Friday, July 25, 2008

Clarification on Relativity

There appears to be some confusion over my previous post on Relativity so I want to produce some further clarification. First, we know that Einstein’s version of the train was used to destroy the concept of “simultaneity” because what is observed on the moving train as being simultaneous was not observed as being simultaneous outside the train. In reality what this demonstrated is that time itself is fluid; there is no objective time. Time, apart from frame of reference, is meaningless. Far from being a defeater to my argument (as Paul C. seems to think), this was my point.

Brian Greene gives his own example of this experiment:

Imagine that the leaders of two warring nations, sitting at opposite ends of a long negotiation table, have just concluded an agreement for a ceasefire, but neither wants to sign the accord before the other. The secretary-general of the United Nations comes up with a brilliant resolution. A light bulb, initially turned off, will be placed midway between the two presidents. When it is turned on, the light it emits will reach each of the presidents simultaneously, since they are equidistant from the bulb. Each president agrees to sign a copy of the accord when he or she sees the light. The plan is carried out and the agreement is signed to the satisfaction of both sides.

Flushed with success, the secretary-general makes use of the same approach with two other embattled nations that have also reached a peace agreement. The only difference is that the presidents involved in this negotiation are sitting at opposite ends of a table inside a train travelling along at constant velocity. Fittingly, the president of Forwardland is facing in the direction of the train’s motion while the president of Backwardland is facing in the opposite direction. Familiar with the fact that the laws of physics takes precisely the same form regardless of one’s state of motion so long as this motion is unchanging, the secretary-general takes no heed of this difference, and carries out the light bulb-initiated signing ceremony as before. Both presidents sign the agreement, and along with their entourage of advisers, celebrate the end of hostilities.

Just then, word arrives that fighting has broken out between people from each country who had been watching the signing ceremony from the platform outside the moving train. All those on the negotiation train are dismayed to hear that the reason for the renewed hostilities is the claim by people of Forwardland that they have been duped, as their president signed the agreement before the president of Backwardland. As everyone on the train—from both sides—agrees that the accord was signed simultaneously, how can it be that the outside observers watching the ceremony think otherwise?

Let’s consider in more detail the perspective of an observer on the platform. Initially the bulb on the train is dark, and then at a particular moment it illuminates, sending beams of light speeding toward both presidents. From the perspective of a person on the platform, the president of Forwardland is heading toward the emitted light while the president of Backwardland is retreating. This means, to the platform observers, that the light beam does not have to travel as far to reach the president of Forwardland, who moves toward the approaching light, as it does to reach the president of Backwardland, who moves away from it. This is not a statement about the speed of the light as it travels toward the two presidents—we have already noted that regardless of the state of motion of the source or the observer, the speed of light is always the same. Instead, we are describing only how far, from the vantage point of the platform observers, the initial flash of light must travel to reach each of the presidents. Since this distance is less for the president of Forwardland than it is for the president of Backwardland, and since the speed of light toward each is the same, the light will reach the president of Forwardland first. This is why the citizens of Forwardland claim to have been duped.

When CNN broadcasts the eyewitness account, the secretary-general, the two presidents, and all their advisers can’t believe their ears. They all agree that the light bulb was secured firmly, exactly midway between the two presidents and that therefore, without further ado, the light it emitted travelled the same distance to reach each of them. Since the speed of the emitted light to the left and right is the same, they believe, and in fact observed, that the light clearly reached each president simultaneously.

Who is right, those on or off the train? The observations of each group and their supporting explanations are impeccable. The answer is that both are right. … The only sublety here is that the respective truths seem to be contradictory. An important political issue is at stake: Did the presidents sign the agreement simultaneously? The observations and reasoning above ineluctably lead us to the conclusion that according to those on the train they did while according to those on the platform they did not. In other words, things that are simultaneous from the viewpoint of some observers will not be simultaneous from the viewpoint of others, if the two groups are in relative motion.

