Undergrad Is there a physical explanation for the relationship between light and space?

[PeterDonis]

when the rock is still in hand it is accelerating "because of gravity"

I meant coordinate acceleration, not proper acceleration, but the point from your previous post that we should be more careful about specifying such things is valid.

There would always be some none zero tidal effect with such changes

With accurate enough measurements, yes, you could, for example, drop two rocks, one slightly above the other, and measure the change in their separation due to tidal gravity. But the point I was making is that this phenomenon is still different from "gravity" as "that which makes the rocks fall at all".

 

[Buckethead]

Yes, as I said above, this is a good approach. So from what you understand, what are the properties of spacetime (not space)? We have mentioned that motion is not one (unless you assume a conspiracy theory of physics). So what other properties have we mentioned here?

Uh-oh, a test! Well it seems spacetime is physical in nature and therefore I suppose you can contain it in a boundary using 4 dimensional points. It also seems you can measure the distance of that boundary using a laser, mirror, and proper time clock. It can expand and carry any object or photon with it as it does so. It can be curved and this is the same thing as tidal gravity, it is flat in the absence of gravity. It can rotate (Lense-Thirring effect or frame dragging) if it is near a rotating body that either surrounds it or is within it.
And most interestingly if it is rotating then any object stationary relative to it and not necessarily at its center, will feel no centrifugal force.

Did I pass?

One point that makes me squint is that I don't know why it is not also allowed to move. It seems motion is just one step beyond expansion. I understand that local tests (such as the MM test) have detected no motion and I get that, but what about motion between large sectors of space such as between galaxies? Is there anything in SR preventing that? And no, I'm not suggesting a spacetime made of "ponderable matter" as Einstein so eloquently puts it.

And as a P.S. when I say I like to visualize spacetime, the way I do so is to remember that if you hold an object stationary above the Earth it is accelerating through spacetime and if you let it go it immediately becomes an inertial frame in spacetime. I use this to stay grounded :)

 

[Buckethead]

That's roughly how fast Alpha Centauri is moving when it makes a full circle around your house in 24 hours. And before you reject that way of calculating Alpha Centauri's speed as ridiculous, consider that it is exactly how you calculate the speed of an aircraft that you see in the sky: distance to moving object times rate of change of angular position.

The point here is that we define speed as the rate of change of the position coordinates with respect to the time coordinate. If we use different coordinates we'll get different speeds, but none of that has any real physical significance.

OK, that makes sense. Thanks.

 

[PeterDonis]

it seems spacetime is physical in nature and therefore I suppose you can contain it in a boundary using 4 dimensional points

Um, what? I have no idea what you are proposing here. Where are you getting this from?

It also seems you can measure the distance of that boundary using a laser, mirror, and proper time clock.

Same response as above.

if it is rotating then any object stationary relative to it and not necessarily at its center, will feel no centrifugal force

Since this is obviously contradictory to observation, whatever model you are using is evidently wrong. But I still have no idea what model it is.

 

[Buckethead]

Excuse me, but why this is true? Solutions of EFE inside a spherically symmetric dense mass object produce spacetime with rotating geodesics where no acceleration is present.
Even in Newtonian mechanics inside a massive object where the acceleration is directly proportional to the distance R from its center and not the inverse of its squared distance. there is rotation without any acceleration felt!

Yes, but isn't that what I said when I said inertia is relative to a spacetime structure...even if that structure is within a rotating sphere!

 

[Buckethead]

Um, what? I have no idea what you are proposing here. Where are you getting this from?

I was extrapolating. Ooops. My logic is that if spacetime is physical in nature and since spacetime is a combination of 3 spatial coordinates and 1 time coordinate I was supposing that a point is spacetime could be identified by a 4 dimensional point. Not so I take it?

 

[PeterDonis]

I say I like to visualize spacetime, the way I do so is to remember that if you hold an object stationary above the Earth it is accelerating through spacetime

No, it isn't. It is experiencing proper acceleration, but it is not "accelerating through spacetime". There is no meaning to the latter idea.

 

[PeterDonis]

My logic is that if spacetime is physical in nature and since spacetime is a combination of 3 spatial coordinates and 1 time coordinate I was supposing that a point is spacetime could be identified by a 4 dimensional point.

