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Saturday, June 18, 2005

Time Travel , Free Will, Ouspensky, Xaj Kalikak, and The Trans-temporal Post-Singularity Ubermind

This entry is motivated by an interesting news article that my friend David Hart forwarded to me, about one of my old favorite topics: time travel.

I'll use the article as an excuse to riff on an idea I had back in the 1980's about the possible transtemporal nature of superhuman minds following the Singularity.

The article is titled "No paradox for time travellers" and appeared on NewScientist.com on 18 June 2005, written by Mark Buchanan. It pertains to a technical paper online at

www.arxiv.org/quant-ph/0506027

Back when I first got serious about science back in my late teens and early 20's, time travel was my top choice of research area -- but after a little while I decided that AI, my second choice, was more likely to be achievable within my lifetime. (EVEN FURTHER DIGRESSION: My third choice was working toward human immortality via biology -- which I'm working on in the background now via my work with Biomind LLC -- but I backburnered that one because I don't enjoy biology personally nearly as much as physics or computer science. To me, it seems that biological immortality will be made possible via a combination of many relatively small insights and leaps -- "big science" like one sees in contemporary biology -- whereas time travel and AI seem more amenable to huge revolutionary insights ... this is one reason the latter interest me more than biology ... the other being that CS and physics have a mathematical elegance that appeals to me, and that biology lacks....)

I learned in the mid-80's, when studying general relativity theory in grad school at NYU, that modern physics deems time travel possible -- but difficult to achieve. Basically, it makes time travel into an engineering problem, but one that would seem to probably require engineering on the scale of making weird configurations of exotic forms of matter and energy ("exotic" meaning physically possible to produce, but incredibly difficult and/or expensive to do so using current technologies). Do-able, but probably not this decade....

Much later I read Kip Thorne's book "Black Holes and Time Warps", which reviews general relativity and its implications as regards time travel (along with other topics), and a host of other related papers, some of which are reviewed and referenced here.

(A much more ridiculous, though amusing, book on time travel is J.H. Brennan's book, "Time Travel: A New Perspective." Brennan gives you practical instructions on how to travel through time. Recommended only for entertainment value. One of the reviewers on amazon.com complains that the methods are inadequate because they can't be practiced by individuals acting alone, they require that time travel be a group activity!)

Anyway, the article Dave forwarded is brief and the bulk of it goes as follows:

The laws of physics seem to permit time travel, and with it, paradoxical situations such as the possibility that people could go back in time to prevent their own birth. But it turns out that such paradoxes may be ruled out by the weirdness inherent in laws of quantum physics.

Some solutions to the equations of Einstein's general theory of relativity lead to situations in which space-time curves back on itself, theoretically allowing travellers to loop back in time and meet younger versions of themselves. Because such time travel sets up paradoxes, many researchers suspect that some physical constraints must make time travel impossible. Now, physicists Daniel Greenberger of the City University of New York and Karl Svozil of the Vienna University of Technology in Austria have shown that the most basic features of quantum theory may ensure that time travellers could never alter the past, even if they are able to go back in time.

The constraint arises from a quantum object's ability to behave like a wave. Quantum objects split their existence into multiple component waves, each following a distinct path through space-time. Ultimately, an object is usually most likely to end up in places where its component waves recombine, or "interfere", constructively, with the peaks and troughs of the waves lined up, say. The object is unlikely to be in places where the components interfere destructively, and cancel each other out.

Quantum theory allows time travel because nothing prevents the waves from going back in time. When Greenberger and Svozil analysed what happens when these component waves flow into the past, they found that the paradoxes implied by Einstein's equations never arise. Waves that travel back in time interfere destructively, thus preventing anything from happening differently from that which has already taken place. "If you travel into the past quantum mechanically, you would only see those alternatives consistent with the world you left behind you," says Greenberger.

Interesting... huh?

What this suggests is that, perhaps, time travel is quite possible and the reason that it seems paradoxical to us is because of our illusion of free will.

I.e. since we think we have free will, we don't like to think that if we go back in time we are constrained to do things consistent with presently observed reality...

I am reminded of Ouspensky's classic novel "The Strange Life of Ivan Osokin" -- where the main character Osokin convinces a magician to send him back in time to live through his life all over again... he's hoping to make his life better, by not making as many stupid decisions as he did the previous time around.