This is a startling conclusion. It is one of the deepest insights into the nature of reality ever discovered. Nevertheless, if long after you set down this book you remember nothing of the chapter except for the ill-fated attempt at détente, you will have retained the essence of Einstein’s discovery. Without highbrow mathematics or a convoluted chain of logic, this completely unexpected feature of time follows directly from the constancy of the speed of light, as the scenario illustrates. Notice that if the speed of light were not constant but behaved according to our intuition based on slow-moving baseballs and snowballs, the platform observers would agree with those on the train. …

The constancy of the speed of light requires that we give up the age-old notion that simultaneity is a universal concept that everyone, regardless of their state of motion, agrees upon. The universal clock previously envisioned to dispassionately tick off identical seconds here on earth and on Mars and on Jupiter and in the Andromeda galaxy and in each and every nook and cranny of the cosmos does not exist. On the contrary, observers in relative motion will not agree on which events occur at the same time. Once again, the reason that this conclusion—a bona fide characteristic of the world we inhabit—is so unfamiliar is that the effects are extremely small when the speeds involved are those commonly encountered in everyday experience. If the negotiating table were 100 feet long and the train were moving at 10 miles per hour, platform observers would “see” that the light reached the president of Forwardland about a millionth of a billionth of a second before it reached the president of Backwardland. Although this represents a genuine difference, it is so tiny that it cannot be detected directly by human senses. If the train were moving considerably faster, say at 600 million miles per hour, from the perspective of someone on the platform the light would take almost 20 times as long to reach the president of Backwardland compared with the time to reach the president of Forwardland. At high speeds, the starting effects of special relativity become increasingly pronounced.

Greene, Brian. (1999). The Elegant Universe. New York: Vintage Books. 34-37 (all italics in original)
Now we have three different examples (Einstein’s, my own, and now Greene’s), all of which really state the same thing. The sequence of events that one observes is dependent upon the relative motion between the observer and what is being observed. While Einstein and Greene both dealt strictly with concepts of simultaneity, it doesn’t take much thinking at all to change this into my own example where we have an event that occurs before another event according to one frame of reference occur after the other event in another frame of reference. In fact, in Greene’s second book (The Fabric of the Cosmos), he gave an illustration of this regarding cuts in the “space-time loaf.” Unfortunately, I’ve loaned that particular book out for the moment. But I will reproduce my own version of cutting the space-time loaf here.

In this picture, we have three events that occur separated by vast distances in space and time. For example, we could say that A is ten million light years from B, and likewise B from C (these are just arbitrary values for the sake of demonstration). We could also say that it takes 10 million years to go from “blue” to “red” to “green.” (Thus, time is going right to left.) Thus, the vertical axis of this diagram represents distance, the horizontal axis represents time.

Now from the perspective of one observer, all the “red” events at A, B, and C occur simultaneously. This observer has a “timeslice” that is directly perpendicular (in our graph). But from another perspective, the “green” event of A is simultaneous with the “red” event of B and the “blue” event of C. This “timeslice” is at a roughly 45 degree angle (both in space—that is distance—and in time—he is in the “future” if time is flowing from right to left).

Now let us give the graph some non-controversial meaning (although you must take note that the graph will not be to scale under these circumstances). Take line A as the life of a star that goes supernova (at green), line B is the life of a star that dwindles to a dwarf star (at green), and line C represents events that occur on Earth until Global Warming melts us (at green). Let’s further say that on Earth, the red dot represents the signing of the Declaration of Independence, and the blue dot represents the construction of the Great Pyramids. The red and the blue dots of the two stars are adjusted accordingly to be arbitrary events that occur at the correct time-scale.

Now obviously the observer that views perpendicularly sees that at the signing of the Declaration of Independence, both stars had the same amount of time left before reaching their ends. However, the observer at the 45 degree angle sees that the supernova star has actually gone supernova while the Great Pyramids are being built!

Now let us give it a little more controversial meaning (again, the graph is not to scale under these circumstances). Let us deal only with lines A and C. Let line A represent the bullet of a gun and let line C represent the finger that pulls the trigger. Line A is: “blue” = bullet loaded, “red” = bullet fired, “green” = bullet kills target. Line C is: “blue” = trigger finger in killer’s pocket, “red” = finger pulls trigger, “green” = finger rubbing killer’s nose. Now in this instance, the distance between line A and C is very, very short. But since a man’s finger and a bullet can never occupy the same space at the same time, there will always be some distance—even if it is only an atom’s length! As a result, the distance to the observer at the 45 degree angle (to both space AND time!) is going to be very, very far away. But the results are the same.

In one perspective, the trigger finger pulls the trigger at the instant the bullet is fired. But in the other perspective, we have the bullet being fired when the killer’s finger is in his pocket. Now the distance to this observer is probably outside the dimensions of our universe and far, far into the future from now. But that observation point does exist in theory. In theory, viewing any two events at the appropriate “timeslice” of the spacetime loaf will yield contradictions in cause and effect. Naturally, these are on such a large scale that for all practical purposes we can ignore them.

