is just the opposite of this.

Yes.

While they come from two different sources, I wouldn't agree that they are two different things. They are both the effect of energy on spacetime. Mass causes geodesics to move toward each other, while negative pressure causes geodesics to move away from each other.

Yes. Although, they are 2 differing forms of energy with differing effects.

If you are saying that the negative pressure which causes space to expand is located at every point in space, I believe that this is the mainstream position. But this doesn't translate into saying that every point in space is expanding, because gravity overcomes this negative pressure several billion times over. It is only when this negative pressure wins out over gravity that space starts expanding.

Well, I have no disagree here. Your point is well taken. I was merely suggesting that the process of spacetime expansion occurs everywhere, even in gravity wells. The effect of expansion is negligible compared to the effect of gravitation when close enough to the COG. I have no disagreement that the net effect inside a galaxy is contraction, and the expansion component negligible. Sound reasonable?

GrayGhost

 

[PeterDonis]

It pretty much turns out that whether or not space is expanding depends on the coordinates you use. For instance, in the case of an empty universe, one set of coordinates gives you a Milne expanding universe, while another set of coordinates gives you an ordinary flat space-time that's not expanding at all.

Isn't this a special case? In the empty universe, objects "at rest" in either set of coordinates are moving inertially (i.e., they feel zero acceleration). In a general non-empty universe, that's not the case; there is a single "preferred" set of coordinates covering the whole spacetime (the FRW coordinates) in which objects "at rest" move inertially. (You can cover a local patch with "flat" coordinates that act like ordinary flat spacetime locally, but they won't work for the whole spacetime.)

Expanding space-time takes the point of view that bodies that are moving or accelerating apart are just following natural geodesics of the space-time.

The other point of view says that any relative acceleration between geodesics must be due to a gravitational force.

But there is an observable, invariant, physical difference between objects that don't feel acceleration and objects that do. Relative "acceleration" between geodesics means relative "acceleration" between freely falling objects whose worldlines are geodesics; but those objects do not *feel* any acceleration, so attributing the relative "acceleration" of their geodesics to a "force" obscures the physical difference I just described. Basically, the gravitational "force" must be a "fictitious" force.

Whereas if you define "expanding spacetime" as the divergence of geodesics (i.e., objects which are moving inertially, and seem to be "at rest" relative to the average of all matter in the universe, find themselves getting further apart with time), then whether or not spacetime is expanding is *not* dependent on the coordinates. You can adopt coordinates in which the objects traveling on the diverging geodesics are not "at rest", but the geodesics themselves will still diverge.

(I know you know all this; I'm just trying to clarify what one has to accept if one takes the viewpoint that any relative acceleration of geodesics has to be due to a "force".)

 

[GrayGhost]

I know you know all this; I'm just trying to clarify what one has to accept if one takes the viewpoint that any relative acceleration of geodesics has to be due to a "force".

Hey, I would like to know everything you fellows know about general relativity, without any time or effort whatsoever, and I'd like to know yesterday. You have any ideas Peter?

GrayGhost

 

[CJames]

Well, I have no disagree here. Your point is well taken. I was merely suggesting that the process of spacetime expansion occurs everywhere, even in gravity wells. The effect of expansion is negligible compared to the effect of gravitation when close enough to the COG. I have no disagreement that the net effect inside a galaxy is contraction, and the expansion component negligible. Sound reasonable?

It sounds like you're saying the same thing I am. I just wouldn't phrase it that way because no expansion is occurring there. I think it would be better to say that the negative pressure very slightly weakens the effects of gravity. Otherwise people start asking if the solar system is expanding, or if meter sticks are expanding, which they are not.

 

[PeterDonis]

Hey, I would like to know everything you fellows know about general relativity, without any time or effort whatsoever, and I'd like to know yesterday. You have any ideas Peter?

I guess that would have to go in a separate thread on tachyons.

 

[GrayGhost]

It sounds like you're saying the same thing I am. I just wouldn't phrase it that way because no expansion is occurring there. I think it would be better to say that the negative pressure very slightly weakens the effects of gravity. Otherwise people start asking if the solar system is expanding, or if meter sticks are expanding, which they are not.

Indeed. Yet, if "the process of" spacetime expansion is occurring inside the solar system, we should not advertize that it is not. It's like a swimming pool being pumped in water at 1 gal/sec while also being pumped out at 2 gal/sec. We could say that the pool loses 1 gal/sec, period, but that would not tell the whole story. However, in many cases here, I do agree it is best to keep it simpler, so touche.

GrayGhost

 

[San K]

No. This expansion is extremely weak. It is so weak even galaxies ahve no trouble holding together. It only has an effect when gravity is virtually zero - out between galaxy clusters.

