# Does spacetime have a future?

1. Apr 10, 2013

### oldGhost1

Firstly, I’m not a mathematician. My understanding of Einstein’s theories comes from popular science books (Cox, Greene, Gardner) so this is at the level of the ‘block universe’ model (or Brian Greene’s loaf, if that’s more familiar) and spacemen flying around the universe. So, on the face of it the ‘block universe’ seems to imply the future is out there, but I don’t think this has to be the case. I think the present moment might be as far as spacetime goes.

Here’s the toy scenario. Spaceman leaves earth and travels to Andromeda and back. By his watch the journey took a year but 6million years have passed for earth.

It’s a familiar ‘time travel’ scenario. However, when viewed externally using the ‘block universe’ model we see a slightly different picture. Implicitly, in drawing a time axis, the model imposes the creation of absolute time. But that’s ok since time is relative to motion so any scale we choose for our time axis will not compromise the outcome of the scenario. We also get the notion of the ‘present slice’, which cuts across space delineating the boundary between past and future, and which is always perpendicular to the time axis. (This is not the same as the ‘now slice’, whose angle deviates from the perpendicular depending on the speed of the protagonist.)

So using the model, both journeys (earth and spaceman) begin at the same spacetime location and come together again at some future spacetime location. Obviously they start on the same present slice. Equally, at their common end point they must again sit on the same present slice, even though one has travelled for a year and the other for 6million. Moreover, this seems to suggest that if we viewed the entire scenario from outside of the model we would see the two journeys (both earth’s and the spaceman’s) running neck and neck in the time direction, exactly on the present slice. So after a tenth of the journey the present slice has moved one tenth of the way along the time axis. At this point earth has aged 600,000 years and the spaceman 36.5 days but they still share the same present slice along with everything else in the universe (everything having aged different amounts depending on their speed). The same goes for any other fraction of the journey you choose. It is simply the case that the rate of time experienced by the spaceman due to his speed of travel is much slower than both that experienced by earth and that of our arbitrary scale for the time axis. This is the benefit of using a model that invokes an arbitrary time rate against which the two journeys can be compared.

The point is, it seems that at no time does the spaceman travel into the future. He stays bound to the universal present along with the earth and everything else. It is the rate of time that changes for him along with everything else that is in motion (i.e. during his journey, on average 1 minute for the spaceman lasts around 11 earth years). So, contrary to the usual ‘time travel’ billing given to scenarios like this one, we don’t need the future to already exist in order for us to appear to travel into it. It is in this respect that I believe there is no need for spacetime to have a future.

Of course this conclusion might stem from the use of an over-simplified model but it does begs the questions, “does spacetime need the past either?” and “could we still use spacetime if we did away with both the past and the future?”

2. Apr 10, 2013

### nitsuj

Look up the definition of future & past, what is the physical significance compared to an "occurrence"/"happening" ect.

[/PLAIN] [Broken]
Hmmm wiki's defining of present time works

Last edited by a moderator: May 6, 2017
3. Apr 10, 2013

### oldGhost1

Sorry, that last paragraph was a bit of an after thought.

The main point was that the normal view of spacetime implies that the future is out there because we can go very fast and travel to it. I was suggesting that it doesn't matter how fast we go, we can't get there ahead of the rest of the universe because we are all sitting on the same present slice.

4. Apr 10, 2013

### nitsuj

I'm suggesting to you to think about what the "future" is.

To be more clear, from a physics perspective it is nothing more than forethought.

The only thing future implies to me is that time keeps going, not anything specific with aging.

Past, present & future are better defined with a "light cone". After reading the definitions of past / future / present read about time-like, light-like & space-like. That is exactly the perspective to interpret your first post.

you're right about it [block universe] not being the "reality", and suppose I may have to add in my opinion.

5. Apr 10, 2013

### Staff: Mentor

But whose present slice? Which slice is the present slice is frame-dependent. For example, suppose someone on Earth is asked, a quarter of the way through the trip, what time it is on the astronaut's clock in his present slice. He gives an answer, which is one quarter of the total trip time by the astronaut's clock.

