B What is the nature of spacetime?

[tim9000]

I've been trying to learn about cosmological expansion (some weeks ago), I think I understand as much as any lay-person could, regarding why everything is moving away from our galaxy. However I still don't understand what spacetime is. The fact that space can deform indicates to me that spacetime is not not a metaphysical thing, but something that has tangible, observable properties. Such as in observing closer galaxies lens more distant galaxies, or that the Alcubierre drive is theoretically possible...or moreover that a 'big rip' could tear the electrons from atomic nuclei, if expansion accelerates.
So if the space part of spacetime itself is getting bigger, and for the aforementioned reasons space is presumably more than just a vacuum of quantum mechanical fluctuations (with various standard model fields in it). Then does humanity actually know what spacetime is, or is it still more or less a mystery?

Thank youP.S. I forgot, of course gravitational waves.

 

[phinds]

Spacetime is a framework in which things happen. It is geometry. It is NOT a "fabric" or other pop-science nonsense. Expansion is just things getting farther apart, not space "stretching" or "expanding". The "big rip" is not in the cards based on our current understanding of cosmology and even if it were that would not make spacetime anything other than a framework. Light does not get "bent" when it passes a massive object, it follows a straight line, BUT ... that "straight line" is in Riemann Geometry (which describes spacetime) not Euclidean Geometry which is why it is described as "bent" from a human point of view.

 

[FactChecker]

There is a trade-off between a person going through time and the same person going through space (at a fast speed). To understand that, time and space need to be put into the same coordinate system. It is similar to the trade-off that a person traveling at a constant speed in two physical dimensions. Suppose a person is traveling at a constant 50 miles per hour. If he goes North at 50 mph, then you know he is not going East or West at all. Likewise if he is going East at 50 mph, you know he is not going North or South at all. In space-time we are always going at the speed of light. If we go at the speed of light in physical space, then you know that we are not moving in time at all. Likewise, if we go full speed in time, then you know we are not moving in physical space at all.

Far from metaphysical, the distortion of space-time is very real. It explains gravity. Einstein's General Relativity is all about that. That is about as "down-to-Earth" as you can get. (Pun intended.)

 

[Dale]

I still don't understand what spacetime is. The fact that space can deform indicates to me that spacetime is not not a metaphysical thing

In science a thing is identified with its measurable properties. So an electron is a thing with a certain combination of measurable properties including mass, spin, and charge.

Spacetime is the thing with measurable properties known collectively as the metric. It includes all of the normal spatial geometry (distance, angles, curvature) as well as similar concepts for time (duration, relative velocity)

 

[bhobba]

However I still don't understand what spacetime is.

Due to the symmetry properties of space and time as measured using rulers, clocks or whatever, its turns out its like space by itself - it can in a sense be 'rotated' so you can't consider them separate. If you have a stick and you can't get it through a door you can rotate it to get it through. The same with space and time.

Here is the technical detail:
http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf

Length contraction, time dilation etc is just like rotating a rod to go through a door - except its 'hyperbolic' rotation.

Thanks
Bill

 

[tim9000]

Spacetime is a framework in which things happen. It is geometry. It is NOT a "fabric" or other pop-science nonsense. Expansion is just things getting farther apart, not space "stretching" or "expanding". The "big rip" is not in the cards based on our current understanding of cosmology and even if it were that would not make spacetime anything other than a framework. Light does not get "bent" when it passes a massive object, it follows a straight line, BUT ... that "straight line" is in Riemann Geometry (which describes spacetime) not Euclidean Geometry which is why it is described as "bent" from a human point of view.

H'mm, yeah I see how light can bend around a galaxy, yet still be traveling 'straight', due to spacetime being a curvature of the geometry itself.
However, (and I don't mean to irritate, but) it is the other implications of proper distances getting bigger (over "time"?) or possibly in a big rip scenario tearing electrons from nucleus. I understand how that sentence is true, just not like how can this 'geometry' becomes this fabric of creation that is tangible with real consequences. And is presumably has properties as I address in my response to Dale below.