I glue two pennies (Earth, Sun) edge-to-edge onto a balloon. Then I put tape across the pennies so they are stuck together (mutual gravity).

I do this again (a star in Virgo galaxy and its planet), so I have two clusters of pennies (Milky Way, Virgo).

I inflate the balloon. If the tape is strong enough then the balloon's inflationary force is far too weak to overcome the tape's strength. The clusters themselves stay together. (Earth-Sun do not change distance).

But the two clusters (Virgo, Milky Way), having no "force" connecting them, move apart as the balloon expands.

hi Dave,

thanks for making, some of, us aware of some interesting theories/hypothesis.

would the distance between virgo and milky-way then be more than it was say, a million years ago?

do we have some proof, such as red-shifting of light etc?

also if the expansion of space is faster than speed of light ...and since there is very little "force" connecting Virgo and Milky-way...wouldn't the galaxies be moving "further away" from each other at some fraction of the speed of light?

 

[Rishavutkarsh]

hi Dave,

thanks for making, some of, us aware of some interesting theories/hypothesis.

would the distance between virgo and milky-way then be more than it was say, a million years ago?

do we have some proof, such as red-shifting of light etc?

also if the expansion of space is faster than speed of light ...and since there is very little "force" connecting Virgo and Milky-way...wouldn't the galaxies be moving "further away" from each other at some fraction of the speed of light?

i agree with him but i want to add one more point if the speed of expansion is more than light then there would come a time when we won't be able to see virgo right?

 

[DaveC426913]

would the distance between virgo and milky-way then be more than it was say, a million years ago?

I picked the name poorly, actually referring to the Virgo Cluster of which we are part. There are clusters outside our own. These are, for the most part, moving away from us all the time.

do we have some proof, such as red-shifting of light etc?

We have evidence of the movements. Our model explains the movements. But there's room for other models.

also if the expansion of space is faster than speed of light ...and since there is very little "force" connecting Virgo and Milky-way...wouldn't the galaxies be moving "further away" from each other at some fraction of the speed of light?

Expansion is proportional to distance; the farther apart two objects are, the faster they are separating. Nearby clusters are moving away at a fraction of c - it's just very small fraction of c.

 

[George Jones]

i agree with him but i want to add one more point if the speed of expansion is more than light then there would come a time when we won't be able to see virgo right?

No.

See posts #55 and #61 in the thread

https://www.physicsforums.com/showthread.php?p=3319935#post3319935.

If these posts are not understandable, ask some questions.

 

[Rishavutkarsh]

No.

See posts #55 and #61 in the thread

https://www.physicsforums.com/showthread.php?p=3319935#post3319935.

If these posts are not understandable, ask some questions.

it means there are some objects in the universe which can't be ever seen or reached by us right?
now then how did they get this far i mean in the time of big bang they were together so after big bang they got farther more then 13.7 billion light years radius (they are also objects and they also follow relativity) because that's the age of universe and nothing can exceed the velocity of light . so what made em get this far?

 

[DaveC426913]

so what made em get this far?

The expansion of space, which is not subject to the restrictions of relativity. Have you been following along?

 

[Rishavutkarsh]

The expansion of space, which is not subject to the restrictions of relativity. Have you been following along?

can't say i was but something made em farther . like two friends bought houses very near before the big bang and with the passage of time they saw each other to go farther and farther (consider them not to be bonded by gravity) so they made sure that they say hi each other everyday now after 13.7 billion years they can't see each other as they have been moved into more distance than 28 billion light years and universe is expanding faster than light. but the thing is that they moved faster than light in respect to each other . as they have moved a distance even more than 28 billion light years in less than 13.7 billion years . isn't that weird huh?

 

[DevilsAvocado]

... as they have moved a distance even more than 28 billion light years in less than 13.7 billion years . isn't that weird huh?

It looks weird if one does not take into account two very important factors:

1. When we say that something is 28 billion light years away now, we mean that we are calculating this distance to the object, where it will be now, but what we see (now) is the light that has traveled for 13 billion years, which then was emitted when the object was only 4 billion light years away from us.
   
   
2. Space is expanding and everything moving inside, including light, has to make its way 'upstream' this expansion, hence it will take light a much longer time to travel a distance, than the first obvious conclusion (think of running at 10 km/h after someone walking at 5 km/h, it will take you longer time to reach that person, than if he stood still).