But the punchline is, while living his life over again, Osokin winds up making the same stupid decisions he did before. He just can't help himself -- he finds himself irresistably drawn to make the same dumb choices even though he vaguely remembers, from his previous times living his life, how annoying their consequences were....

Osokin iterates around again and again -- repeatedly living his life then getting the magician to send him back to the past to live his life over again -- each time failing to correct his stupid decisions.

But then, after the N'th iteration, he finally he achieves enough awareness that when he meets with the magician he realizes it's stupid to revisit his life again, without changing the nature of his mind -- and he agrees to join the magician's mystical sect and get tutored in the True Path....

Ouspensky's point of course is that normal humans don't have free will but basically live like deterministic machines pushed by their unconscious and emotions -- but if you join his Gurdjieff/Beelzebub sect, you can achieve real free will! (BIG DIGRESSION: Needless to say, I don't accept this philosophy, though I do find some germ of truth at the core of it. In my view, there is absolute freedom in the universe at a certain level -- the level Peirce called First -- and then there are patterns in the universe at another level -- the level Peirce called Third -- and there are subtle connections between First and Third, wherein some patterns seem to have more freedom associated with them than others.... It may well be that human-mind-patterns can achieve more freedom, in a sense, via practicing meditative and mystical disciplines like the ones Ouspensky preached -- though of course these practices can also lead to a bunch of delusions. But I don't believe that any practice can lead to a fundamental breaking-out from the world of determinism and delusion, which is pretty much what Ouspensky taught. It's a big exaggeration, unfortunately -- the only hope for breaking out of delusion altogether is to go totally beyond your human mind, which Ouspensky didn't really succeed in doing; he may have had awesome moments of insight, but he still remained human with all the beauty and flaws and screwiness implied thereby, blah blah blah....)

OK -- so Ouspensky's novel gave a funny twist on Nietzsche's Eternal Recurrence ... but it also seems somewhat relevant to these recent ideas about time travel.

The time-travel idea from the Greenberger and Svozil paper basically suggests that if we went back in time we'd find ourselves in the position of Ivan Osokin -- unable to make decisions other than the ones we're "postdestined" to make, so as to cause the future to come out as it's already known it's going to come out....

Ergo, the conclusions of Greenberger and Svozil hold up except in the presence of Ouspenskyan magicians!! ;-))

But another interesting possibility arises here. It may be that our present reality is not consistent with there having been time travelers going back into our past doing interesting stuff. However, sometime in the future there may be a time-travel-ful period full of time travelers cycling around and around -- and the world during that period may be whacky enough that the consistency of existence-of-meddling-time-travelers with observed reality is obvious...

Indeed, this is what I've often suspected. Once time travel is invented, maybe we'll be able to travel back in time fairly freely -- but only back to the point where time travel was invented -- not before. The Greenberger and Svozil results suggest that travel back before the invention of time travel may not be possible -- or may be possible only with very strict constraints -- because it can't be done too freely and still be done consistently with the world as it's known to be during that period (e.g. our period and our past). But once time travel is invented, free and whacky time travel from the future back till that point may well be consistent with the world after that point.

This suggests that the history of the universe may be divided into two periods: temporally forward and temporally bidirectional.

This is a fun vision of the post-Singularity world.... Post-Singularity may be post-temporality, in a sense. superhuman AI creates time machine, starts up the rampant-time-travel domain, and all heaven breaks loose ;-)

Yeah yeah, this is whacky speculation, I know. But it's not impossible according to known physics, and nor is it philosophically nonsensical.

The key point is that there may be consistent solutions of the universe's physics equations, according to which the universe at time T is consistent with time travellers from after T coming back and messing with the universe at time T in interesting ways that are obvious and noticeable to the folks living at time T.

The universe at our present time is consistent with time travelers from the future coming back and messing with our past, but not in ways dramatically noticeable by us. Of course, it's possible that time travelers did come back and mess with our past in ways that were important to us -- maybe that's the cause of the origin of life, the Big Bang, etc. -- these ideas have been explored in numerous science fiction novels. But even if so, this level of time-travel-based interference is pretty minimal compared to what may be possible in the post-Singularity period.

In some whacky, interesting but amateurish science fiction I wrote in the late 1980's (part of my never-finished meta-novel Wargasm), I described a character named Xaj Kalikak, who traveled into the future and practiced excessive time-travel until he'd revised the past and his own mind so many times that, in effect, the various loops of time-travel-induced-bidirectional-causation organized themselves into an intelligent mind. Instead of feedback loops of electricity in the brain, feedback loops of causation over time self-organized into a superintelligent mind. Perhaps this sort of thing will come true, and the superhuman mind following the Singularity will be transtemporal in a way we can't even imagine....

