|
|
Causalities
Via Mr. Moles, an excellent explanation for laypeople of why FTL travel is time travel given special relativity.
If you scroll down, I posted a long comment on why it is not strictly correct to say that an FTL/time-travel universe requires you to abandon causality, and an excursus on some of the kinds of causalities that might obtain.
Posted by benrosen at May 12, 2005 11:26 AM | Up to blogWe could call this "orphaned effects" or "vanished history" causality, in the sense that we could observe effects, in such a world, whose causes "never happened".
Aha! Thanks, Ben -- that was my missing idea.
Posted by: David Moles at May 12, 2005 01:45 PMit is not strictly correct to say that an FTL/time-travel universe requires you to abandon causality
I'd say that Richard Baker (author of the cited web page) is using a strict definition of causality, while you are using a looser one.
But you and I have had this discussion before. :)
Posted by: Ted at May 15, 2005 05:17 PM`When I use a word,' Humpty Dumpty said, in rather a scornful tone, `it means just what I choose it to mean -- neither more nor less.'
`The question is,' said Alice, `whether you can make words mean so many different things.'
`The question is,' said Humpty Dumpty, `which is to be master -- that's all.'
Alice was too much puzzled to say anything; so after a minute Humpty Dumpty began again. `They've a temper, some of them -- particularly verbs: they're the proudest -- adjectives you can do anything with, but not verbs -- however, I can manage the whole lot of them! Impenetrability! That's what I say!'
`Would you tell me please,' said Alice, `what that means?'
`Now you talk like a reasonable child,' said Humpty Dumpty, looking very much pleased. `I meant by "impenetrability" that we've had enough of that subject, and it would be just as well if you'd mention what you mean to do next, as I suppose you don't mean to stop here all the rest of your life.'
`That's a great deal to make one word mean,' Alice said in a thoughtful tone.
`When I make a word do a lot of work like that,' said Humpty Dumpty, `I always pay it extra.'
-- https://www.sabian.org/Alice/lgchap06.htm
Posted by: Benjamin Rosenbaum at May 16, 2005 10:09 AMI responded more on-topically and less whimsically on Rich's board. Executive summary: John Calvin's causality deserves the name.
Posted by: Benjamin Rosenbaum at May 16, 2005 10:39 AMYou're going to have all Five Forms enumerated before the year's out. I just know it.
Posted by: David Moles at May 16, 2005 01:42 PMThat would be fun, then I'd have some material for a sequel... :-)
Posted by: Benjamin Rosenbaum at May 16, 2005 01:47 PMYep, I often feel that I've stepped through the looking glass when I have a discussion with you, Ben. :)
I take that as a high compliment.
Posted by: Benjamin Rosenbaum at May 17, 2005 09:57 AMBecause I am that kind of obsessive, I've been thinking over the Five Forms and may post something about them soon. But in the meantime, though, I ask you: under what system of causality may cornbread count the reals?
('"I'm trapped at a local maximum!" wails the great wolf.')
Posted by: Dan Percival at May 17, 2005 02:59 PMHitherby Dragons rocks!!!!!!!!!!!!!
Posted by: Benjamin Rosenbaum at May 17, 2005 03:43 PMI don't know why, but this seems like a good time to move from causality over to ethics and bring up Michael Patton's Can Bad Men Make Good Brains Do Bad Things?
Posted by: David Moles at May 17, 2005 07:39 PMThe only thing that makes life possible is permanent, intolerable uncertainty; not knowing what comes next. - Ursula K. LeGuin
Posted by: Michael Musson at May 19, 2005 10:47 PMOn a side note, it occured to me yesterday that the "orphaned effects" model is the "parallel universe" model as percieved by someone who stays in one universe and doesn't time travel.
Posted by: David Moles at May 20, 2005 01:00 PMHmmm.... maybe. Clever physicists might come up with experiments designed to distinguish them (which clever philosophers could then debate)...
Posted by: Benjamin Rosenbaum at May 20, 2005 01:03 PMPresumably you mean a "parallel universes" model where you cannot choose which universe you travel into? Certainly a lot of SF assumes that you can, in which case a non-traveling observer might see things like a traveler appearing, saying, "Well, I'm going home now. See you later," disappearing, reappearing, and saying, "Hey, I'm back. Did you miss me?"
(Of course, that's also consistent with the "orphaned effects" model, too, but the parallel universe model would be a more parsimonious explanation.)
As for experiments, David Deutsch claims that the multiverse is proved by the ability of quantum computers to solve problems that require more computational power than is available in a single universe. Of course, this argument doesn't persuade everyone.
