Spacetime 'loaf' according to Fabric of the Cosmos

[Dannen]

Spacetime 'loaf' according to "Fabric of the Cosmos"

From what I learned watching Brian Greene's "Fabric of the Cosmos" episode on Nova, if you look at spacetime like a loaf of bread, then each 'slice' depends on your relative speed compared to another point in the loaf. This I have no problem with, but it really got confusing when he mentioned that an observer billions of light years away would see an older image of Earth if he traveled away from it. Upon seeing this my mind immediately asked the question, does that mean time travel BACK in time is possible, or does it simply mean the light traveling from Earth to the observer is older.

To simplify, if an exotic means of travel existed, where you could instantly warp 10 billion light years without breaking the speed of light limit (via a wormhole or whatever), would you then end up 200 years in the past if you stepped through the wormhole after traveling away from Earth, and 200 years in the future after traveling towards Earth? (You'll know what I mean if you have seen that episode, where the alien's 'slice' in spacetime is relative towards a distant past Earth slice when he's traveling away from Earth, but when he's traveling towards Earth his slice is connected with a future Earth).

How I understand spacetime is that it always moves forward, but at different speeds depending on gravitational force and relative speed, so traveling back in time should never be possible (it just moves forward at different speeds, but there's always a NOW, you've just aged at different speeds depending on where you are in the Universe). But the scenario depicted in Greene's show seemed to imply otherwise.

 

[dEdt]

This I have no problem with, but it really got confusing when he mentioned that an observer billions of light years away would see an older image of Earth if he traveled away from it. Upon seeing this my mind immediately asked the question, does that mean time travel BACK in time is possible, or does it simply mean the light traveling from Earth to the observer is older.

This isn't quite accurate.

When we look out into space, we are always seeing an image that was produced in the past, for the simple reason that light takes a finite amount of time to reach us. Although it is true that an observer billions of light years away will see an image of us from our past, this isn't what Greene is trying to say -- he's pointing out something much deeper that comes from the special theory of relativity. What Greene is saying is that different observers in relative motion will measure time differently. In particular, two events that I consider to have happened simultaneously will, to another observer moving relative to me, take place at different times.

In special relativity, it isn't possible to exploit this effect to travel backwards in time. However, wormholes -- if they even exist -- complicate matters and theoretically allow travel backwards in time, though perhaps for different reasons than you mentioned.

How I understand spacetime is that it always moves forward, but at different speeds depending on gravitational force and relative speed, so traveling back in time should never be possible (it just moves forward at different speeds, but there's always a NOW, you've just aged at different speeds depending on where you are in the Universe). But the scenario depicted in Greene's show seemed to imply otherwise.

Don't think of spacetime as moving. It is a static structure. Time dilation effects -- such as the gravitational time dilation that slows time down near the surface of a planet or star, or time dilation due to motion that slow down a moving clock -- are best thought of as arising from, respectively, the curvature of spacetime and the fact that two observers measure time differently.

 

[PeterDonis]

an observer billions of light years away would see an older image of Earth if he traveled away from it.

It's been quite a while since I watched this show, so I don't remember Greene's exact words; but I suspect you're misinterpreting him here.

First, consider an observer far away from Earth, who is seeing images of Earth as he moves. No matter what his state of motion is, the successive images of Earth that he sees are properly ordered in time: that is, for example, he sees the image of Earth at noon UTC on January 1, 2014 before the image of Earth at 12:01 pm UTC on January 1, 2014. Changing his state of motion will change how fast the "Earth time" contained in the images he sees changes (because of the relativistic Doppler effect), but it will never change the *order* of "Earth times" in the images.

Second, Greene's usual reason for discussing what happens when an observer far away from Earth changes his state of motion is to say that this changes what event on Earth is happening "now" from the distant observer's standpoint. For example, suppose the distant observer starts out at rest relative to Earth, and he judges that noon UTC on January 1, 2014 is happening "right now" according to him. If he then starts moving away from Earth, he will judge that some event *before* noon UTC on January 1, 2014 is happening "right now" according to him; conversely, if he starts moving towards Earth, he will judge that some event *after* noon UTC on January 1, 2014 is happening "right now" according to him. (These are standard consequences of how inertial frames work in SR.)

If the observer is far enough away, such as a billion light years, even small changes in his speed relative to Earth (say on the order of meters per second) can change the Earth event he considers to be happening "right now" by years. But this has nothing to do with the actual images of Earth that he sees; at the instant he changes his speed, the image of Earth he sees does not change (it is of Earth a billion years ago, if he's a billion light-years away); all that changes is how fast the "Earth time" in the images he is receiving changes. The change in what Earth events he judges to be happening "right now" is a coordinate change; it's a change in the frame of reference he uses to describe events, not a change in the events themselves.

 

[PeterDonis]

How I understand spacetime is that it always moves forward, but at different speeds depending on gravitational force and relative speed, so traveling back in time should never be possible (it just moves forward at different speeds, but there's always a NOW, you've just aged at different speeds depending on where you are in the Universe). But the scenario depicted in Greene's show seemed to imply otherwise.

There are a number of issues with this way of viewing things. This previous thread on the same subject goes into some of them:

https://www.physicsforums.com/showthread.php?t=676547&highlight=spacetime+loaf

The main issue, IMO, is that, as dEdt pointed out, spacetime does not move; it is a 4-dimensional geometric object that just is. It is possible to view individual objects as "moving" along their worldlines in spacetime, but this view has issues too; a better way is just to view objects as their worldlines (or world tubes, if we are talking about extended objects instead of idealized point particles), i.e., as geometric objects contained in spacetime that are just there, not "moving".

The other main issue, IMO, is that "now" is not a physical thing; it's just a convention. There are many ways of slicing up spacetime into "now" slices, but none of them make any difference to any actual physical observables. The physical invariant is causal relationship: saying that two events are spacelike separated is an invariant statemen, but saying that they both happen "now" is not.