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

[Rishavutkarsh]

the speed of light is C and the age of universe is 15 billion years so can't we assume that the radius of the universe can't be more than 15 billion light years? also has the speed of light changed since the beginning of the universe?

[ghwellsjr]

The universe is actually closer to 13.7 billion years old and the radius of the observable part of the universe is about 13.7 billion light years since the speed of light has always been exactly C. But we assume that the universe is also expanding in the opposite direction and, in fact, in all directions and so there is much more to the universe than we will ever be able to see.

And there are parts of the universe that are moving away from us at faster than the speed of light.

[Rishavutkarsh]

And there are parts of the universe that are moving away from us at faster than the speed of light.

faster than speed of light is it possible ? please elaborate and explain it's evidence

[DaveC426913]

We believe the universe may be as wide as 156 billion light years.

Relativity forbids massive objects reaching or exceeding c. It says nothing about the expansion of space. Space is expanding and galaxies are moving along with it.

[cephron]

Someone please do correct me if I'm wrong, but I think I have a good way to explain...

No object can move through space at the speed of light relative to another object. No star, meteor, or spaceship will ever pass by earth at a speed equal to or greater than c.

But the expansion of space means that the further away something is from you, the greater the growth of the distance between the the object and you (ie. getting increased distance per unit time). It's almost as if huge amounts of empty space are spawning between the objects every second.

So, neither object is actually "moving" at c, but the growth of space between them is greater than 299,792,458 m/s.

[San K]

We believe the universe may be as wide as 156 billion light years.

Relativity forbids massive objects reaching or exceeding c. It says nothing about the expansion of space. Space is expanding and galaxies are moving along with it.

Does that mean the distance between sun and earth (in a sense) is not the same as it was say, 1 or 10 billion years ago?

though light would still take 8 mins then and now?

however it would be hard to talk of distance then and now.....but I am not a relativity expert

[WannabeNewton]

bcrowell already wrote up an FAQ on this:
http://physicsforums.com/showthread.php?t=508610

[DaveC426913]

Does that mean the distance between sun and earth (in a sense) is not the same as it was say, 1 or 10 billion years ago?

though light would still take 8 mins then and now?

however it would be hard to talk of distance then and now.....but I am not a relativity expert

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.

[pervect]

the speed of light is C and the age of universe is 15 billion years so can't we assume that the radius of the universe can't be more than 15 billion light years? also has the speed of light changed since the beginning of the universe?

You might take a look at Ned Wright's FAQ. Here's one part that addresses one of your questions.

http://www.astro.ucla.edu/~wright/cosmology_faq.html#DN


If the Universe is only 14 billion years old, how can we see objects that are now 47 billion light years away?

When talking about the distance of a moving object, we mean the spatial separation NOW, with the positions of both objects specified at the current time. In an expanding Universe this distance NOW is larger than the speed of light times the light travel time due to the increase of separations between objects as the Universe expands. This is not due to any change in the units of space and time, but just caused by things being farther apart now than they used to be.


There is a certain amount of convention involved in defining distances and velocities of very distant objects due to the curvature of space-time. One part of the convention hinges on the issue of "now", the notion of "now" in cosmology is logical and self-consistent, but subtly different from the SR notion of "now" of any particular observer.

[CJames]

faster than speed of light is it possible ? please elaborate and explain it's evidence

An object with mass can never overtake a beam of light, but if space itself is expanding, the distance between two objects can expand at faster than the speed of light. This is possible in the theory of general relativity, where it is possible for geodesics to diverge from one another at this rate.

The strongest evidence that this has occurred in reality is the experimental evidence for the theory of the inflationary universe. Inflation is a quantum theory that predicts the universe underwent several quantum fluctuations during its formation. These fluctuations caused space to expand at faster than the speed of light, which explains the uniformity of the observable universe.