Now we ask the astronaut what time it is on Earth clocks in his present slice a quarter of the way through the trip. He will *not* say a quarter of the total trip time! He will say that hardly any time at all has elapsed on Earth, because he has only been traveling for a few days and the Earth is moving away from him at almost the speed of light, so its clocks are running a lot slower.

I don't want this to turn into another interminable twin paradox thread, so I'll leave it at this: the real lesson of spacetime is that the idea of a "present slice" is not a good thing to focus on. To really understand spacetime, you need to understand causal structure: light cones.

6. Apr 10, 2013

### oldGhost1

I know what you mean Peter but don't we have a special case in this model. By drawing a time axis haven't we imposes absolute time on the model and we can use that as the reference in disputes over time. I know the clocks aren't going to match between earth and the spaceman and I think I pointed that out when I said their rates of time won't match. All the example is really considering is their paths through the time dimension of the block universe. It makes no difference that the spaceman is increasing his separation from earth. All of that kind of happens in 3D space. And the whole of 3D space sits on the present slice of this model. The present slice then advances at our arbitrary rate set by our labelling of the time dimension. It doesn't matter how fast you travel in 3D space, the whole of space advances at the same rate along the time axis.

Just to be clear, I know the clocks won't match. And I'm not suggesting that earth or spaceman time will match the arbitrary time units chosen for the time axis. All I meant was that even though spaceman takes a year and earth takes 6million, they both arrive at their destination at the same moment of spacetime. And using the rules of this model they both made their entire journeys sitting on the same present slice.

7. Apr 10, 2013

### Staff: Mentor

Yes, oldGhost, I understand all that, but my point is that you have arbitrarily picked the Earth's direction in spacetime as the time direction. If you picked the astronaut's direction in spacetime as the time direction, you would get the same kind of model for spacetime, but it would have a different set of present slices, and it would say that the astronaut is the one with the fastest rate of time flow, not the Earth. The block universe model does not say the Earth's direction in time is the "right" one.

8. Apr 10, 2013

### oldGhost1

ok Peter, I think I see what you're saying. I'll have to go away and give it some thought. May be a little while...

9. Apr 10, 2013

### pervect

Staff Emeritus

Firstly, I wouldn't expect any differences in physical predictions from a philosophical position such as "block time".

Secondly, there isn't any "absolute time" in SR, and I don't understand why you think there should be from your example. It's possible that you are using the term "absolute time" to mean something different from what I think it means.

You might try filling in your defintions and expanding your logic. Meantime, I'll give you my best understanding of absolute time:

In relativity, the times measured by the different observer's clocks cannot be absolute time, for if it was, the clocks would agree when they reunite (absolute time flowing without regards to anythign external).

And any notion that singled out a particular clock as keeping "absolute time" would be incompatible with the notion of relativity that there is no preferred frame of reference.

10. Apr 10, 2013

### nitsuj

Much better said than Greene, and he's a "physics author"!

11. Apr 10, 2013

### nitsuj

This point is actually the same as your second point.

I think it is from the perspective of any object. Like a rock, or some other inanimate object (no "magical" free-will accelerations please ).

Of course as the poster said this is just a model.

Are we considering deltas of physical composition? Or just time? The clocks will "agree" when they reunite; in the sense that the OP had described, proper time. their age will be different.

Again it's a model, you know this is describing a proper time perspective, and you know that is the same as a geometric perspective of time, at least as a geodesic path.

I'd imagine that the poster knows this is an abstract, a model to show time as a geodesic path, derived from 3D.

Seems the same to me as the perspective of a photon. (does those photon things ever get to accelerate?)

If you disregard any concern for aging, what does it matter how old what ever object is whatever "age". Future / past are of no physical consequence to the present.

For calculations & understanding past/future are course crucial, but that's just philosophical stuff...

