Speed of light effected by expansion of space?

[Chalnoth]

I don't see it there. I already pinpointed the mistake.Maybe you didn't understand. If you refer distances to the expanding space, you will have a constant v as the distance is the same.That's not an accelerating universe.But it is. So v=Hd is wrong.But it isn't. So where is the mistake?In that you say the both simultaneously.

v = Hd is correct. It's just that H changes with time. At any given time, the recession velocity between two points, with "at the same time" laid out by the two points seeing the same temperature CMB, will be v = Hd, where d is the distance between those points. This picture works whether you're talking about an accelerated expansion or not. The only part that is relevant is that the universe is, on large enough scales, homogeneous and isotropic to some observers.

Oh is it? Why is th light cone the way it is and not distorted? We have to redifine spacetime interval, space like events and time like events

Light cones are very distorted by the expansion of space. As for redefining the space-time interval, I hope you are aware that as compared to special relativity, general relativity does do this, as it takes into account the curvature of space-time.

 

[rasp]

Stretching would be a more accurate term.


Space-time is expanding. In General Relativity, space-time is seen as an entity in and of itself, with its shape determined by the matter that inhabits it. The existence of matter in the universe induces curvature in space-time, which, when we look at just the space components, looks like space is stretching or expanding.

Space has what type of characteristics that stretches or expands with time? How are you defining space, that it might stretch as if it were actually the same as its balloon analogy?

 

[Chalnoth]

Space has what type of characteristics that stretches or expands with time? How are you defining space, that it might stretch as if it were actually the same as its balloon analogy?

Well, technically, space-time has curvature that looks to observers like ourselves as if space is expanding.

 

[rasp]

Well, technically, space-time has curvature that looks to observers like ourselves as if space is expanding.

Space has no characteristic that I am aware of. It doesn't "look" like anything to observers. It has no primary meaning but is defined only secondarily as distance in relationship to the objects it separates.

 

[marcus]

Space has no characteristic that I am aware of. It doesn't "look" like anything to observers. It has no primary meaning but is defined only secondarily as distance in relationship to the objects it separates.

I agree. At least in cosmology we can assume that space has no physical material existence, it is not a substance like rubber.
The balloon analogy is not a mechanical model but a device to help people visualize. Think only of the surface of the balloon---all existence concentrated on the 2D surface. No rubber.

Space has what type of characteristics that stretches or expands with time? How are you defining space, that it might stretch as if it were actually the same as its balloon analogy?

You answered your own question. There is no physically existing space. There is, however, geometry. Once can make measurements. One can measure the angles of a triangle. there is an idea of a straight line. Of distance. As you indicated, geometry is primary. Space is "only secondary", as you said.

Can we call this backdrop the balloon? Well, then what of the balloon itself? Is it moving? If so, what is moving?...

A common perspective on the universe is to consider the backdrop to be the CMB---the microwave background. Light left over from ancient matter which was approximately uniformly distributed (before it began to curdle and clump) and of an approximately uniform temperature.

One can tell one is moving relative Background if there is a doppler hotspot ahead of one, and one can measure the speed by the dopplershift. One has an idea of rest with respect to Background.

It's convenient. They use it to analyze data. It is convenient to think of the background as not moving. then each of the galaxies has some proper motion relative background which can in many cases be estimated. These proper motions are normally rather slow. Not part of the expansion pattern.

This thread has evolved far beyond me, can I interject back to my original question? I understand that the galaxies are not moving per se at velocities greater than c, but are only in relation to each other as "the "backdrop of dynamic geometry" expands. Can we call this backdrop the balloon?
Well, then what of the balloon itself? Is it moving? If so, what is moving?...

It is convenient to think of the backdrop as not moving. It is a handy anchor point, a reference for all other motions. I would prefer not to call it "the balloon" because the balloon is just a visualization aid.

I guess a communication problem might be that I believe that geometry exists (not as a substance but) as a pragmatic reality. And you might not believe this. It would make it hard to communicate if that is true. Let me explain how I think that geometry exists.

GR equates the gravitational field to the geometry. The gravitational field is nothing else but the geometry. Geometry is as real as gravity. And it as real as the pragmatic fact that I can measure angles and distances. Moreover geometry is not naturally Euclidean. It evolves. At any given place we have no right to expect it to be static or flat. GR explains why in certain circumstances it will be approximately flat. Why in others it will be expanding or contracting according to some pattern.

Some other branch of physics may explain why the gravitational field (i.e. geometry) exists. Here we just take as given that it exists and that it evolves according to the main GR equation.

So distances between stationary observers (at rest w.r.t. background) increase according to some pattern (Hubble law) and this is not surprising.

And space is not a substance, neither is geometry a substance.

You might enjoy reading Rovelli's parable of the whale. I will see if I can find a link.
This links gets an early draft the whole book,
http://www.cpt.univ-mrs.fr/~rovelli/book.pdf
Look at section 1.1.3 "The physical meaning of general relativity," page 7.

And also more elaboration, with quotes from Einstein and others, in section 2.3.2 "The disappearance of spacetime". On pages 52 and 53.