Inflationary theory made several predictions about the universe that weren't predicted by any other theories. These predictions have been experimentally verified with striking accuracy by the WMAP satellite and other studies of the cosmic background radiation.

[abbott287]

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.

What exactly is it that is expanding?? Also, would that mean casualty can be violated because two objects are seperating from each other faster than the speed of light?

[WannabeNewton]

This is possible in the theory of general relativity, where it is possible for geodesics to diverge from one another at this rate.

Is there a way to see this come out naturally from the equation of geodesic deviation?

[pervect]

Is there a way to see this come out naturally from the equation of geodesic deviation?

Try Ned Wright's cosmology FAQ again http://www.astro.ucla.edu/~wright/cosmology_faq.html#SS

Why doesn't the Solar System expand if the whole Universe is expanding?

There's also a reference to a paper by Cooperstock http://xxx.lanl.gov/abs/astro-ph/9803097

See section 2


2 Equations of motion in the LIF
In this section we find the equations of motion for a particle in the LIF using the geodesic
deviation equation. We refer the reader to the Appendix for the details of the calculation.


A short and simplified version is that if the solar system is expanding in terms of it's Fermi frame (the LIF frame mentioned in section 2), it's because it's loosing mass. (in particular, the mass element defined by M in the Schwarzschild geodesic, which will also be equal to the Komar mass, for example).

The dominant mass-loss mechanism is the sun radiating it's energy away, an effect mentioned in the paper but one that is not of cosmological origin. There might be some very very very small cosmological effect due to dark matter.

Cosmologically we know that rho, the mass density (measured locally) is going down,but this doesn't imply that the solar system is loosing mass, necessarily. Dark matter flux is one of the ways that it _might_ be loosing mass due to cosmological effects. And of the effects we do know about, solar radiation dominates, though it wouldn't usually be thought of as cosmological.

[CJames]

What exactly is it that is expanding??

Space itself is expanding, or more accurately, geodesics are diverging from one another over time. This has no effect on what is happening inside galaxies or solar systems, however, because in these systems geodesics are converging.

Also, would that mean casualty can be violated because two objects are seperating from each other faster than the speed of light?

No. Casualty violation would only occur if a worldline traveled outside of the light cone. In other words, it would only occur if an object were to overtake a beam of light. Causality violation doesn't occur because the two objects will never interact with one another.

[GrayGhost]

What exactly is it that is expanding?? If galaxies are moving away from us at greater than the speed of light, due to whatever reason, doesnt that mean the light could never reach us? Also, would that mean casualty can be violated because two objects are seperating from each other faster than the speed of light?

What's expanding is the very spacetime itself. Maybe you prefer to call it the fabric of spacetime? Everything goes for the ride while the cosmos expands.

I am no expert wrt GR, but here's my 2 cents based on what I've read myself ...

Imagine a point in space, where a light source was originally emitting. You were then some distance X away. If spacetime did not expand, it would take the initial photons a duration of T=c/X to reach you. However, since spacetime is stretching everywhere at every moment, the photon has more space (and thus time) to traverse than the original distance X, because it expands as the photon travels. If the expanse separating the POE and yourself were large enough, then the expanding spacetime can prevent a photon from ever reaching you. It seems conceivable to me, that a photon could reach you from (say) the birth of a galaxy some 10 billion years ago, but soon fade from view forever. The way I look at it, it's somewhat analogous to a radially inbound photon attaining an escape velocity "but due to the expansion itself". You have to remember, every point in spacetime is expanding, all the time. The greater the vast expanse, the sooner approaching photons will never be able to reach you, and eventually become outbound.

FAIK, this is no violation of the general theory. Light's invariant speed is assumed true in any local area of spacetime no matter what part of the vast expanse one considers, or when. So the issue of a photon no longer being able to be viewed from another distant perspective is a superpositional effect which does not violate GR.

GrayGhost

[CJames]

You have to remember, every point in spacetime is expanding, all the time.