Last edited: Apr 10, 2013
12. Apr 11, 2013

### oldGhost1

Ok, good comments all round. I have a better idea of where I’m going wrong now but I’m still not quite there.

Firstly, as my use of the terms absolute time and present slice have caused confusion I’ll try to be more precise.

My use of the term absolute time refers just to the model in the sense that the model is effectively a graph with a co-ordinate system onto which we have placed the whole of spacetime. Implicit to any graph is an origin where all axes intersect and from which absolute co-ordinates can be obtained (absolute time being one of them). There is no absolute co-ordinate system in the real world, but there is in this model. It’s only a model.

Use of a present slice is also restricted to this model and is not to be thought of as the equivalent of a real ‘now slice’. Within this model the present slice projects perpendicular to the time axis and allows us to take a snapshot of every clock in the universe. You can then take another snapshot from further along the time axis and compare the amount by which each clock has changed. From this you could deduce such things as
1) Clocks that show the least passage of time have been travelling faster than most of the other clocks.
2) Clocks that show the most passage of time have been travelling slower than most of the other clocks.
3) Clocks that show identical passages of time have been travelling at the same speed as each other (no relative motion between them)

Now, probably two areas where I go wrong with this model are
1) It brings to mind a Euclidean 4D space with all axes perpendicular whereas reality is non-Euclidean.
2) It tends to encourage me to think of 3D space being separate from time as opposed to being intertwined as spacetime. This was the sense in which I laboured the point about the present slice. If 3D space has no time dimension then by implication the whole of 3D space must be in the same moment. A part of me still finds that argument compelling but I’m sure I’ll be put right on that.

However, the original question was “does spacetime have a future?” and I’d like to just tweak the original scenario to try to get at an answer.

Spaceman on earth. He starts a clock running that simply counts the passage of earth years. Spaceman flies to Andromeda and back. He has engine trouble on the outward journey so flies slower on the way there than on the way back. Flight takes him 1 year. As he lands the earth clock ticks over to 6 million.

We now have two events in spacetime – the starting of the earth clock and the earth clock ticking over to 6 million. Plot these two events on our block universe model such that when a line is drawn between them it runs parallel to the time axis (don’t know why I’m doing that but it seems I need to specify a direction of some sort). Now adopt a scale for the (absolute) time axis. Because I’m lazy I’m going to say these two events are 100 time units apart. Now use a present slice to record the clock readings of the earth clock and the spaceman at the points 0, 50 and 100 along the time axis.

At time 50 (half way between start and finish events)
Earth clock reads around 3 million
Since spaceman has engine problems he has had to travel slower than he would have liked to this point. He is roughly ¾ of the way to Amdromeda but because of his slower speed his clock shows roughly 200 days have passed.

At time 100 (finish line)
Spaceman managed to travel much faster and by doing so his clock ran slower. He covered the remaining 5/8 of journey in 165 days, so his clock reads 1 year.

This is the sense in which the original question of “Does spacetime have a future?” was asked. The traditional interpretation of the spaceman scenario is that he has travelled to a future earth. I’m suggesting that high speed travel simply slows the spaceman’s passage through time enough for the earth (and everything else) to keep up. There is no need for a future earth because earth was effectively keeping pace with the spaceman along the time axis the whole time. So spacetime doesn’t need a future that is predefined in order for us to appear to travel there.

13. Apr 11, 2013

### Passionflower

This would be true for an Euclidean spacetime, however it is Minkowskian (or Lorentzian if we include curvature).

The slicing of the 'loaf' in Minkowski spacetime is done with a hyperbolic angle and, in simple terms, that means that each angle is equivalent. Hence there is no preferred cut through the 'loaf' and thus no preferred time direction.

14. Apr 11, 2013

### ghwellsjr

The speed of clocks (and everything else) is relative to the coordinate system so two clocks can be traveling in different directions at the same speed and have relative motion between them and yet show identical passages of time.