The brown line on the diagram is the worldline of the Earth. The yellow line is the worldline of the most distant known quasar. The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day. The orange line shows the present-day distance between the quasar and the Earth, about 28 billion light years.

http://en.wikipedia.org/wiki/Metric_expansion_of_space#Understanding_the_expansion_of_Universe

 

[CJames]

it means there are some objects in the universe which can't be ever seen or reached by us right?
now then how did they get this far i mean in the time of big bang they were together so after big bang they got farther more then 13.7 billion light years radius (they are also objects and they also follow relativity) because that's the age of universe and nothing can exceed the velocity of light . so what made em get this far?

The theory of inflation says that objects were close enough to interact with each other when the universe was first created, but a phase change in the quantum field released energy into the universe, causing the distance between these objects to expand at faster than the speed of light for a short period of time.

This is why two objects which were 13.7 billion light years away from each other 13.7 billion years ago still had about the same temperature.

 

[Rishavutkarsh]

oh you mean the friends can never see each other again ? now you get a lesson don't buy house near a friend because time can change things ... i km can become 13.7 billion light years. i feel bad for them both :(

 

[JDoolin]

The brown line on the diagram is the worldline of the Earth. The yellow line is the worldline of the most distant known quasar. The red line is the path of a light beam emitted by the quasar about 13 billion years ago and reaching the Earth in the present day. The orange line shows the present-day distance between the quasar and the Earth, about 28 billion light years.

http://en.wikipedia.org/wiki/Metric_expansion_of_space#Understanding_the_expansion_of_Universe

I notice that the Ben Rudiak Gould's lambda CDM image cuts off at the bottom at 700 million years ABB (After Big Bang). If I'm reading it correctly, the expansion rate of the universe is fastest where the cone is flared out, and slowest if the cone is vertical.

I thought I recalled a gif animation on Ned Wright's page (though it may have been somewhere else) that went all the way back to the first instant. The particles started out co-located, yet not causally connected. Then they moved away from each other at great speed (via the stretching of space), and then slowed down to a velociy where light could travel between them.

Extrapolating from Gould's image, if the base of the cone goes horizontal, something like that may have happened before 700 million years.

oh you mean the friends can never see each other again ? now you get a lesson don't buy house near a friend because time can change things ... i km can become 13.7 billion light years. i feel bad for them both :(

When the cone flares out enough, can signals cease between two previously neigboring (i.e. causally connected) particles? I wonder whether the theory is similar to the black hole situation (but more symmetrical), where the person falling into the black hole falls in in finite time, while the person watching sees him fall closer and closer into the event horizon, but never falling in.

In the lambda CDM cosmological model, where the stretch of space exceeded the speed of light, perhaps both parties would see the last light of the other eternally redshifting to infinity, while continuing to experience their own time normally.

 

[Anamitra]

The red line does not look like a null geodesic if infinitesimal segments are considered.Strictly speaking we should consider light cones at each and every point of the null geodesic[red-line], maintaining the time axis parallel to itself. [Incidentally all infinitesimal segments lying on the light cone do not make 45 degrees with the time axis. We can always wrap smooth curves on a light cone which are of a mixed character----to be precise any smooth curve[with delta_t not equal to zero] wrapped over the light cone is of a mixed character[generally speaking] comprising spacelike and null segments].

Is the following Wikipedia statement[in your link] in conformity with the above considerations?
"In particular, light always travels locally at the speed c; in our diagram, this means that light beams always makes an angle of 45° with the local grid lines."

 

[Dale]

The red line does not look like a null geodesic if infinitesimal segments are considered.

It is hard to tell exactly, but it looks pretty close to me.

 

[Anamitra]

By introducing the concept of conformal time with the FRW metrics we have light cones whose generators make 45 degrees with the time[conformal ] axis.
We consider a general type of a FRW metric [in simplified form] :
{ds}^{2}{=}{dt}^{2}{-}[{a}{(}{t}{)}]^{2}{[}{dx}^{2}{+}{dy}^{2}{+}{dz}^{2}{]}
Writing,
{dt}{=}{a}{(}{t}{)}{d}{\eta}
we have for the null geodesics,
{d}{\eta}^{2}{=}{dr}^{2} ----------- (1)
where,
{dr}^{2}{=}{[}{dx}^{2}{+}{dy}^{2}{+}{dz}^{2}{]}
Equation (1) gives us a picture of the light cone as we know in special relativity so far as the coordinate speed of light is concerned..
Alternatively we may do the following:
{ds}^{2}{=}{dt}^{2}{-}[{a}{(}{t}{)}]^{2}{[}{dx}^{2}{+}{dy}^{2}{+}{dz}^{2}{]}
Or,
{ds}^{2}{=}{dt}^{2}{-}{dL}^{2}------ (2)
Where,
{dL}^{2}{=}{[}{a}{(}{t}{)}{]}^{2}{[}{dx}^{2}{+}{dy}^{2}{+}{dz}^{2}{]}
Again we have the Special Relativity picture at each point of time with equation (2).

