What is the nature of spacetime?

[tim9000]

Preface: I do sort of get that spacetime is a 4d geometry (time as like a different axis to space, that's not really something I'm concerned with)

I'm really trying hard to understand this...

It does not...

see above. Spacetime does not define the distance it is just a framework in which thing exist and have distance from each other.

I've heard it said that things moving at superluminal speed are explained as that they 'are not really moving, the space (Proper distance) between them is getting bigger'. I'm trying to reconcile that with what you're saying.

Now you are getting off int ether theory which was debunked a LONG time ago and is pretty much banned on PF. Space is not a medium.

Right, apologies. If the binary black-holes are spinning, how does spacetime take energy away from their orbit radius, if not as a medium? Also, what field in the standard model (something which I am new to) takes the energy and propagates the gravitational ripple?

As a warmup exercise, try thinking about the ordinary spatial geometry of a non-Euclidean surface like the surface of a 2-sphere (e.g., the surface of the Earth). A "straight path", i.e,. a geodesic, in this geometry is a great circle. Now, is this "re-defining" what a straight path is? "Re-defining" compared to what? Is it "making" distances between points be "different"? Different compared to what? The geometry just is what it is.

What I was getting at (I had galaxy lensing in mind) to put it in terms of your analogy would be like if you pushed your finger into the geometry of the sphere in the middle of the 'straight line' (the geodesic) as you depress the geometry, the straight line curves in and back out around your finger, but traveling along the geometry of the sphere its a straight line. since you've pushed your finger onto the sphere, (like the mass of a galaxy) it has been deformed, and so to travel along the straight line, the geometry re-defines that the straight line follows the depression of the sphere (geometry).

You're not fully grasping what "spacetime geometry" means.

Maybe not, but I hope that clarifies what I meant by 're-defining', and when I said 'changing' I meant strictly in the context of making galaxies further apart through expansion (space getting bigger).

A spacetime that contains gravitational waves has "ripples" in its geometry, yes. But the ripples aren't due to anything "changing"; they are just part of the spacetime geometry. Nothing has to "change" for the ripples to be there; the 4-dimensional spacetime geometry already contains within it all of the "ripples" over "time".

Right, so there is no standard model field propagating the ripples, the geometry is propagating the gravitational waves (and taking the energy away from orbits)...I need to ponder on this, trying to keep in mind that spacetime is not a 'medium'...hmm curvature with the absence of local mass, it's like the curvature is self-propagating ripples over time and space...
So say as the ripple passed through the reflector/detector, and it was some fraction the width of a hydrogen atom or nucleus, did this mean that if we were watching a single atom (I know you can't due to Heisenberg's uncertainty prin) but just for arguments sake, would that mean as the ripple passed through the atom that we were watching, we would have seen the actual width of the atom get smaller from our reference frame, because the space the atom was occupying got compressed as the ripple passed through it?

Much appreciated, thanks again

P.S. I know the analogy of galaxies as coins sprinkled through and embedded in the big rubber blob that is stretched from all sides to represent expansion is a fallacy, but I am struggling to understand expansion in any other (geometry) way.

 

[tim9000]

Another post script: I found what I was eluding to:
https://www.physicsforums.com/insights/balloon-analogy-good-bad-ugly/

It is only the 4th point that I have a problem understanding. I'm sure this is completely MY short-coming, but this 'metric expansion of space' seems oddly un-scientific, as we attribute observable effects to something un-measurable, I think I can accept a pure (GR) geometry, with no other properties. However I find it hard to picture this allowing for distinctly different types of distances, to be valid and permitting superluminal recession.

 

[phinds]

Another post script: I found what I was eluding to:
https://www.physicsforums.com/insights/balloon-analogy-good-bad-ugly/

It is only the 4th point that I have a problem understanding. I'm sure this is completely MY short-coming, but this 'metric expansion of space' seems oddly un-scientific, as we attribute observable effects to something un-measurable, I think I can accept a pure (GR) geometry, with no other properties. However I find it hard to picture this allowing for distinctly different types of distances, to be valid and permitting superluminal recession.

But in point of fact, what I said in the article is scientific and the opposite, being unsupported (and unsupportable) by empirical evidence, would be UNscientific.

