# Spacetime immutable?

1. Dec 12, 2008

### alphachapmtl

Cause of relativity, Lorentz transformation and non Euclidean geometry, it is said space and time can't be viewed as separate entities but must be merged into spacetime (because there is no universal time valid for all observers).

So: This spacetime is immutable. It is a fixed structure, unchanging in time (there being no time outside of spacetime). There is no such thing as an expanding spacetime (of course an observer like us following his world line may see an expanding space).
Am I right?

Some have told me I am wrong, and the expansion of the universe proves it. But I think they don't understand what I mean.

2. Dec 12, 2008

### Staff: Mentor

I think both descriptions are reasonable. You can look at a cone and say "it gets bigger" meaning that as you go down the axis the diameter of every cross section is larger than the diameter of the last. Or you can look at a cone and say "it stays the same size" meaning that the cone is one single unchanging geometric object, not a collection of separate circles.

The disagreement seems to be purely semantic.

3. Dec 12, 2008

### MeJennifer

You are completely right!

4. Dec 12, 2008

### Naty1

Interesting questions....

I think most would agree that Newton's view of absolute space and absolute time was supplanted by Einstein's relativity...neither is viewed individually as immutable.

Lee Smolin says (Fabric of the Cosmos)

He illustrates constant velocity as a straight line in spactime, uniform acceleration as a corkscrew shape...

Yet Peter Bergmann, a student of Einstein says (The Riddle of Gravitation)

I think it would be a mistake to be dogmatic either way...context IS relevant.

Spacetime doesn't seem immutable to me : before the big bang there was none, now there is apparently some, so a change took place. It doesn't seem it necessarily always existed. Dynamically curved spacetime seems real enough: Spacetime is constantly shaped by mass,energy,pressure as things move about...so whether it's "immutable" in that sense is not obvious to me.

If the expansion of the universe isn't a type of spacetime evolution/change, what is it? As space expands, the shape of spacetime necessarily changes as uniform energy density expands, galaxies move away from each other and accelerate.
But I would not claim it necessarily invalidates aspects of spacetime immutability....depends on what you mean.

5. Dec 12, 2008

### JesseM

It depends how you define "change". Say we are looking at the surface of a sphere, and we place a z-axis in 3D space in such a way that it passes through both poles of the sphere. Then it would be correct to say that "at points further down along the y-axis than the south pole of the sphere, the sphere is not present", but this is only a "change" because you are switching the part of this space you're looking at, we could also say that the sphere itself is not changing just because you're inspecting points further down than the south pole. Of course this analogy isn't perfect, because the curved 2D surface of the sphere is sitting in a 3D "embedding space" while there is no need to postulate a higher-dimensional spacetime that curved spacetime is sitting in (although you can model it that way if you wish), but without such an embedding spacetime your phrase "before the big bang" doesn't even seem to make sense.
But "constantly shaped" seems to presuppose a dynamical view where we have curved space which is changing over time. You can slice up 4D spacetime into a stack of 3D surfaces, something known as a "foliation" of the spacetime, and then draw up rules which tell you how the surfaces must evolve if you are given an initial surface...but this doesn't work for all possible spacetimes (my understanding is that it only works for 'globally hyperbolic' spacetimes, and that spacetimes with closed timelike curves are not globally hyperbolic, I don't know if there are any spacetimes without closed timelike curves that are not though). The basic equations of GR are not dynamical in my understanding, they just relate the curvature of spacetime at every point to the mass/energy at that point, and so the challenge is to find entire 4D spacetimes which satisfy these relations at every point.
"Expansion" of the universe only makes sense in the context of a foliation which slices up the 4D spacetime into a series of 3D sections. Think about DaleSpam's analogy in which we cut up a 3D cone into a stack of 2D cross-sections:

6. Dec 13, 2008

### Phrak

To be absolutely pedantic, the statement makes no sense as you intended it to mean. No offense implied.

In the same vein one could try this: Spacetime is immutable. It is a fixed structure, unchanging in distance.

What you are talking about is a model of spacetime, where we pretend we are standing outside of it, looking at it as a static entity. It's a very useful model. But as someone around here likes to state, "the map is not the territory."

Last edited: Dec 13, 2008
7. Dec 13, 2008

### Naty1

Is anything in the universe "immutable"?? I can't think of anything...

Is a photon in special relativity immutable? Without gravity it may exist without change except for position. In the actual universe, gravity will curve its path, transform its energy and frequency (as red or blue shift) and so I'd say it is NOT immutable...Black Holes, Stars, planets, galaxies all seem dynamic...none last "forever".

8. Dec 14, 2008

### Staff: Mentor

Hi Naty1,

It is just a different way of looking of things. In one you consider a point particle to be a 0-D object (point) which occupies a single time-varying point in space. In the other you consider a point particle to be a 1-D object (line) which occupies an entire fixed set of events in spacetime. In the first, movement is seen as an actual change, but in the second movement can be seen as simply the slope of an unchanging line in some coordinate system.

Of course, since a slope is a change in one variable over a change in another variable I think it is still reasonable to talk about things changing and moving even in the second context, as long as you realize that you are refering in some sense to a specific way of slicing up a 4-D geometry into an ordered series of 3-D subsets.