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Time Travel Simulation Resolves “Grandfather Paradox”

154 points| markmassie | 11 years ago |scientificamerican.com | reply

124 comments

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[+] zrm|11 years ago|reply
> In the presence of CTCs, quantum mechanics allows one to perform very powerful information-processing tasks, much more than we believe classical or even normal quantum computers could do

That seems like an understatement if I'm understanding it correctly.

Imagine you have a "time machine" and you want to solve some arbitrary computable problem. You try a prospective solution and see if it's correct. If not, you send the next prospective solution back to be tried on the next go around the time loop. Once you arrive at the correct solution, you send that same solution back so that the iteration stops there. Then the loop repeats indefinitely with the correct solution so that the probability of exiting the loop at the correct solution approaches infinity.

It would literally be the end of the world as we know it. P=NP. Forget about quantum cryptography, that would break all public key cryptography, all cryptographic hash functions. It would obsolete algorithmic complexity theory by effectively turning every finite space algorithm into an O(1) algorithm. It would probably bring Strong AI.

But it still couldn't break a one-time pad.

[+] terhechte|11 years ago|reply
There's a chapter in the brilliant fan fiction "Harry Potter and the Methods of Rationality" where Harry gets access to a Time-Tuner, i.e. a time machine from the Harry Potter universe, and this is the first experiment he envisions and performs.

HPMOR is a really great book.

https://www.fanfiction.net/s/5782108/17/Harry-Potter-and-the...

[+] maaku|11 years ago|reply
Or, instead of receiving the next iteration you end up with a piece of paper with "DON'T MESS WITH TIME" written in your own shaky handwriting.

The space of possible stable outcomes is much larger than just the ones carrying the outcome of the computation.

[+] possibilistic|11 years ago|reply
It wouldn't be a constant energy algorithm though, would it? For each successive optimization iteration, you would have to expend energy. Does that energy get put back with every rewind of the clock? If so, energy is also infinite.

I wonder what the time-energy-complexity trade-offs are?

As an aside, I would gladly pay someone to walk me through the math and physics sometime. (Any grad students in Atlanta are more than welcome to take me up on that offer... I might even try Skype.)

[+] tjhance|11 years ago|reply
www.scottaaronson.com/papers/ctc.pdf

Shows that (with or without quantum computing) you can do all of PSPACE using a CTC (in polynomial time) and no more.

[+] onion2k|11 years ago|reply
It would probably bring Strong AI.

A CTC is effectively a computer that can process a loop instantly, regardless of how complicated it is. Given that, we could design an AI machine that could analyse an arbitrary amount of data in any depth without regard to how long it'll take. More than that, everything happens in one 'tick' of whatever is controlling the CTC, so there aren't any issues around asynchronous processing. It just 'goes away'. Such a machine would never have to wait for another process to finish. Strong AI would be pretty much a certainty - we'd be able to brute force any problem.

[+] wuliwong|11 years ago|reply
I wonder if you'd run into some sort of energy problem. Like, this time machine would require some sort of energy and incur some amount of wear and tear on during each pass. The amount of possible solutions to today's cryptography might make this brute force level of effort, even with a time machine, infeasible. I feel like nasty old thermodynamics may preserve our world still. :)

Granted, I'm way way out of my depth here. I have a Ph.D. in physics but I studied nonlinear oscillators, relating them to problems in neuroscience.

[+] rst|11 years ago|reply
Beyond P=NP: this actually gives you a constant-time solution for any problem where it's possible to enumerate candidate solutions, regardless of how long it takes to do so. So, we'd have ANYTHING=O(1).
[+] baddox|11 years ago|reply
What algorithm would you run on this machine to yield strong AI?
[+] ww520|11 years ago|reply
One-time pad is just a generated key used once. The "time machine" will break it by trying out all keys in the key space in the time loop. If time is not an issue, brute force method pretty much breaks any crypto.
[+] TheLoneWolfling|11 years ago|reply
My pet theory:

You create a paradox, it just keeps looping (you go back in time and kill your grandfather -> you don't exist -> you don't build the time machine and go back -> your grandfather lives -> you exist -> you build the time machine etc). But every time around the loop there is a certain amount of actual randomness.

Perhaps that atom decays this time around, or that transistor erroneously conducts due to shot noise.

So all we see is the final "fixed point". The iteration where everything ends up going just right to avoid a paradox - perhaps the gun fired prematurely, or the time machine didn't work, or a passing airplane dropped an engine on you, or...

From the perspective of any time traveler, it ends up being as though the universe is conspiring against you if you try to do anything that would cause a paradox.