So once again, we can relate this back to what I’ve said about the logical before. Cause and effect is determined by what logically must occur before another thing can happen, NOT by what temporally occurs. Usually the logical and temporal correspond, but when it does not we have evidence that we have to adjust our frame of reference. There will be some frame of reference where that cause will temporally precede its effect, but that might not be our observational frame of reference. Our frame of reference, taken at face value, would cause us to be mistaken.

By the way, I also point out that this is the basis of the Lorentz transformation equations anyway. Those equations in essence seek to show the relationship between various frames of reference. And the point isn’t that cause and effect are destroyed at all—that’s never been what I claimed. Rather it’s the fact that cause and effect are temporally meaningless when there is no objective time; instead, they can only remain logically meaningful.

Logical precedence is not bound by frame of reference; it is the objective quality that causes must precede effects. Temporal “before” are strictly bound to frame of reference; it will always be a subjective quality. On Earth, it usually matches the objective frame of reference because the relative speed between observer and observee remains very small.

Hopefully that helps clear it up a bit.

1. Unfortunately you are still in error - not because you are stupid (you are not) but because you have failed to take into account one very important factor. That factor is the necessity that an observer must be within the light cone of a particular cause in order to observe it to begin with.

In your version of the spacetime loaf, you assume that it is possible for an observer to view any sequence of events (causes and effects) in any order, simply by placing themselves at the correct angle to observe a particular slice of spacetime. This is not the case because an observer must themselves be located at a specific point within spacetime in order to view any sequence of events - specifically, they must be within the light cone of those events.

Let's take a particular event, say a bullet being fired, and agree that any effects of that cause must be in its future light cone. In order to observe the bullet being fired, however, an observer must also be within its future light cone - and consequently will always see any effects after the initial cause. The outer edge of the light cone places a limit on the possible perspectives that an observer can have of that chain of events - i.e. it limits the "angle" that may be achieved in viewing a spacetime slice of those events.

Specifically (and contrary to your example) it is impossible for an observer to gain a sufficiently "angled" perspective to observe an effect happening before the cause - because in order to do so they would need to be outside the light cone of the cause, and would not in fact be able to observe it in the first place.

2. Peter, I have to agree with Paul C. Imagine that the photons reflected by the finger on the trigger create a spherical envelope expanding at the speed of light. Because c is faster than the mechanical chain of causality from trigger to bullet, the finger-on-trigger image envelope encloses the bullet before it is fired. Thereafter the image of the bullet being fired moves out in its own envelope, but that envelope is always within that of the trigger finger. So all observers see the finger on the trigger first. The chain of causality makes the effect "too close" to the cause to be seen before the cause.

I like the example of the light at the middle of the table at the treaty signing. In fact, I was thinking of a light at the mid-point of the train to trigger Adam and Bill. I just want to be clear that if Charlie does see Adam and Bill press their buttons simultaneously while the train is moving that means that the bomb sees Bill's signal in both Charlie's and the trains reference frames and the train does not blow up.

3. Peter, I have to agree with Paul C. Imagine that the photons reflected by the finger on the trigger create a spherical envelope expanding at the speed of light. Because c is faster than the mechanical chain of causality from trigger to bullet, the finger-on-trigger image envelope encloses the bullet before it is fired. Thereafter the image of the bullet being fired moves out in its own envelope, but that envelope is always within that of the trigger finger. So all observers see the finger on the trigger first. The chain of causality makes the effect "too close" to the cause to be seen before the cause.

I like the example of the light at the middle of the table at the treaty signing. In fact, I was thinking of a light at the mid-point of the train to trigger Adam and Bill. I just want to be clear that if Charlie does see Adam and Bill press their buttons simultaneously while the train is moving that means that the bomb sees Bill's signal in both Charlie's and the train's reference frames and the train does not blow up.

4. Sorry for the double post.
Jason

5. Not to dog-pile, but I concur with Jason and Peter C: I still believe relativity enforces the directionality of causation regardless of reference frame.

