Showing posts with label Relativity Theory. Show all posts
Showing posts with label Relativity Theory. Show all posts

Monday, January 28, 2013

Symmetry principles

Here is an interesting inductive argument about the restricted Principle of Relativity in Einstein's little popular book on relativity:

But that a principle of such broad generality should hold with such exactness in one domain of phenomena [mechanics], and yet should be invalid for another [electrodynamics], is a priori not very probable.
This is induction across laws: from the laws of mechanics having a property, we infer that the laws of electrodynamics have it as well. If induction is within a natural kind, this induction would require there to be the natural kind law.

One can take the Principle of Relativity to be a second-order law (cf. Earman). That's not the only way to think about it. We could, for instance, imagine the following metaphysics: We are realists about ordinary laws, like those of mechanics and thermodynamics, and we think that God has produced these laws. But in choosing which laws to produce, God followed certain "artistic principles". One of these artistic principles is the Principle of Relativity (and similar symmetry principles). I don't know what advantages of this over a hierarchical view on which there are higher order laws that constrain lower order ones. But it's worth thinking about.

Tuesday, October 25, 2011

More about functionalism about location

Functionalism about location holds that any sufficiently natural relation, say between objects and points in a topological space, that has the right formal properties (and, maybe, interacts the right way with causation) is a location relation.

Here is an argument against functionalism. Functionalism is false for other fundamental physical determinables: it is false for mass, charge, charm, etc. There is a possible world where some force other than electromagnetic is based on a determinable other than charge, but where the force and determinable follow structurally the same laws. By induction, functionalism is probably false for location.

Some will reject this argument precisely because they accept something like functionalism for the other physical determinables, and hence deny the thought experiment about the non-electromagnetic force--they will say that if the laws are structurally the same, the properties are literally the same.

I think there is a way to counter the above argument by pointing out a disanalogy between location and other fundamental physical determinables (this disanalogy goes against the spirit of this post, alas). Let's say we live in an Einsteinian world. A Newtonian world still might have been actual. But, plausibly, the Newtonian world's "mass" is a different determinable from our world's mass. Here's why. In our world, mass is the very same determinable as energy (one could deny this by making it a nomic coextensiveness, but I like the way of identity here). In the Newtonian world "mass" is a different determinable from "energy". Therefore either (a) Newtonian "mass" is a different determinable from mass, or (b) Newtonian "energy" is a different determinable from energy, or (c) both (a) and (b). Of these, the symmetry of (c) is pleasing. More generally, it is very plausible that fundamental physical determinables like mass-energy, charge, charm or wavefunction are all law bound: you change the relevant laws (namely, those that make reference to these determinables) significantly, and you don't have instances of these determinables.

But location does not appear to be law bound. "Location" in a Newtonian spacetime and a relativistic spacetime are used univocally. You can have a set of really weird laws, with a really weird 2.478-dimensional space (for fractional dimensions, see, e.g., here), and yet still have location. Maybe there are some formal constraints on the laws needed for locations to be instantiated, but intuitively these are lax.

Plausibly, natural (in the David Lewis sense of not being gerrymandered) physical determinables that are not law bound are functional. If location is a natural physical determinable, which is very plausible on an absolutist view of spacetime, then it is, plausibly, functional. I think an analogous argument can be run on relationism, except that the fundamentality constraint is a bit less plausible there.

One might question the claim that natural physical determinables that are not law bound are functional. After all, if the claim is plausible with the "physical", isn't it equally plausible without "physical"? But the dualist denies the claim that natural determinables that are not law bound are functional. For instance, awareness seems to be a natural determinable (whose determinates are of a form like being aware of/that ..., and nothing else), but the dualist is apt to deny that it's functional.

In any case, one interesting result transpires from the above. It is an important question whether location is law bound. If we could resolve that, we would be some ways towards a good account of spacetime (if it is law bound, proposals like this one might have some hope, if based on a better physics). The account I give above of law boundedness is rather provisory, and a better account is also needed.