[+] DennisP|11 years ago|reply
This sounds like the Novikov self-consistency principle.

Say you have a wormhole on a billiard table. It curves around and goes three seconds backward in time. You roll a ball into the wormhole, aimed such that after it exits the wormhole, it will knock its earlier self off the path so that it never enters the wormhole. Paradox.

Except when you try it, instead of emerging along the pathway you aimed, it emerges along a slightly different path, and strikes its earlier self only a glancing blow. And why did it emerge along a different path? Because it was struck a glancing blow.

http://en.wikipedia.org/wiki/Novikov_self-consistency_princi...

[+] ZoFreX|11 years ago|reply
If your theory was the correct one, could we use that effect to perform computation - perhaps condensing 1000s of years of computation into a few minutes, with the result encoded in which steady state it settles on?
[+] JoeAltmaier|11 years ago|reply
I like to imagine that time travel is chancy, and the 'time tunnel' collapses each time a paradox is imminent.
[+] sandycheeks|11 years ago|reply
When I was younger I thought a lot about the physics of traveling back in time but I always seemed to hit a brick wall with spatial coordinates.

Where we are in the universe today is very far from where we were in the universe yesterday based on the movement of the earth alone. Add to that the movement of our solar system, galaxy, cluster, supercluster and movements I am not even aware exist and it becomes really far away. Grandpa would probably be light years away from me and my time machine.

Am I missing something here, because I've never heard this mentioned by anyone else?

[+] Steuard|11 years ago|reply
It's a valid issue. You wouldn't need to worry about any component of your motion that's "constant velocity" (so, inertial straight-line motion), since all inertial reference frames are equally valid. But you would need to keep track of curving motion (like the rotation of the Earth, orbit around the Sun, Sun circling around the galactic core, etc.).

You might be able to wave your hands and claim that the time machine follows paths back in time along natural world-lines in curved space-time (gravitational geodesics), which will at least get things like orbiting around the Sun right (and galactic motion as well). But I think you'd still need some way to keep the machine's path rotating on the surface of the Earth rather than falling back and forth through the center of the planet.

[+] TheLoneWolfling|11 years ago|reply
Most of the time this is handwaved over, for bunches of reasons. Part of it is that there is no one valid frame of reference: you can't just say "this stays stationary" - because what does that even mean? Stationary relative to what?

If you mean "you go wherever inertia would take you in that amount of time, with no acceleration", then if you go backwards a multiple of a year you end up pretty close to Earth (quick approximation: the Sun's acceleration in its orbit in the milky way is ~2*10^-10m/s/s, which works out to ~100km in a year, ~400km in two years, etc.). In actuality you could probably get somewhat better range by letting your velocity build up to intercept Earth-that-was at the target time. (You'd need to take into account a bunch of things for best accuracy: the Earth's orbit is not "perfect", the moon's phase, the acceleration of the Sun, etc, but we know most of that.)

You probably would end up needing to make multiple jumps, pausing in-between to let Earth's (or another planet's, or even the Sun's) gravity well readjust your velocity to what is needed for your next jump.

This means that you'd need to build in re-entry capability into the machine (as you are unlikely to have the precision necessary to be able to jump into atmosphere at a sane velocity), and potentially maneuvering delta-v. Note that with a time machine you lose conservation of momentum, which makes things a lot easier. You can change the direction of your velocity vector by jumping back in time and interacting with your past self. You can potentially use this to get "free" (read: reactionless) velocity out of any gravity well.

[+] jdjb|11 years ago|reply
If you can travel backwards in time (or even just stop time) you can be at any spatial location you desire in the entire universe (since you have essentially infinite speed).
[+] stan_rogers|11 years ago|reply
That is a major plot point in Spider Robinson's Callahan's Con. (Look, his first few Callahan stories were charmingly quirky, and I got into the habit of reading them. This is not an endorsement of his larger oeuvre, okay?) In that case, the cosmic microwave background was used as the inertial reference, probabilities were the main problem to solve (we'd be well beyond the relative simplicity of the three-body problem), and little details like delta-v were not merely hand-waved away.
[+] kevincennis|11 years ago|reply
It's been almost 10 years, so I may be mistaken... but I think the director of Primer mentioned this in the DVD commentary.

EDIT: Right, not really part of the plot. I just think I remember him (in the commentary) talking about some of the "trickier" aspects of writing a story about time travel, and I think he mentioned the fact that nobody ever really addresses the positional aspect.

[+] growse|11 years ago|reply
Moreover, imagine I write down some information, then wait for exactly 6 months for the earth to take me far away from that point in space. If I now travel 6 months minus 1 nanosecond back in time with that piece of paper, but preserve my spacial position, haven't I just 'transmitted' information through space faster than light can?
[+] bengali3|11 years ago|reply
whats your reference for coordinates?