Posted by: Ted at May 20, 2005 02:20 PMI was thinking of a fairly limited parallel universe model -- really not so much parallel as "alternate" -- in which time travel into the past would cause a timeline to fork, but in which there wouldn't necessarily be any way to move directly from one branch to another.
If you also assume that time travel is one-way -- that once you've gone back and caused the fork, you're on the branch you've created, and there's no way to get back to your original branch -- then I think the question of whether to apply the alternate-universes model or the orphaned-effects model becomes entirely philosophical.
On the other hand, if you've got time gates, rather than time machines ("Mozart in Mirrorshades"), or you've got time machines tethered to an origin point (Niven's Hanville Svetz stories), then it's clear to travelers, at least, that they should apply the alternate-universes model.
Posted by: David Moles at May 20, 2005 03:16 PMOkay -- now can we think of a set of experimental results for which the "orphaned effects" model *rather* than the "parallel universes" model is the most parsimonious explanation?
I suppose repeated attempts and failures to get "back to your original timeline" might suggest that your original timeline "isn't there to get back to"?
Posted by: Benjamin Rosenbaum at May 20, 2005 04:24 PMA lot depends on the exact mechanism. I was thinking on the flight back from Chicago about traversible wormholes; if you've got those, you can walk from one timeline to another, so it's pretty clear what's going on.
But, if there are naturally occurring traversible wormholes, and there are alternate universes, then I think I can show that that leads to the creation of an infinite number of alternate universes as soon as you accelerate one end to create your time differential -- it's sort of a recursion thing. And that seems like an unnecessary multiplication of entities.
Posted by: David Moles at May 20, 2005 07:18 PMA lot depends on the exact mechanism. I was thinking on the flight back from Chicago about traversible wormholes;
Ah, that's different. We started off talking about FTL, but wormhole don't involve that; they used a closed timeline curve instead. Most discussions of wormholes that I've read conclude that Novikov's principle of self-consistency applies. No changing the past allowed.
But, if there are naturally occurring traversible wormholes, and there are alternate universes, then I think I can show that that leads to the creation of an infinite number of alternate universes as soon as you accelerate one end to create your time differential -- it's sort of a recursion thing. And that seems like an unnecessary multiplication of entities.
If you're talking the Many-Worlds interpretation of QM, "unnecessary multiplication" is why a lot of people object to it in the first place; every single event spawns another universe.
But if you're not talking about the MWI, why would creating a time differential necessarily spawn an infinite number of alternate universes?
But if you're not talking about the MWI, why would creating a time differential necessarily spawn an infinite number of alternate universes?
Only if you assume that time travel = branching timelines (and of course ignoring the quantum effects that are predicted to enforce chronology protection). I don't have my notes on me, but my thoughts went something like this:
Some time ca. the Big Bang, a wormhole is created, with two mouths, A and B. Go into A, come out of B, and vice versa. Both on the same timeline, both within the same universe, no problem.
Now, move A -- take it somewhere and bring it back, subjecting it to a little time dilation along the way. Moving from A to B now takes you back in time; moving from B to A now takes you forward in time. (I may have this backwards, but anyway, you're familiar with the idea.)
So some time later I (or J. Random Fundamental Particle) enter A, and come out of B in the past -- changing B's future, creating a branching timeline. B still leads to A, and still leads to the future -- but on my original timeline, not on the branch, not to the future that I'd reach by just hanging around.
Meanwhile, mouth A is still present on this timeline. If I enter A again, going farther into the past (or if I wait around till the time I originally entered A, on that other branch) I create yet another branch.
And there's mouth A waiting for me again. Lather, rinse, repeat.
There's a certain tree-falling-in-the-forest aspect to it -- do the branches exist until I travel (or something travels) through the wormhole? But my intuition is that the number of branches is at least countably infinite. Or am I missing something?
Posted by: David Moles at May 23, 2005 02:01 PMI'm still convinced that time is an illusion of consciousness, and that all possible states in all possible universes exist as discrete entities simultaneously, and that they're only interconnected by consciousness. My consciousness perceives a particular sequence of universes and arranges them contextually to make sense (or "chronologically," if you insist on including the illusion of time...).
However, for the sake of argument, I'll make some comments on the wormhole model proposed by David.
Say you've got the arrangement David described. Wormhole A points to wormhole B in the past, while wormhole B points to wormhole A in the future. So you go through wormhole A in Universe 0 (U0), coming out wormhole B and creating an alternate future, which I'll call U1. You look around, change history, then decide you were better off in the first place. You go back through B to U0's A.