My understanding is that this isn't entirely accurate. The distance between galaxies in a super cluster is not expanding. Anything that is gravitationally bound isn't affected by the expansion, only objects that are gravitationally separated from one another are.

[GrayGhost]

My understanding is that this isn't entirely accurate. The distance between galaxies in a super cluster is not expanding. Anything that is gravitationally bound isn't affected by the expansion, only objects that are gravitationally separated from one another are.

Is it that gravitation is a superpositional effect that keeps galaxies held together as such even in light of spacetime expansion (everywhere all the time), or that "spacetime itself expands less" if large gravitational fields are present in the region? It appears you assume the latter.

GrayGhost

[CJames]

Is it that gravitation is a superpositional effect that keeps galaxies held together as such even in light of spacetime expansion (everywhere all the time), or that "spacetime itself expands less" if large gravitational fields are present in the region? It appears you assume the latter.

GrayGhost

I'm not an expert in the subject by any means, but my understanding is that spacetime doesn't expand at all in areas where things are gravitationally bound.

I assume this because of the nature of geodesics. Two objects that are being separated by the expansion of the universe have diverging geodesics. Two objects that are gravitationally bound to one another have converging geodesics.

You can't have geodesics that simultaneously converge and diverge at the same time. Right?

[Jaynte]

We believe the universe may be as wide as 156 billion light years.


Who believe's that?
The visible universe is 12 billion light years, thats why we believed the universe was 12 billion years old before, but now we have calculated indirectly that the universe is about 13.7 billion years old.

[George Jones]

We believe the universe may be as wide as 156 billion light years.

The radius of the observable universe is 13.7 billion light-years. The radius of the observable universe is 47 billion light-years. The size of universe is at least 78 billion light-years. The popular media have arrived at 156 billion light-years by incorrectly doubling 78 billion light-years.

These statements are seemingly contradictory, but, actually, they are all consistent with current cosmological theory and observations. Why? Because space and distance in cosmology are strange things!

If two different, but correct, ways of measuring distance are used to measure the width of a room, then, to the accuracy of the methods, the results will be same. This is not true in cosmology! Because of spacetime curvature, there is no unique correct concept of spatial distance.

Light travels at a certain finite speed, so the image of any object that we see now is formed by light that left the object some number of years ago. The lookback distance of the object is defined to be the same number of light-years. "the radius of the observable universe is 13.7 billion light-years" uses lookback distance.

Another type of distance is proper distance. Here, "proper" is used in the same sense as "property", not in the same sense as "correct". While the definition of lookback distance considers us and an object at two different times, proper distance considers us and an object at the same instant of cosmic time. "the radius of the observable universe is 47 billion light-years" uses proper distance at the time now.

While lookback distance and proper distance are defined differently, they are both correct. Given distance using one definition, it is possible to calculate the distance given by the other definition. For example, a lookback distance of 13.2 billion light-year corresponds to a proper distance of 31.7 billion light-years.

And there other definitions of cosmic distance. It is important to keep in mind which definition is being used.

Now on to the 78 (156) billion light-year figure. Current cosmological theories indicate that although 4-dimensional spacetime is curved, 3-dimensional space is very close to being flat. For the sake of a shorter explanation, let's assume that space is flat.

Even if space is flat, it might be connected in strange ways, like in the video game Asteroids. In Asteroids, if you fly off the top of the screen, you immediately appear in the same place at the bottom of the screen. Similarly for the sides of the screen. Maybe the universe is connected up in the same way.

A few years ago, some physicists looked at cosmological data and conclude that if the universe is connected like an Asteroids screen, then the width of the Asteroids screen is at least 78 billion light-years. Note: 1) this is something quite different then the size of the observable universe; 2) the popular media took this 78 billion light-year width or diameter incorrectly as a radius and doubled it to get 156 billion light-years.

http://arxiv.org/abs/astro-ph/0310233

[ghwellsjr]

If spacetime did not expand, it would take the initial photons a duration of T=c/X to reach you.
Don't you mean T=X/c?

