Spacetime and relativity - am I understanding this part of it correctly?

Factual Questions
1

Am in middle of reading The Fabric of the Cosmos by Brian Greene, which is a fascinating book. However, I’m plagued by an inability to fully grasp some of the concepts he talks about - I read his analogies, and have a general sense of understanding, but am not totally sure I read it right. Or, maybe it’s not me, but the whole damn concept of relativity.

Anyway - in one section he talks about how spacetime exists, fully, in that the past, present and future always exist. To explain, he gives an analogy, which I will paraphrase here in order to make sure I understand.

Assume you have three people - yourself, Bob Betelguese, and Amanda Andromeda, each sitting in a chair reading the daily newspaper for June 17, 2005 (or whatever year it is in their terms, but it’s the exact same “day”). Bob and Amanda are each X billions of light-years from you, in opposite directions. Let’s say all three of you are at exact rest (disregarding the movement and rotation of planets etc). You each also have the ability to take a mental snapshot of the universe as it exists right now - in that you can take that snapshot and examine any portion of it you like, and it will show you exactly what everything looked like at the instant you took it.

So you, Bob and Amanda, all at rest, take this snapshot at the exact same time. Because you are at rest relative to each other, your snapshots will be identical. Amanda will see you reading the June 17, 2005 paper, and you will see her doing the same. Ditto for Bob and you.

Now, however, if you get up and start walking, say “directly” at Bob (and therefore away from Amanda), things change. Now all three are no longer at rest relative to each other. So the snapshots will change. Let’s say all three people take a snapshot exactly 1 second after the previous one, but this time you are moving towards Bob. The snapshots, when compared against each other, are now drastically different. Your snapshot will show Amanda (or Amanda’s world) many years in the past…and even weirder, your snapshot of Bob’s world will show his world many years in the future. Even though, for you, only a second has passed.

I think I understand this part - but please correct me if I’m wrong. Another question I have is what would Amanda’s snapshot show of you and Bob - if her snapshot even exists, seeing as from your snapshot, she may not even have been born yet.

Ow, my head hurts.

2

No, it’s pretty much the whole damn concept of relativity that’s confusing. You’re in good company.

To answer your questions: Yes, you have the situation correct; if you start moving towards Bob and away from Alice, then what you would observe as “the present” everywhere in the Universe would be what you saw as “the future” for Bob back when you were sitting still, and “the past” for Amanda.

As for Amanda, what she sees in her snapshot depends crucially on whether she’s moving or not. If she’s still sitting still on her version of June 17, 2004, she would see you and Bob reading the June 17, 2004 papers. If she then gets up and starts walking towards you and Bob, she’ll see what would have been some number of years in the future for you, and even further in the future for Bob. (In fact, if the three of you are evenly spaced, then she’ll see Bob twice as far in future as you, i.e. if she sees you ten years in the future, she’ll see Bob twenty years in the future.)

The reason for all of this has to do with how you define “now” in special relativity. The way it’s usually thought of is in terms of light pulses: Suppose you sent out a flash of light towards Amanda at 1:00 PM, and you observe the same pulse of light reflected back to you at 3:00 PM; you would then surmise that the pulse of light reached Amanda at 2:00 PM. Now suppose you start moving away from Amanda. The pulse of light takes the same amount of time to get to Amanda, but since you’re moving away from it, it takes longer to get back to you. If it gets back to you at, say, 3:30 PM, you would conclude that the pulse got to her at 2:15 PM. So when you start moving away from Amanda, you conclude that an event taking place fifteen minutes ago (according to your measurements when you sat still) is really taking place now.

That’s a rough sketch of it, at least. Let me know if you have further questions (or if you wouldn’t mind a bit of algebra being brought into the discussion — it makes things so much easier…)

3

Sorry to pick a nit but you can’t take a snapshot of the universe as it exists right now. If Bob is five million light years away you can only take a snapshot of him reading a paper that is five million years old.