But beyond that (and to echo a point Peter C made earlier), how can you claim to have divorced the notion of temporal causations from logical causation when in order to distinguish the “logical” cause from its effect you must still first check to see which of two events occurred (temporally) first in some “privileged” reference frame? Isn’t doing that just a back door admission that “logical causation” (as you’ve defined it) is still synonymous with “temporal causation”?

Perhaps I can best make my point by asking you to define a method for distinguishing a cause from its effect that makes no reference whatsoever to any timeline. I’d contend that if you can’t do that, then you’ve failed to establish that there is, in fact, any difference between “logical” and “temporal” causation.

6. Okay, let's start small then (this is for any of you guys who wish to respond, although it directly uses the terminology Paul C. used).

Would you agree that all the observers of the events in Einstein's train (and in Greene's version) are within the "light cone" of all the events that occured?

7. Peter: yes. If they were not within the light cone of the events, they would not be able to observe anything.

It occurred to me today that it might be easier to illustrate this using Greene's own example. Where would an observer have to be standing in time and space in order to observe the president of Forwardland signing the treaty before the lightbulb came on?

8. BTW, one other thing.

Jason said:
---
Because c is faster than the mechanical chain of causality from trigger to bullet, the finger-on-trigger image envelope encloses the bullet before it is fired.
---

Except the speed of the causative action doesn't matter. All that matters in the loaf illustration is that there is a distance between the place where two events occur. And to keep within modern theory, we can go all the way down to Planck length in distances (below that is theoretically--not just mechanically--impossible to detect), which is still vastly smaller than the distance between an atom and its electrons.

At this point, it might help if you think in terms of scale. Imagine zooming in so that the atoms that make up the finger and the atoms that make up the bullet equivalent to galaxies of stars.

In any case, I would also ask if we weren't dealing with causality here, but were instead dealing solely with two different and non-related events, would you have any problems at all with anything that I've said so far?

9. Paul said:
---
If they were not within the light cone of the events, they would not be able to observe anything.
---

Okay, so given this then within the same "light cone" some people view some events as occuring simultaneous to other events, while other view those same events occuring one before the other (as long as the various observers are in different relative motion). This is, of course, the point Einstein made (I'm sure you'll agree, so I'll just ask my next question):

Is it possible for someone in the same "light cone" to see event A occur before event B while someone else (in a different relative frame) can see event B before event A? (At this point, assume no causality.)

10. At this point I cannot see a way how that would be possible.

11. Peter, the speed of causation has to matter. If it was faster than c, then you would indeed see the effect before the cause. As it stands, though, the signal from the cause has to reach the effected object for the effect to be caused. How does the bullet know to leave the gun if the signal of the trigger hasn't reached it? How does any observer see the effect and yet not see the signal from the cause, which has to reach the point at which the effect happens in order for there to be an effect in the first place?

Take the example of the supernova and the building of the pyramids. Suppose Egyptians see the supernova and decide it is an auspicious moment to build the pyramids. So the supernova causes the building of the pyramids. Now suppose the Egyptians have a disco ball hanging in a palm tree that reflects light in all directions. When looking through your telescope you see the Egyptians pointing up at the supernova and there in the disco ball is the image of the supernova reflected towards you. So you have to see the light from the supernova at least as soon as you see the Egyptians deciding to build the pyramids. In fact, because the light you see is reflected, it is not taking the shortest path, which is a straight line (in curved space a straight line will appear curved, etc. but that doesn't alter this discussion). So light from the supernova should definitely reach you before you see the Egyptians seeing it.

As for non-causally related events, I agree that there is such a thing as a propter hoc fallacy. As for the initial discussion between you and Paul, I don't know how deep I want to get into that :). I will note that light does not experience time; as soon as it is emitted it is absorbed as far as the photon is concerned. (Not only is a clock moving at the speed of light stopped, but the distance the photon would "see" is contracted to nothing). So from light's perspective you could have an effect at the same time as a cause, just not before. As for questions in quantum mechanics like Schroedinger's cat (looking in the box determines whether cat is alive or dead) I'm not sure that looking in the box could be considered the "cause" of the cat's death; just the point at which we know its dead (or alive). I'm not sure if that is what you meant by quantum mechanics causing uncertainty in direction of causality though.