Friday, June 24, 2011

Memory theory, fission and faster-than-light influences

Standard memory theories of personal identity says that what is necessary and sufficient for identity is a chain of memories (or, more precisely, quasi-memories) and the absence of fission or fusion of memories. Now suppose:

  1. If we keep fixed the laws of nature and miracles don't happen, then what is done five light years from earth at t cannot affect whether I am on earth five minutes after t (keeping a constant reference frame throughout).
Suppose physicalism is true. Then it is in principle possible to perform the following operation: record the state of my memories, freeze me, and send the records to a location five light years from earth. At that location the records can be downloaded into a fresh brain. So, suppose my memories have been recorded, I'm frozen, and the records are five light years from earth, where, at time t, someone is deciding whether or not to download those records into a fresh brain. At the same time (in this frame), I am being thawed. If they download the records into a fresh brain, then at t I will experience fission, and cease to exist according to standard memory theories. But that violates (1): whether they download the records into a fresh brain affects whether I am on earth five minutes after t.

One can get out of this problem, at the cost of other weirdness, by allowing one to survive fission. Another way is to deny physicalism—without physicalism it is not clear that memories can be transfered, as they may not be entirely brain-based.

But one might also try for the following solution. Suppose they do download the memories into a fresh brain. Fission doesn't count as occurring then. After all, reference frames are arbitrary, and so such a "then" would be arbitrary. Fission only counts as occurring when one of my memory-continuants is in the forward light-cone of another of my memory-continuants. And that will happen five years after the operation, and hence will not violate anything like (1). I don't know how attractive this view about fission is. It would be weird to build into a memory view something so tied to the physics of our world. One would need to say something about how the memory view changes in worlds with different physics. I still think a better move is just to deny the memory theory. But this interesting move would be worth thinking about.

Thursday, September 9, 2010

Backwards causation

It is commonly thought that a cause C metaphysically cannot have an effect in its past. I see two simple ways of making sense of this principle in a relativistic framework:
  1. A cause can only have effects in the future half lightcone centered on it.
  2. A cause cannot have effects in the past half lightcone centered on it.
But I think neither of these is a plausible candidate for a metaphysical principle. Consider what (1) and (2) respectively say in a flat spacetime:
  1. A cause at (x,t) can only have an effect when the effect is at a spacetime location (y,u) such that |xy|<c(ut).
  2. A cause at (x,t) cannot have an effect at a spacetime location (y,u) when |xy|<c(tu).
But these just don't seem to be plausible candidates for a metaphysical principle, though I suppose one might think that they could be consequences of a physical principle. The same applies to the more complicated versions we'd need in a non-flat spacetime.
If we want (1) or (2) to be non-trivial metaphysical principles, we need to replace the references to lightcones by something of more metaphysical than physical significance. A plausible approach is to define the future half lightcone of a as the set of spacetime points states of affairs at which can be affected by a cause at a. But then (1) becomes simply the claim that causes can have effects only in spacetime, which is controversial and fails to capture the backwards causation intuition.
Now (2) is the claim that that a cause at a spacetime location b cannot affect anything at a spacetime location a when a is such that something at a could affect something at b. This is, in effect, a principle tailored to rule out causal loops. But if that's the intuition behind it, we might as well just say there are no causal loops, and be done with it. And if we do that, then we will have ruled out some, but not all, instances of backwards causation.

Tuesday, October 21, 2008

Relativity theory, promises and promulgation of laws

In one earlier post, I suggested the principle the basic laws of morality, just like those of physics, should be reference frame invariant. In that post, I offered some examples of the application of this theory, albeit ones that were not of much interest. In a later post, I have offered an application of the principle to the abortion debate, but the principle did not really decide any issue, but simply deepened the discussion. But now I have what is to me a much more interesting pair of applications.

I promise you never to sit on your late wife's favorite bench which happens to be on my front lawn. I thus create an obligation for myself (an amazing power, isn't it, the power to create obligations?). A while later you release me from the promise. Your release destroys the obligation (so a part of my power of promising was a power to give you the power to make the obligation cease to obtain).