If you think that distant galaxies are breaking the universal speed limit (in terms of proper motion) just because they have a high recession velocity, how do you think they are achieving the greater than infinite energy that this requires?

 

[PeterDonis]

if you pushed your finger into the geometry of the sphere

Yes, but this is not a good analogy, because spacetime does not get "pushed"; it doesn't get changed from a flat geometry to a curved geometry. It just is a curved geometry, because of the presence of matter and energy. The matter and energy can't be created or destroyed, so there is no physical meaning to the scenario you are imagining, of taking a flat spacetime geometry, adding some matter, and thereby "pushing" it into a curved shape. The flat geometry you imagine as being there before the "pushing" process does not exist; and what's more, there is no way of saying that a particular point in the curved geometry that actually exists corresponds to any particular point in some imaginary flat geometry that would have existed had the matter and energy not been there. The idea of such a flat geometry, although it seems intuitively plausible, has no physical meaning and is best avoided if you really want to understand the curved 4-d spacetime geometry.

it's like the curvature is self-propagating ripples over time and space...

This is one way of looking at it, yes--it has an obvious analogy to EM waves propagating through empty space.

However, there is also another way of looking at it. The 4-d spacetime geometry does not have to "propagate" anything; it just is. And if there is matter and energy in one region of that spacetime geometry, in a particular configuration, then the geometry in other regions will have "ripples" in it. Nothing has to "propagate"; it's all just a global solution of the Einstein Field Equation with particular geometric properties.

would that mean as the ripple passed through the atom that we were watching, we would have seen the actual width of the atom get smaller

How would you measure the "width" of the atom?

 

[tim9000]

I've been meaning to get back onto this thread for ages, and a couple of times I had written a partial reply, but before I could send it, my laptop would have to reset and I'd lose my progress.

If you think that distant galaxies are breaking the universal speed limit (in terms of proper motion) just because they have a high recession velocity, how do you think they are achieving the greater than infinite energy that this requires?

I'm [certainly] not saying that any of the science is wrong, I'm saying that it's my short-coming in that I can't understand how spacetime gives rise to these different types of movement (and distance). I'm sure they're not breaking the universal speed limit, I'm just trying to understand how they're not. As I posited earlier "it's like the geometry of spacetime is just constantly redefining how big space is, redefining the framework on/in which everything sits/exists (it is this far apart, now it is this far apart)" but someone said that wasn't a good way to think about it.

It just is a curved geometry, because of the presence of matter and energy.

I "understand" that the spatial geometry is not flat, in my head I was picturing that it was parabolic, like a sphere, but I'm aware it could be hyperbolic. Admittedly though I don't really understand how to picture this 4-D curved geometry in my head (I'd like to understand it better). Anyway my crude example was merely trying to discuss how I was picturing how Space can act as a magnifier lense to light traveling through it (in a straight line..."straight" being what spacetime says it is).

you imagine as being there before the "pushing" process does not exist; and what's more, there is no way of saying that a particular point in the curved geometry that actually exists corresponds to any particular point in

So...wouldn't you have to model the clumping of large masses as a sort of depression in (an already curved) Spacetime to get the gravitational lensing effect?

This is one way of looking at it, yes--it has an obvious analogy to EM waves propagating through empty space.

However, there is also another way of looking at it. The 4-d spacetime geometry does not have to "propagate" anything; it just is. And if there is matter and energy in one region of that spacetime geometry, in a particular configuration, then the geometry in other regions will have "ripples" in it. Nothing has to "propagate"; it's all just a global solution of the Einstein Field Equation with particular geometric properties.

This concept (that I don't get) of 'just is' seems to be starkly similar to what I'm trying to fathom regarding super-luminal movement. To me you're saying 'the spacetime geometry looks like this at this instant, then it looks like this the next instant' like if you roll a ball along the floor and say 'it is here, now it is here' like no link between it's journey, like the universe defined it's space and time to be here, then it redefined it's space and time to just be on the other side of the room' like a solution to a linear movement equation (I haven't delved into Einsteins filed equation yet).

How would you measure the "width" of the atom?