There is a trade-off between a person going through time and the same person going through space (at a fast speed). To understand that, time and space need to be put into the same coordinate system. It is similar to the trade-off that a person traveling at a constant speed in two physical dimensions. Suppose a person is traveling at a constant 50 miles per hour. If he goes North at 50 mph, then you know he is not going East or West at all. Likewise if he is going East at 50 mph, you know he is not going North or South at all. In space-time we are always going at the speed of light. If we go at the speed of light in physical space, then you know that we are not moving in time at all. Likewise, if we go full speed in time, then you know we are not moving in physical space at all.

Far from metaphysical, the distortion of space-time is very real. It explains gravity. Einstein's General Relativity is all about that. That is about as "down-to-Earth" as you can get. (Pun intended.)

That is actually a really good way of putting it, nice sort of vector-ie way of putting it.

Spacetime is the thing with measurable properties known collectively as the metric. It includes all of the normal spatial geometry (distance, angles, curvature) as well as similar concepts for time (duration, relative velocity)

I sort of understand that, how would you define it? I understand that is has these quantum fluctuations (creation and destruction of particles spontaneously, really fast) as well as these fields through it (Higgs, electromagnetic...and others? Sorry, what are they?)
I'm trying to get my head around the QED and QCD vacuum wiki pages.
Presumably these quantum fields in the standard model are are of this spacetime geometry, I.e. when the light travels around a galaxy, the electromagnetic field is distorted by the mass of the galaxy it passes around so that 'straight' from the perspective of the light or the EM field is around the galaxy?Thanks all!

 

[Dale]

I understand that is has these quantum fluctuations (creation and destruction of particles spontaneously, really fast) as well as these fields through it (Higgs, electromagnetic...and others? Sorry, what are they?)
I'm trying to get my head around the QED and QCD vacuum wiki pages.
Presumably these quantum fields in the standard model are are of this spacetime geometry, I.e. when the light travels around a galaxy, the electromagnetic field is distorted by the mass of the galaxy it passes around so that 'straight' from the perspective of the light or the EM field is around the galaxy?

GR is a classical (non quantum) theory. None of this is going to help you understand GR.

 

[pervect]

I've been trying to learn about cosmological expansion (some weeks ago), I think I understand as much as any lay-person could, regarding why everything is moving away from our galaxy. However I still don't understand what spacetime is. The fact that space can deform indicates to me that spacetime is not not a metaphysical thing, but something that has tangible, observable properties. Such as in observing closer galaxies lens more distant galaxies, or that the Alcubierre drive is theoretically possible...or moreover that a 'big rip' could tear the electrons from atomic nuclei, if expansion accelerates.
So if the space part of spacetime itself is getting bigger, and for the aforementioned reasons space is presumably more than just a vacuum of quantum mechanical fluctuations (with various standard model fields in it). Then does humanity actually know what spacetime is, or is it still more or less a mystery?

Thank youP.S. I forgot, of course gravitational waves.

I would say that the fundamental observable phenomenon of space-time is the ability to measure distances, and time intervals. You can pretty much regard this as being done with rulers, and clocks. If you wax philosophical, you can probably agonize a lot over what a ruler and a clock really is. As far as science goes, we have an operational procedure based on the SI standard for measuring both.

I can dig up a quote for the "SI meter" and the "SI second" definition if one is needed, but it should be easy to find.

Space time is geometry, and we can regard geometry as the study of distances. Angles a a part of geometry, but if we have distances, we can compasses drawing circles, and we can imagine measuring distances along the arcs of these circles, and those define angles, so we can define angles in terms of distances. Thus we don't need to regard geometry as being about angles and distances, since we can define angles in terms of distance. We can regard geometry as being fundamentally about distances.

It's helpful to introduce the concept of coordinates to talk about geometry, though not strictly necessary. Since it's not strictly necessary, I will avoid it for now.

Space-time geometry takes a rather funny turn, in that there turns out not to be two separate sorts of distances (spatial distances and time distances, usually referred to as time intervals), but only one sort of "distance", an observer independent interval known at the Lorentz interval. The relationship between the Lorentz interval and the SI concepts of time interval and distance is one of the topics of special relativity, and the reason that we view space-time as a single unified entity rather than two separate concepts of space and time.

But you can compute the space-time interval knowing only how to measure distances and time intervals. So if you understand distances and time intervals, you have the tools needed to understand the Lorentz interval.

There are some tricky aspects about distance that I've glossed over, but the main point I'm trying to make is that you can regard space-time as being all about distances, and that we have operational procedures for measuring distance via instruments we call rulers and clocks.