12. Maybe some math will help.

I’m open to correction but I think the following proves conclusively that Relativity preserves the order of causation:

Imagine a gun being fired in a 1 dimensional stationary reference frame. In a coordinate system defined within that frame, let the trigger of the gun be located at x1and let the end of the gun barrel be at x2. To simplify the math let x1 = 0. Let’s assume the gun barrel is positioned such that x2 is a positive number. Let t1 be the time in the stationary frame when the trigger is pulled, and let t2 be the time in the stationary frame when a bullet leaves the end of the barrel. Again, to simplify we’ll let
t1 = 0 seconds.

Now, in addition to the stationary frame, imagine a reference frame moving at speed v with respect to the stationary system. In the moving system let X1 be the position of the trigger, X2 be the position of the end of the barrel, T1 be the time when the trigger is pulled and T2 be the time when the bullet leaves the gun barrel.

According to the Lorentz transform we have:

T1 = B[t1-v(x1)/c*c] = 0
(since t1 = x1 = 0)

and

T2 = B[t2-v(x2)/c*c]

where,

B = 1/SQRT[1-(v*v)/(c*c)].

The question now is whether T2 can ever occur prior to T1 for some v. Under our assumption that
x1=t1=0, this equates to: can T2 ever be negative?

For T2 to be negative we must have:

t2 - v(x2)/c*c < 0.

Solving for v, we obtain:

v > t2(c*c)/x2.

Since x2/t2 is the velocity of the bullet (remembering that distance = rate * time), let us define Vg as that velocity and write:

v > (c*c)/(Vg).

This result means that if t2 < 0, then either v or Vg must exceed the speed of light. Of course, neither condition is allowed by Special Relativity.

13. “Is it possible for someone in the same "light cone" to see event A occur before event B while someone else (in a different relative frame) can see event B before event A? (At this point, assume no causality.)”

If we’re assuming no causality, then I’d say “yes”.

From my previous post I claimed that the condition for T2 to occur prior to T1 (for T2 to be negative) is,

v > t2(c*c)/x2.

If I’m right about the above condition, and if the events at t1 and t2 are *not* causally related (i.e. the bullet leaving the barrel is independent of the trigger being pulled), then there are no limitations on the possible values that x2/t2 = Vg can take. This means that Vg can exceed c, resulting in T2 < 0, even though t2 > 0.

14. Just to clarify.

In my first example I've assumed that the bullet is initially aligned with the trigger at t1 and leaves the barrel at t2, which makes x2/t2 = Vg the average velocity of the bullet.

In the second example I *don’t* assume this: the events at t2 and
t1 are independent, so x2/t2 = Vg is not, in general, the bullet’s velocity. Thus the meaning of Vg in the second example is not the same as the first.

I fear my sloppy nomenclature creates the impression that the bullet speed in example two can exceed c. It can’t.

To avoid this confusion, perhaps I should have used two guns being fired independently in the second example and compared, say, the times at which the bullets leave their respective gun barrels. In that scenario there are clearly no limitations on the values that t1 and t2 can take.

15. Jen,

Thanks for the math! I will look it over. However, I also realized today that I don't need to prove there's an observation position where the cause comes before the effect, because everyone agrees that we can have causes simultaneous with effects. Indeed, I see that Jason pointed this out as well in one of his comments since I last looked.

So I actually was trying to over-prove my case anyway. The simple proof for why the logical "before" is what is relevant to cause and effect is because there is no temporal "before" during simultaneous events.

Let us take the situation where on the train, Adam and Bill press their buttons and the train blows up because Adam's signal reaches the bomb before Bill's does; Charlie sees both signals arriving simultaneously, but the train explodes.

Now reverse them. This time, Bill's signal (from his perspective) gets there before Adam's signal. The train does not blow up. But Charlie still views both signals as arriving simultaneously.

Therefore, from Charlie's perspective, there is no difference between the two cases. Yet the outcome is different. Charlie will not be able to temporally demonstrate cause and effect here; yet the logical cause and effect still stands.

16. Hi Peter,

In order for cause and effect to occur simultaneously, you’d have to have a reference frame moving at the speed of light, which violates Relativity. Adam and Bill’s mass approaches infinity as their speed approaches c. So causes most definitely cannot be simultaneous with effects under Relativity.

But even if cause and effect *were* to appear inverted (or simultaneous) to Charlie in some imagined world, logical causation is still dependent on a temporal ordering. Why? Because you claim the ‘cause’ of the explosion is still the individual who acted *first* in the moving frame—though you’ve yet to explain just what it is that makes Adam’s and Bill’s the “appropriate” frame.

