Question regarding relativity and "infinite" speed - WTF?!

JJM 777 said:
It looks like I will again end up neither understanding nor believing that the chronological order of remote events would be relative, while the chronological order of local events is not.
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You make that statement like it is something to be proud of.
 
JJM 777 said:
It looks like I will again end up neither understanding nor believing that the chronological order of remote events would be relative, while the chronological order of local events is not.

If events within 0.9 light cones distance from each other are "local" and "chronologically ordered", I cannot see why events within 1.5 light cones from each other do not become chronologically ordered with each other, by a witness at half-way between them for whom they both are "local" and "chronologically ordered". Similarly, any distance of n light cones is theoretically bound chronologically together by a chain of local observers in between, at intervals short enough not to leave anywhere a gap longer than what is accepted as "local".
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No you seem to be thinking that the chronological order is Euclidean (past and future separated by a plane) in some small enough region, but that is not correct. The only ordering of events is Minkowsky (past and future separated by a light cone) no matter what the scale. We use the word "local" not because events are ordered in a small enough region but because the ordering depends on the location. Whether it is a mile, an inch or an Angstrom apart the ordering of events in different locations is different. The differences are just too small to see at small distances. But the differences accumulate and so your chain of observers will just be forced to conclude that there is a difference between adjacent observers even if they cannot see it.
 
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JJM 777 said:
I agree that interaction takes time, it happens at a speed. Everything what happens, happens at a speed and takes some time.

This notion alone does not negate the possibility that all existence might be simultaneous.
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Strictly speaking, that's probably correct - logically, there might exist theories with finite propagation of influence but universal simultaneity.

But that wasn't my point. The point was that all interactions taking place at finite speed makes it possible logically for there to be no unique "now". Moreover, according to all the experimental evidence that possibility is reified in the form of special and general relativity.

As for the rest of your post, go read an introductory book on relativity, like this one: http://www.bartleby.com/173/1.html .
 
JJM 777 said:
If events within 0.9 light cones distance from each other are "local" and "chronologically ordered", I cannot see why events within 1.5 light cones from each other do not become chronologically ordered with each other, by a witness at half-way between them for whom they both are "local" and "chronologically ordered".
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If I send (A) an 0.75c signal in all directions, which triggers an event (B) 0.75ly to my left, and triggers another event (C) 0.75ly to my right, the A-C ordering is invariant, and the A-B ordering is invariant, but the B-C ordering is not. I cause them both (they're both in my light cone) but they do not cause each other.

Go ahead, JJM. Do the math. Don't just say "I guess there's an observer who X", construct the observer, assign him coordinates, and show that there's a causality-paradox. There isn't.
 
JJM 777 said:
It looks like I will again end up neither understanding nor believing that the chronological order of remote events would be relative, while the chronological order of local events is not.
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It looks to me as though you're either unfamiliar or uncomfortable with the mathematical notion of a partial order.

In what follows, I'm going to assume the special theory of relativity is applicable.

JJM 777 said:
If events within 0.9 light cones distance from each other are "local" and "chronologically ordered",
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Light cones often overlap without coinciding, so it's hard to make sense of "0.9 light cones distance" between two events.

Let's call your events e1 and e2. There are four possibilities:
  1. e1 and e2 are exactly the same event.
  2. e1 lies within the past light cone of e2.
  3. e1 lies within the future light cone of e2.
  4. e1 lies outside the light cones of e2, and e2 lies outside the light cones of e1.
With possibilities 1, 2, or 3, all observers will agree on the chronological relationship between e1 and e2. With possibility 1, e1 and e2 happen at the same time and place. With possibility 2, e1 happens before e2. With possibility 3, e2 happens before e1.

With possibility 4, different observers may disagree about whether e1 happened before or after e2 or at the same time.

JJM 777 said:
I cannot see why events within 1.5 light cones from each other do not become chronologically ordered with each other, by a witness at half-way between them for whom they both are "local" and "chronologically ordered".
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If e1 and e2 lie outside each others' light cones, then any witness W to those events will see them at events w1 and w2, where w1 lies within the future light cone of e1 and w2 lies within the future light cone of e2. Furthermore the world line of W connects w1 and w2, so events w1 and w2 must be ordered in time, and all observers who see both events w1 and w2 will agree on the order of events w1 and w2.

Suppose, without loss of generality, that w1 precedes w2. That tells you nothing about the chronological relationship between e1 and e2. Witness W may be able to calculate that e1 happened before e2 in W's coordinate system, but some other witness may be able to calculate that e2 happened before e1 in that other witness's coordinate system. When e1 and e2 lie outside each others' light cones, the results of any such calculation are coordinate-dependent.

When e1 and e2 lie outside each others' light cones, there is no absolute sense in which they are ordered in time. The ordering you get by combining causality with local chronologies is not a total order; it's a partial order.

That's a mathematical fact with implications for computer science as well as relativity. See, for example, chapter 2 of
W D Clinger. Foundations of Actor Semantics. PhD dissertation, MIT, 1981, MIT AITR-633. http://dspace.mit.edu/handle/1721.1/6935​
 
sol invictus said:
Well, there are obviously no rules for what's going to help someone understand something. But to me, talking about infinite speed for light is very misleading (especially when you add that it's not an infinite velocity, which simply doesn't make sense). If you watch a light pulse go by, it definitely moves at finite speed: c. If you watch two light pulses approach head-on, their relative speed is 2c - a bit difficult to understand if you'd been told that the speed of light is "infinite", no?

If you were yourself moving very close to c, you'd see objects approaching you at nearly speed c (again, finite), but the distance to them would be shortened due to length contraction and therefore they'd arrive in a very short time. So in no case are there any infinite speeds involved.
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I find Mitch's use of 'infinite' not only utterly incorrect but very misleading.

Simplification is one thing; abuse of concepts is another.
 
JJM 777, to see how events in one frame of reference that are simultaneous are not necessarily simultaneous in another frame of reference, take a look at this graphic. As others here have said, the observation of events all boils down to one thing: the speed of light (since to observe something it must be seen). And since all observers in all frames of reference will agree on the speed of light, that means that they MUST view things like the passage of time differently (hence the idea of simultaneity between reference frames being defunct). This forms the foundation of the effect of time dilation, which is an extremely well-documented and proven effect.

Let me tackle this from another direction: JJM 777, do you accept the experimental verifications of time dilation in special relativity? If so, then you must give up on some of these ideas of yours where you seem to be insisting upon some kind of special, absolute frame of reference. If not, then please explain why not.
 
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