 

[FactChecker]

That is actually a really good way of putting it, nice sort of vector-ie way of putting it.

If you like that way of explaining relativity, I highly recommend the book "Relativity Visualized" by Lewis Epstein. I got that idea from his book. I really enjoyed reading it.

 

[PeterDonis]

or that the Alcubierre drive is theoretically possible

"Theoretically possible" in the sense that it is a valid mathematical solution of the Einstein Field Equation, yes. But it is a solution that in all probability does not describe an actual physically possible state of affairs. The examples of gravitational lensing and gravitational waves are better since we know they actually happen.

 

[Narasoma]

Spacetime is the thing with measurable properties known collectively as the metric. It includes all of the normal spatial geometry (distance, angles, curvature) as well as similar concepts for time (duration, relative velocity)

How do we know that spacetime is "there" and not just an "illusion" made by our brain? I mean, we "see" things, but we don't actually "see" the spacetime itself. While metric is just a mathematical property of a spacetime model, i.e. differentiable manifold. By the way, is it possible to make a model of the spacetime using some mathematical objects other than a differentiable manifold, or, more generally a topological space?

 

[jbriggs444]

How do we know that spacetime is "there" and not just an "illusion" made by our brain? I mean, we "see" things, but we don't actually "see" the spacetime itself.

What difference does it make?

 

[FactChecker]

How do we know that spacetime is "there" and not just an "illusion" made by our brain? I mean, we "see" things, but we don't actually "see" the spacetime itself. While metric is just a mathematical property of a spacetime model, i.e. differentiable manifold. By the way, is it possible to make a model of the spacetime using some mathematical objects other than a differentiable manifold, or, more generally a topological space?

"spacetime" is the idea that explains the time and distance measurements that we observe in the universe and in physics experiments. If we ignore measurements, what is left to be called "knowledge"?

 

[Narasoma]

What difference does it make?

Of course, something which is "there" is different from something which is the result of our conception. However, whether that difference has a significant physical effect or not, I don't know.

 

[Dale]

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

I am with jbriggs444 on this. This question and its answer don't matter. Whether it is all in our head or not we have a theory which accurately predicts the outcome of measurements involving clocks and rulers.

 

[Narasoma]

"spacetime" is the idea that explains the time and distance measurements that we observe in the universe and in physics experiments. If we ignore measurements, what is left to be called "knowledge"?

Is there any way to formulate a measurement other than using metric?
(But this is just a restriction to my earlier question)

 

[Narasoma]

I am with jbriggs444 on this. This question and its answer don't matter. Whether it is all in our head or not we have a theory which accurately predicts the outcome of measurements involving clocks and rulers.

Maybe it's just a matter of philosophy. But to me it's still bothering.

 

[FactChecker]

Is there any way to formulate a measurement other than using metric?
(But this is just a restriction to my earlier question)

It's important to understand that the distortions of space and time measurements apply to ANY method of measurement: the aging of a human, the vibrations of atoms, the time for Mercury to orbit the Sun. It means that we can take an atomic clock to the top of a mountain and it will have run faster when we bring it down and compare it with a lower-altitude clock. The distortion also explains gravity. That is in Einstein's general theory. So it is not just an intellectual mind-game.

 

[Narasoma]

It's important to understand that the distortions of space and time measurements apply to ANY method of measurement: the aging of a human, the vibrations of atoms, the time for Mercury to orbit the Sun. It means that we can take an atomic clock to the top of a mountain and it will have run faster when we bring it down and compare it with a lower-altitude clock. The distortion also explains gravity. That is in Einstein's general theory. So it is not just an intellectual mind-game.

Hm, this is getting further from my question whether we can make a model for spacetime other than using differentiable manifolds. In our solar system scale, GR gave a very accurate prediction. However, there still some mysteries out there, dark matter and dark energy for example. We say that there is a dark matter and dark energy is because we keep GR the way it is, or in other words, we keep a differentiable manifold as our model of the spacetime.

 

[phinds]

Hm, this is getting further from my question whether we can make a model for spacetime other than using differentiable manifolds. In our solar system scale, GR gave a very accurate prediction. However, there still some mysteries out there, dark matter and dark energy for example. We say that there is a dark matter and dark energy is because we keep GR the way it is, or in other words, we keep a differentiable manifold as our model of the spacetime.