As for seeing a different time when you start to move that is at best a misleading way of stating what happens. Think in terms of space time dilation. This came about as a way to solve problems caused by the speed of light being an absolute. The speed of light in a vacuum is always the same no matter how you measure it. If you have a locomotive travelling on the tracks at 0.5c and it has a headlight the velocity of that light is the same no matter who measures it. You could be on the train, standing beside the track or on another train going the opposite way but the speed of light for the headlamp would be the same.

This has been done experimentally to see if light has a medium that it travels through like sound waves travel through matter. It was considerably less exciting than a train going 93,000 miles per second but showed there was no invisible “either” as a wave medium. Look up Michelson Morley interferometer to learn more.

When we move we dilate time and space. The train that is moving will be seen as shorter by an outside observer and its clock will be going slower. The clock slowdown has been tested experimentally by taking two matched atomic clocks and flying one around the world on an airliner. When they got back the clocks were out of sync by the amount of time predicted by relativity. Not much as the velocity of the plane is is a tiny fraction of that of light but measurable.

4

Padeye
Thanks - I actually do understand (well, I think I do) that part, but I don’t think that’s what Mr. Greene is implying. He’s addressing a different situation - this is the section where he’s talking about all pasts/presents/futures existing in some sense. And he specifically was talking about a theoretical snapshot of the universe sans the lightspeed limit - because he does mention that just because in this theoretical snapshot Bob might know our future, there’s no way he could actually get a message to us to tell us about it - because the messages are constrained by the speed of light. It’s a more theoretical point he’s trying to get across.

MikeS
Thanks also - if you feel like throwing in algebra go for it. As for your Amanda, I guess I meant what would her snapshot show if I’m the one who is moving. One second ago, we’re all at rest, so we have the same snapshot. Then I get up to move towards Bob, so I see his future and Amanda’s past (or vice versa?). But at that same instant, what does Amanda’s snapshot show? She’ll still see Bob, since they’re both still at rest relative to each other, but I guess (since I’m moving away) she’ll see my past?

5

<cockeyed squint> I don’t think you can have a valid though experiment if you first disregard the most fundimenal constant of relativity then add it back in.

I could be completely wrong, and probably am, but I think he’s just doing a really weird and IMO poor illustration of the effects of time dilation. I can see into the past by looking at anything. Something a mile away is 1/186,000 second in the past. The moon is about 1-1/4 seconds in the past, the sun eight minutes. I can look into the future and see tomorrow but it will take 24 hours. :smiley: If I don’t want to wait I can just run really fast. If I go fast enough then one hour on my watch will take 24 hours to a stationary observer.

Of course there is more than one way to look at all this and I may just need to understand his model better.

6

If you’re uncomfortable with the snapshots, just wait a while. Instead of taking a snapshot of the Universe as it is right now, take a snapshot of it as it was five million years ago (thus giving you time to see things five million lightyears away). Start moving and repeat the process, and you’ll have a different snapshot, because your notion of when “five million years ago” is will have changed.

7

No, I think Greene is just illustrating the lack of a universal, absolute time coordinate. How do you transform between two reference frames, one moving relative to the other? The “Galilean relativity” transformation is
x’ = x - vt
t’ = t
which seems intuitively obvious; it just says that for the moving frame, the origin is shifted, at time t, by vt, because the observer is moving with velocity v. The time coordinate stays the same; the two observers agree on what happened at time 0, time 1, etc. But, though it may seem obvious, this is not correct. The transformation of coordinates which obeys Einsteinian relativity modifies both the space and the time coordinates, so that there is no agreement on what happened at time 0, i.e., on what constitutes a slice of constant time.

This is distinct from the problem of information propagation. Of course it will take some time for me to become aware of a faraway event, but I can deduce when the event happened by subtracting the signal propagation delay from the time I saw it. The point is that for observers moving relative to each other, they won’t agree on what times to assign to these events.

8

yes, thank you! That explains what I think Greene is doing so much better than how I tried to do it.