[JDoolin]

Because of spacetime curvature, there is no unique correct concept of spatial distance.


But are there well-defined concepts of spatial distance?

[abbott287]

What's expanding is the very spacetime itself. Maybe you prefer to call it the fabric of spacetime? Everything goes for the ride while the cosmos expands.

I am no expert wrt GR, but here's my 2 cents based on what I've read myself ...

Imagine a point in space, where a light source was originally emitting. You were then some distance X away. If spacetime did not expand, it would take the initial photons a duration of T=c/X to reach you. However, since spacetime is stretching everywhere at every moment, the photon has more space (and thus time) to traverse than the original distance X, because it expands as the photon travels. If the expanse separating the POE and yourself were large enough, then the expanding spacetime can prevent a photon from ever reaching you. It seems conceivable to me, that a photon could reach you from (say) the birth of a galaxy some 10 billion years ago, but soon fade from view forever. The way I look at it, it's somewhat analogous to a radially inbound photon attaining an escape velocity "but due to the expansion itself". You have to remember, every point in spacetime is expanding, all the time. The greater the vast expanse, the sooner approaching photons will never be able to reach you, and eventually become outbound.

FAIK, this is no violation of the general theory. Light's invariant speed is assumed true in any local area of spacetime no matter what part of the vast expanse one considers, or when. So the issue of a photon no longer being able to be viewed from another distant perspective is a superpositional effect which does not violate GR.

GrayGhost

Thanks for the reply.

First off, I guess this brings up the question of how do we determine what is moving away from each other due to a force, or if space is just being created between them??? Second, if we figure out how this "space" (space time fabric I take it, whatever that is, dark matter maybe?) is being created and make a space building machine, could we then just "create space" between a rocketship and earth and move them apart faster than the speed of light? I know I am swimming way above my head, but I am trying to fill it all in as fast as I can. Thanks for taking my questions seriously, and to all taking the time to help! EDIT: One more question...what do all of you take to stop the migraine headaches all this hard thinking brings on? :)

[GrayGhost]

Don't you mean T=X/c?

Indeed sir. Thanx for the correction. Missed that on my proof-read. T=X/c it is !

GrayGhost

[GrayGhost]

I'm not an expert in the subject by any means, but my understanding is that spacetime doesn't expand at all in areas where things are gravitationally bound.

I assume this because of the nature of geodesics. Two objects that are being separated by the expansion of the universe have diverging geodesics. Two objects that are gravitationally bound to one another have converging geodesics.

You can't have geodesics that simultaneously converge and diverge at the same time. Right?

One might imagine a geodesic that spans from one galaxy to a distant other galaxy. Consider that geodesic locally near either galaxy, while ignoring it everywhere inbetween, and the 2 segments of said geodesic should diverge under continued cosmic expansion (I would figure). Yet, it's still one geodesic in grandier. At any local point in spacetime anywhere, it should appear to converge.

I'd assume your response is what the community would consider to be appropriate. However, let's assume there is a medium of spacetime, and then there are the curvatures thereof. The medium expands under expansion, due to the presumed yet unknown dark energy. I was just wondering whether the medium could be expanding even within a gravity field, while the gravity well maintains it's exact configuration (potential and gradient relative to the COG)? IOWs, could the medium stretch even inside the well, while the well maintain's its precise shape? If the extent of mass dictates the well's geometry, and the mass does not change even during expansion, then maybe an expansion of spacetime inside the well (due to dark energy everywhere) would go unbeknownst within galaxies.