That part is fine. But I don't see how you are getting from that to stuff about a "boundary".

 

[Buckethead]

That part is fine. But I don't see how you are getting from that to stuff about a "boundary".

If you draw a line between 2 of these spacetime points then would you have a line? If so what if you planted 4 points. Wouldn't you have some kind of spacetime tetrahedron? This is what I'm calling an object with a boundry.

 

[Buckethead]

No, it isn't. It is experiencing proper acceleration, but it is not "accelerating through spacetime". There is no meaning to the latter idea.

By proper acceleration do you mean proper acceleration through space?

 

[PeterDonis]

If you draw a line between 2 of these spacetime points then would you have a line? If so what if you planted 4 points. Wouldn't you have some kind of spacetime tetrahedron? This is what I'm calling an object with a boundry.

Drawing arbitrary lines doesn't make an object. There has to be something there. If the only thing there is spacetime itself, spacetime doesn't have any kind of boundary like you are describing.

By proper acceleration do you mean proper acceleration through space?

No, I mean proper acceleration that is measured by an accelerometer and felt as weight.

 

[John Morrell]

I think your line of thought with boundaries only really works if you can draw a boundary, the inside of which is space-time and the outside of which is not. That sounds to me like its related to the concept of the edge of the universe, though to be honest I don't have any knowledge about theoretical work done about that.

Space-time is not an object; you can't move it, what would it be moving relative to? You can't touch it, it's just a place-time. Using the word 'physical' makes me think that you are imagining that there is some true-er space that space-time is embedded within, which I don't believe we have any evidence of.

 

[Dale]

Uh-oh, a test! Well it seems spacetime is physical in nature and therefore I suppose you can contain it in a boundary using 4 dimensional points. It also seems you can measure the distance of that boundary using a laser, mirror, and proper time clock. It can expand and carry any object or photon with it as it does so. It can be curved and this is the same thing as tidal gravity, it is flat in the absence of gravity. It can rotate (Lense-Thirring effect or frame dragging) if it is near a rotating body that either surrounds it or is within it.
And most interestingly if it is rotating then any object stationary relative to it and not necessarily at its center, will feel no centrifugal force.

Very good. Now you are thinking about what properties it has. You are not completely correct on those properties but you are closer than most pop sci sources.

Spacetime has geometrical properties. In the language of Riemannian geometry it is a 4 dimensional pseudo-Riemannian manifold with signature (-+++). This means that it has an invariant notion of distance (known as the spacetime interval) and at each point there is one dimension of time (the - signature above) and three dimensions of space (the +++ signature). In local rectilinear coordinates the spacetime interval can be written $ds^2=-dt^2+dx^2+dy^2+dz^2$. From that you can obtain invariant notions of angles and curvature and related concepts. You can also define parallel transport, what it means for a line to be straight (geodesic), and how to take derivatives in the manifold.

Right now, that is just a bunch of terminology to you, but the bottom line is that spacetime has geometrical properties. Those properties are described by the math of Riemannian geometry.

One point that makes me squint is that I don't know why it is not also allowed to move

Because experiments designed to detect that motion have consistently not detected it. It is not that we arbitrarily said "no motion allowed", we did experiments and it seems that it doesn't move. Our model reflects that fact

 

[puzzled fish]

It can expand and carry any object or photon with it as it does so. It can be curved and this is the same thing as tidal gravity, it is flat in the absence of gravity. It can rotate (Lense-Thirring effect or frame dragging) if it is near a rotating body that either surrounds it or is within it.
And most interestingly if it is rotating then any object stationary relative to it and not necessarily at its center, will feel no centrifugal force.

As many have said before in their posts spacetime does not move. You accelerate or rotate relative to the distant galaxies and do not feel any force because your worldline is a geodesic through a given spacetime solution of the EFE equations. This is a manifold with a metric that underlies all its properties.
You do not have to go as far as exotic solutions like the Kerr metric to see this. The familiar Schwartzschild solution in the vacuum is enough. Satellites rotate around with respect to the the distant galaxies ( I do not use Earth here, because where Earth begins we have to use a different spacetime inside it) without any force or acceleration felt because their orbits are geodesics in the Schwartzschild vacuum spacetime solution.

