Tuesday, February 27, 2007

Cause and Effect

Part I: The Andromeda Paradox
Okay, science and philosophy fans, this one's for you. There's been a lot of discussion recently about Desmond's strange trip to the past and apparent ability to see the future. I believe that both are signs he has become a living causal paradox -- one that highlights some startling aspects of special and general relativity, and raises interesting problems of time and free will. To understand, let's begin with Desmond's namesake, Mr. David Hume.

Hume was an empiricist and believed that we can only know what experience tells us. One of his great philosophical contributions was the notion that causation is really nothing more than our observation of the conjunction of two events. We see A followed by B enough times and infer that there must be a necessary connection between them -- i.e., A causes B. Hume argued that this inference was faulty no matter how often A is followed by B. Constant conjunction is not synonymous with necessary connection.

Hume's claim is pretty wild when you think about it. He basically argued that there's no reason beyond our own experience to think the sun will rise tomorrow. This argument was a punch in the mouth to metaphysics, and spurred a number of convoluted attempts (e.g., by Kant) to preserve some notion of causality that preceded experience. I won't bore you with the details -- suffice it to say that this argument is very important to the history of philosophy but less so for our purposes.

Fast forward to Albert Einstein, whose special theory of relativity radically reshaped our conception of time. One key aspect of the theory is the relativity of simultaneity. If events A and B are separated in space (i.e., not causally related) people in relative motion (e.g., walking and standing still) won't agree whether A and B happened simultaneously, or A was followed by B. This lack of absolute simultaneity, which is a function of the speed of light being constant, has some pretty freaky consequences.

In four-dimensional spacetime, your "present" is the three-dimensional universe comprised of the unique set of events at the intersection of your past and future light cones -- i.e., your plane of simultaneity. When people move at different relative velocities to another, they have different planes of simultaneity and thus different sets of "present" events. At any given moment, in other words, your 3-D universe differs in content from the 3-D universes of people moving around you. Some of their future events are in your present, and vice versa.

This yields what theoretical physicist Sir Roger Penrose terms the Andromeda Paradox. To paraphrase: Desmond, who happens to be walking in the direction of the Andromeda galaxy, passes Charlie singing Oasis on the street. As a result, events in the Andromeda for Des (e.g., the launch of an invading space fleet) will be ahead of those same events in time for Oasis Charlie -- possibly by hours, days, or even weeks. In Charlie's "present," the Andromadeans may still be deciding whether to launch!

This disparity makes no difference to either man because the events in question are too far away to affect them (i.e., outside the causal boundaries set by their light cones). It does, however, raise some difficult questions for free will. As Sir Roger asks: "If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability." And if that launching is predetermined -- in Charlie's universe at least -- how can the Andromadeans' decision to do so truly be free?

Things get even weirder if we posit some way for Charlie and Desmond to affect events in the Andromeda. Pretend there's a method of communication (e.g., subspace radio) that allows instantaneous contact across the universe. An Andromadean warns Des that the invasion fleet has launched. Des walks back to warn Oasis Charlie, who then contacts the Andromadean generals. Charlie's crooning soothes the savage beasts, and he persuades them not to launch the fleet. As a result, free will is preserved at the cost of causal paradox...

It's improbable but theoretically possible that a similar phenomenon explains Desmond's limited precognition on the Island. Desmond witnesses Charlie's death and contacts A, who is light years away. A tells B, whose plane of simultaneity is such that Charlie has not yet died. B contacts Desmond just in time to avert Charlie's death. The main problem with this scenario (aside from the identities of A and B) is that special relativity forbids the transmission of information at speeds faster than the speed of light.

That doesn't preclude the existence of hypothetical particles that are already moving faster than light. Tachyons, for example, are a Star Trek staple, and were used in Watchmen to interfere with Dr. Manhattan's ability to see the future. There's also quantum entanglement, whereby two particles can affect each other instantaneously -- what Einstein called "spooky action at a distance." Our best bet, however, is probably conventional communication via shortcuts through spacetime (e.g., wormholes).

For that latter possibility, however, we need to introduce Einstein's general theory of relativity, so this is probably a good place to break.