GrayGhost

[WannabeNewton]

One might imagine a geodesic that spans from one galaxy to a distant other galaxy. Consider that geodesic locally near either galaxy, while ignoring it everywhere inbetween, and the 2 segments of said geodesic should diverge under continued cosmic expansion (I would figure). Yet, it's still one geodesic in grandier. At any local point in spacetime anywhere, it should appear to converge.
GrayGhost

Huh? Geodesic deviation involves the changing separation between two neighboring geodesics. How would you construct a separation vector from a single geodesic and make it point to itself and still measure any divergence/convergence? Also, how could \frac{D^{2}\xi ^{\alpha }}{D\tau ^{2}} be both positive and negative at the same time?

[rede96]

Second, if we figure out how this "space" (space time fabric I take it, whatever that is, dark matter maybe?) is being created and make a space building machine, could we then just "create space" between a rocketship and earth and move them apart faster than the speed of light?


I'm no expert in this area but like you, find it really interesting. However I would imagine that the conservation of energy principle would mean that we couldn't 'create space'. But like I said, what do I know!

As for the head aches, I find switching the PC off and going to the pub helps tremendously. :0)

[pervect]

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.

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. It's not as much in the spirit of relativity, perhaps, but in most non-cosmological circumstances I find it more useful, it gives some feeling of "cause" and "effect".

So when you attribute gravity to a force, the only way a bound system (like the solar system, for instance) can expand or contract is if the force changes. If you are in a position where you can define a mass (which isn't always possible), then you can say that the force changing implies that the mass is changing.

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.

[CJames]

One might imagine a geodesic that spans from one galaxy to a distant other galaxy. Consider that geodesic locally near either galaxy, while ignoring it everywhere inbetween, and the 2 segments of said geodesic should diverge under continued cosmic expansion (I would figure). Yet, it's still one geodesic in grandier. At any local point in spacetime anywhere, it should appear to converge.

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

I'd assume your response is what the community would consider to be appropriate. However, let's assume there is a medium of spacetime, and then there are the curvatures thereof. The medium expands under expansion, due to the presumed yet unknown dark energy. I was just wondering whether the medium could be expanding even within a gravity field, while the gravity well maintains it's exact configuration (potential and gradient relative to the COG)? IOWs, could the medium stretch even inside the well, while the well maintain's its precise shape? If the extent of mass dictates the well's geometry, and the mass does not change even during expansion, then maybe an expansion of spacetime inside the well (due to dark energy everywhere) would go unbeknownst within galaxies.

GrayGhost

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

[CJames]

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.

[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. :wink:

[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 occuring 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 wanna 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. :wink:

[George Jones]

i agree with him but i wanna 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

http://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

http://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 wierd 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 wierd huh?

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

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.


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).


http://upload.wikimedia.org/wikipedia/commons/thumb/3/32/Embedded_LambdaCDM_geometry.png/450px-Embedded_LambdaCDM_geometry.png

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_expans ion_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]

http://upload.wikimedia.org/wikipedia/commons/thumb/3/32/Embedded_LambdaCDM_geometry.png/450px-Embedded_LambdaCDM_geometry.png

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_expans ion_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."

[DaleSpam]

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]]

[JDoolin]

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]]

Is it increasing in the diagram? If I understood the idea correctly, we have:

c^2 d\tau^2 = c^2 dt^2 - a(t)^2 dx^2

which simplifies to:

c^2 = \frac{a^2 dx^2}{dt^2} \overset ? = constant

which would be the speed of light (squared) when using the physical distance.

But the speed of light (squared) in the comoving distance would be

\frac{dx^2}{dt^2} = \frac{c^2}{a(t)^2}

which would be slowing down as a(t) increases.

(Edit: Now that I look at the diagram again, it does appear that the physical distance speed of light is increasing, i.e. c^2 = \frac{a^2 dx^2}{dt^2} \neq constant. Is that a particular feature of the Lambda-CDM model, or is it just a badly drawn speed-of-light line?)

[bcrowell]

The mentors have discussed this thread and decided that it is time to close it. Please note that we have a FAQ entry on this topic: http://physicsforums.com/showthread.php?t=508610