To reiterate my earlier comment, for your argument about logical causation to go through, you need to first explain what makes something the cause of an event without recourse to any temporal ordering of events in any reference frame.

17. Jen said:
---
Adam and Bill’s mass approaches infinity as their speed approaches c.
---

Yes, but light moves at c without having an infinite mass. And since light most certainly does exist, then that is sufficient for my argument.

I'm not dealing with that which is actually possible for human to observe (for that matter, even Einstein's train example is never going to be observed in real life), but rather what is theoretically possible.

Jen said:
---
But even if cause and effect *were* to appear inverted (or simultaneous) to Charlie in some imagined world, logical causation is still dependent on a temporal ordering. Why? Because you claim the ‘cause’ of the explosion is still the individual who acted *first* in the moving frame—though you’ve yet to explain just what it is that makes Adam’s and Bill’s the “appropriate” frame.
---

Actually, my definition of a cause is irrespective of temporality. My actually definition of a cause is "That which is a necessary precondition for a specific effect." The only thing about temporal order is that in our frame of reference, we view them temporally. We'll never get to the speeds necessary to violate this.

This is an important philosophical point because cause and effect still functions even without temporal existence. That is, before spacetime, logical causality would still be valid. And the existence of light is all that's necessary to demonstrate that a non-temporal framework is valid (even if we do not take into consideration the instant "before" the Big Bang).

Jen said:
---
To reiterate my earlier comment, for your argument about logical causation to go through, you need to first explain what makes something the cause of an event without recourse to any temporal ordering of events in any reference frame.
---

Ultimately this is a metaphysical question. It's a question of ontology (being). And if we include Quantum Mechanics into the equation, it affects physics too.

And this also brings up the fact that Quantum Theory does deal with signals that move faster than the speed of light (because if you send two particles in opposite directions know that they have opposite spin but not knowing which one either particle has, they both behave as if they're spinning both directions; but as soon as you measure one and collapse it to a definite spin, it forces the other particle to instantaneously take the opposite spin regardless of how far away it is). Also, you have particles that spontaneously "burst" into existence with "no cause" (but then that's because they're looking for a temporal cause), and there are anti-particles that acts as their twin particles only they're going backwards through time, etc.

Ultimately, time itself ought to be a two-way street (in physics, the equations would work either way), and it's only the oddity of entropy that gives time a "direction" from our point of view. But if time flowed backwards, then we'd have effects preceding causes; and mathematically the physics works this way (again, ignoring entropy).

I likewise believe that time, as we think we know it, is a myth. But that's another story :-)

18. My point was that in your thought experiment Bill and Adam must be moving at the speed of light for the events to be simultaneous, which would be impossible. If you have another thought experiment in mind that can show simultaneity of cause and effect in a Special Relativistic framework without violations, then I stand corrected.

Yes light does not have mass and so is not subject to restrictions on speed, but that fact alone doesn’t salvage the original thought experiment.

At one point you say,

“Actually, my definition of a cause is irrespective of temporality. My actually definition of a cause is ‘That which is a necessary precondition for a specific effect.’ The only thing about temporal order is that in our frame of reference, we view them temporally. We'll never get to the speeds necessary to violate this”

But later you seem to punt on the question of just what a cause *is* by putting it into the category of ontology and metaphysics.

And yet somehow you can say with certainty what constitutes the “cause” and what constitutes the “effect” with respect to Bill, Adam, and the explosion. Where does that certainty come from if not the temporal ordering of events in some reference frame?

On the one hand you don’t seem to want to commit to a solid answer; on the other hand you’d need to have that solid answer to ever know the explosion wasn’t actually the cause of Bill’s and Adam’s actions.

So I ask again. Without some ordering of events, how do you know that the explosion isn’t actually the cause in your thought experiment?

Thanks for the discussion.

19. Jen said:
---
Yes light does not have mass and so is not subject to restrictions on speed, but that fact alone doesn’t salvage the original thought experiment.
---

Actually, I don't think you understood what the original thought experiment was for. (This isn't a slight, it's just that you weren't part of the original discussion, of which this has departed a great deal!)