Just as a hypothetical for argument sake, that the current model would expect to happen to the Space/geometric framework in which the atom exists as the gravitational wave passed through it.There was a Vsauce video:
where he said [in so many words] that the Earth has a net shift in the background radiation, leading to the conclusion that the Earth is moving, but wouldn't the background radiation itself sort of be like the marker for the framework of where spacetime was at the 'big bang'? Like, if you were not shifted in any direction, you'd be 'stationary with respect to spacetime', or atleast the background radiation? (but from what I remember of Einstein there is no such thing)

Thanks

 

[phinds]

... To me you're saying 'the spacetime geometry looks like this at this instant, then it looks like this the next instant' like if you roll a ball along the floor and say 'it is here, now it is here' like no link between it's journey, like the universe defined it's space and time to be here, then it redefined it's space and time to just be on the other side of the room' like a solution to a linear movement equation

No, a movement equation implies proper motion. Cosmological expansion (recession) does not involve proper motion. You might find it helpful to see the description in the link in my signature, which builds up to the appropriate concept by starting with the "normal" balloon analogy but getting rid of the problems inherent in that analogy.

 

[tim9000]

Specific to that one point of my last post:

No, a movement equation implies proper motion. Cosmological expansion (recession) does not involve proper motion. You might find it helpful to see the description in the link in my signature, which builds up to the appropriate concept by starting with the "normal" balloon analogy but getting rid of the problems inherent in that analogy.

Yeah I did that some months ago. What I'm saying is that to me that 'fixed analogy' sounds like the loaf of bread with the things in it is baking over time forever, forever getting bigger, and what I'm saying is that the rising/baking of the bread itself is like a constant re-definition of the loaf. (thus the olives in the loaf haven't expanded any energy to be further away)

 

[phinds]

Specific to that one point of my last post:

Yeah I did that some months ago. What I'm saying is that to me that 'fixed analogy' sounds like the loaf of bread with the things in it is baking over time forever, forever getting bigger, and what I'm saying is that the rising/baking of the bread itself is like a constant re-definition of the loaf. (thus the olives in the loaf haven't expanded any energy to be further away)

OK, I see what you mean but that seems to me to be just a particular way of looking at expansion. In other words, you ARE, I think, seeing is as just geometry, which is what it is. The geometry of spacetime is changing with time in a way that carries things away from each other if they are not bound by gravitational or other forces and you are calling the change a "re-defiintion".

 

[bhobba]

What I'm saying is that to me that 'fixed analogy' sounds like the loaf of bread with the things in it is baking over time forever,

Forget analogies you read in popularizations - they confuse when thought about carefully enough because they are just meant to get across the flavor.

Here is what's going on. Locally - ie in a small region - you can find a region of space-time that is inertial ie particles move with constant velocity without any force. Its like a sphere - pick any small region and its like euclidean geometry. But overall it behaves a lot differently - continue lines they will meet etc etc. The same with GR - locally its very common-sense - overall you get strange behaviors like curved and expanding space-time that in everyday experience looks like a force between objects etc etc.

Thanks
Bill

 

[PeterDonis]

I don't really understand how to picture this 4-D curved geometry in my head

Nobody can picture a 4-D geometry in their head. The best anyone can do is to visualize lower dimensional analogues or projections. That's why we don't depend on visualization to solve problems in GR; we use math.

wouldn't you have to model the clumping of large masses as a sort of depression in (an already curved) Spacetime to get the gravitational lensing effect?

No. The spacetime is curved because of the presence of the masses; the masses don't add any curvature, they are the source of the curvature to begin with.

To me you're saying 'the spacetime geometry looks like this at this instant, then it looks like this the next instant'

No. I'm saying that what you are calling different "instants" are just different places in the same spacetime geometry. The spacetime geometry doesn't change; it already contains all the "instants".

I haven't delved into Einsteins filed equation yet

Then you're missing a lot of context. I recommend Sean Carroll's online lecture notes:

https://arxiv.org/abs/gr-qc/9712019

wouldn't the background radiation itself sort of be like the marker for the framework of where spacetime was at the 'big bang'

No. There is no such thing. You keep on thinking of spacetime as changing. Spacetime doesn't change. The spacetime geometry already contains all the information about "change" through the entire history of the universe; what you are thinking of as "change" is just different places in the same spacetime geometry. The Big Bang is a place in the spacetime geometry of the universe that is very far away from the place in that geometry where we on Earth today are; and the background radiation we are seeing today is in the same place in the geometry as we are, also very far away from the place in the geometry where the Big Bang is.