But when did these things happen? When did the obligation not to sit on the chair come into existence? When I promised I wouldn't, or only when the promise reached you? And when did the obligation cease? When you said you release me, or only when the release reached me? Of course, if we're speaking face to face, the question is only of theoretical interest—but, still, it is a genuine interest, I think. But what if you live four light-years away, and we speak by radio? Then, did I become bound when I made the promise, or only four years later, when you heard the promise? And did I become released when you uttered the words releasing me from the promise, or only four years later? In such a case, the question is not just of theoretical interest.

It turns out that there is a very natural way to decide this question when we apply invariance, assuming that making promises and releasing from them is a matter of basic laws of morality. Suppose that we said that the obligation comes to exist when you hear my promise. But then the law would not be invariant. For five minutes after I have sent my words to you over the radio, it will be true in some but not all reference frames that you have already received the message. So, it will depend on reference frame whether I may sit on the bench then or not. Invariance will be violated. (Note that it will not help much to say that what is relevant is my reference frame. For extended substances do not in general define a unique reference frame. Besides, if my reference frame matters so much then, absurd, I'll be able to affect when the obligation applies simply by running really fast in some direction or other.)

If, on the other hand, I say that the promise is binding on me as soon as I have made it, then this rule is invariant. For the rule, basically, says that the obligation obtains when I am in the forward light-cone of the promise-making, and this is a reference-frame invariant relationship.

One might think that just as I am bound as soon as I sent the promise, so too am I released as soon as you sent the release. But here things are quite the opposite. For if I were released as soon as you sent the release, invariance would be violated—for, we would have to ask, in which reference frame is the "as soon as" measured. But invariance will obtain if I specify that my obligation ceases as soon as the release gets to me.

So we have a pretty good argument, based on invariance, for when promises come to bind and when we are released from them. The obligations, as it were, exist at the site of the promiser, and hence come to exist when the promiser speaks, and cease to exist when the promisee's release arrives at the promiser. Of course, further questions can be asked—when is the exact moment of sending, for instance. But those questions, I think, do not concern the basic practice of promise making/keeping itself—maybe answers to those questions can be left to custom or the prudent legislator.

Here is a different application. When a legislature passes a law, when does the law become morally binding on me? (I don't care about the question when it becomes legally binding, since only moral normativity matters in the end.) When the law is passed? Or when the law is promulgated? Or when the promulgation arrives? Intuitively, it would seem unfair if I were bound as soon as the law were passed, since I would have no way of knowing about the law as soon as it were passed, and surely the law is to be a guide to my rational deliberation. I think Aquinas makes something like this argument. But it would be nice to have an argument without so much that is controversial. Well, that's easy. The rule that the law is binding morally on me when promulgated violates invariance (imagine that the law is one of the Galactic Empire, and there is no faster than light travel, so it can take years and years to reach me), since we would have to ask: "In which reference frame?" The same problem obtains for the question: "When the law is promulgated?" (e.g., when the legislature radios it out to the subjects). But "When the promulgation arrives to me" is invariant, since it is a question of my being bound.

Now there is a problem with this answer. Generally, it is taken that ignorance of the law is no excuse. So, it seems, I can be bound by laws that were never communicated to me. Three answers are available. The first is that the "ignorance" saying only applies to legal binding—morally, ignorance of positive law is a perfectly fine excuse. The second is to modify my initial formulation: I am bound at the first time at which it was reasonably possible for me to have found out about the legislation had I set my mind to it. This, too, is invariant. The third is to combine the first two answers. Certain basic laws, such as laws proclaiming the constitution of a new nation, only become morally binding when the subjects hear of them. As part of the proclamations of these laws, the subjects hear how and where they can find out about additional laws. But then further laws becoming binding when one can reasonably find out about them. This, too, is invariant.

In any case, the answer "When the legislator makes the law" is not a good one. So we have an argument for Aquinas' thesis that promulgation is essential to the bindingness of a law. Secret treaties do not bind those ignorant of them, at least not morally.

