Can someone help a novice unbeliever?

[rasp]

I posted this last week and got no replies. Let me try again. What I am looking for is a basic understanding if the relativistic changes in time and space as described in SP lorentz contractions are useful in understanding the absolute expansion of space (whatever that may be)? Thanks!

Original Post --------------------------------------------------------------------------------

It seems to me that the expansion of space is a dynamic event different in principle then the relativistic events which are dealt with by the lorentz transformations. Have there been experiments to determine that it is only space that is expanding and not also a type of ongoing gravitational time dilation to explain the stretching (or redshift) of the wavelength of light?

For it would seem to me that if assume a metric of space expands while a metric of time remains the same, then c would increase as the sum of the function delta space/delta time.

Also, I know the lorentz transformations can be used for length contraction, but are they bidirectional? Can they be used to imply the observed length expansion of the universe from a particular coordinate system like the earth?

Finally, does the Minkowski spacetime invariant provide a preferred worldview for distance and time? Thanks!

 

[JesseM]

I posted this last week and got no replies. Let me try again. What I am looking for is a basic understanding if the relativistic changes in time and space as described in SP lorentz contractions are useful in understanding the absolute expansion of space (whatever that may be)?

The Lorentz transformation is specific to inertial reference frames in the "flat" spacetime of special relativity, while the "expansion of space" (and spacetime curvature due to gravity in general) requires the larger theory of general relativity, which only reduces to special relativity "locally" (when you zoom in on very small regions of curved spacetime). The speed of light is always c as measured in local inertial frames, but in non-local coordinate systems covering large regions of curved spacetime, the coordinate speed of light need not be c (in fact even in special relativity, if you pick a non-inertial coordinate system the coordinate speed of light can vary).

 

[rasp]

The Lorentz transformation is specific to inertial reference frames in the "flat" spacetime of special relativity, while the "expansion of space" (and spacetime curvature due to gravity in general) requires the larger theory of general relativity, which only reduces to special relativity "locally" (when you zoom in on very small regions of curved spacetime). The speed of light is always c as measured in local inertial frames, but in non-local coordinate systems covering large regions of curved spacetime, the coordinate speed of light need not be c (in fact even in special relativity, if you pick a non-inertial coordinate system the coordinate speed of light can vary).

OK, Thanks. Can you answer further
1) Does the quanta metric (i.e. the interval of space and time) (as opposed to the elapsed total distance of space or time between inertial frames, as described by lorentz) changes in GP due to gravity? and
2) is that what results in the change in the value of the speed of light?

 

[JesseM]

OK, Thanks. Can you answer further
1) Does the quanta metric (i.e. the interval of space and time) (as opposed to the elapsed total distance of space or time between inertial frames, as described by lorentz) changes in GP due to gravity?

Not sure what you mean. It doesn't really make sense to talk about the "total distance of space or time between inertial frames", since every inertial frame is just a coordinate system that fills all of spacetime in SR. The point of the Lorentz transformation is that if you know the position and time coordinates of a specific event in one frame, then the transformation can be used to find the position and time coordinates of the same event in another frame.

Also, what do you mean by "quanta metric"? In GR we just have the "metric" which can be used to find the time or distance along an arbitrary path through spacetime, like the time elapsed on the worldline of a particular object between two events on its worldline, as measured by a clock which moves along with it. The metric is indeed different in a spacetime which is curved by gravity than it is in the flat spacetime of SR, if that's what you're asking.

 

[PeterDonis]

You might find http://www.astro.ucla.edu/~wright/cosmo_01.htm" helpful in understanding how the cosmological coordinate system used in discussing the "expansion of space" relates to the frames used in special relativity.

 

[rasp]

Not sure what you mean. It doesn't really make sense to talk about the "total distance of space or time between inertial frames", since every inertial frame is just a coordinate system that fills all of spacetime in SR. The point of the Lorentz transformation is that if you know the position and time coordinates of a specific event in one frame, then the transformation can be used to find the position and time coordinates of the same event in another frame.

Also, what do you mean by "quanta metric"? In GR we just have the "metric" which can be used to find the time or distance along an arbitrary path through spacetime, like the time elapsed on the worldline of a particular object between two events on its worldline, as measured by a clock which moves along with it. The metric is indeed different in a spacetime which is curved by gravity than it is in the flat spacetime of SR, if that's what you're asking.

Sorry, for the confusion as I am not a physicist. What I mean, by a quanta of space or time is a hypothetical non-continuous interval, such as with mass or energy. I am specifically wondering how space can expand everywhere unless this hypothetical interval expands, or unless more intervals are dynamically created? Thanks

 

[rasp]

Or, not to be pig-headed and think that space and time are unrelated, I am open to a hypothesis that the explanation of cosmological space expansion is a result of the change in the speed of light or the dilation of time.

 

[JesseM]

Sorry, for the confusion as I am not a physicist. What I mean, by a quanta of space or time is a hypothetical non-continuous interval, such as with mass or energy. I am specifically wondering how space can expand everywhere unless this hypothetical interval expands, or unless more intervals are dynamically created? Thanks

Quantized spacetime isn't part of GR so your question can't be answered in the context of relativity. In a hypothetical quantum theory of gravity spacetime may be quantized, but if it were spacetime that was quantized rather than just space, then each quanta would presumably be very brief and I imagine there would be no issue of individual quanta needing to expand along with the universe, if you divided 4D spacetime into a series of 3D spacelike slices than the quanta making up each subsequent slice would be different from the previous one (I think something like this would be true in the spin foam approach to quantum gravity). This is just speculation though, since as I said there is no established theory of physics that includes quantized spacetime.

 

[rasp]

Quantized spacetime isn't part of GR so your question can't be answered in the context of relativity.