Earth Center? Solar Center? Galaxy Center? ... Universe Center?

hmm traveling backwards along the 4th dimension by itself sounds like we are NOT traveling in the other 3.... so where would the atoms (that originated from your banana at 9:25am 3 days ago) go if we merely changed their value on the 4th axis? does their xyz stay locked at the current values or revert back to their previous values.

[+] bithive123|11 years ago|reply
The time travel show "Seven Days" from the 90s dealt with this -- sometimes the time machine would end up stuck underground or floating out in space.
[+] wuliwong|11 years ago|reply
You are not alone! I've thought a lot about how much we move in space while we "sit still" on earth. :)
[+] camelNotation|11 years ago|reply
My pet theory:

Quantum mechanics is a statistically based science because we have yet to discover the constants that would unify it with general relativity, making this entire thought experiment irrelevant.

Imagine if you are watching 10 parallel strings ripple up and down at various frequencies. Viewed from the side, it would at first glance appear chaotic, but by observing the behavior long enough and recording where the activity occurred over time, you could statistically predict where the strings would be at any given time.

However, if you were aware of the number of strings you were viewing and the frequencies at which they were moving, you could formulate a precise theory of exactly what you were viewing and what you would view at every point in the future.

That is the current state of physics. Quantum mechanics is seeing without understanding the rules governing the system, so predictions and observations are made using statistics instead of constants. Once we discover the constants, the current theories will be entirely obsolete and articles like this will become relics.

[+] ep103|11 years ago|reply
yeah. I remember some ~7 years ago reading about a research team that stated that they had rewritten many of the fundamental equations of (some branch of) quantum physics to show that they could be written in a completely deterministic manner. They said that while such equations weren't likely to be useful (due to the limitations of our testing technology), it was an important result, particularly when it comes to understanding the underlying science. And they were very upset that basically no one paid their result any real attention.
[+] smokel|11 years ago|reply
Apparently, Stephen Hawking organized a time travel experiment in 2009. There was also the Time Traveler Convention in 2005 [1]. If people keep organizing such events, future time travellers may be at a loss as to which one to attend.

[1] http://web.mit.edu/adorai/timetraveler/

[+] aaronbrethorst|11 years ago|reply
My favorite "layman's" argument for why time travel, as it's been classically described in science fiction, can't exist is that we haven't been overrun with tourists from the future.
[+] DCKing|11 years ago|reply
Well, the argument is that quantum indeterminism implies quantum time travel is possible, because the grandfather paradox is solved/migitated by indeterminism in which the grandfather paradox is still a valid outcome. However, quantum indeterminism itself is not yet completely undisputed; some theoretical physicists such as Gerard 't Hooft maintain that quantum mechanics can be both deterministic and consistent with current experiments.

This also raises the following question - if quantum mechanics is undeterministic, then the macroscopic world is at least probabilistic. If probabilistic systems allow the possibility time travel on the quantum scale, would the grandfather paradox also not be solved on classical scales? Since it is possible that me killing my grandfather in the past would fail with some very small probability (due to various quantum effects adding up), would the grandfather paradox then not also be solved in this case? I'm not sure if I'm interpreting the article correctly.

[+] axilmar|11 years ago|reply
If time travel exists, then it cannot be a simple rewind of the universe's tape. Because if that was the case, then rewinding the tape to a time that your father was not born would mean that you will also not be born, and thus there wouldn't be any time travel, since neither you nor anyone else would be able to witness it.

Thus, in order for time travel to work, it means to rewind the tape and add yourself to the tape at a moment you did not exist before. Thus, if you killed your father, your replica wouldn't be born, but you wouldn't stop to exist.

Therefore, the whole 'grandfather paradox' is not a paradox at all: if time travel exists, then you would simply exist in a universe where a replica of you will exist or not, depending on how events play out.

[+] afro88|11 years ago|reply
Not so fast - who says you become a "replica" in the first place? Assuming time travel replicates things, then yes, what you said holds true.

But as I understand it you don't replicate, your time just loops back on itself. So looping back to a time before you were born and killing your father would create a paradox.