I think it's pretty cool that one can get such fairly specific answers to difficult normative questions simply out of relativity theory. I think one could probably also get similar answers if one had a causal theory of time (whether it was relativistic or not). And that is not a coincidence because I think the relativistic theory of time is, basically, a causal theory of time.

Wednesday, September 10, 2008

Relativity Theory and abortion

In an earlier post, I offered the principle that just as the laws of physics should be invariant under change of reference frame, so should the laws of morality. One consequence of that is that various inside-outside distinctions are not going to be significant of themselves. Here is an interesting little consequence of that: Any argument that abortion is permissible based on the fact that abortion takes place inside the body of the woman cannot be right, since the claim that the fetus is inside the woman's body is not invariant under coordinate transformations.

This doesn't mean that the argument is thoroughly refuted. But it does mean that the mere geometrical fact that the fetus is within the woman's body is insignificant. There may, however, be more significant related invariant facts about dependence, burden, etc. The invariance move does not, thus, settle the discussion, but moves it forward, by forcing the pro-choicer arguer to give a fuller story about the distinction in invariant terms, which terms non-coincidentally are going to be descriptively richer, thereby deepening the debate.

Of course, one doesn't need relativity theory to show the problem with the principle that one can do what one likes as long as it is within the confines of one's body. One can also proceed by counterexample. If one accidentally swallowed Whoville, one would not be permitted to follow that up with a drink of something intended to kill all the Whos.

Tuesday, July 1, 2008

Distant stars

We are sometimes amazed that we are seeing the distant past when we look at distant stars. But just about always when we look around, we see the past--light takes time to come to us from the objects. Why is it more amazing when we see the more distant past? And anyway, isn't the measure of temporal distance relative to reference frame?.

Wednesday, February 20, 2008

Psychological identity and faster than light causation

In 2010, data from your brain is scanned and recorded in duplicate on two hard drives, while the original is destroyed. One hard drive is sent off to a station in orbit in the alpha-Centauri system, and it arrives there within ten years. The other remains on earth, in a special vault. An automated process in the vault is guaranteed to grow a new brain in 2050, and imprint the saved data on that brain. If that is the whole story, then according to materialist psychological identity theorists who ground personal identity in chains of (quasi-)memories, you will thereby be resurrected.

But now consider this oddity. Suppose that at the same time (in respect of some reference frame—it shouldn't matter which one), the scientists on the station around alpha-Centauri happen to grow a brain and imprint your data on it. Then you have undergone fission: there are two copies of you. The standard resolution of fission cases is to say that you then do not exist—all the other options are more absurd. This means that the scientists on the station have it within their power to prevent your being resurrected on earth, simply by imprinting your data on a brain at the same time as the machines on earth are doing so. And this ability of theirs is not limited by the speed of light. In fact, in some reference frames it will be true to say that because they imprinted your data on a brain shortly after the vault on earth has done its work, you weren't resurrected in the vault on earth (but instead were the victim of fission). This may well seem absurd.

The scientists near alpha-Centauri, then, have counterfactual control over whether you're resurrected on earth. Is this counterfactual control a form of causal control? Well, on theories of causation on which counterfactual dependence between wholly distinct events (the scientists' pushing of buttons is wholly distinct from your resurrection, it seems) entails causation, the answer will be affirmative. So, materialist psychological identity theorists who accept accounts of causation like that seem to have to admit that faster than light causation is physically possible (I say "physically", because no part of my story seems to violate any law of nature).

Saturday, February 9, 2008

Morality and Relativity Theory

Einstein tells us that basic laws of physics should be invariant under change of reference frame. Is the same true of basic laws of morality? What would that mean? I think it would mean that any law of morality which is not invariant under change of reference frame can only be a consequence of a more general moral law that is invariant together with some conditions explaining why, contingently, things are arranged in some particular manner in space-time as to give rise to the non-invariant law. (Similarly, the non-invariant law about dropped objects near the earth moving in the direction of the center of the earth follows from an invariant Einsteinian law together with contingent facts about how matter is distributed in our vicinity.)