I don't think dark matter has anything to do with GR. Am I missing something?

 

[Ibix]

I don't think dark matter has anything to do with GR. Am I missing something?

I think one has to posit something like dark matter to make GR consistent with the observed rotational profile of galaxies. However, to address what I suspect is narasoma's point, that doesn't mean that we didn't consider modifying GR rather than proposing a new kind of matter. It's just that the modified gravity theories haven't panned out and there is increasing indirect evidence for a kind of matter we haven't seen directly yet.

 

[phinds]

I think one has to posit something like dark matter to make GR consistent with the observed rotational profile of galaxies.

But wouldn't the same be true for Newtonian mechanics? In fact, wasn't it an application of Newtonian mechanics to the rotational speed that led to the realization of dark matter? My point being that dark matter per se isn't needed for GR it's just that there is something (that we call dark matter) that affects the rotational speeds and the flatness or near-flatness of the universe. I may just be tying myself in a knot w/ definitions here.

 

[Ibix]

But wouldn't the same be true for Newtonian mechanics? In fact, wasn't it an application of Newtonian mechanics to the rotational speed that led to the realization of dark matter? My point being that dark matter per se isn't needed for GR it's just that there is something (that we call dark matter) that affects the rotational speeds and the flatness or near-flatness of the universe. I may just be tying myself in a knot w/ definitions here.

I see what you're getting at. I think we're talking slightly at cross purposes. I agree that you don't need dark matter to make GR work, but you do need some invisible source of gravity to make it describe galaxies correctly. I was interpreting the question as "why do we add dark matter instead of thinking of revising GR", the answer to which is that we did try revising gravity (Newtonian gravity - you are right) but couldn't make it work, especially in light of more recent observations. Subject to the usual "all science is our current best guess" caveats, of course.

 

[Narasoma]

I don't think dark matter has anything to do with GR. Am I missing something?

Fact : We "saw" ordinary matter acted strangely
Conclusion : We said that there is "something" caused that strangeness.

But this conclusion has been taken because of keeping GR in mind. My question is if we formulate spacetime and its dynamic using mathematical objects other than differentiable manifold, maybe we didn't see dark matter or dark energy again. But this is just my brute force imagination.

 

[PeterDonis]

if we formulate spacetime and its dynamic using mathematical objects other than differentiable manifold

Can you give specific examples of theories along these lines that are being investigated? We can't discuss personal speculations.

 

[Ibix]

But this conclusion has been taken because of keeping GR in mind. My question is if we formulate spacetime and its dynamic using mathematical objects other than differentiable manifold, maybe we didn't see dark matter or dark energy again. But this is just my brute force imagination.

That's kind of the point I was making. We have considered alternatives (e.g. MOND: https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics), and the wiki article links to papers as recent as 2012 on the subject. But my understanding is that unmodified GR plus dark matter is generally considered to be the better hypothesis given our current state of knowledge.

 

[Dale]

this is getting further from my question whether we can make a model for spacetime other than using differentiable manifolds

If that was your question then you should have worded it this way, not is it "an 'illusion' made by our brain". That overly provocative wording completely obscured this intention.

I am almost certain that we can make a different mathematical model. Generally it is possible to make many different models that are mathematically equivalent. Like Newtonian and Lagrangian mechanics.

However, those would just be considered different formulations of the same theory, not a new theory. It would still be GR unless it led to different predictions.

 

[PeterDonis]

We have considered alternatives

MOND still models spacetime as a differentiable manifold. Narasoma is talking about not using a manifold structure at all.

 

[PeterDonis]

Generally it is possible to make many different models that are mathematically equivalent. Like Newtonian and Lagrangian mechanics.

Both of those use differentiable manifolds to model spacetime. That's a big part of why they can be shown to be mathematically equivalent. Showing mathematical equivalency between a model that uses a differentiable manifold and a model that doesn't is a much taller order.

 

[Narasoma]

If that was your question then you should have worded it this way, not is it "an 'illusion' made by our brain". That overly provocative wording completely obscured this intention.

I am almost certain that we can make a different mathematical model. Generally it is possible to make many different models that are mathematically equivalent. Like Newtonian and Lagrangian mechanics.

However, those would just be considered different formulations of the same theory, not a new theory. It would still be GR unless it led to different predictions.