 

[rasp]

Marcus wrote:"GR equates the gravitational field to the geometry. The gravitational field is nothing else but the geometry. "

Isn't it then more accurate to say the geometry or gravitational field is expanding rather than saying space is expanding?
I still see no reason in attributing an expansion of space when space is defined as having no substance. We commonly think of the elapsed stretch of time (not an interval of time) as increasing without attributing the increase to a physical process, do you think of space similarly?

 

[Chalnoth]

Space has no characteristic that I am aware of. It doesn't "look" like anything to observers. It has no primary meaning but is defined only secondarily as distance in relationship to the objects it separates.

It has as much reality as the electromagnetic field. The shape of space determines the paths of objects within it. It's not quite so simple as the distance, then, but also includes the motions of objects.

 

[Chalnoth]

Isn't it then more accurate to say the geometry or gravitational field is expanding rather than saying space is expanding?

That doesn't make a whole lot of sense, though.

I still see no reason in attributing an expansion of space when space is defined as having no substance.

It does, though. See gravitational waves. It's not the same sort of substance as stuff you can pick up, but then lots of things we are now aware of fall into that category.

We commonly think of the elapsed stretch of time (not an interval of time) as increasing without attributing the increase to a physical process, do you think of space similarly?

Well, it sort of depends upon what you mean. The appearance of the passage of time is tightly wound up with the increase of entropy, and is rather difficult to explain clearly. Heck, I'm not even sure if it's clearly understood yet.

 

[rasp]

And space is not a substance, neither is geometry a substance.

You might enjoy reading Rovelli's parable of the whale. I will see if I can find a link.
This links gets an early draft the whole book,
http://www.cpt.univ-mrs.fr/~rovelli/book.pdf
Look at section 1.1.3 "The physical meaning of general relativity," page 7.

And also more elaboration, with quotes from Einstein and others, in section 2.3.2 "The disappearance of spacetime". On pages 52 and 53.

Thanks, I particularly liked the classical definitions of space as either an "object" (Newtonian) or a relationship (Aristotle). And now I understand space as a dynamical entity, which may be better described as a gravitational field with a particular local strength and shape.

Can I prevail upon you for another 2+ questions? Let me know if I'm off base with questions for which I lack the proper prerequisite knowledge for this forum?

1. Is the "expansion of space" equally understandable as the "weakening" of the cosmological gravitational field?

2. We can imagine a constant speed, C = d/t , changing if we alter the relationship between a quanta of space and a quanta of time. In GR this seems to be happening with the "stretching" of space. Is it also proposed to be "happening" with the shrinking of time?
2a. What would be the difference in saying space is expanding vs "space-time" is expanding?

 

[Chalnoth]

1. Is the "expansion of space" equally understandable as the "weakening" of the cosmological gravitational field?

No, I don't think so. If you take the situation of de Sitter space, for instance, then the space-time geometry is actually independent of time, even though it's undergoing accelerated expansion. There certainly is no weakening of the field in that case.

2. We can imagine a constant speed, C = d/t , changing if we alter the relationship between a quanta of space and a quanta of time. In GR this seems to be happening with the "stretching" of space. Is it also proposed to be "happening" with the shrinking of time?
2a. What would be the difference in saying space is expanding vs "space-time" is expanding?

Well, first, space expanding makes sense, because we're talking about how space changes as a function of time. How would space-time change as a function of time? The prospect doesn't make any sense.

As for your previous question, I'm not quite sure what you're asking here. In General Relativity, the speed of light is always equal to c, as long as it's measured relative to the velocity of an observer at the location of the light beam. The only reason it might be something different if you're considering the speed of light far away is that subtracting speeds at different points in General Relativity is an invalid operation. Therefore any distant speed we talk about will be arbitrary.

 

[Chalnoth]

When you look at the geometry of space-time, there is no notion of change in that geometry. It's as if the entire history of the universe were laid out on a single sheet of paper. This isn't the way that we see time. We don't see the entire history laid out before us: we see moment by moment passing sequentially. And as such, we tend to think of space and time as being very different things: we think of our universe as expanding. But in terms of General Relativity, you might instead just say, "well, our universe has some space-time curvature of such and such character".

 

[rasp]

But it is perfectly possible to look at light (or even non-relativistic objects) traveling between far-away points at speeds that appear to exceed that of light.

and then
The only reason it might be something different if you're considering the speed of light far away is that subtracting speeds at different points in General Relativity is an invalid operation.

Are you saying 2 contradictory things here?

My question is very basic. Restated, I'm asking, Do the same physicists who envision a stretching of space also talk about a shrinking of time? And could that account for the appearance of light traveling at speeds greater than C between far away objects.

 

[Chalnoth]

Are you saying 2 contradictory things here?

No. I'm saying that relative speeds are only well-defined at a single point. That is, I can say how fast something is traveling past me in an unambiguous way. But I can't say how fast something is moving towards/away from me far away in an unambiguous way.

My question is very basic. Restated, I'm asking, Do the same physicists who envision a stretching of space also talk about a shrinking of time? And could that account for the appearance of light traveling at speeds greater than C between far away objects.

No, that doesn't make any sense to me.

 

[Chronos]

Ack, space and time are indivisible, one does not exist without the other. Its pi and the radius of a circle. Space without time is meaningless. The Ricci metric clearly illustrates this point. imo.