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A or B theory of time?

Marin

Marin

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Narushima said:
Very good.

You just need to take the idea a little further. You said that the time intervals are dependent on a reference frame.

Now suppose we are talking about more than one event - two bombs going off in my example - which are not causally connected.

The time interval between those two events is not the same for different reference frames, in other words, it depends on the reference frame.

So here is the question:

Which reference frame is the 'real' one?

Suppose in one frame bomb 1 goes off at X seconds and bomb 2 at Y seconds after (this time they do not blow simultaneously for simpler illustration). In a different frame even if bomb 1 also goes off at X seconds on the clock, bomb 2 will not - bomb 2 will go off at Z seconds after.

So when did bomb 2 go off, Y or Z seconds after?

There is no reason why we should accept the answer of one reference over the other (as long as they are both inertial frames but never mind that) - they are both 'correct.'
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Ok, I follow you here, the following paragraph is where we part.

Narushima said:
Your own thought experiment about the ball is more subtle and would be equivalent to saying that bomb 1 goes off at 'X seconds' in all reference frames. The problem is that 'X seconds' doesn't exist in the first place because time is always measured as the temporal movement of events, e.g. each tick of the clock. Because relativity affects the duration of temporal movements how any event is experienced temporally will always depend on the reference frame.

So while it is true that your ball popped into existence, it is impossible to define the exact 'moment' when it did so. Which means that even if we use t = 0 in the big bang as the original reference point, just because you saw that ball pop into existence 14 billion years, 3 months, 2 days, 4 hours, 20 minutes and 33 seconds later does not mean someone in a different reference frame will agree with you - a different reference frame will report that time as being slightly different (how different depends on how close to c the frame has been moving and for how long).
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The crucial thing in my example of the ball was to show that there is only a finite reach of events we can pass through given the maximum possible speed is c. The duration of these events may be different in each frame and the exact moment of their refference may vary, but what matters is (like you said) that the order of the events is intact. So the ball would have to begin to exist in all frames at a certain point. What matters is wether this existence is in the past or present of a refference frame.

Now, as we've concluded, present and past are relative based on one's frame but the amount of frames is finite. (Or rather the reach in which all refference frames are positioned is limited by the maximum speed that is c.) So the question at hand is "Is an event in the past for all refference frames?". I'll visualize:

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In the upper sketch there is a hypothetical scenario in which all observers share the same position, speed and velocity thus they all share the same refference frame and in that refference frame the event that occured (which is in a certain interval of X seconds, with the amount being dependant on the frame the observer belongs to).

The bottom sketch presents a widened frame (marked green) in which an observer going at maximum possible speed of c is held. Now since from the point of the initial frame, with a limited reach of c, the observer can only go so far if the event is beyond his reach (even beyond the amount of time he can steal or add) the event will still be in the past. Now since the only other frames would be those with lower speeds, the difference in time compared to the first refference frame in the upper sketch would only be smaller, the event is objectively in the past because it belongs in the past of all refference frames.

In case my use of the word "time" is confusing, just replace it with number of events. Suppose the observer moving at c (bottom sketch) is moving through an amount of events set in X at a given increased or slowed down rate, if the event that we're trying to reach is beyond the limit of the events we can skim through (in difference to the initial frame) then it belongs in what we deem past.

I hope this makes sense as I'm tired and don't really know how to properly explain it better than this.

Narushima said:
In other words there is no such thing as "absolute time" - a single reference frame which we can use as a reference for comparison to all others because the laws of physics are the same in all reference frames (again assuming they are inertial reference frames).

One final thought experiment for you: imagine that we have a set of metre rulers and we mark a point on each of them, e.g. 1.1 cm or something. Now suppose we stretch the entire rulers by varying amounts (our rulers were made of highly elastic material capable of permanent deformation). This is basically what time dilation does to our experience of time in relativity except that we have no reference metre ruler to begin with because all rulers come into existence stretched to different lengths.
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Ok, there may not be an absolute refference frame but there is an absolute order of events. Now if events are ordered as preceeding or succeding, there must be a certain interval between them. (In contrast to simultanious events.) It doesn't matter how that interval is perceived as in the eyes of an observer, if the interval is beyond reach of all observers (all refference frames basically) then that interval is out of grasp for the observers, therefore not a part of their reality anymore in the same sense as the events that are in their grasp.
 
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