 

[PeterDonis]

What I'm saying is that to me that 'fixed analogy' sounds like the loaf of bread with the things in it is baking over time forever, forever getting bigger, and what I'm saying is that the rising/baking of the bread itself is like a constant re-definition of the loaf.

If you define the "loaf" this way, then the "loaf" is space, not spacetime.

 

[Jlister]

What about quantum fields & the rapid expansion at the beginning? Are we in a position to suggest what may have been the first quantum field or, were they all there from the start? Why the rapid expansion, something about strong nuclear forces?

The further we go back the greater the energy density, the heavier the particle to a maximum of the whole universe? So, initially there's no spacetime, then spacetime with a single universal quantum field, then two fields (universe & universe-1), etc...?

 

[PeterDonis]

Are we in a position to suggest what may have been the first quantum field or, were they all there from the start?

Quantum fields don't appear or disappear; they're everywhere in spacetime. The only question is what state they're in.

Why the rapid expansion, something about strong nuclear forces?

No. The rapid expansion was because at the end of inflation, a huge amount of energy got put into the Standard Model quantum fields--electrons, quarks, gauge bosons--so that they were at very high temperature, and they were expanding rapidly because inflation had caused everything to expand rapidly.

So, initially there's no spacetime, then spacetime with a single universal quantum field, then two fields (universe & universe-1), etc...?

No. Once more: spacetime doesn't change. There is only one spacetime describing the universe; that spacetime simply has different quantum field states at different places in the spacetime geometry.

 

[Jlister]

Quantum fields don't appear or disappear; they're everywhere in spacetime. The only question is what state they're in.

The state includes this & that particle at this & that time? Ah, plug in the time dimension to get which particle is where & which way it's going. The state doesn't change, the state is the state. Thee state; a universe is characterized by its state.

No. The rapid expansion was because at the end of inflation, a huge amount of energy got put into the Standard Model quantum fields--electrons, quarks, gauge bosons--so that they were at very high temperature, and they were expanding rapidly because inflation had caused everything to expand rapidly.

So, an initial inflation & *then* the superluminal expansion? All the while, the fields are there but, with a certain amount of energy given the state of evolution of ... space? When the energy currently in the electrons/quarks/gauge bosons (the mass of these particles) "arrived" there, the assumed quantum harmonic oscillators that make up these fields expanded, ostensibly? Would there be a commensurate cooling & hence shrinking of the previously energetic fields?

No. Once more: spacetime doesn't change. There is only one spacetime describing the universe; that spacetime simply has different quantum field states at different places in the spacetime geometry.

I added "time" to "space" just before i posted... important to keep these things straight.

 

[Dale]

To me you're saying 'the spacetime geometry looks like this at this instant, then it looks like this the next instant' like if you roll a ball along the floor and say 'it is here, now it is here' like no link between it's journey

Consider the shape of a trumpet https://goo.gl/images/WgdSjL

You could think of this as a circle (a 1D line which is a closed loop) whose circumference grows over time. You could also think of it as its own static 2D shape which has certain static features like a length, a surface area, certain symmetry, etc. which don't require you to view it as a series of circles.

 

[PeterDonis]

The state includes this & that particle at this & that time?

Yes.

an initial inflation & *then* the superluminal expansion?

What "superluminal expansion" are you talking about? If you mean the current expansion, it's only "superluminal" if you look at objects far enough apart and use coordinate speed in standard FRW coordinates, which has no physical meaning anyway.

All the while, the fields are there but, with a certain amount of energy given the state of evolution of ... space?

No, the Standard Model fields initially got their energy when it was transferred from the inflaton field at the end of inflation.

When the energy currently in the electrons/quarks/gauge bosons (the mass of these particles) "arrived" there, the assumed quantum harmonic oscillators that make up these fields expanded, ostensibly?

No. The quantum fields don't "expand"; they just have a state at each event in spacetime. The states of the SM fields at events in the region of spacetime just after the end of inflation are much higher energy than the states of the SM fields at events in the region of spacetime before the end of inflation.

I added "time" to "space" just before i posted... important to keep these things straight.

But you didn't. My comment applies to your post after you corrected it, not before. You are using the word "spacetime", but you're still thinking of it as space--as something that can "expand", "change", etc. That is what you need to fix.