Heh.

15 comments:

Tom Buckner said...

There's a completely separate way of deriving non-paradoxical time travel if we consider time travel as equivalent to travel to other possible Tegmark universes isomorphic to our past (I'm referencing Julian Barbour's ideas of Platonia, with each Now being like a snapshot). I once wrote a long, humorous e-mail to my friend Michael in which I explained this (it's lost, but I'll briefly paraphrase:)

Say you go back in time and kill your grandfather. Do you disappear? No: there you stand, covered in his blood, with the memory of having killed him. Now let's say you go back to the present. You now exist in the present, with the memory of having killed him. The copy of you that left in the time machine is not there, having left.
But suppose you met your exact quantum copy: would you both explode or something? Why would that happen? My reply is that you stop being exact copies almost instantly. Facing each other, they see different views of the room, breathe different atoms of air, and so on. As time passes, they must pile up slightly different experiences, as though they were very, very identical twins, but nothing more. Their memories may match, but only up to the point of their meeting.

Suppose, having just returned from killing Gramps, you travel back in time and kill yourself before you can kill Gramps? Then there you are, covered in Gramps' blood, standing over your own dead body, and Gramps is wondering what the hell is going on.
So you decide to go back to the present and have a stiff drink. With shaking hands you strip off your bloodsoaked shirt and try to mix a martini, but then you come bursting in the door with a flame thrower. This would never have happened if you'd left time/Tegmark travel alone, you poor sod.

The catch is that travel in Platonia is different from time travel as we usually understand it; instead of linear travel along the single path we believe to have led us here, in Platonia we would need essentially infinite knowledge about where we are trying to go, which suspiciously resembles the infinite energy needed to exceed light speed (i.e. tachyonic travel to the past). And you need a comparable amount of data on the place you started to get back! Also, if we do live in Platona, there are many possible pasts which will derive our present Now arrangement of matter/energy, just as there are many possible futures deriving from it (this is why I have previously used a chessboard as a metaphor for the arrangement of particles in a Tegmark universe: one would need to know the positions and types of particles/pieces, but also the rules governing their movement).

Am I mistaken, or is there a great divide between physicists who calculate what happens if there is one universe and those who assume many?
If we posit many universes, the backwards-traveling waves are probabilistically constrained from manifesting in their own past timeline, but in Platonia there are many other timelines for them to manifest in. Perhaps this means that we WILL invent time travel, but the paradoxical past effects are prevented in this timeline. And perhaps such travel is inherently one-way.

James MacAulay said...

"The time-travel idea from the Greenberger and Svozil paper basically suggests that if we went back in time we'd find ourselves in the position of Ivan Osokin -- unable to make decisions other than the ones we're "postdestined" to make, so as to cause the future to come out as it's already known it's going to come out...."

Osokin's situation sounds different than the one described by the Greenberger and Svozil article: apparently only some soul-thing or mind-shard of Osokin's travels back in time, rewriting itself over Osokin's original mindware at the destination time. Perhaps the magician is only sending back particular parts of Osokin's mind which can conveniently form some basic memories but have no ability to alter behaviour (somehow...).

The article, on the other hand, seems to be talking about classical time travel where whole bodies, brains, and minds cease to exist at some time and suddenly appear some time earlier. In this case, I can't see how you can get around the fact that there is a fully functional human being suddenly appearing in the past, with lots of uncanny knowledge of the future (assuming that this strange new time travel technology isn't violently destructive to the human form, of course).

What I'm getting at is that regardless of whatever notions of free will we bring into the picture, a fully functional human body and brain will act using the same heuristics and cortical algorithms (or whatever) that it does when it departs in the future. If I go back in time before I was born with the intention of killing my parents, then when I arrive in the past with an identical body and brain I will still have those intentions.

Whatever "free will" is, it is *not* some Cartesian Theatre-goer removed from reality which must *act on* reality to get reality to do stuff. If we say "there's no free will" then we are still left with this body and mind which act in particular ways when presented with particular stimuli. If, instead of a human, we sent a simple robot back in time to kill my parents, it would be a little easier to see how powerful physical-law-bending trickery would be required to assure the prevention of the slaughter.