Ugh. This is the boring universe I left in the first place, you go back through A to B.
Now, there are two possibilties with this A & B system, which David didn't clarify - either A and B each point to a specific time and place, A being, say Judea around 30 CE, and B being Fairfax, VA around 2005 CE - or A points to Judea 1975 years before B, so that the time is moving for both points on the wormhole. I'll assume that time is moving for both points on the wormhole and move on.
So you're bored with U0 again, and you go through A again, and you're back in U1 at B again, a little later in time than you were the first time you went through. Now suppose that rather than going back to U0, you travel through space to the location of A and go through to B. Now you've created U2, simultaneously generating a new universe and defining the sound of 1980s pop-rock in one fell swoop.
So you're in U2, and you go back through B, to U1, then you go to B in U1 and go back to U0. If you go through A at this point, you're in U1 again.
Except upon reflection, I don't think this is what happens. I think every time you go through A, you generate a new universe, and every time you go through B, you go back to the universe from which the new one was generated. Let me think through this interpretation. Thanks for your patience.
So you start in U0, you go through A, creating U1. You go through B, and you're back in U0. Going through A now creates U2. Now you go to A in the current universe, and you create U3. Going through B at this point puts you back to U2. You travel through space to B. Does that send you back to U1, or does it create U4? I think you're back in U1. Go through A, and THAT creates U4.
Okay, so let's regress to U0. What happens if you go through B at this point? Do you remain in U0, only at a point in the future? I think so. Then if you go through A to get back to your own time, it actually sends you through to U1. If you then go back through B, I think you come out in your own future, having missed a number of years by virtue of having gone through B in the first place.
I think maybe the universe makes more sense if you go through A consistently. Even though on a space-time-continuum level, you're creating a new universe each time, I think on a continuity level, causality would be easier to contextualize than going through B.
Hrm. I don't know if I've said anything useful, but I think I may have said something true...
Posted by: Matt Hulan at May 23, 2005 02:49 PMI have an almost religious terror of getting this deep into this sort of conversation without math.
Is any of this how wormholes are purported to work?
Posted by: Benjamin Rosenbaum at May 23, 2005 02:59 PMTrust slashdot to provide...
An article linked from /. to BBC:
https://news.bbc.co.uk/1/hi/sci/tech/4564477.stm
As for getting deeper into the conversation without the math, I think (as this article seems to confirm) that any conversation about wormholes is by nature a philosophical conversation, not a scientific conversation. Adding "the math" doesn't take the conversation out of the realm of speculation, it simply gives the speculation rules and structure.
Rules and structure are useful, moving the philosophy from opinion to logic, but I don't know that logic makes the philosophy any more true...
Posted by: Matt Hulan at May 23, 2005 04:24 PMYeah, I'd have to sit down with a pencil and draw some diagrams (and throw lots of them away) to be sure of what I was talking about.
The "time is moving" model is the one Kip Thorne posits in Black Holes and Time Warps. There is math behind it. I don't think there's any math behind the branching timelines idea. (And without branching timelines, there's apparently good math behind the idea that traversible wormholes with time differentials, were they to exist, would destroy themselves before they become traversible, due to vacuum fluctuations undergoing something analogous to audio feedback.)
I don't believe in consciousness, per se, so the idea that time is an illusion of consciousness doesn't do much for me. I think time is a useful concept for describing relationships between possible states of the universe that we see as being causally connected, whether or not we treat all possible states equally, or some as potential and some as actual. (Side note: of course, you can't really talk about states of the universe without also positing some reference frame.)
Posted by: David Moles at May 23, 2005 05:48 PM[David]
Only if you assume that time travel = branching timelines (and of course ignoring the quantum effects that are predicted to enforce chronology protection).
Okay, but it sort of sounds like you're assuming your conclusion as a premise.
What I thought you were talking about was traversible wormholes between two different universes. Then you could perform time dilation on one mouth without spawning any additional universe; you'd simply create a situation where, for example, two objects entering a wormhole mouth a year apart in one universe would exit the wormhole mouth in the other universe ten years apart. (Assuming that time originally "passed" at the same "speed" in both universes, of course.)
If both mouths of the wormholes open onto the same universe (and if the wormhole doesn't destroy itself via quantum fluctuations), then I think the best guess is that the Novikov self-consistency principle holds. From what I've read of Kip Thorne, that's the conclusion he drew from his calculations; no branching timelines for him.