Part II: The Chronology Protection Agency
Einstein's theory of general relativity throws a fresh curve in the causation mix. Special relativity treats spacetime as uniformly flat, but general relativity posits that mass literally warps the geometry of spacetime. This contrast raises the intriguing possibility of circumventing light's speed limit by exploiting these warped geometries. The trick is to find something sufficiently massive to wrinkle spacetime in the required way. Luckily, the implosion of Swan Station supplies the perfect fudge along these lines.

Say Swan was in the process of imploding into a small black hole, warping spacetime around the Island. Activation of the Fail-Safe caused the black hole to evaporate, releasing a blast of hypothetical Hawking radiation that punched a wormhole in spacetime. Theoretically, someone could send information through the wormhole at sub-light speed, allowing Desmond to change Charlie's immediate future. And here's where the brain-frying really begins -- it's also paradoxically possible that Desmond can alter his own history via the warp and wormhole.

To see why, recall the light cone we used to illustrate the relativity of simultaneity. In special relativity, where spacetime is flat, Desmond's future light cone is always pointed away from his past. In general relativity, however, the curvature of spacetime can theoretically cause his future light cone to tip. If it tips far enough, Desmond's future light cone can intersect with his past, creating a closed timelike curve. Somehow, Des exploited such warped spacetime geometry to project himself mentally into the past, leaving an imprint of his future self behind.

This obviously creates the potential for massive paradox. Since Des only went back a few years, he couldn't cause the (grand)mother of all paradoxes by killing a parent or grandparent. As we saw, however, his residual memory of the future almost made him to propose to Penny, which paradoxically would mean he never went to the Island to turn the Fail-Safe key. Indeed, Desmond's mere hesitation has already altered the timeline to create small paradoxes. As others have noted, Penny kept a copy of their last photograph the "first time" around.

At this point, you may be wondering whether the very paradoxical character of these causation scenarios renders them impossible by definition. Remember, however, what Hume said about causation -- it's always an empirical question. There's no reason to rule out causal paradoxes independent of experience. This leads most physicists to speculate that the universe operates somehow to prevent or otherwise correct for such paradoxes. One famous speculation in this regard is Stephen Hawking's Chronology Protection Conjecture.

Hawking's conjecture is that the laws of physics are such that backwards time travel can only take place at microscopic scales, thereby preventing causal paradox. He uses the metaphor of a Chronology Protection Agency, "which prevents the appearance of closed timelike curves and so makes the universe safe for historians." An alternative approach is the Novikov Self Consistency Principle, which permits backwards time travel at the macroscopic level, but posits that the universe self-corrects against any alterations to the past that would yield causal paradoxes.

If this all sounds familiar, it should. The Jeweler (appropriately named Ms. Hawking) played the role of Chronology Protection Agent, preaching something similar to the Self-Consistency Principle. As she said to Desmond: "The universe, unfortunately, has a way of course correcting." Des is part of a closed timelike curve caused by his activation of the Fail Safe. If he chooses not to go to the Island, the result will be major causal paradox, triggering a catastrophic course correction that restores consistency by destroying the world -- we all die.

It may even be that Des can now mentally project himself at will through space-time. The clue is the red shoes in his flashback, which are an obvious reference to the ruby slippers in the Wizard of Oz. As Glinda the good witch says to Dorothy at the end of that story: "You've always had the power to go back to Kansas." When asked why she didn't tell Dorothy sooner, Glinda replies: "She wouldn't have believed me. She had to learn it for herself." Despite his helpless pleas to "please let me go back," I suspect Des already has this power-- he needs to learn to believe in himself.

And that brings me to my closing speculation, which is that the Others are a kind of Chronology Protection Agency ("CPA") fighting against creation of causal paradox. They use the Island as a quarantine zone where living sources of such paradox can be confined and taught (brainwashed?) to control their abilities. Perhaps Juliet was "recruited," at least in part, to prevent her from creating paradoxes that require catastrophic course corrections. She's being held as long as it takes to conquer her demons and indoctrinate her into the CPA Code.