Anonymous said...

Trying to be faithful to the formalism used, one finds that we get ourselves all tangled up in nonsense when we conflate wavefunctions with particles. Wavefunctions extend from Big Bang event horizon to some point at infinity (in a open universe). Superposing some McTaggartian A or B-series on top of all these waves and what obtains?

Stephen

Anissimov said...

*claps* Nice speculation. The idea of spacetime-loop-instances of a single person coalescing into a superintelligent mind seems to be new. If quantum wavefunctions going back in time always interfere destructively with earlier states of the universe, then how can a time traveller exist coherently in the past? I don't understand.

daddycaylor said...

To anissimov's question: It seems that a time traveller to the past could have an "additive" effect, i.e. add additional details to the past that don't conflict with his the past that was previously affected by him/her. This would imply that the traveller could not travel back to physical locations that are too close to the locations he/she was before.

To the "time travel can't go back before time travel was invented" thought: Doesn't this imply that time travel can never be invented? Think about the very moment that time travel is invented, and think about the above statement in quotes. Then how can we truly say at that point that time travel (to the past) has been invented, if it can't be done?

On how "observer moment"-based reality relates to this: Are these "waves" made of objective space-time events? Or would a time traveler's waves add or destroy "events" only as he/she experienced them or remembered them?

Bob Mottram said...

One of my favourite sci-fi novels, called "Slaughter house five" by Kurt Vonnegut gives a very similar scenario in which the main character travels in an uncontrolled random way to different parts of his own lifetime.

I think time travel (backwards at least) probably is impossible, otherwise we would have a lot of Japanese tourists from the future turning up to photograph the quaint practices of early 21st century life.

On the other hand as you say in theory time travel should be possible. Perhaps on the rare occasions when people think they see ghosts or UFOs perhaps these are actually instances of time travel.

Altman said...

Feynman used to joke that there is only a single electron in the universe, whirling back and forth through time -- hence the reason that all electrons are indistinguishable is that they are in fact all the same electron. All of existence, including the emergence of conscious observers, arises from this wildly meandering path of a single electron through space and time. cf. Wheeler-Feynman absorber theory and later transactional interpretation of quantum mechanics by Cramer.

Li and Gott have also proposed that a universe undergoing early inflation could spontaneously give rise to "baby universes," one of which by means of a closed timelike curve would turn out to be the original universe. An arbitrarily advanced civilization could artificially produce basement universes which tunnel through to the initial "big bang" in the same manner.

bnutwit said...

I keep thinking, where does looking into the past(sky) using telescopes fit in this. Does instant travel to a distant star to see how its environ looks 'now' constitute time travel. If so when we return did we travel to past (from the star's point of view). Suppose our galaxy lies in between two far away galaxies say G1 and G2 and that G2's view of G1 is thru our galaxy, then if we change all the red wavelengths from G1 passing thru our galaxy to blue (let us assume we can do this galaxy wide), so did we change G1's timeline with regards to G2 worldline. I know that sounds confusing, but does someone get my drift.

Another point, if we are expanding since big bang, let us reduce(project) our 3D space to 1D and include time as the second Dimension. Since we are expanding from a single point, every 't' is a latitude on the surface of a 3D sphere. Let us say Big bang is North Pole, then Past is higher latitude and Future is the reverse, we have not reached the equator yet (will there be a equator if there is no crunch?). So going to past is traveling North and future is South. Since we keep moving south at a constant rate any changes made at a particular latitude after we moved from it will never catch up with us until we stop or travel North. This means that we actually hop from one multiverse to another at every 't'. If the number of 't' since big bang is 'N' then at next 't' there will be 'N+1' multiverses. Hmm...., ok, instead of equator being Zero latitude, let us make North pole as zero, then at each 't' exactly 'N+1' new timelines are possible, any change in timeline 'n' will continue to propagate to 'n+1' , but at next 't' Multiverse 'n' will be overwritten by Multiverse 'n-1'. So what is the ideal value for 't'. Does time travel has a quantum time limit much like the uncertainity principle???

Colin said...