 

[GeorgeDishman]

How do we know that spacetime is "there" and not just an "illusion" made by our brain?

If I have a clock ticking on my desk, I can watch the hands move round for a minute. You could sit opposite me with your own clock and watch yours do the same and a screen between us so we can only see our own clocks. In each case, the motion and even the "passing of time" might only be in my imagination. However, if we start together when one says "go" and put our hands after a minute has passed, they will go up together. What stops our hands going up at different times? They say "time flies when you're having fun" so if I enjoy the experiment more than you, my hand should go up before yours. That suggests both clocks are operated by a physical process which is some way depends on a common aspect of the universe in which we live, an objective measurable we call "time" which we share in the experiment by both clocks being at rest in a common inertial frame and at the same gravitational potential.

There are alternative explanations, your clock showing the time I imagine for example, but they rapidly become indistinguishable from pure solipsism in which "I think therefore I am" but my clock and yours, and in fact you and all the rest of the universe are only figments of my imagination.

There is another simpler argument too, if time is only in our imagination, how did the universe evolve from the hydrogen/helium primordial mix to permit life to exist if time is only imagined by lifeforms? All of this is getting very philosophical though.

 

[tim9000]

OK, I see what you mean but that seems to me to be just a particular way of looking at expansion. In other words, you ARE, I think, seeing is as just geometry, which is what it is. The geometry of spacetime is changing with time in a way that carries things away from each other if they are not bound by gravitational or other forces and you are calling the change a "re-defiintion".

I feel like I might finally be getting somewhere with communicating this difficult subject [for me as a layman]

Forget analogies you read in popularizations - they confuse when thought about carefully enough because they are just meant to get across the flavor.

Here is what's going on. Locally - ie in a small region - you can find a region of space-time that is inertial ie particles move with constant velocity without any force. Its like a sphere - pick any small region and its like euclidean geometry. But overall it behaves a lot differently - continue lines they will meet etc etc. The same with GR - locally its very common-sense - overall you get strange behaviors like curved and expanding space-time that in everyday experience looks like a force between objects etc etc.l

I appreciate that analogies are a double edged sword and this is the subject where they are least effective, but...
I understand you're saying that on the huge scale of the universe and galaxies spacetime looks very different do down here on little old Earth, but that doesn't explain that from our reference frame a galaxy is over there one minute, then over there the next. An ignorant caveman such as myself using merely his own two eyes [and a computer] would conclude that space/distance itself has grown, but that is not the case because space is itself merely a framework.

No. The spacetime is curved because of the presence of the masses; the masses don't add any curvature, they are the source of the curvature to begin with.
No. I'm saying that what you are calling different "instants" are just different places in the same spacetime geometry. The spacetime geometry doesn't change; it already contains all the "instants".
Then you're missing a lot of context. I recommend Sean Carroll's online lecture notes:

https://arxiv.org/abs/gr-qc/9712019
No. There is no such thing. You keep on thinking of spacetime as changing. Spacetime doesn't change. The spacetime geometry already contains all the information about "change" through the entire history of the universe; what you are thinking of as "change" is just different places in the same spacetime geometry. The Big Bang is a place in the spacetime geometry of the universe that is very far away from the place in that geometry where we on Earth today are; and the background radiation we are seeing today is in the same place in the geometry as we are, also very far away from the place in the geometry where the Big Bang is.

Thanks for the link.
Yeah I think I already knew what you were saying about curvature, then again maybe I was saying something wrong and I don't.
Say you pooled all the mass of the universe into some sort of uber-super-massive black hole, would there be the extreme curvature around/in it, then expanding out for ever the curvature of the universe would tend to be euclidian out at infinity?
I'm kind of uncomfortable with this 'spacetime' framework containing all the information of the universe, although I except that you may well be completely correct. But it just sounds like sort of an 'everything is predetermined' sort of thing, that would certainly give fuel to the argument that time is sort of an illusion. But yeah I don't know random quantum fluctuations - God playing dice, the big bang itself doesn't seem to [in my mind at least] fit with that model of existence...also with the heat death of the universe won't all that information be lost anyway...or I suppose the information is just spread infinitely thin until it just exists as a technicality.
Anyway back onto my original point and how you addressed it, taking it to what I infer is its logical conclusion: Space isn't actually getting bigger it kind of is already bigger, just not yet...fair comment?
Like if I took two billiard balls near each other on the table (representing galaxies) then moved them further apart (forgetting that I used energy to do so) and said the time it took to do so made up for the increase in space between them, like they're sort of interchangable sides of the same coin.