 

[nitsuj]

I meant coordinate acceleration, not proper acceleration, but the point from your previous post that we should be more careful about specifying such things is valid.
With accurate enough measurements, yes, you could, for example, drop two rocks, one slightly above the other, and measure the change in their separation due to tidal gravity. But the point I was making is that this phenomenon is still different from "gravity" as "that which makes the rocks fall at all".

Mostly because of this forum and regularly accurate and insightful posters like you that I get to sometimes follow what's being discussed; thanks for that! :D

 

[nitsuj]

I don't know why it [space or spacetime?] is not also allowed to move. It seems motion is just one step beyond expansion.

what physical effect is there to see "it" move?

I haven't read much about it but have read somewhere on the forum that the term expansion as in the expansion of "space" is not intuitive.

Here is a link to the wiki on Hubble's law which IS the expansion of the universe. The is no talk of moving space, spacetime or anything of the sort. It also said "expansion of the universe is better called "Hubble Flow". I like that because it highlights that all is being done is making a measurement between points...the results are the results...there is nothing extra brought to the results such as saying the space is moving. One thing is for sure...large distances increase the Doppler effect on "light" over time. Note "light speed" is always invariant.

lol what the heck is a parsec?? Is it possible to get an intuition for that unit?

In other words if you observe space moving, you can say space moves. Given there only seems to be spacetime (not just 3d space alone) and it's geometric in nature the concept space moving doesn't make sense to me. That said when first learning about spacetime, I too imagined "space" as moving. The more learned the less that made sense.

 

[Herman Trivilino]

If you draw a line between 2 of these spacetime points then would you have a line?

I suggest you start there. Each point is an event, so think of an example of two events and plot them in spacetime. Then consider whether the interval between them is timelike, spacelike, or lightlike. And what that means for this line that you're using to connect those two points.

Physics is not some exercise in visualization and analogy. Those are just things people use to describe and learn the physics. Physics is about an understanding of Nature, so in this case think of two naturally-occurring events, how the points in spacetime represent those events, and what that line you've drawn represents about the behavior of natural objects. It's the behavior of those objects that's important, the physics is just a tool used to understand that behavior.

 

[Dale]

@Buckethead regarding boundaries, spacetime is modeled as a manifold, which requires that all boundaries be open. So if there is a boundary then it is not the kind of boundary that you can place a point on.

 

[Dale]

why we can't really say whether or not a distant galaxy is actually moving away from us at a given speed?

Sorry it took a while to get back to this, but it is an important point.

In spacetime geometry the velocity between two objects is a kind of angle. If two objects collide then their spacetime "worldlines" intersect at a single event and the angle of that intersection is easy to calculate.

However, if two worldlines don't intersect then in order to compare their velocity you have to move one vector to where the other is without turning it. This is called parallel transport.

It turns out that in flat spacetime parallel transport is independent of the path, but in curved spacetime it is not. Consider a sphere with a vector on the equator pointing north and another vector on the exact opposite side of the sphere also pointing north. If you parallel transport along the equator then you get the angle between them is 0, but if you parallel transport along longitude lines then you get 180 deg.

So in a curved spacetime there simply is no unambiguous way to compare the velocity of two distant objects.

 

[Buckethead]

@Buckethead regarding boundaries, spacetime is modeled as a manifold, which requires that all boundaries be open. So if there is a boundary then it is not the kind of boundary that you can place a point on.

In the same way that a small triangle can be defined on a globe for example (a Euclidean representation of a non-Euclidean manifold) can't we section off 4d spacetime into a 3d space the same way? This is an approximation, but still, doesn't it allow for a boundaried section of spacetime to be defined and to exist physically?

 

[Buckethead]

I suggest you start there. Each point is an event, so think of an example of two events and plot them in spacetime. Then consider whether the interval between them is timelike, spacelike, or lightlike. And what that means for this line that you're using to connect those two points.