Ben, from my reading of Greenberger and Svozil's paper no, their results do not suggest that time travel back before the invention of time travel may not be possible. This may be so for other reasons but their results do not suggest it.
According to their conclusions their results suggest a quantum mechanical reason why inconsistent time loops (eg going back in time to murder yourself) cannot occur.
This does not rule out self-consistent time loops that do not change the past (eg if you met a mysteriously familiar-seeming old man who gave you plans to make a time machine and after a life-time of work you built one and went back in time and gave the plans to your younger self, that would be allowed under this theory (although it may be ruled out for other reasons). Another example of a consistent time loop would be going back in time and arranging for your mother and father to meet. This would explain their constantly expressed gratitude for the stranger who introduced them - a stranger who appeared to be heavily disguising his facial features.
Greenberger says that their quantum mechanical explanation banning inconsistent time loops may have implications for free will. He said to media that if you went back to try to kill your younger self you could find yourself changing your mind and being unable to go through with it.
The question here would be how quantum mechanical effects would manifest on the macro-scale, such as in the brain of a person. Or, as James MacAulay astutely suggests, a simple robot was sent back to do the job. How do quantum processes manifest on the macro scale? This is an unanswered question at the moment I think.

Bnutwit asked whether instant travel to a far away star is a form of time travel. It's all semantics. According to the theory of special relativity there is no such thing as "instant" travel. However if you came back from the distant star you would find yourself to have aged less than the people left behind on earth so that could be regarded as a form of "time travel into the future." (twin paradox). But it is not what sci-fi regards as time travel.
We see the stars as they were a long time ago because of the finite speed of light so we are "looking back into the past" - again not sci-fi time travel.
According to the Special Theory of Relativity there is no global "instant" time - it is different for different observors moving with respect to each other.
But the General Theory of Relativity does posit that there is an "absoluteness" about the world-lines of whatever through space-time and allows for the possibility of closed time-loops (time-travel).

regards, Colin

Colin said...

Ben, from my reading of Greenberger and Svozil's paper no, their results do not suggest that time travel back before the invention of time travel may not be possible. This may be so for other reasons but their results do not suggest it.
According to their conclusions their results suggest a quantum mechanical reason why inconsistent time loops (eg going back in time to murder yourself) cannot occur.
This does not rule out self-consistent time loops that do not change the past (eg if you met a mysteriously familiar-seeming old man who gave you plans to make a time machine and after a life-time of work you built one and went back in time and gave the plans to your younger self, that would be allowed under this theory (although it may be ruled out for other reasons). Another example of a consistent time loop would be going back in time and arranging for your mother and father to meet. This would explain their constantly expressed gratitude for the stranger who introduced them - a stranger who appeared to be heavily disguising his facial features.
Greenberger says that their quantum mechanical explanation banning inconsistent time loops may have implications for free will. He said to media that if you went back to try to kill your younger self you could find yourself changing your mind and being unable to go through with it.
The question here would be how quantum mechanical effects would manifest on the macro-scale, such as in the brain of a person. Or, as James MacAulay astutely suggests, a simple robot was sent back to do the job. How do quantum processes manifest on the macro scale? This is an unanswered question at the moment I think.

Bnutwit asked whether instant travel to a far away star is a form of time travel. It's all semantics. According to the theory of special relativity there is no such thing as "instant" travel. However if you came back from the distant star you would find yourself to have aged less than the people left behind on earth so that could be regarded as a form of "time travel into the future." (twin paradox). But it is not what sci-fi regards as time travel.
We see the stars as they were a long time ago because of the finite speed of light so we are "looking back into the past" - again not sci-fi time travel.
According to the Special Theory of Relativity there is no global "instant" time - it is different for different observors moving with respect to each other.
But the General Theory of Relativity does posit that there is an "absoluteness" about the world-lines of whatever through space-time and allows for the possibility of closed time-loops (time-travel).

regards, Colin

Colin said...

Ben, from my reading of Greenberger and Svozil's paper no, their results do not suggest that time travel back before the invention of time travel may not be possible. This may be so for other reasons but their results do not suggest it.
According to their conclusions their results suggest a quantum mechanical reason why inconsistent time loops (eg going back in time to murder yourself) cannot occur.
This does not rule out self-consistent time loops that do not change the past (eg if you met a mysteriously familiar-seeming old man who gave you plans to make a time machine and after a life-time of work you built one and went back in time and gave the plans to your younger self, that would be allowed under this theory (although it may be ruled out for other reasons). Another example of a consistent time loop would be going back in time and arranging for your mother and father to meet. This would explain their constantly expressed gratitude for the stranger who introduced them - a stranger who appeared to be heavily disguising his facial features.
Greenberger says that their quantum mechanical explanation banning inconsistent time loops may have implications for free will. He said to media that if you went back to try to kill your younger self you could find yourself changing your mind and being unable to go through with it.
The question here would be how quantum mechanical effects would manifest on the macro-scale, such as in the brain of a person. Or, as James MacAulay astutely suggests, a simple robot was sent back to do the job. How do quantum processes manifest on the macro scale? This is an unanswered question at the moment I think.