15. Apr 11, 2013

### WannabeNewton

What is your precise (if possible mathematical) definition of future? For example when talking about Minkowski space-time, there always exists a conformal isometry of Minkowski space-time into a specific open subset of what is called the Einstein static universe. The topological boundary of this open subset (called the conformal infinity of Minkowski space-time) contains two points of relevance: past time-like infinity and future time-like infinity. All time-like geodesics of Minkowski space-time (the paths that free massive particles travel on) start at past time-like infinity and end at future time-like infinity.

These are best visualized through conformal diagrams although I can't seem to find a good one on the internet that depicts this at the very moment. I'll try to keep looking or maybe someone else knows an internet resource that has good diagrams.

16. Apr 11, 2013

### Passionflower

Yes, but to avoid any confusion past and future time-like infinity are not actually single points in spacetime.

But for instance in a Milne universe the past time-like infinity could actually be considered a single point in spacetime however future time-like infinity could not be.

The Milne universe is interesting in that each spatial point in this universe is at the center. Similar to the idea that there is no preferred direction for hyperbolic angle of a spacetime slice.

17. Apr 11, 2013

### WannabeNewton

Indeed and this would be easier to see if the explicit coordinates on $O\subseteq S^{3}\times \mathbb{R}$ used for $\tilde{g_{ab}} = \Omega^{2}\eta_{ab}$ were listed and past and future time-like infinity were concretely defined in terms of the coordinates like you would see in textbooks but I fear that might make things too mathematical / complicated for the OP and take away from some possible physical insight that could be gained from a conformal diagram if I could just find one! Aaaargh!

18. Apr 11, 2013

### Bill_K

19. Apr 11, 2013

### WannabeNewton

20. Apr 11, 2013

### Staff: Mentor

You don't need to specify a direction when you draw the time axis, because you already specified a direction when you specified the two events. They are both on the Earth's worldline, which defines a specific direction in spacetime. So the time axis you've adopted is just the Earth's worldline.

But there's nothing in spacetime itself that makes the Earth's worldline special. You could just as easily pick any other worldline, such as the astronaut's, and make it the time axis of your block universe diagram, and you can still make all of the same physical predictions.

(Note that, in your scenario, there *is* a sense in which the Earth's worldline is special. But that still doesn't make it special enough, so to speak. See below.)

And so did the Earth itself. The difference is that the Earth took 6 million years by its own clock to get to that particular future Earth, whereas the astronaut took much less time. (I think you recognize this, since you say something sort of like it later on in your post. But I don't think you fully realize the implications. See below.)

Why the difference in elapsed time? Because, once you've picked those two particular events in spacetime (Earth at time zero, Earth at time plus 6 million years), you have also picked out one particular worldline, the Earth's worldline, as special with respect to those two events: the Earth's worldline is the one along which the maximum amount of time elapses between the two events. *Any* other worldline that passes through those two events must have less elapsed time, whether it's the astronaut's or anyone else's.

But once again, the Earth's worldline is only special with respect to those particular events; it's not special with respect to spacetime as a whole. So you can't make arguments about spacetime as a whole using facts about particular events or particular worldlines between those events, when the events are only singled out by the fact that you picked them.

But once again, this will be true *regardless* of whose worldline you pick as the time axis, as long as it's inertial. You can pick the astronaut's outgoing worldline as the time axis and make exactly the same kind of statement: there is no need for a future astronaut because the astronaut was effectively keeping pace with the Earth along the time axis the whole time.

Yes, in your scenario the astronaut has to turn around and come back to Earth, but that's a feature of your particular scenario; it doesn't show anything about spacetime itself. You could just as easily construct a scenario where the astronaut flies off, and some time later by Earth's clock aliens attach a device to Earth that causes it to fly off in the same direction as the astronaut but even faster, so it eventually catches up to the astronaut. In *that* scenario, it would be natural to pick two events on the astronaut's worldline--his leaving Earth, and Earth catching up to him--and make *those* the two events that define the time axis. Then everything would look the same as in your scenario, but with the astronaut playing the role of the Earth and Earth playing the role of the astronaut. Both scenarios are compatible with the laws of SR, so you can't say either one is privileged over the other.

