The Metaphysics of Special Relativity
It should be pointed out right away that theories of physics come with their accompanying metaphysics. This word, "metaphysics," has acquired negative connotations because of the extravagance of traditional discussion in the philosophic field of metaphysics, and also as a consequence of the emergence of a school of thought, Analytical Philosophy, which rallied the claim that traditional metaphysical are generated out of misuse of language or abuse of logic.
Yet a metaphysics of a theory is simply a collection of the objects that satisfy the theory's existential commitments. For instance, Newtonian Mechanics is committed ontologically to the existence of space and time as ill-defined and inert but actual entities, and also advances the convenient metaphysical fiction that forces operate on points in which the masses of bodies are concentrated. Once it was thought that, in its metaphysics, a physics shows us what kinds of things the world really contains. This view, however, seems untenable in light of the problems that metaphysical debates come upon. If a theory were to be abandoned because of difficulties that arise out of its metaphysics, then we could find ourselves easily bereft of theories in physics - even though we would have no other reason for abandoning the theory. The justification of keeping a theory in physics is ultimately pragmatic: if it works, you keep it (of course,we would need to be clear as to what "works" means but metaphysical oddities don't seem to qualify as grounds for abandoning a theory in physics.) By the sake token, physicists do not have the kind of privilege they think they have when it comes to describing what kinds of things exist in the universe! This is not well known.
As an example, let us consider the following paraphrased Leibnizian critique of the metaphysical commitments of Newtonian Mechanics. Like any science, Newtonian physics accepts the principle that everything that comes under the purview of our investigations, and which could have been otherwise, has a complete explanation. Yet, space and time, which are in the metaphysics of the theory, violate this principle. Since any item x, or event y, could have been located somewhere else, or could have happened at some other time, there ought to be a complete explanation as to why the item, or event, is located, or eventuated, where or when it is. We can provide such complete explanations within the theory for moving objects and such, but not with respect to initial positions of objects (or times of events) in absolute terms. This is because all points of space, and all units of time, do exactly the same job with all others. As we say, space and time are isotropic. This means that the metaphysical commitments of the theory to space and time violate the principle of sufficient reason (available complete explanation) which the theory accepts. Yet, the theory works and is kept in spite of any problems with its metaphysics.
In light of the above we can explore relativistic metaphysics. Einstein proposed a solution to a problem that had generated a crisis in physics. Put together, Newtonian Mechanics and Electromagnetic Field Theory generated an inconsistent theory. Yet, this joining was inevitable since Newtonian physics could not account for the behavior of waves. The problem is this: in Newtonian physics, speeds are additive; if you run on top of a moving platform, your speed for the observer on the ground is the addition of the speed of the platform and your individual running speed. In Electromagnetic Theory, however, the speed of a wave was set as constant through the characteristic medium of the wave. Additively thinking, it should take longer for someone who is chacing you to catch up with you if you are running away than if you are running toward the pursuer. But, with constant wave speed, this may not be the case. Needless to say, Newtonian theory was the intuitive one and any effort to reconcile the two theories was putting a premium on keeping intact Newtonian thinking. This privileged the view that there must be a characteristic medium of light - the ether - which "conspires" to create the un-Newtonian anomalies observed. When, however, two engineers, Michelson and Morley, cleverly set up an experiment that proved that there is no ether, the field opened to Einstein's model for the reconciliation of mechanics with wave theory. There is a view that Einstein's theory, moving in the opposite direction from everybody else, absorbed Newtonian Physics into the counter-intuitive Electromagnetic Field theory, but this is controversial.
Next, we briefly examined what Einstein did in the Relativity Theory, minus the mathematical equations of the theory, so we can also set up the Metaphysics of Relativistic Physics.
Einstein kept Galileo's principle (that, for inertially moving systems, operation of the laws of nature cannot be used to differentiate one moving system from another - meaning, if you try to play ball on a moving airplane, you won't detect anything different about how the laws of nature work in comparison to playing ball on the ground of the - moving - earth.) Then, Einstein added only one other principle: all inertially moving systems measure the same speed of light, which is given as a universal constant.
Suppose you are a spaceship traveling in space and try to figure out crucial parameters by using your instruments. You can only trust your knowledge of the Relativistic Physics (the available equations of the theory and the universal constant which is given as the speed of light.) You emit light beams and use them to calculate the speed of light. You get an incorrect number but the theory gives you equations into which you plug your information. Using those equations, you figure out two things: by how much your spaceship has shrunk in the direction in which you are moving; and by how much your system-clocks have slowed down relative to another moving system you left behind last time you synchronized clocks. This is not so surprising. Like any speed, the speed of light is defined as distance over the time it takes to cover that distance: so, to get the "right" or constant speed of light, both spatial and temporal quantities need to be manipulated. This is the foundation of the oddity, you might have heard about - that objects shrink and clocks slow down. Physics practitioners take these effects to be real rather than pragmatic adjustments which give us the right mathematical result within a given theory. Let us not discuss this further here.