Bnutwit asked whether instant travel to a far away star is a form of time travel. It's all semantics. According to the theory of special relativity there is no such thing as "instant" travel. However if you came back from the distant star you would find yourself to have aged less than the people left behind on earth so that could be regarded as a form of "time travel into the future." (twin paradox). But it is not what sci-fi regards as time travel.
We see the stars as they were a long time ago because of the finite speed of light so we are "looking back into the past" - again not sci-fi time travel.
According to the Special Theory of Relativity there is no global "instant" time - it is different for different observors moving with respect to each other.
But the General Theory of Relativity does posit that there is an "absoluteness" about the world-lines of whatever through space-time and allows for the possibility of closed time-loops (time-travel).

regards, Colin

Nick K said...

I'm not at all qualified to talk about any of this (I don't even know what isomorphic means)but doesn't 5-dimensional theory assert that all possibilities, or all quantum waveform positions, all exist simultaneously, along with all their outcomes, in a region of space currently inaccesible to us?
If we for the moment regard the 5th dimenion as a "flat surface" containing all possibilities, and the 4th dimension as an individual's timeline, at each point on this line only one of the possibilities can be played out. However, as all possibilities already exist, we are unable to change anything - only to divert our timeline to a different universe where the change was inevitable.

MCP2012 said...

Ben: Current meta-physics (as distinguished from metaphysics--but see the late David Lewis' *Plurality of Worlds* for his take on ontological realism regarding modal-logic "possible worlds"...) would seem to suggest that there are many (if I'm not mistaken, at least 5) different senses or aspects of Multiversality. Tegmark, Andrei Linde, Smolin, Dave Deutsch, Saul-Paul Sirag (in his own way) and many others would, if I'm not mistaken, posit an ontology that entails that "time travel" is travel (or access) to an alternate spacetime, or even hyperspacetime. That is, it is literally travel to a (in many ways similar or identical) different spacetime in which event x either fails to occur, or occurs differently, etc. Deutsch & Tegmark, again if my reading of them isn't mistaken [can't guarantee this though!] seem to imply that physically-ontologically possible worlds are indeed pretty much isomorphic--or a better way to put would be *co-extensive*--with modal-logic's possible worlds (again, cf. Lewis, above). Now such different possible worlds may or may not be accessible by us technolgoically (yet), but they may, at least in-principle, be accessible (indeed, traverseable) by/with technology that we can't yet fully (or even partially?) conceive. My intuition (for whatever it's worth...) is that such trans-world access and travel is indeed in-principle quite doable, and that it's only a matter of time (!!!!) before we or our cognitive-intellectual descendents figure out the nuts-&-bolts how-to of it all. Both Saul-Paul Sirag and Jack Sarfatti, e.g., posit the possibility of full-fledged hyperspatial engineering. Which means we (or our descendents) would take-on more-or-less "Q"-like powers/abilities. Just my 2-cent rumination(s)...Great blog, Ben! Best wishes getting backing for Novamente A.S.A.P.!!

Francis said...

Ben:
Please finish 'Wargasm,' it sounds like it'd be a hoot. Now that Kurt Vonnegut and Robert Anton Wilson aren't around any more, we need another transcendence on paper to remind us it can still be done. My bro' would go for it as well; he got through 'Infinite Jest' twice. Thanks for kicking me in the gray matter.
I should let Petey talk for himself but he has said now and again that thanks to what he's seen in Hugh Everett, PhD.'s many-worlds interp of quantum theory, there might be possible sub-paths within an established path for any cohesive sentient unit of matter to effect a certain number of changes in a time-travel situation and still end up back where s/he began. Assuming that's what he wanted. So much for Ray Bradbury's 'Sound of Thunder.' In fact, maybe there's a minimum number of fluctuations in any given path that must remain unchanged for the sentient unit
to do as described above.
Makes me wonder if possibly Ouspensky's short story and the above view of quantum mechanics are not just dissimilar ways of saying almost the same thing.

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