[Ben]
I have an almost religious terror of getting this deep into this sort of conversation without math.
I don't understand; you were happy to talk about what you called the "orphan effects" model without resorting to mathematics. I don't think any of us really has the math background to analyze this at the level a real physicist would.
Posted by: Ted at May 23, 2005 11:18 PMYou're right, of course, Ted, that the real math of wormholes would be beyond me -- so my comment was sloppy.
What I meant to say -- after reading Matt's long post -- was "my head is starting to hurt".
:-)
Posted by: Benjamin Rosenbaum at May 24, 2005 12:04 AMAh, okay.
Posted by: Ted at May 24, 2005 12:14 AM[David]
I don't believe in consciousness, per se, so the idea that time is an illusion of consciousness doesn't do much for me. I think time is a useful concept for describing relationships between possible states of the universe that we see as being causally connected, whether or not we treat all possible states equally, or some as potential and some as actual.
[Me]
If you don't believe in consciousness, what does it mean that something does or does not "do much for me?" If "time is a useful concept for describing... the universe that we see as... etc." useful to whom, and who is it that does the seeing?
I don't mean to be confrontational, I'm just curious in what you DO believe in, if not consciousness. You can point me to a link, if you've already gone over this in detail...
Posted by: Matt Hulan at May 24, 2005 01:00 PMNo problem, Matt. I wouldn't say I have any sort of fully formed or self-consistent theory of consciousness, but some of my thoughts and/or some of the ideas that have influenced me can be found here, interspersed among other things. For the purposes of this discussion, what I mean to say is that I'm comfortable with theories of time that fail to explain our perception of time, because I don't consider qualia to be admissible evidence. (We all assert that we're conscious, but I don't think any of us can prove emperically that anyone else is; and philosophical attacks on the problem tend to lead into arguments that, to me, seem nonsensical, like Putnam's argument against the brain in the vat.)
Ted, I may very well have assumed what I was trying to prove, but I didn't realize it until I'd worked through the consequences. Having done that, I tend to agree that the Novikov principle is the version that makes the most sense.
(Dammit, I was hoping to get some of the SFnal eyeball kicks of many-worlds abuse without having to posit a preexisting multiverse and infinite multiplication of entities. Back to square one...)
Posted by: David Moles at May 24, 2005 02:09 PMMatt, see also this particular comment of mine in that discussion thread.
Posted by: David Moles at May 24, 2005 02:12 PMTed and/or David, can we take some time at Wiscon with a blackboard, so you can show me what you're talking about with the wormhole example?
Posted by: Benjamin Rosenbaum at May 24, 2005 02:41 PMSure!
Posted by: David Moles at May 24, 2005 04:39 PMP.S. Ben, I think (viz. the consciousness digression) you need a radio button for "I am an automaton, posting to your weblog in response to its actual content." :)
Posted by: David Moles at May 24, 2005 04:40 PMOkay, now that Ted has explained this in the Madison, WI airport --
If both mouths of the wormholes open onto the same universe (and if the wormhole doesn't destroy itself via quantum fluctuations), then I think the best guess is that the Novikov self-consistency principle holds.
From what I understood, what you mean is that general relativity implies that the Novikov self-consistency principle holds -- that is, self-consistency is already implicit in general relativity.
But it sounds like it's also a falsifiable hypothesis. The "radical rewrite hypothesis" isn't logically inconsistent -- it's just forbidden by general relativity (which is to say, evidence for it would force a revision of general relativity).
You set up an experimental apparatus for shooting a billiard ball through a wormhole. The billiard ball is meant to emerge from the other end in time to strike itself before it goes in, keeping it from going in -- the grandfather paradox in the lab.
Kip Thorne's calculations, according to Ted, say that general relativity demands that what you see is this: the ball shoots toward the entry wormhole. Just before it hits, its future self emerges from the exit wormhole and strikes it a *glancing blow* -- just enough to drive it into the entry wormhole at such an angle that it can emerge, strike itself a glancing blow and clatter to the ground.
Given that I can't follow the math, it seems natural to me that this would be already implicit in the assumptions of general relativity.
Consider the following result:
So you get your experimental apparatus set up. You write on your billiard ball "Professor Thorne was here 8/23/2045" with a Sharpie. Then you launch it through the wormhole.
But before it can enter, another billiard ball flies out of the exit wormhole, strikes the first a solid blow, and both of them clatter to the floor of the lab.
Now there are two billiard balls on the ground, both of which say "Professor Thorne was here 8/23/2045" in black magic marker.