If you define the "loaf" this way, then the "loaf" is space, not spacetime.

Okay, the loaf is one axis, the other axis is the oven?
Much like expansion/inflation this thread has gotten away from me again, I'll have to get the the rest hopefully tomorrow.
CHeers!

P.S. Did anyone comment on that 'red shifting' sort of indicating a vector for the planet wrpt the cosmic background radiation? [possibly, I haven't read far ahead in the thread yet to know]

 

[PeterDonis]

that doesn't explain that from our reference frame a galaxy is over there one minute, then over there the next. An ignorant caveman such as myself using merely his own two eyes

You don't see galaxies "jump" from one place to another, discontinuously, with your own eyes. Nor do you see that with any actual measurements. Everything moves smoothly. You seem to be misinterpreting what our cosmological models actually say. They do not say that "space expansion" means things move discontinuously.

Say you pooled all the mass of the universe into some sort of uber-super-massive black hole

That is a different spacetime--a different solution of the Einstein Field Equation. It is not one that can describe the entire universe; it can only describe an isolated object within the universe, excluding the rest of the universe. So this question is not well-defined and doesn't have a meaningful answer.

it just sounds like sort of an 'everything is predetermined' sort of thing

Classical GR is a fully deterministic theory, so yes, "everything is predetermined" as far as GR models are concerned. But GR models don't capture everything about "reality". Our cosmological models based on GR only tell us the large-scale average structure of the universe. They certainly don't tell us every single event at every scale. Cosmology can't predict what you are going to do tomorrow.

I don't know random quantum fluctuations - God playing dice, the big bang itself doesn't seem to [in my mind at least] fit with that model of existence

That's because GR is not a quantum theory. Nor is it a theory of everything. You shouldn't expect it to explain everything.

Space isn't actually getting bigger it kind of is already bigger, just not yet...fair comment?

IMO no. Here is how I would put it: a spacelike slice taken through the observable universe that passes through the event of the Earth "now" has a larger volume than a spacelike slice taken through the same set of worldlines--the same "pieces of matter" that are in the spacelike slice through Earth "now"--at the end of inflation. Notice how I didn't use a single word implying change; I just described two different "slices" taken out of the geometry of spacetime and compared their volumes.

the loaf is one axis, the other axis is the oven?

I don't think this helps any. You need to think of spacetime as a thing, not as a process.

 

[GeorgeDishman]

Like if I took two billiard balls near each other on the table (representing galaxies) then moved them further apart (forgetting that I used energy to do so) and said the time it took to do so made up for the increase in space between them, like they're sort of interchangable sides of the same coin.

It might help to consider the difference between "space" and "spacetime". Objects last for some duration so can you think of two balls that start in contact for a short while then move apart through space as a function of time as being like a forked branch when visualised in spacetime?

 

[Mister T]

How do we know that spacetime is "there" and not just an "illusion" made by our brain?

I recommend you change that question to the following statement: Spacetime is a model made by our brain.

More generally, this is often a confusion. You're mixing up the model with the thing being modeled. The natural world is what it is. People make models in an attempt to understand it, predict it's behavior, and build stuff.

Once you sort this out in your mind you'll see that your question is based on a misconception. When you study physics you're studying the models, the construction of those models, the use of those models, and the connection between those models and the behavior of Nature.

 

[secur]

Hello tim9000,

The Principle of Relativity (POR) says there is no way to determine, experimentally, an absolute velocity or an absolute reference frame. So any observer can suppose, if he likes, that his own velocity is zero, in his own "rest frame". That led Einstein to dismiss the Newtonian concept of absolute space and time. He didn't actually say it didn't exist, rather it's meaningless scientifically, since we can never determine it. But let's not get into what exactly he did, or didn't, say - that's not important. The point is that in 1905, and still today, the POR holds. Only relative motion has meaning, not absolute.

But today there's a new wrinkle: the Cosmic Microwave Background, CMB. Its existence is not a "law of physics", but it happens - accidentally, as it were - to define a practical "rest frame" for the universe, against which we can compare our motion. It turns out, as you know, that our galaxy is moving through it at a moderate speed, much less than c.