The Wikipedia model seems to have used unmodified time[and not conformal time]. If the distance represented is the coordinate distance, we should get[rather we are supposed to get] the Special Relativity picture of the null geodesics[so far as infinitesimal sections are concerned]] after transforming to conformal time[from unmodified time]. But from the picture it is not clear [and quite difficult to say]whether the red line will finally cater to the required properties of the null geodesics.[after the transformation.]
[If Wikipedia has used physical distance for the picture the situation would become much more difficult]

 

[Anamitra]

We consider the following equation again:
{ds}^{2}{=}{dt}^{2}{-}[{a}{(}{t}{)}]^{2}{[}{dx}^{2}{+}{dy}^{2}{+}{dz}^{2}{]}
For a null geodesic:
\frac{dx}{dt}{=}\frac{1}{{a}{(}{t}{)}}

dx/dt should be a variable thing[function of time]----this does not seem to hang with the constant 45 degree depiction in the Wikipedia model:"In particular, light always travels locally at the speed c; in our diagram, this means that light beams always makes an angle of 45° with the local grid lines."

[Only x-coordinate has been considered in the above relation. One may consider both x and y coordinates to get a better picture]

If the picture represents a plot of conformal time against coordinate distance we get the same light cone picture as we have in Special Relativity.The red line contains segments that do not make 45 degrees with the conformal time axis

The same holds true if coordinate time[unmodified] is plotted against physical distance[The Special Relativity picture of the light cone should hold true-the red line does not seem to be following it every where--it is not at 45 degrees to the time axis at all points]

 

[JDoolin]

Here's what the wikipedia article says about the diagram.

"The narrow circular end of the diagram corresponds to a cosmological time of 700 million years after the big bang; the wide end is a cosmological time of 18 billion years, where one can see the beginning of the accelerating expansion which eventually dominates in this model. The purple grid lines mark off cosmological time at intervals of one billion years from the big bang. The cyan grid lines mark off comoving distance at intervals of one billion light years. Note that the circular curling of the surface is an artifact of the embedding with no physical significance; space does not actually curl around on itself."​

Looking path of the light through each individual rectangle, it appears that sometimes the light covers only 1B LY in 1 billion years, and in others (notably the time between 1 billion years and 2 billion years) the light covers several billion light years.

Is that consistent with c d\tau^2 = c^2 dt^2 - a(t)^2dx^2?


To follow the path of a photon, set d\tau = 0, and derive:
(repeating what Anamitra already said.)

\frac{\mathrm{d} x}{\mathrm{d} t} = \frac{c}{a(t)}

I'm pretty sure this \frac{\mathrm{d} x}{\mathrm{d} t} refers to how fast the beam travels according to the purple grid lines (representing Δt= 1BYears) , and cyan grid lines (representing Δx=1B LY).

 

[Anamitra]

Here's what the wikipedia article says about the diagram.

"The narrow circular end of the diagram corresponds to a cosmological time of 700 million years after the big bang; the wide end is a cosmological time of 18 billion years, where one can see the beginning of the accelerating expansion which eventually dominates in this model. The purple grid lines mark off cosmological time at intervals of one billion years from the big bang. The cyan grid lines mark off comoving distance at intervals of one billion light years. Note that the circular curling of the surface is an artifact of the embedding with no physical significance; space does not actually curl around on itself."​

Looking path of the light through each individual rectangle, it appears that sometimes the light covers only 1B LY in 1 billion years, and in others (notably the time between 1 billion years and 2 billion years) the light covers several billion light years.

Is that consistent with c d\tau^2 = c^2 dt^2 - a(t)^2dx^2?


To follow the path of a photon, set d\tau = 0, and derive:
(repeating what Anamitra already said.)

\frac{\mathrm{d} x}{\mathrm{d} t} = \frac{c}{a(t)}

I'm pretty sure this \frac{\mathrm{d} x}{\mathrm{d} t} refers to how fast the beam travels according to the purple grid lines (representing Δt= 1BYears) , and cyan grid lines (representing Δx=1B LY).

"The cyan grid lines mark off comoving distance at intervals of one billion light years."

One billion light year is a comoving distance--it does not change with time as we proceed upwards along the time axis.But the graduations are widening as we go up along the time axis--so these graduations mark off the physical distances[the increasing physical distances] corresponding to the comoving distance of one billion light years [with the advancement of time]

The quantity [physical distance/time] is increasing for the light ray.

[Physical distance= a[t]*comoving distance[comoving distance=coordinate distance between labels that do not change with time]]