Does space have a velocity in spacetime?

[eaglechief]

Hello, i try to find some opinions on these points

a) If a brane action in a bulk is defined, in that case, that a brane is modelwise moving through a bulk, how is this ratio defined? Is this a regular "velocity" in that meaning, that space is being passed in a period of time?

b) If a 4D-Einstein-Spacetime is chosen, where space itself is a slice cut through spacetime, how can the ratio, with which the space is moving through time, be defined? I suppose a "space per time" fails due to it is more a "time per X", but what is X?

Thanks in advance for answers.

 

[PeterDonis]

how is this ratio defined?

I'm not sure exactly what you're referring to. Do you have a specific reference that we can use as a baseline for discussion?

Is this a regular "velocity" in that meaning, that space is being passed in a period of time?

I don't think so, by analogy with the GR case--see below.

how can the ratio, with which the space is moving through time, be defined?

It can't. Spacetime is not something that "space moves through". Slicing a spacetime into spacelike slices is just that--you have a family of spacelike slices that, taken together, cover the spacetime. There is no sense in which one spacelike slice "moves through spacetime".

 

[eaglechief]

Thanks for your reply, Peter.

I am trying to put a different light on the attributes how "space" and "time" are defined. As far as i do understand GRT and FRW-Models, "space" is just a static cut through spacetime in form of a slice. Perhaps there occur some interesting effects, if space is modelwise treated more as a dynamic part of the spacetime. Therefore it makes sense to me to ask how a spacelike hypersurface (being "space") really moving through time could be described. To do this, one needs to define a ratio, how this "moving" can be expresses, comparable to a velocity inside the space of our perception, setting ds/dt and gaining v. In some papers i came across statements like "branes moving through the bulk" and i wonder how this "moving" is defined, because one could ask "how fast ist the brane moving?".

 

[PeterDonis]

As far as i do understand GRT and FRW-Models, "space" is just a static cut through spacetime in form of a slice.

That's one way of interpreting "space", yes; but you have to allow for the fact that different spacelike slices can have different geometries, so a given spacetime won't necessarily have a single "space"; it will have an infinite number of different possible "spaces", depending on which slice you look at. Each such slice is just a particular slice cut out of the entire spacetime; there is no invariant way of correlating one slice with another, and a given slice certainly doesn't "move"--it's just a particular subset of the whole spacetime.

Perhaps there occur some interesting effects, if space is modelwise treated more as a dynamic part of the spacetime.

It isn't. There are other ways of formulating GR which do view "space" as a dynamic thing (for example, the "superspace" formulation, which John Wheeler was a proponent of), but these formulations don't view "space" as moving through spacetime. In models that use spacetime, "space" doesn't move through it; "space" is just a label for a spacelike slice, and you can pick any slice you want.

Therefore it makes sense to me to ask how a spacelike hypersurface (being "space") really moving through time could be described.

No, it doesn't make sense. See above.

 

[Chronos]

You can overlay a grid on spacetime, but, you can't overlay spacetime on a grid. To quote Einstein, space has no ponderable properties. How do you define motion for an entity devoid of ponderable properties

 

[eaglechief]

Hi Chronos, thanks for your reply.
"How do you define motion for an entity devoid of ponderable properties"
--> that's the point.

If we may talk about a green meadow approch, besides ART, by using a grade 4 spacetime, with three degrees of freedom for space and one degree of freedom for time, i do think it's allowed to ask about the "speed" in radial direction.

let me explain by using the illustration of a flat D2-circle. The circumference of the circle should represent the R^3 space, the entire circle the (R^3*T^1) spacetime. Any radius drawn from the centre of the circle M to any point on the circumference P should represent the dimension of time T^1.

Now let's point the focus on two "slices" of space, one with radius r1 and one with radius r2 = 2*r1. The point P should be an moving object in space. Let P have on the first slice an angle (alpha) and on the secon slice an angle (alpha + x). If we compare the both slices of space, one can see, that object P has changed position in space (has moved on the circumference) as well as object P has moved "in time" (in radial direction away from M), due to it has increased radius.

Now the approach is: geometrically we can describe the both "rates of change", the radial as well as the rate of change on the circumference only, in the same way, by drawing vectors. At this step, we do not care, that we have a model of spacetime, we only analyse geometrical attributes of a point P in a D2 circle. What holds us back to draw a vector from the center of the circle M to point P on the circumferences with radius r1 and r2 and ask about the direction and amount of the movement of point P away from center M ? In my opinion: not much. The challenge is in my eyes to define a "rate of change of time" being the same as a "velocity of time"

Greetings
eaglechief