Einstein hesitated from drawing metaphysical conclusions from all this but his erstwhile Math teacher, Minkowski, did not show similar restraint and claimed that the success of the theory shows that the fabric of the universe is actually a manifold in which space and time are bound together in one unifying entity that is to be called spacetime. Given that Newtonian space and time were obscure items - fraught with problems and generating paradoxes - spacetime is not any less obscure. This has been often missed. It is not unusual to celebrate in Einstein's success the defeat of Newtonian space and time. This is true since Newtonian space and time were most emphatically disjoint (and characteristically different in the one-directionality of time, but not of space). Nevertheless, spacetime is itself to be regarded - in the naive Realist manners of physicists - as a substance. You must have heard that the universe, engendered by the Big Bang, is spacetime and is to be compared to a baloon that was explosively blown (a baloon that is not anywhere itself, since there is no Newtonian space within which spacetime is situated.)
In sum: given that the equations of the theory require spatial and temporal quantities to be co-manipulated to get us the right speed of light (which is a constant), then, the stuff of the universe must itself be space-and-time together (so that they can be actually co-flexible.) Einstein's equations are like the discarded ones of Lorenz - but Lorenz, unreconstructed Newtonian at heart, had taken the objects themselves to suffer internal changes rather than space-and-time to be a flexible stuff that is constitutive of the universe.
The fun comes next. What kind of universe is this? What does it mean to say that we are situated in spacetime and how is this different from the more "intuitive" Newtonian world in which we could be situated in space with time "flowing" over us in only one irreversible direction?
The Block Universe
We have seen that relativistic physics requires an ontology of spacetime - a substantival manifold that has space and time joined together, so that we have to speak of four dimensions rather than the traditional three-dimensional fabric of Newtonian space "over" which time "flows" in an irreversible direction. (Notice the tortured metaphorical language that the Newtonian metaphysical commitments require, by the way.) The oddity of relativistic physics follows from stipulating that only the speed of light is to be measured as a universal constant by all moving frames - all other spatiotemporal truths are relative to each frame of motion with no global or absolute truths in this respect. (No, this is not a vindication of clueless postmodernism; the theory is itself prescriptive, with inexorable equations handed down to us as to how things are supposed to be working. There is, however, a shock value to this. Who would have ever thought in the tradition that spatial and temporal truths - and truths about what events are simultaneous - are relative to moving frames??)
As a substantival entity, spacetime must have its characteristic geometry. We can see this intuitively - Minkowksi bravely stipulated it, betraying also the typical Realist manners of a scientist. (Realism about x is the view that the x we are talking about exists independently of anyone thinking about it.) Nevertheless, our intuitions can ascribe a geography to space rather than to time. Whether you can ever travel to point z, or whether you can ever have access to the technology that allows you to travel to point z, point z in the geography of space is always there (notice the independence from time, hence "always"). It can be in principle accessed at any time if getting from here to there is feasible. Now, in the relativistic universe, we have time implicated and interwoven within the fabric of things. This sounds initially like the stuff of science fiction: events, not objects, must be in our geography now. This is because the kind of thing that you can characterize only by using BOTH spatial and temporal attributes (in spacetime) is an event - not an object. But what does it mean to have a four-dimensional geography of events? This is what is sometimes called the block universe. All events, not only present anywhere but also past and future relative to anyone are present - except we may or may not be able to access them. This opens the door to speculation about time travel as a possibility that is not inconsistent with our physics. When H. G. Wells wrote his Time Machine, he was speculating in science-fiction style but modern physics seems to permit at least the theoretical option of time travel. Moreover, the logician Kurt Godel proved mathematically that there is at least one conceivable geometry of spacetime (not our own universe's but a possible geometry), which is such that: by moving forward in our conventional time we actuall go into the realm of past events. (The geometry of this universe would be like a knot, in which you move into the earlier twists of the material as you actually move straught through.)
Einstein was not pleased with his friend Godel's proof. This is because Einstein was well aware that time travel scenaria generate paradoxes and apparent contradictions. If the theory cannot rule such logical anomalies out, there is a problem. It becomes urgent, then, to examine and try to sole the apparent paradoxes of time travel. (Of course, given the pragmatic bent of working science, if the model works you keep it regardless of philosophic problems that accrue when you contemplate it.)
Time Travel Stories
When you read or watch time travel stories, do you usually detect inconsistencies generated by the time travelling component?
Paradoxes of Time Travel
Paradoxes of Time Travel are discussed extensively in philosophic literature.