I can imagine, even if I can't follow the math, where this result would be problematic from the point of view of all kinds of principles of physics -- conservation of mass/energy and of momentum, for instance (though maybe the wormhole mechanism somehow makes up the differences there?)
The next question is, though: if we did in fact actually observe this, could we make up an elegant, naturalistic theory that would account for it?
I expect we could.
And I expect one camp of interpreters would say "there are two balls, one sent by the Professor Thorne of a parallel universe, who is wondering where his ball went, one sent by this Prof. Thorne" and the other would say "there are two balls, one from a timeline which was erased by its successor timeline, leaving only this ball as evidence that it ever existed. When did it exist? Why, three beta-seconds ago along the t-beta time axis, of course."
Are there experiments which could determine which of these interpretations is correct?
Well, if Prof. Thorne is standing there holding two balls and a paper airplane comes out of the wormhole exit with a note saying "what happened to my ball?" we would assume the former, but I'm not sure *that* makes any sense with the original setup (that there is only one entry and exit for the wormhole, and they're both in this Prof. Thorne's lab).
So this is the point at which I think I *would* actually need to understand the math to say anything meaningful. It's easy from this point on to postulate things that sound sensible but are in fact nonsense, *given* the (unclear to me) constraints under which the experiment was set up.
But nothing has yet convinced me that Prof. Thorne holding two billiard balls *cannot happen*, nor that if it did *no scientific explanation would be possible*, though I am perfectly willing to believe that it would force a vast revision of physics-as-we-know-it.
I think you're right. My instinct is that the alternate timeline hypothesis (given the phenomenon of the two signed billiard balls) may not be very parsimonious but is not falsifiable. The erased timelines hypothesis is more parsimonious but is disprovable by the paper airplane.
Posted by: David Moles at June 1, 2005 02:30 PMWell, if Prof. Thorne is standing there holding two balls and a paper airplane comes out of the wormhole exit with a note saying "what happened to my ball?" we would assume the former, but I'm not sure *that* makes any sense with the original setup (that there is only one entry and exit for the wormhole, and they're both in this Prof. Thorne's lab).
That's the problem. The wormhole supposedly connects the two mouths bidirectionally. You should be able to look through the mouth that the billiard ball exited, and see the apparatus that launched it. This was true before time dilation was applied to one of the mouths; why should it no longer be true after time dilation is applied? When did the wormhole switch from connecting two points in the same universe to connecting two points in different universes, and why?
And what's on the other side of the wormhole mouth that you were aiming your own billiard ball at? Still another universe? If so, then why should your shooting billiard balls into it or toward it have anything to do with billiard balls exiting the other mouth?
When I talked to Ben, I mentioned that when I Googled the radical rewrite conjecture, I found stuff like this:
For a rather more violently radical point of view permit me to propound the Radical Rewrite Conjecture wherein one posits a radical rewriting of all of known physics from the ground up. Suppose, for instance, that one models spacetime by a non-Hausdorff differentiable manifold. What does this mean physically? A non-Hausdorff manifold has the bizarre property that the dimensionality of the manifold is not necessarily equal to the dimensionality of the coordinate patches [26]. From a physicist's perspective, this idea has been explored somewhat by Penrose [25].Crudely put: while coordinate patches remain four dimensional in such a spacetime, the dimensionality of the underlying manifold is arbitrarily large, and possibly infinite. Local physics remains tied to nicely behaved four dimensional coordinate patches. Thus one can, for instance, impose the Einstein field equations in the usual manner. Every now and then, however, a passing wave front (generated by a “branching event”) passes by and suddenly duplicates the whole universe.
(from a paper by Matt Visser at https://arxiv.org/pdf/hep-th/9202090)
Superficially it sounds like alternate timelines, but I don't feel qualified to use this as a basis for further arguments. However, it seems that Visser's conclusion (at least back in 1992, when he wrote that paper) was that time travel via wormholes is very likely impossible for other reasons.
I am too slow for the internet. Consider this a late and off-topic trackback:
Posted by: Dan Percival at June 6, 2005 07:31 PMAh, yes, I forgot: no links allowed. Follow my name link, it's the top journal entry at the moment.
Posted by: Dan Percival at June 6, 2005 07:32 PMLinks are allowed! At least, I'm pretty sure links are allowed. Perhaps your tag was malformed? Or have my MT settings changed somehow?
Here is Dan's movie review.
Posted by: Benjamin Rosenbaum at June 7, 2005 10:45 AM