[+] TeMPOraL|11 years ago|reply
I'm starting to adopt the idea of Scott Aaronson that since we have a lot of evidence suggesting that P != NP, we should treat physic ideas as less probable of being true if they make P=NP as a side effect.
[+] vbit|11 years ago|reply
Say I go back in time. Does it mean I disappear from the time I was in? And I'm in two places at a point in the past (the me from that time and the me from the future)? Now if I want to go back to the time I came from, do I join back at the exact time I left (which means no one would notice my travel), or would I have to travel back to the time I left + the elapsed time I spent in the past? And if I really did return to the exact time I left, does that really mean no one noticed my leave? Because I'm sure when I left time continued and somebody noticed.
[+] afafsd|11 years ago|reply
In the form of time travel being talked about, the answers are:

a) Yes, you disappear from the time you were in.

b) Yes, you're in two places at once for the duration between your arrival and your departure

c) Forwards travel in time doesn't cause too many philosophical problems (since we're already doing it) which is why nobody talks about it. But there's no requirement to wind up exactly where you started.

[+] stinos|11 years ago|reply
Can someone enlighten me: what is this simulator they speak of? It doesn't seem answered anywhere in the article what it is, whether it's software, let alone how it works. Yet the whole article relies on it. Does it act on real protons? Or are they simulated as well?

And, most important, why do they trust a simulation device built by humans who hardly understand the matter completely, when the device is then used to make assumptions about that same matter? Is it somehow proven this simulator is correct? And how did that happen?

[+] jessriedel|11 years ago|reply
This is a poor article. It is reporting on a simple table top device created by researchers eager to misrepresent their work. It tells us essentially nothing about quantum mechanics or CTCs.

We don't know how quantum mechanics behaves in the presence of CTCs. There are multiple, mutually incompatible proposals for extending QM in this regime that all make identical predictions in normal, causal spacetimes (i.e. the only sorts of spacetimes we have access to). Deutch has one extension of QM, and it suffers from serious internal consistency problems, but there are others.

Since this experiment takes place without CTCs, it can't tell us anything we didn't already know. It's literally just a toy device that is sorta described by the same math as a certain system with CTCs in QM_Deutch would be, if you squint your eyes hard enough. But you could say the same thing about a computer simulating QM_Deutch in software. It tells you nothing about whether the universe actually obeys QM_Deutch in the presence of CTCs ... if they exist at all.

Similarly deceptive bits of "research" in the news often appear that claim to find quantum gravity effects on table-top experiments.

http://www.space.com/5052-black-hole-effect-created-lab.html

In all these cases, the scientists will eagerly over-represent their work to the journalist, and the journalist will eagerly gobble it up and write eye-catching headlines about new breakthroughs in physics, but the heart of the claim will be buried in the article and subtly couched in weasel words. And if you actually try to drive down at it by asking probing questions, the journal and scientist will retreat to much, much less exciting claims and you will never be able to prove they intended otherwise.

[+] phpnode|11 years ago|reply
All hypothetical time machines must also be space machines, i.e. they must take into account the movement of the planets, the galaxy, the universe to avoid materializing their passengers in the middle of space or the centre of the sun. My question is what frame of reference would they use?
[+] claar|11 years ago|reply
This is exactly what always bothers me in time travel movies.

You never hear about the poor time traveler who got the calculation slightly wrong and ended up deep in space or inside of a mountain.

[+] TheLoneWolfling|11 years ago|reply
You can use a time machine as a very good space drive.

"All" you do is jump back / forwards in time repeatedly so that gravity pulls you in the direction you want to go. (In actuality: good luck plotting a flight path)

Want to get to 20% of the speed of light? Sit in freefall near Jupiter for 5 weeks (assuming 20m/s/s acceleration), jumping forward / backward in time as appropriate to stay in roughly the same spot relative to Jupiter.

[+] axilmar|11 years ago|reply
I do not think that there can be a Grandfather Paradox. If one goes back in time, he/she will simply be removed from the state of the universe as it is now and be added to the state of the universe at the target past date. He/she could then go on killing their father before they were born, but nothing will happen to them except not meeting with themselves as babies.
[+] chippy|11 years ago|reply
I've enjoyed thinking about the following:

It must be almost impossible to time travel back in time. But it could be possible, given unlimited time. Thus, given that at some point in the unlimited future, time travel would occur, how can we increase the chances now of being visited by these future time travellers?

[+] onion2k|11 years ago|reply
It's quite possible that the problem with paradoxes stems not from them being 'impossible', but from our limited cognitive tools failing to equip us to think about them.

Sort of like people in ancient times believing you can't predict the motion of the planets because they didn't have calculus yet.

[+] stevewilhelm|11 years ago|reply
I would like to see a unified explanation that describes how our current modes of time travel work.

How does the matter that comprises my car and myself successfully get from Palo Alto to The Mission every morning?

[+] u124556|11 years ago|reply
If you had a program that generated a random number, and somehow send a hash of said number to the past to be used as a salt to generate itself. Would the new random number be truly random?