So, you mean that if we want to build a new theory, it is not enough just by changing of our "modelisation"?
I haven't considered that.

 

[Dale]

So, you mean that if we want to build a new theory, it is not enough just by changing of our "modelisation"?
I haven't considered that.

Yes. It is not universally divided this way but in my understanding the usual division is that different theories make different experimental predictions. If they make the same experimental predictions but have different philosophical viewpoints then they are different interpretations. If they make the same predictions and have the same philosophy but have different math then they are different formulations.

 

[Herman Trivilino]

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

Would you ask that same question of time? Of space?

 

[tim9000]

Hi all,

Spacetime is a framework in which things happen. It is geometry. It is NOT a "fabric..."

I've re-read the thread trying to keep in mind that 'spacetime not a fabric'.

Disclaimer: I only just looked up what Modified Newtonian dynamics and differentiable manifolds WERE. In-fact I only learned SR and am quite new to GR.

I've had a bit more of a think on what you said like the geometry of spacetime is 're-defining' what direction a straight path is.
Unfortunately despite your best efforts, I'm still struggling.
I would get that a fabric containing things could stretch, but you said it was merely a geometry.
How can a mere frame-work actually make things be more distant? It's like spacetime is constantly re-defining how big the distance between distant objects is. I understand that mass tells spacetime how to curve, but It's like spacetime is a sort of definition frame-work for the universe, to tell matter how to move, yet as seen in expansion, its not just like spacetime is a passive definition, spacetime is itself actively re-defining how far things are apart, like actively changing.

To harp on about this again: 'gravity waves', aren't they a ripple in the "geometry" of spacetime? To me it seems like this geometry which is sort of the passive instruction set for telling matter about space and time, is actually acting like a physical medium.

the "SI meter" and the "SI second..."

Admittedly I'm still yet to get a chance to read through the derivation of the Lorentz transformation.
As I said I am no expert on GR. Isn't the definition of a second based on a cesium atom, but I'm not sure if that is a valid standard throughout reality? Like which frame of reference to look at the atom is objectively the one...from the reference of the atom itself...but then you can't measure anything outside that frame using the atom...I struggle with this sort of time (and to a much lesser extent 'space') is in the eye of the beholder thing...I would like to have a more developed perspective, I am just woefully ignorant of things outside my field.

Thanks in advance for any more thoughts, (and everyone's patience).

 

[phinds]

How can a mere frame-work actually make things be more distant?

It does not, any more than it makes a spacecraft move from Earth to the moon or it makes you get farther from home when you walk down to the corner store. Things cosmological move apart for two reasons. I recommend the link in my signature. You move from your home to the corner store because your legs expend energy.

It's like spacetime is constantly re-defining how big the distance between distant objects is.

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

I understand that mass tells spacetime how to curve, but It's like spacetime is a sort of definition frame-work for the universe, to tell matter how to move, yet as seen in expansion, its not just like spacetime is a passive definition, spacetime is itself actively re-defining how far things are apart, like actively changing.

Don't know how you get to that but it has an element of truth although I think not in the way you are seeing it. If an asteroid moves close enough to Earth to be attracted by our gravity and fall to Earth, then according to GR, it IS spacetime that causes it to move to Earth, but it is the mass of Earth that "tells" spacetime to make that happen by making a "straight" line head for Earth.

To harp on about this again: 'gravity waves', aren't they a ripple in the "geometry" of spacetime? To me it seems like this geometry which is sort of the passive instruction set for telling matter about space and time, is actually acting like a physical medium.

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.

 

[PeterDonis]

I've had a bit more of a think on what you said like the geometry of spacetime is 're-defining' what direction a straight path is.

...

How can a mere frame-work actually make things be more distant?

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.

It's like spacetime is constantly re-defining how big the distance between distant objects is.

You're not fully grasping what "spacetime geometry" means. "Time" is one of the dimensions of spacetime. Spacetime doesn't "change" things; distances don't "change" in spacetime. The spacetime of our universe just has a 4-dimensional geometry with a particular curvature, and particular curves within that geometry are related in particular ways. The 4-dimensional spacetime geometry already contains within it all the "distance" relationships over "time"; nothing has to "change".

To harp on about this again: 'gravity waves', aren't they a ripple in the "geometry" of spacetime?

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".

 

[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.