Now, consider those distant galaxies which, naively, are receding from us at speeds approaching c. Standard cosmology says that there are more distant galaxies, receding even faster than light. How can this be, when c is a speed limit that nothing can surpass?

Here's the key fact. According to everything we know, at the location of those distant galaxies, they're moving through the CMB at speeds comparable to ours. So from their point of view, they're nowhere near the speed of light. From their point of view, we're the ones receding at an enormous speed.

The way to make sense of this is to accept that the CMB does, in practice, define an "absolute rest frame" of the universe. All galaxies are moving slowly by that standard. But spacetime itself is expanding. That's why very distant galaxies can recede faster than c, even though relative to their local space they're approximately stationary, just like us.

The speed-of-light limit applies only to our motion relative to local space. It has nothing to say about the expansion of spacetime. That expansion can be (much) faster than light speed.

This is just an intuitive picture, of course, but as such it's valid I believe. Study the FLRW solution of Einstein's field equations, and the physics related to the surface of last scattering (the origin of the CMB) for the exact situation.

 

[PeterDonis]

spacetime itself is expanding

No, space is expanding (at least, on the interpretation you are describing). Spacetime does not expand; it doesn't change. It just is.

 

[secur]

No, space is expanding (at least, on the interpretation you are describing). Spacetime does not expand; it doesn't change. It just is.

True. For something to expand it has to be changing in time, which "spacetime" can't do. In the "Block Universe" all times exist at once - although even the term "at once", or "simultaneously", implies an instant of time, which is not right.

But to say it "just is" implies it must be taken on faith, no further explanation possible - that also is not right. And it brings up Bill Clinton's objection: it depends what you mean by "is".

We don't really have the language to describe the situation; there's no substitute for the math.

Apart from that, don't you agree this is a sensible intuitive picture, getting across the basic idea?

 

[tionis]

I heard that space is doubling itself every some to the minus some every second. Is this true, and if it is, is there a difference between expanding and doubling? To me, expanding space is sort of like stretching and doubling is like exponential. Let me see if I can explain what I'm asking: suppose I take a region of space and I put it inside a geometrical shape, if space is doubling, then I should see the number of geometrical figures increase exponentially, whereas with expansion, I only observe one geometrical shape grow. Which is it?

 

[GeorgeDishman]

I heard that space is doubling itself every some to the minus some every second.

What you saw was talking about the cosmological effect called "inflation" which, if it is correct, finished around 10^-32s after some fiducial "start".

To me, expanding space is sort of like stretching and doubling is like exponential

If it expands by 100%, it has doubled, and if it expands by 100% in every period T, then the result is exponential so there isn't really a difference. If inflation is the correct model, then it doubled very rapidly during that period, perhaps doubling every 10^-34s.

Since inflation stopped, expansion has been much slower and at a variable rate so not exactly exponential. Currently distances are increasing on average by 1% roughly every 140 million years, 10.8 billion years ago it was 1% every 44 million years and in the far future the current indication is that it may settle to a constant value of 1% in about 175 million years.

 

[tionis]

Thanks, George. What I heard the professor say is that space is currently expanding by that amount every second. I think he was referring to dark energy. The difference in my mind is that two objects in the same cube of space I referred to earlier, separated by a distance, but without going outside the imaginary boundaries of said cube, would not grow apart if space was doubling itself because it would just duplicate itself around that cube as oppose to the cube growing in size which would then separate the two objects within. My understanding is that every second there is more space than before, so is this because space cannot occupy the same space of another piece of space and so it duplicate itself? Is all very confusing lol.

 

[PeterDonis]

don't you agree this is a sensible intuitive picture, getting across the basic idea?

Not really, since it leads to a number of common misunderstandings, some of which appear in this thread.

Which is it?

Neither, really. When people talk about "expansion of space", they are talking about a feature of a particular set of coordinates. The direct physical observable is redshift--we observe light from distant galaxies to be redshifted, and the redshift gets larger as the galaxies get further away from us (though the distance itself is not observed directly, we observe brightness and angular size and infer distance from that--the actual direct correlation is between redshift and brightness/angular size). The "expansion" is what we get when we put all this data into a model using FRW coordinates and look at coordinate distances as a function of coordinate time. None of this implies the things you are saying.