This is interesting because I understand the timelike, spacelike, or lightlike relationship between the two dots and it makes me wonder about 4 equally spaced events in spacetime. One could say (tongue in cheek) this is a spacetime tetrahedron, but since the relationship between any two of those four points could be either timelike, spacelike, or lightlight, this "tetrahedron" would be a twisted time/space shape that could not be visualized. But could it still be said to be real and physical?

Physics is not some exercise in visualization and analogy. Those are just things people use to describe and learn the physics. Physics is about an understanding of Nature, so in this case think of two naturally-occurring events, how the points in spacetime represent those events, and what that line you've drawn represents about the behavior of natural objects. It's the behavior of those objects that's important, the physics is just a tool used to understand that behavior.

I clearly see what you are saying here, and I don't disagree. I suppose I use analogies to try and see if I can understand what possible direction the models are allowed to go since I do not have the talent to do it strictly through math (alas...).

 

[Dale]

In the same way that a small triangle can be defined on a globe for example (a Euclidean representation of a non-Euclidean manifold) can't we section off 4d spacetime into a 3d space the same way? This is an approximation, but still, doesn't it allow for a boundaried section of spacetime to be defined and to exist physically?

You are mixing up two separate things. One is the boundary and the other is a foliation. Sectioning off a 3D sub manifold is called foliation. The sub manifold is a manifold in its own right so it also has open boundaries.

 

[Herman Trivilino]

This is interesting because I understand the timelike, spacelike, or lightlike relationship between the two dots and it makes me wonder about 4 equally spaced events in spacetime.

Yes, but did you think about examples of two events? Like a fist hits a desk here, and hammer hits a nail there?

One could say (tongue in cheek) this is a spacetime tetrahedron, but since the relationship between any two of those four points could be either timelike, spacelike, or lightlight, this "tetrahedron" would be a twisted time/space shape that could not be visualized. But could it still be said to be real and physical?

I can easily imagine a square with points (0,0), (0,1), (1,0), and (1,1) where the first number is the one-dimensional space coordinate and the second number is the time coordinate. I plot those four points on a spacetime diagram and I have a square. I can think about actual events represented by each corner, that is where and when they occur. I can think about the set events that occur inside that square and the set of events that occur outside that square.

There's nothing particularly difficult or twisted about it.

I clearly see what you are saying here, and I don't disagree. I suppose I use analogies to try and see if I can understand what possible direction the models are allowed to go since I do not have the talent to do it strictly through math (alas...).

You're expending more effort to avoid the math than it's worth. And it's leading you astray. See above.

 

[Nugatory]

In the same way that a small triangle can be defined on a globe for example (a Euclidean representation of a non-Euclidean manifold)...

Yes, a small enough region of spacetime can always be considered flat with a three-dimensional Euclidean space embedded in it. (This is an approximation, but it gets better and better as the region in question gets smaller and smaller, so we can make the approximation arbitrarily good by considering a sufficiently small region of spacetime). However...
[/quote]can't we section off 4d spacetime into a 3d space the same way?...doesn't it allow for a boundaried section of spacetime to be defined and to exist physically?[/QUOTE]No. There are two concerns here. First, the division of the region into space and time is still frame-dependent (observer-dependent; coordinate-dependent). Different observers moving at different speeds relative to one another will make up their Euclidean subset out of different points in the region. It's easiest to see this if you consider that each observer's notion of space is "all the events that share the the same time coordinate", and this is inherently coordinate-dependent.

And second, all we've done is identified a mathematical relationship between the coordinates of points in that region of spacetime. There's no way of getting from there to "exist physically".

 

[Buckethead]

Yes, a small enough region of spacetime can always be considered flat with a three-dimensional Euclidean space embedded in it. (This is an approximation, but it gets better and better as the region in question gets smaller and smaller, so we can make the approximation arbitrarily good by considering a sufficiently small region of spacetime). However...

can't we section off 4d spacetime into a 3d space the same way?...doesn't it allow for a boundaried section of spacetime to be defined and to exist physically?

No. There are two concerns here. First, the division of the region into space and time is still frame-dependent (observer-dependent; coordinate-dependent). Different observers moving at different speeds relative to one another will make up their Euclidean subset out of different points in the region. It's easiest to see this if you consider that each observer's notion of space is "all the events that share the the same time coordinate", and this is inherently coordinate-dependent.