So now we have two different models that both say spacetime doesn't need a future, that it only needs everything up to the "present slice", but with *different* present slices cut at different angles through spacetime. If we take this at face value, it tells us that, if we insist that any single present slice "exists", then they all have to "exist". This is the sort of argument people like Brian Greene use to justify their claims about the "block universe". Others, like me, take the opposite course: all this shows is that the concept of a "present slice" is not a good concept. If I don't insist that a present slice "exists", then I don't have to worry about whether the "future" exists either. I can focus on the things that don't depend at all on such unanswerable questions, like causal structure: which events can be causally connected to which other events?

21. Apr 11, 2013

### oldGhost1

ok guys, that's great. Thanks for all your help (even the information overload from Wannabe was nice to see).

I guess my take home message from this is that, disarmingly simple though the block universe model looks, it takes a lot more understanding of the subject than I had to fill in the blanks and use it correctly. And anyone with the required knowledge probably wouldn't bother using this model anyway. At that rate I guess I'm lucky to have gotten any replies at all. Thanks again guys.

One last things.
Can anyone recommend some decent books on GR and SR (for a non mathematician)

22. Apr 11, 2013

### Staff: Mentor

Kip Thorne's Black Holes and Time Warps is a good non-technical book on GR (it also covers some of SR). It also has a lot of good discussion of the historical development of GR which is interesting in its own right.

23. Apr 11, 2013

### oldGhost1

nice one. Thanks Peter

24. Apr 12, 2013

### oldGhost1

Sorry guys I’m back again.

This is still just about on the topic of how spacetime represents the ‘future’. The following is a passage from “Relativity Simply Explained” by Martin Gardner (p82). I read the first paragraph as saying every object sits in (and is integral to) its own world line in 4D spacetime. It’s the second paragraph I’m struggling with. How can you graph the world line of an object moving unpredictably, for example that of a firework rocket that is triggered by the decay of a radioactive isotope? Mr Gardner doesn’t expand on this point so how exactly does the world line handle unpredictable events?

“In relativity theory, every object is a four-dimensional structure lying timelessly along its world line in the four-dimensional world of spacetime. If an object is considered at rest with respect to the three space coordinates, it is still travelling through the dimension of time. Its world line will be a straight line that is parallel with the time axis of the graph. If the object moves through space with uniform motion, its world line will still be straight, but no longer parallel with the time axis. If the object moves with non-uniform motion, its world line becomes curved.
Strictly speaking, one should not say that an object moves along its world line, because ‘moves’ implies movement in time, whereas time is already represented by the world line. The world line is no more than a convenient way to graph the motions of an object in three-space. The fact that a Minkowski graph is, in a sense, a static, timeless picture of the world has nothing whatever to do with the question of whether the future is or is not completely determined by the present. An object moving in a random, unpredictable way can be graphed by a world line just as easily as an object moving in a predictable way. After an event has occurred, its Minkowski graph does indeed freeze the event in a timeless ‘block universe’, but this has no bearing on the question of whether the event had to happen the way it did”

25. Apr 12, 2013

### Staff: Mentor

By knowing how it moved after you have observed it to move; for example, after you have observed the rocket being triggered. You can't predict in advance exactly when the rocket will be triggered, but once it has been you can observe its trajectory and draw a spacetime diagram of it, showing the rocket sitting at rest until some particular time and then flying off.

In other words, to draw a spacetime diagram you have to know the entire history of the spacetime you are drawing a diagram of. Gardner's point is that this fact is independent of how you get the knowledge: you could get it by having already observed it, or you could get it by making a deterministic prediction of the entire history from some initial conditions. But even in cases where the latter is not possible, you can still do the former.