The space/time loaf of bread

[Starstuffer]

Perhaps I am red-shifted, but I just saw a video demonstrating space/time as a loaf of bread and depending on how it is "sliced" an observer would see different times across space. I am having a hard time wrapping my head around this theory. I can see how an observer from afar would see my past, and if their speed, direction and distance relative to me remain constant, they would always be time delayed by the same amount. Time would pass at same rate for both of us. My issue is the loaf theory postulates that should the observer start moving towards me they would catch up with my present and start to see my future. I think it more likely that they would observe me moving slower to the point where, as the distance closed, they would catch my present but never my future.

 

[Bill_K]

Perhaps I am red-shifted, but I just saw a video demonstrating space/time as a loaf of bread and depending on how it is "sliced" an observer would see different times across space.

This is not about what a distant observer would "see", but rather what he would regard as "now", which in SR is a tenuous concept at best. His "now" changes every time his rest frame changes.

What he can see and act on is limited by the finite speed of light, i.e. things in the past. It's only later, after light has had a chance to propagate across the intervening distance, that he can say, "oh yes, that was happening then."

 

[Starstuffer]

The concept of "now", a distant observers now, my now etc. I get. But the demo I saw framed all of this as though all of space/time exists in my conception now. From Big Bang to Big Crunch (or whatever your persuasion) and to see any part of it, I need only change my observing conditions.

 

[Bill_K]

The concept of "now", a distant observers now, my now etc. I get. But the demo I saw framed all of this as though all of space/time exists in my conception now. From Big Bang to Big Crunch (or whatever your persuasion) and to see any part of it, I need only change my observing conditions.

I'd say the demo is not to be relied on in that case. What "exists" is a philosophical question, and what seems to exist "now" is frame dependent. According to one distant observer I have not been born yet, while according to another I am already six feet under. Nothing of practical significance either way.

 

[PeterDonis]

My issue is the loaf theory postulates that should the observer start moving towards me they would catch up with my present and start to see my future.

This is a very misleading use of the word "see". Further comments below.

I think it more likely that they would observe me moving slower to the point where, as the distance closed, they would catch my present but never my future.

You are correct. Light travels at a finite speed, so a distant observer cannot receive light signals from your future just by changing their state of motion relative to you.

 

[JVNY]

Here is a prior discussion of the space-time loaf: [thread]248893[/thread].

 

[pervect]

Ignoring for now the philosophical issues (the concept of existence, for instance), the concept behind the space-time loaf, the "relativity of simultaneity", is an important concept in relativity.

So I can't comment on the particular presentation you are talking about, but I can say that the idea behind the space-time loaf is a valid and important one.

It might be helpful to read different treatments of the issue (the issue being the relativity of simultaneity) if the "space-time loaf" formulation isn't making sense.

The relativity of simultaneity is addressed more formally by Einstein's train paradox (which you will also see a lot of discussion of). Einstein's original formulation can be found online, at http://www.bartleby.com/173/9.html


There are other treatmens along the same line - I recall reading a paper that claimed Einstein's original formulation, while logically sharp, was confusing to students. But I don't recall allegedly less confusing presentation of the idea anymore.

I believe a lot of the confusion arises from trying to disentangle two separate concepts, that sometimes get conflated. These are simultaneity and causality. Two events are simultaneous if they happen to share the same time coordinate. This is observer dependent. Cause and effect is not observer dependent, a cause always proceeds an effect according to every observer.

The old idea of absolute time had a universal "past" that caused a universal "future". In relativity, since there isn't any universal "now", there isn't any universal "past" nor any universal "future".

To use the bread analogy, space-time as whole is a loaf, there isn't any way to separate universally "past" from "future" until you cut the loaf. And the way you cut the loaf depends on the observer.

But cause and effect still happens , it's reformulated as a relationship between individual events rather than as a global concept. Cause and effect in relativity is determined by light cones. While A lot of texts talk about light cones, a specific reference doesn't come to mind. Basically every event has a past light cone, which is the past of that event, and a future light cone, which is the future event. Sometimes events occur outside the light cone - when A is outside B's lightcone, B is outside A's lightcone. Two events outside each other's lightcone have a designation, they are called "spacelike separated", and different observers will order them differently. There isn't any issue with causality, because no cause can propagate faster than the speed of light.

 

[Starstuffer]

Thank you all for your replies.

 

[JVNY]

Starstuffer, also note that the spacetime loaf video is misleading in depicting the space component of spacetime. The video shows the moving alien's bread slice to be longer than the stationary alien's bread slice (the blade that cuts a slice for the moving alien is the hypotenuse of a right triangle of which the blade that cuts the slice for the stationary alien is a side). The opposite is actually true because of length contraction.

 

[yuiop]

I have created this diagram to help illustrate some of the concepts that are being discussed here:

https://www.physicsforums.com/attachment.php?attachmentid=67593&stc=1&d=1394744076

A and B are initially at rest in frame S in the year 2014. The line of simultaneity is represented by the horizontal blue line connecting A and B at events e1 and e3. By prior agreement they both instantaneously accelerate to high speed to the right simultaneously in 2014 as measured in S. The line of simultaneity is now represented by the tilted red line connecting events e1 and e2 in the new rest frame of A and B.

By a naive interpretation, from A's point of view in A's new reference frame, B has shot into the future of frame S and is "now" (by A's new definition of now) in the year 2021 of the old reference frame S. However it is not as straight forward as that simple interpretation suggests. When an extended objects accelerates to a new reference frame the clocks do not automatically synchronise themselves. B had to wind his clock back by 3 years at the acceleration event (e3) so that his clock would be re-synchronised with A in the new reference frame. B had to wait a further 3 years of his own proper time to arrive at the event (e2) that A called "now" when A accelerated in 2014. There was no magical leap into the future as far as B was concerned and B had to manually adjust his clock. While A assumes that B was at event e2 immediately after the acceleration event, A does not see where B actually was, until the light from that event (the light blue line) arrives back at A in the year 2018 of the new reference frame or the year 2023 in the old reference frame and anything could have happened to B in the intervening years to prove A was wrong in his assumption of where B was in his new concept of "now" in the year 2014.

In the year 2018 of the new reference frame, A can look back and have real information about the events e1, e2 and e3 as they are all in his past light cone and can now say with some objectivity that B was at event e2 when A started accelerating at event e1 in the year 2014, but from the point of view of his new reference frame, B started accelerated to the new reference frame, 3 years earlier than A. This is a perfectly valid interpretation of past events, but at no time does A or B have information about the future before it happens beyond an educated guess. To me, the unpleasant aspect of the spacetime loaf concept, (which I believe is closely related to the block universe idea), is that it implies the future is predetermined.

 

[yuiop]

I am reposting this diagram, as the link to the image in the previous post has been reported as broken.

Perhaps a moderator can combine the two posts and delete the redundant post with the broken link?