Anyway, you said:
---
But later you seem to punt on the question of just what a cause *is* by putting it into the category of ontology and metaphysics.
---

Far from being a punt, this is actually putting it in the correct context. Causality ultimately ends up being a metaphysical issue. And I don't think any physicist would ultimately quibble with that. After all, the goal of physics (at least those seeking the ToE/GUT), is to be able to encapsolate that which is true for all frames of reference. This is why the General Theory of Relativity is an advancement over the Special Theory of Relativity; the General Theory incorporated gravity--another force--and it did so by examining another framework, and showing that gravity was equivalent to constant acceleration.

So if the laws of physics cannot explain something (namely, causality) at a specific framework that does exist (namely, the speed of light) then we are left with an incomplete theory. That theory may work fine for most things--Newton's physics was good enough to get us to the moon and back--but it will not be complete. So even if we say that sub-c velocities always have causes temporally preceding effects, this still doesn't address the fact that cause and effect occur when there is no temporal existence at the speed of c.

So look at it from the perspective of a photon. I press a key on my computer and a character appears on my screen a split-second later. From the photon's perspective, however, there is no "split-second later." There is no temporal cause and effect; yet it remains real that from my framework my pressing a key preceded the character appearing on the screen. The universe is real for both me and the photon's perspective. Defining causality in the basis of time makes it impossible to speak of cause and effect for the photon; yet the universe the photon "experiences" is different than the universe it would "experience" if my fingers didn't cause the character to appear on the screen (via the convulted route of electrical circuits, etc.).

You said:
---
Without some ordering of events, how do you know that the explosion isn’t actually the cause in your thought experiment?
---

Because explosions, by definition, need causes. They don't just happen.

Now this is an insight that I got because I'm temporally based. That's true enough. But having discovered this from a temporal position, I can still think about the implications it would have for that photon. And that means I realize that even if we compress all events into a singularity of time the explosion is still caused by something, even though the cause and the effect do not follow sequentially in time. As a result, in an ultimate sense, I argue that cause and effect cannot be temporally linked; they have to be logically linked. It's only if there's a logical linkage that we can have cause and effect without the passage of time.

20. I don’t believe the perspective of a photon helps your case.

From the perspective of a photon you get a singularity. In the case of a singularity, the meaning of an “event” becomes indeterminate, and there is therefore no way to know what a photon “perceives” from its reference frame. Given that they are themselves “events”, this indeterminacy includes “cause” and “effect”.

Singularities, I believe, are one reason physicists long ago began suspecting that Relativity is incomplete. They are also a problem for the Big Bang.

21. The last few posts have got me thinking about a couple of questions I've had from time to time on light speed and timeless perspective. First off, with the train or photon, how does it "fit" between its departure station (emission point) and arrival station (absorption point). Remember that at least the train has, within its reference frame, length in the direction of travel, while it sees the universe as contracted down to nothing in that same direction of travel.

More seriously is the question of actual "awareness" in a light-like timeframe. With the train moving at c, from Adam and Bill's perspective there won't be time for their signals to move an atom's length much less reach the bomb. How can they even be aware of anything since their trip is instantaneous? How can there be any physical action in the train's reference frame?

It's OK for a photon to be timeless because it is both mindless and unchanging (frozen) with no moving parts or thoughts to think. I'm not too sure about anything else though.

22. Peter,

I just realized this:

In the limit as v approaches c, the rate of time in the moving frame approaches zero (due to time dilation). So if anything a photon (in its rest frame) sees a frozen-snapshot-in-time of our world, which is the exact opposite of seeing all events simultaneously. With just a snapshot, a photon actually wouldn’t have opportunity to see even *one* example of causation.

I still stand by what I said about singularities, but I wanted to fire this off because I think it'll do a much better job of convincing you that SR won't help your argument.

23. Forgive me for saying so, Peter, but you seem to be really stretching to find something that will support your initial point. My original contention was that it is impossible to talk about a logical before without a temporal before as the basis - and despite offering three different examples, you have failed to deliver a single case where the logical before is not based on a temporal before. The irony of course is that the identification of a logical before in each case is causally and temporally related to the occurrence of a temporal before - it is impossible to talk about a logical before until after a temporal before has been observed!

Give us a single case of a logical before that exists without any temporal before as a reference point, and you will have proved your point convincingly. My contention is that you cannot provide any such case, and that the "logical before" is founded entirely on the particular experience of a "temporal before". It is irrelevant of whether different frames of reference under relativity confuse the situation from the perspective of a particular observer - and I think both Jen and Jason have identified the key weaknesses in your current modified argument. A single case will suffice to prove us wrong, and I look forward to seeing it.