Could this abstract observation have any actual consequences? Suppose Georgina believes that when she works unowned land, by natural law the land becomes hers (cf. Locke), and by natural law she gains mineral rights to what is below the surface of the land she has worked. That doesn't seem right. What counts as being "below the surface of the land she has worked" depends on the reference frame. So it can't just be a basic moral law that one gets whatever unowned stuff is below where one worked. A story must be given explaining the lack of invariance. And probably the easiest way to do this is to say that if there is any such acquisition of mineral rights, it comes from a non-invariant positive law. This isn't very interesting, since I assume we knew that there is no natural acquisition of mineral rights.

There could, however, be some slightly more interesting consequences in other areas. For instance, in sexual ethics, it follows that considerations based on the shapes of organs, as well as ones based on inside-outside distinctions (what is in one reference frame a cup that is red on the outside, green on the inside, with juice within is in another reference frame a cup-shaped object that is green on the outside, red on the inside, with juice adhering to the outside due to odd gravitational fields), should not be of basic relevance, absent some further story. Instead, basic moral rules about sexuality should involve reference-frame invariant concepts such as contact, causation, teleology, intention, and consent. This is helpful—it focuses the philosopher's mind on what the morally relevant features of the activities are. (I've used this in a comment to argue that the use of condoms to prevent HIV transmission within a married couple is unacceptable within a Catholic sexual ethics.)

Thursday, December 13, 2007

Long snakes and Relativity Theory

This is an exercise in some rather gruesome metaphysics of parthood. If you don't like gruesome examples, stop reading. There will be a payoff, though--a defense of animalism.

Imagine a long snake, all stretched out, and for simplicity assume uniform linear mass distribution. Let's say the length of the snake is 10 meters and its diameter is 0.1 meters. Suppose that something cuts off the rear 1/4 of the snake, and the cut happens at near-light speed--maybe a blade descends on the poor snake at 90% of the speed of light. Suppose that almost instantaneously before the blade touches the unfortunate snake, a butterfly almost instantaneously brushes its wing against the tip of the snake's tail and never has any other contact with the snake or its bits. (Let's say "almost instantaneously" means "in the amount of time during which light travels 0.01 meters.) Then, it seems, butterfly touched the snake. Call the reference frame in which the above description takes place "frame A". But, it is a fact that then there is a reference frame, call it "frame B", in which when the butterfly touched the snake, the tail was already cut off. It seems that in this reference frame, the butterfly did not touch a (or the) snake--he merely touched a cut-off tail.

It follows that the following propositions cannot all be true:

  1. In frame A, the butterfly touched the snake.
  2. In frame B, the butterfly did not touch the snake.
  3. Whether two substances touch does not depend on the reference frame.

So we must deny at least one of (1), (2) or (3). Note that affirming (1) and (2) and discarding (3) would have the interesting consequence that whether battery has been committed depends on the reference frame. For suppose that an accident cuts off my leg at near light speed. Then there can be a situation where you very quickly mutilate the "foot" at the end of that leg (I put it in quotation marks, because there is an issue whether a disconnected foot is a foot) just before the leg is cut off. By exactly the same reasoning, then, in one reference frame it seems you've committed battery--you've mutilated a part of me--and in another you haven't. (In neither reference frame do I feel the mutilation, because the leg is cut off before the nerve signals come from the "foot" to my central nervous system.) I don't think whether battery has been committed should differ between reference frames. (Would you be guilty in one frame and innocent in another?)

So, I need to reject either (1) or (2) or both. It seems to me that (1) is harder to deny than (2). To deny (1) we would have to allow that the tail is fully connected to the snake, and yet not a part of it because it is about to be cut. So, we should deny (2). Hence, something can be a part of a body even though it is already severed from the body.