My apologies in advance if I am confusing the question with the wrong terms. But with your patience, let me try once more.

What is the working explanation for the expansion of cosmological space? Surely, it can not be as simple as "distance increases between objects when they move away from each other"?

The common literature speaks about the "stretching of space". This seems to imply a metric for space that is changing, and it's why I thought there had to be a relativistic effect to explain the change, i.e. every interval of space stretches from some measure to some new measure.

Does the changing speed of light in a cosmological setting imply changes to a basic metric of space and time? Or is the changing speed of light fully explained by identifying the geodesic path that light takes through a gravitationally induced curved spacetime?

 

[JesseM]

What is the working explanation for the expansion of cosmological space? Surely, it can not be as simple as "distance increases between objects when they move away from each other"?

The common literature speaks about the "stretching of space". This seems to imply a metric for space that is changing, and it's why I thought there had to be a relativistic effect to explain the change, i.e. every interval of space stretches from some measure to some new measure.

Fundamentally GR does not deal with a metric on space, but a metric on spacetime, which gives some notion of the "length" of arbitrary paths in spacetime, like the time along the timelike worldlines of actual objects, or the distance along spacelike paths (which cannot represent the path of any actual object because they'd represent an object moving faster than light in a local sense--each point on a spacelike path would lie outside the future light cone of other nearby points on the path). The Einstein field equations describe the relationship between the metric of spacetime and the distribution of matter and energy--how matter/energy curve spacetime. The field equations just describe the local relationship, so what physicists in GR look for are entire global "solutions" that satisfy the field equations everywhere.

In the case of cosmology, the simplest solutions for a universe filled with matter are different cases of the Friedmann–Lemaître–Robertson–Walker metric (FLRW metric for short). Again, these are entire 4D curved spacetimes, not descriptions of space expanding over time. But 4D curved spacetime can be sliced up into a series of 3D sections, something known as a "foliation". It's hard to visualize slicing up a 4D surface, but we can drop the number of spatial dimensions from 3 to 1 and then visualize a curved spacetime surface as a curved 2D surface where one dimension is space and one is time. Then the spacetime corresponding to an "expanding universe" could be something like the surface of a cone or an American football, and the foliation could consist of slicing it into circular cross-sections, with each cross-section further from the tip being larger than cross-sections closer to the tip (in the case of a football, the largest cross-section would be at the center and then cross-sections closer to the tip on the other side would get smaller again, analogous to a universe that expands from a Big Bang, reaches a maximum size, and shrinks again until it collapses in a Big Crunch, which is what you get if you plug a sufficiently high matter density into the FLRW metric). One point to realize is that for a given curved spacetime surface, the foliation is not unique--just as you can slice a cone into cross sections at different angles to get different-looking conic sections, so you can slice a 4D spacetime into a series of 3D cross-sections at different "angles" too and get different-looking spatial slices. So, in a given spacetime there is no unique truth about how space is changing over time, it depends on how you define "simultaneity" (which events at different points are defined to have happened at the same time-coordinate).

But with the FLRW spacetimes, there is a particularly simple type of foliation that cosmologists tend to use, one in which the 3D slices are what's called "hypersurfaces of homogeneity"--the 3D slices are chosen such that the matter in each slice is distributed in a perfectly uniform way, with a uniform density at every point. With such a foliation the distance between an arbitrary pair of particles of matter does continually increase over time (I believe you could define this distance in any given 3D slice in terms the shortest spacelike path between particles that is confined to that slice), and the local density of matter continually decreases. So, this is basically where the notion of the "expansion of space" comes from. But this idea isn't really fundamental, what's fundamental is that these are curved 4D spacetime solutions which satisfy the Einstein field equations at every point. For some criticisms of the whole language of "expanding space", see this paper which was discussed on this thread, along with this paper as well.

Does the changing speed of light in a cosmological setting imply changes to a basic metric of space and time? Or is the changing speed of light fully explained by identifying the geodesic path that light takes through a gravitationally induced curved spacetime?

Again, GR only says that light moves at c in a local sense, in the locally inertial frame of an observer right next to the light at any given point on its worldline. Even in flat SR spacetime there is no requirement that light move at c in a non-inertial coordinate system (and all global coordinate systems in curved spacetime will be non-inertial), so this doesn't really depend in any specific way on the metric. It might even be possible to find a coordinate system in a FLRW spacetime where light does continue to have a coordinate speed of c everywhere, just as you can do with Kruskal-Szekeres coordinates in the curved spacetime around a nonrotating black hole (which I discussed on this recent thread).

 

[rasp]

Fundamentally GR does not deal with a metric on space, but a metric on spacetime ...then the spacetime corresponding to an "expanding universe" could be something like the surface of a cone or an American football, and the foliation...called "hypersurfaces of homogeneity"--the distance between an arbitrary pair of particles of matter does continually increase over time (I believe you could define this distance in any given 3D slice in terms the shortest spacelike path between particles that is confined to that slice), and the local density of matter continually decreases. So, this is basically where the notion of the "expansion of space" comes from. But this idea isn't really fundamental, what's fundamental is that these are curved 4D spacetime solutions which satisfy the Einstein field equations at every point. For some criticisms of the whole language of "expanding space", see this paper which was discussed on this thread, along with this paper as well.

Jesse, thanks for your detailed answer and the references to the thread and papers, which describe a question very similar to mine. All have been helpful. But the answers are only satisfactory as particular solutions to particular equations and are difficult to relate to conceptually.

I fear that physicists will never again provide a logical conceptual framework, but will revel in their own making of mathematical models unrelated even to their own conception of reality. There will be those who speak of reality through math, and then the others, we poor souls who must either accept or reject, but will never understand.