And second, all we've done is identified a mathematical relationship between the coordinates of points in that region of spacetime. There's no way of getting from there to "exist physically".

OK, I understand everything you've said here and it makes sense, It seems that even if spacetime we're physical any observer would simply see a distorted view of it compared to any other observer and because time is also part of the coordinate system, when it (or even each particular coordinate) exists would also be in question. However with regard to your second concern, there (in my mind) may still be indications of physical existence. The strongest example being the Lense-Thirring effect as described by Puzzled Fish above where you have a space surrounded by a thick sphere. It is my understanding that if you place stationary test point particles anywhere inside this sphere and you set this sphere spinning, the particles will begin to orbit the center without any forces being felt by the particles. This to me indicates the space inside the sphere is spinning and the particles are simply stationary relative to this space. This space would also be spinning relative to the space located outside the sphere (and far enough away as not to be influenced by it). Now I'm sure I'm missing something here as I'm paraphrasing what I learned elsewhere about the Lense-Thirring effect, but if what I'm saying is true, then wouldn't this be considered one physical space rotating relative to another physical space? Perhaps I'm suppose to replace my use of the word space with spacetime to make what I'm saying more accurate, and that could throw a wrench in the whole thing.

 

[nitsuj]

It maybe possible to call that Alcubierre drive thing a "moving" space, that's apparently possible with math from gr.

 

[Buckethead]

It maybe possible to call that Alcubierre drive thing a "moving" space, that's apparently possible with math from gr.

Yes! Thank you for that reminder. And in such a moving space where the ship is stationary relative to the spacetime warp, the ship experiences no acceleration.

 

[puzzled fish]

The strongest example being the Lense-Thirring effect as described by Puzzled Fish above where you have a space surrounded by a thick sphere. It is my understanding that if you place stationary test point particles anywhere inside this sphere and you set this sphere spinning, the particles will begin to orbit the center without any forces being felt by the particles. This to me indicates the space inside the sphere is spinning and the particles are simply stationary relative to this space. This space would also be spinning relative to the space located outside the sphere (and far enough away as not to be influenced by it). Now I'm sure I'm missing something here as I'm paraphrasing what I learned elsewhere about the Lense-Thirring effect, but if what I'm saying is true, then wouldn't this be considered one physical space rotating relative to another physical space? Perhaps I'm suppose to replace my use of the word space with spacetime to make what I'm saying more accurate, and that could throw a wrench in the whole thing.

No, no, puzzled fish didn't say that... The sphere, which is a planet or a star does not have to rotate. The planet has radius R and is homogeneous everywhere (density = constant). In Newtonian mechanics, you can put inside a disk of radius R with its center the center of the planet and rotate it with constant angular velocity, without any acceleration or forces noticed anywhere on the disk, because the "centrifugal force" anywhere on its surface matches the acceleration inside the planet which is directly proportional to r = distance from its center. Now the spacetime inside the Earth or Sun isn't like that and you cannot find such a disk, but for two points close enough this is a good analogy.
The same thing happens to a satellite when it rotates outside the Earth, there isn't any force, because its orbit is a geodesic in the Schwartschild solution of the Einstein Field Equations in the vacuum. The solution is called a metric and it has been explained before in this thread.
Acceleration force means only one thing: deviation from geodesic. Because you are not being exerted any forces upon on acceleration with regard to distant objects doesn't mean that space is moving with you: it only means that your worldline is a geodesic in a curved spacetime.

 

[Dale]

even if spacetime we're physical

Spacetime is physical. It has physically measurable geometric properties. It just doesn't have motion.

The strongest example being the Lense-Thirring effect

A spiral staircase also rotates without moving.

You need to understand that these experiments have been done. It isn't scientists saying space doesn't move, it is experiment saying space doesn't move and scientists finding models which match that experimental fact.

 

[Dale]

It maybe possible to call that Alcubierre drive thing a "moving" space, that's apparently possible with math from gr.

A shortcut doesn't have to move to get you to your destination sooner.