Maybe then Juliet can, if she chooses, return to the world working as a CPA Agent. This work might include recruiting others like her, much as she was recruited by Ethan and Alpert. It may also involve intervening to prevent causal paradox (and thus course correction) like Ms. Hawking did in Desmond's flashback. The latter task could even entail shifting back and forth between different parts of the timeline to be in the right place at the right time. Only fools, after all, are enslaved by time and space...


Harbringer said...

Greetings BigMouth, thank you for your blogs, they are often quite informative and thought provoking. This particular post was very interesting to read, and although not being a learned physicist myself, I think I was able to wrap my brain around the concepts to some degree.

A big question that I have is, what is the distinction between reality and perception of reality? I ask because, if ones perception dictated reality, then one would perceive the events occuring light years away as present time (e.g. stars that have burned out millions of years ago but that we see shining brightly in the night sky) correct? Therefore in this example, if information that travelled at "meta-light" speed could be relayed back and forth to effect the outcome of a decision akin to the Andromeda example, you would be presented with the paradox in question.

However, if time was a constant and regardless of how it was perceived events occurred along the timeline, then although your perception of the star still burning would be accurate, the reality of it would not be. Your perception would simply be misled and incorrect. I will try to use a smaller space-frame to bring my point to light.

A star explodes. One planet in the stars orbit is closer then the other. The people on that planet are incinerated sooner and are aware of the star's explosion faster then the next planet down the line. Just because the next planet's inhabitants are aware of thier demise later then the first planet, it doesn't change the fact that the star exploded at a determined place in time.

If you stretch that example out over an extreme distance of space, in which you would need information to travel faster than the speed of light to effect the situation, it still wouldn't change the star exploding at a very precice moment on the timeline.

If perception dictates reality (which I tend to believe) then those theories make a lot of sense to me, but if outside of one's perception of reality there is an actual confirmed point at which an event occurs then regardless of your distance from the event it seems theoretically impossible to change. Furthermore, the perception of the council that is making the decision creates its own reality, and although that decision won't effect Charlie's Oasis cover for millennieum, it has already been established.

I'll be the first to admit that my argument holds little water, mostly stemming from the fact that I don't completely understand the theories, but it seems to me, that ultimately it comes down to how fast information can be relayed, and that your distance from the situation, regardless of how many light years away you are is irrelevant. I don't see how something is occuring sooner to someone halfway to the Andromeda system than it is to someone half again as far away, outside of thier own perspective.

In any case, I would welcome your thoughts or further explination if you have an understanding of it. Elsewise, I think you are pretty spot on with the Desmond theory, although reaching a bit with the Others having so great a role in the universe. They seem a bit too mundane in thier actions to me to have so great a responsibility.


Bigmouth said...

Harbringer: Thanks! You may not be a physicist (neither am I) but you've put your finger on the main problem with this post. It turns out that the Andromeda Paradox -- like the Twin Paradox -- isn't actually paradoxical at all! The apparent paradox results from two observers computing time according to their inertial frame of reference. Once the proper coordinate transformations are performed to compensate between the different inertial frames, the paradox disappears. That's a fancy way of saying the apparent paradox results from the perceptual lag to which you allude in your exploding star hypothetical.

That doesn't, however, address the potential paradoxes created by general relativity and closed timelike curves. I continue to believe that the implosion of Swan warped spacetime so that Desmond's past and future light cones briefly intersected. In that moment, his past and future minds got crossed, yielding the confused prescience Des now exhibits. I also fully believe this trip has introduced paradox into the timeline that will eventually manifest concretely on the show. On that point, a poster on the fuselage named hearingvoices raises an intriguing possibility. Dharma's experiments in time travel may paradoxically be responsible for creation of the fourtoes statue! I'm not personally ready to go that far, but it's a fascinating scenario to ponder.

Finally, stay tuned for my follow up post about an astrophysicist named J. Richard Gott. He's written extensively about doomsday equations, time travel, and causal paradox -- I suspect he may be the inspiration for some big ideas on the show.

Bigmouth said...

PS: I should also say many thanks to koralis and wearegettingnowhere of the fuselage for clarifying the science behind the Andromeda Paradox.