One paradox is generated by the prospect of duplication of a unique individual. There is no specific reason for outlawing traveling to a past or future time unit at which the traveling person meets an earlier or later version of himself or herself. This violates the principle of numerical identity, according to which there can only be one individual at any moment who lays claim to being a certain person. If this is a logical principle, not a physical one, then the violation of the principle gives rise to a logically impossible situation. If the theory we have implies a necessary falsehood, then at least one of the theory's sentences must be false. Yet, we have no candidate sentence in the theory, which we can remove. Hence the paradox - proving validly a conclusion that cannot be true, from premises that are put down as true. We will see subsequently a suggested solution to this paradox. (If solvable, a paradox is not genuine; it is a puzzle.)
Another paradox is known famously as involving a situation in which you return to the distant past and you assassinate one of your ancestors before he or she had procreated. There is no reason provided by the theory to presume that, if time travel is possible, such an attempt would not succeed. Yet, if the attempt is successful, the assassinated ancestor never procreates and it cannot be you who is carrying out the endeavor. So, it is presumed as true that you assassinated your ancestor and yet it is also impossible that you exist - let alone that you do anything. Once again, a contradiction looms. More precisely, a logically impossible situation is to be accepted as logically possible if time travel is available - but this cannot be the case since what is impossible in any sense cannot also be possible in that same sense. We will visit suggested solutions to this conundrum.
Another paradox is the following. You visit yourself in the past to pass on information as to how to build a time machine. But you were able to build the time machine in question since you are visiting your earlier self. How did you build this machine in the first place? Well, it is because your future self passed back the relevant technical information. But your future self accessed this information only because he or she was able to build a time machine - which, information, became available by the future self who visited the earlier self... And so on, ad infinitum. Here we have an infinitely regressive loop. Since Aristotle, infinite regressive series of explanations have been viewed as absurd: it is like having a complete explanation and, at the same time, not being able to produce it! (In non-intuitionistic or classical mathematics, we can deal with infinite series without constructing procedures by, for instance, using the kind of proof known as proof by contradiction.)
The name of David Lewis, deceased Princeton philosopher and science fiction afficionado, rightly comes to mind whenever time travel problems are discussed. Lewis thought that he had a simple test about feasibility of time travel: if it is possible to cover all the relevant details of situations arising in time travel scenaria, then we should accept that time travel does not necessarily lead to logical absurdities. In this respect, it is crucial to have some science fiction samples to point to, which succeed in covering "enough" about details without running into contradictions. (Vagueness clings to "enough" here but you can consult Lewis' writings on the subject to check if additional details are forthcoming.) Lewis himself distinguished two such science fiction stories -- "All You Zombies" and "By His Bootstraps," both by Robert Heinlein.
A proposed solution to the self-duplication puzzle. We need a revision of what accept as our theory of personal identity. (Personal identity, in philosophy, is the study of what makes you the same person over time, notwithstanding the changes you do undergo. It turns out to be a recalcitrant subject -- surprisingly from the point of view of the unsuspecting everyday person.) We need to switch allegiance to a controversial theory of personal identity, known as Mereology. According to this view, you are never entirely present at any one given time-unit; only your relative temporal part is present at any one moment. It is like saying that it is an error to touch any part of your arm or leg and demand that you have yourself spatially encapsulated in that one spot. What you have there is only a spatial part of the whole that constitutes you spatially. We do the same with your temporal slices: at any time unit t, a person X, is present then only as temporal part X-t. The added reinforcement for this theory is that the block universe (see above), which relativistic physics seems to be inflicting on us, also requires the mereological view of personal identity. Mereology is not popular but it has a solution to the duplication problem we saw above: when "you" visit "you" at t, it's only the t(k+n)-part of you visiting the tk-part of you. So, we don't have a duplication of you - no violation of numerical identity: two of your temporal parts are squeezed into the same point - like pressing two spots on your body some together.
A proposed solution to the ancestor paradox we saw above. It is true that you "can" kill your ancestor - we have no reason for revising our view of free action and agency now. But being able to do this does not imply that you must succeed. Since you are able to meet this ancestor during your time traveling peregrinations, this means that the totality of things works out so that you cannot succeed in assassinating your ancestor when you try. This last occurrence of "can" needs attention. This point is due to Lewis. What do we mean when we say that you "cannot" succeed in killing your ancestor? Didn't we say earlier that you surely can do this - you are free and able, and nothing is presumed different about the experiences we have when we time-travel. The answer is that two different sense or meanings of "can" are involved here - so we have no contradiction if we say that, "yes, you can kill the ancestor" in the sense of being able to do so, but also "you cannot kill the ancestor" in a different sense of "can" that has to do with historical possibilities. To paraphrase David Lewis' example, "you could speak Chinese but you can't speak Chinese as it is."
Can you think of a solution for the third paradox presented above?
© 2014 Odysseus Makridis