 

[tionis]

Neither, really.

Hi Peter. I found the video. The statement starts @ 31:15. Is the professor wrong?

 

[PeterDonis]

I found the video.

We're not talking about pop science interpretations. Yes, many pop science sources will talk about "space expanding". So will professors when they are trying to give analogies to lay people. But the actual physics is what I described.

Is the professor wrong?

He isn't "right" or "wrong". He's talking about an interpretation, not about the actual physics. He's not trying to give you an actual physical model that you can use to draw physical conclusions. He's just making an analogy for people who don't know the physical model and don't want one.

 

[tionis]

He isn't "right" or "wrong".

But Peter, he gave a very specific number for the doubling of space every 10^-35/s . Where did he pull this one from lol?

 

[PeterDonis]

he gave a very specific number for the doubling of space every 10^-35/s

First, he's talking about the inflationary epoch there. It has nothing to do with what's happening today.

Second, that number still describes a coordinate-dependent quantity, at least if you're going to use the phrase "doubling of space" to describe it. You have an equation in the model where the spatial scale factor is an exponential function of time. The number he gave is just the time constant in the exponential. But if you're looking for an actual physical invariant described by that number, it isn't "doubling of space"; the invariant is the rate at which comoving observers see other nearby comoving observers accelerating away from them (the technical definition is the expansion scalar of the congruence of comoving worldlines).

So the professor is right that the number he gave occurs in the model and has a specific technical meaning there. But he's neither right nor wrong, physically speaking, when he says that the number describes "doubling of space"; that's an interpretation, not the actual physics.

 

[tionis]

Awesome explanation. Thank you!

 

[secur]

Apart from that, don't you agree this is a sensible intuitive picture, getting across the basic idea?

Not really, since it leads to a number of common misunderstandings, some of which appear in this thread..

But any intuitive picture leads to misunderstandings. If it were exactly correct it wouldn't be an "intuitive picture", rather it would be "real physics". As you say, in this thread, there are a number of common misunderstandings due to pop-sci "intuitive pictures". That's unavoidable when teaching any complex subject. Leonard Susskind mentions somewhere that what you tell beginners must be a bit wrong; you can't nail it all down in the first hour. The goal is: by the end of the semester, make sure all those necessarily imprecise statements are corrected in the student's mind.

You can't reject an intuitive picture on the grounds that it isn't exactly right: none are. You could, on those grounds, refuse to give a beginner any intuitive idea at all, just throw them into the most difficult details, sink or swim. But that goes against basic and universal pedagogical practice.

Note that your assertion "spacetime just is" is also an intuitive picture. To say the past "is", or the future "is", is meaningless in the English language. Correct is: "the past was" and "the future will be". This is not just a quibble, and it's not just about grammar. In all human experience, only the present "is", not the past or future. When the student hears that statement, they get an intuitive picture which has some validity ("Block Universe") but strictly speaking makes no sense. It "leads to a number of common misunderstandings", to say the least. Does that mean it's no good? No. By the end of the semester they'll understand what you mean by this statement which is, prima facie, simply a grammatical error.

This pedagogical issue, although quite germane to this thread, is tricky. It demands expertise in theory of education, language, philosophy. So it's really not worth pursuing.

 

[cube137]

Not really, since it leads to a number of common misunderstandings, some of which appear in this thread.
Neither, really. When people talk about "expansion of space", they are talking about a feature of a particular set of coordinates. The direct physical observable is redshift--we observe light from distant galaxies to be redshifted, and the redshift gets larger as the galaxies get further away from us (though the distance itself is not observed directly, we observe brightness and angular size and infer distance from that--the actual direct correlation is between redshift and brightness/angular size). The "expansion" is what we get when we put all this data into a model using FRW coordinates and look at coordinate distances as a function of coordinate time. None of this implies the things you are saying.

The above is interesting description. So one can say space is really an illusion as we are only inferring from the brightness/angular sizes and redshifts and inferring "distance" from them as well as any expansion. This may be why quantum entanglement works and why space can be united with time because space is not what we think it is.. only an illusion. But then when we see a car moving in front of us. Can we say we only observe the other car sizes, colors and ours and infer spaces from that. Or is space only an illusion when referring only to redshift or Big Bang? How do you apply it to everyday spaces?