How long can this weird state of affairs go on? I don't really know. We could say that it goes on until the part is severed in all reference frames. But while that is an attractive idea, it neglects the fact that we are talking about organic parts, and what matters here is organic connections, not relativistic connections. The relevant scale of velocities is the speed of the fastest organic signals, not the speed of light. Suppose that the snake's brain sent a nerve signal to the tip of the tail, and the nerve signal passed the cut-point just before the cutting began. Because nerve signals move much slower than light, before the nerve signal arrives at the tip of the tail, it will already be the case that in all reference frames the tail is severed. Still, I think the tail might count as part of the snake, as long as the signal is traveling there. Let's say the signal tells the tip of the tail to wiggle. Maybe we can say that while the tail yet wiggles under the influence of that nerve signal, the tail is a part of the snake.

Does any of this matter, except as abstruse metaphysics? Maybe. Take animalism, the theory that you and I are animals. A standard objection to animalism is that we can survive as brains in a vat, but a brain in a vat is not an animal. However, the above considerations suggest that, at least for more complex beasts like snakes and humans, connection to the nervous system has a relevance to determining what still is and what no longer is a part of the body. The nervous system, then, has a kind of centrality in more complex animals from the organic point of view. And this makes it plausible the animal could survive as an organism when pared down to just a nervous system, assuming appropriate life-support mechanisms. And it is not a far leap from that to suppose that we can survive as organisms with just central nervous systems, and maybe even with just the central part of the central nervous system, namely the brain (in a vat, of course).

Now, if animalism is true, then we were all once fetuses--I was the numerically same organism as a fetus. Thus, a human fetus is one of us, and presumably killing it is wrong. Thus, we have here a loose line of argumentation from Relativity Theory to the wrongness of abortion. Isn't philosophy fun?

Saturday, November 17, 2007

"We want to live forever"

We want to live forever. What does that mean? First suggestion: I want it to be the case that at every future time I exist. But that's not enough. For suppose that time itself will come to an end in five minutes, and I will live for the next five minutes. Then at every future time I will exist, but my desire to live forever will surely not be satisfied by living for five minutes.

Second suggestion: I want it to be the case that at every future time I exist, and that the future be infinite. But that may be too much. My desire to live forever could, perhaps, be satisfied by the following scenario: I live in a universe with infinitely many very, very widely separated inhabitable stellar systems. After a year, I enter into a spacetime machine that can move me to an arbitrary point in spacetime, and this transports me back in time exactly one year (relative to some single reference frame) and moves me to another inhabitable planet, far from anywhere that I've lived before. I live there for a year, and this repeats. If t is a time two years from now, I do not exist at t on this scenario. However, I do live forever in subjective time--I have an infinitely long life, though it is all wound in on itself within a single year. Granted, it's a nuisance to have to get to know a new place every year, even though I do get to keep memories from the other places I've been. But this nuisance has nothing to do with the satisfaction of my desire to live forever. But I could live forever in the ordinary way, and have that nuisance happen to me--I could be every year transported to another planet, far away from where I have ever been before, but not transported back in time.

I want to suggest that it doesn't really matter whether I'm transported back in time every year or not. Third suggestion: What we want is an infinite future life, regardless of how that future life is arranged in spacetime. On this suggestion, it is subjective or personal time that matters vis-a-vis living forever. I think much the same is true with respect to many other temporally charged ethical matters--when only one individual matters, it is her personal time that matters, and when there are multiple individuals mattering, it is their group interpersonal time that matters (imagine a group of individuals all zigzagging back and forth across spacetime).

And if we have the idea that we should take as ontologically more basic what is more significant to us as persons (taking ethics as first philosophy, or something like that), then we will adopt personal time as the focal or primary sense of temporality. If we do this, we will be B-theorists, because we will have little need or room in our ontology for an objective impersonal moving present. I suspect this approach is faithful to both Einstein's notion of the relativity of time and to the basic insight in the Aristotelian idea of time as the measure of change (just take time to be the measure of change within each given substance, but do not insist on embedding these changes within a single temporality).

A related issue is discussed here.