Sunday, September 2, 2012

Thought Experiment on Entropic Restrictions in Time Travel

In a discussion of time travel, questions will come up about freewill and causation.  I have always found this conversation frustrating because the common view is just so plainly wrong.

The common view is the one espoused in Back to the Future, which arguably is where most Americans get their understanding of time travel. (I guess as opposed to empirical time travel science?)  Everyone knows this so I don't even have to summarize it, but here goes:  You go back in time but you have to watch out that you don't accidentally change anything, because if you change something because then you will change the future.  In particular, you need to make sure that your introduction to your parents when they were in high school doesn't keep them from falling in love, or else you would undo your own existence, the fact of which alone should point out that there is something screwy here.

In this idea, because you can change the future you came from, there are different "timelines".  When you go back in to the past you go to a different timeline or split the universe or whatever and the effects of your meddling will be in the new timeline and not the one you came from.

So why do we think there are multiple timelines?

Let me propose a much simpler resolution: there is one timeline, you cannot change the past, and any interaction you have with the past had already been recorded in the time before you left.

The problem with getting this is that we do not see the intervening period between Marty hooking up his own parents and entering the Delorean.  In the movie as it is scripted, things are wrong, but in a more correct film, it would look something like this:

Marty shows up out of a time machine in the 1950s.  He meets his parents as teenagers and introduces them.  They fall in love (and remark on what a great name "Marty" would be) and get married and have Marty.  While they're falling in love, Marty gets back in the time machine and returns to the 1980s.  We have some thirty years of film of his parents buying their first house, shopping for groceries, going to neighborhood parties, until finally they conceive a child.  Thinking back to the kid they met in high school who played guitar to the song when thy fell in love, they name their new son Marty.  Marty grows up, learns to play guitar, and eventually meets a crazy weatherman who has invented a time machine.  He gets in the time machine.  Marty shows up in the 1950s.  He meets his parents as teenagers and introduces them.  They fall in love (and remark on what a great name "Marty" would be) and and get married and have Marty.  While they're falling in love, Marty gets back in the time machine and returns to the 1980s.

The point is it is consistent.  The beginning half of the movie (showing Marty interacting with his parents before we see him travel back in time) and the ending half (after the audience sees Marty travel back in time and interacting with his parents) are the exact same footage.  You wouldn't even need to shoot it twice.  Nothing different happens.

This will obviously introduce huge limitations on what kind of time travel is possible.  If time travel is possible at all (and probably isn't) then it must present a self-consistent chain of causation.

Part of the problem with seeing this is most people think of causation in terms of human interaction and not in terms of energy, momentum and entropy.  As long as the "major stuff" still works out, it's okay if small things change, where the major stuff tends to be personal interactions.  It's okay that Marty pushed billions of atoms outside of the place they were "supposed" to be, as long as the people who are "supposed" to fall in love did and your motivation for time-traveling isn't distorted.

So instead of thinking of just character motivation and development having to be consistent between past and changed past, think in terms of the energy and momentum of every particle in the universe having to be consistent between original past and changed past.

That doesn't leave a lot of room for difference.  Actually, maybe no room at all.

I think the principle problem, and the one that doesn't get explored enough, is the connection between entropy and causation within the scope of time travel.  I would argue, in order to keep space-time self-consistent, time travel is only possible to regions where the total entropy of the universe was exactly the same as it was when you left - which is a huge restriction on time travel as it means you can't travel in time.

To illustrate this point, suppose that in my mad science laboratory, I have an insulated bowl of water which I call (1), a Stirling engine, and a TARDIS.  When the experiment begins, another insulated bowl of water (2) is spit out of the TARDIS.  The two bowls are then use as heat reservoirs for the Stirling engine (see video), which will use any heat difference between them to do useful work (which might be used to power a lightbulb).  After this is done, the two bowls are in thermal equilibrium.  The bowl we had at the beginning of the experiment (1) is now put in the TARDIS and sent back in time to the beginning of the experiment (thus there are two time-copies of the same bowl in this experiment, possibly at different temperatures).
single reservoir as heat sink and source with time-travel

This experiment is essentially using the waste heat from an entropic process (the heating up of (1) during the Stirling cycle) to then act as the heat source (2) for that same process.  At some point, (1) must be heated to the initial temperature of (2), which will involve a non-entropic heat transfer.

Just an example, suppose (1) is at 70 degrees and (2) is at 150 degrees (and I'm an American so I'm using real degrees, not your wimpy Celsius froo-froo).  The Stirling engine will run until both are at (150+70)/2 = 110 degrees, producing some amount of work W.  At that point, in order to get (1) up to the same temperature as (2), an additional 40 degrees must be transferred from (2) to (1) raising its temperature above equilibrium, which can only be done if the Stirling engine is run in reverse.  To run it in reverse will take the same amount of work W that was generated, so that work from the engine caused by sending a warm bowl back in time wasn't able to exert energy on anything - it had no effect on the past.

If you want to say that the temperature of (2) at the beginning doesn't have to equal the temperature of (1) at the end of the experiment, then that creates problems about where the work is coming from.  Or where the bowl at temperature (2) is coming from.  If you want to say this situation creates an alternate timeline, then there's infinitely many of them stretching in both directions - timelines "further up" from you will have a Stirling engine that generates more and more work from this experiment, and timelines "further down" from you will eventually have no work generated.  So, in the above example, you start with (2) at 80 degrees higher than (1) at 150 degrees, and both end ad 110 degrees.  If you send this 110 bowl back, then (2) is only 40 degrees higher than (1) and both will end at 90 degrees.  When you send the 90 degree bowl back, then (2) is only 10 degrees higher than (1), etc.  But, also, you got your 150 degree bowl from an alternate experimenter who ran this with an initial heat difference of 160 degrees!  That is, his (2) started at 230 degrees.  He got his (2) from another guy, whose (2) started at 390 degrees, and above him it was 710 degrees and above him 1350 degrees.  Ad nauseam.  Eventually there is some lucky son of a gun who has an infinite heat difference and can power his entire civilization in to extragalactic expansion for all eternity.  Which is absurd.

Because heat transfer is the most fundamental thermodynamic thing (it is, for instance, how you manage to move about), this same reasoning can effectively be applied to any possible interaction of the future with the past.

I think simply put, time travel is completely ruled out by entropic considerations.  If not ruled out, then the effect that the future can have on the past is severely limited.

If there are any errors in my thinking here, then please do not hesitate to point them out to me.


S said...

The main thing that jumps out at me is this: Once Marty is grown, why don't his parents recognize him as the person who introduced them in high school? After all, they did name him after him so you think that would jog their memory. I wish I better understood your description regarding entropy and causation in time travel to proffer a decent discussion, but alas I fall short. However, I now know what a Stirling engine is, so I've learned something new today. Thanks :)

Accountants London Lady said...

I'd always been a little sceptical of the idea of time travel I must say, but this articulate explanation only confirms my suspicions that, as you point out, the future cannot change the past!

Unknown said...

An eyebrow raising take on time travel! However I think you might be purposefully digging yourself a circular trench you can't get out of here. If you sent the bowl back and the past you doesn't bother to send it back again, does that not change the past? Then there's extra energy sent back in time and floating about in the past world and you have added energy to a limited system. If I say there's less energy in the future now, how did that continuity work if there's more energy in the past? I'm not sure we've covered all possibilities. Right now, you are subscribed to a single timeline that is seemingly ruled by causality and fate. What if we send back a Tardis filled with boiling air and a live poodle. You cool and open the tardis. The poodle is dead and you bury it. How can you send it back again? What happened to the energy sent to the past? In my mind, either time travel is not possible, period or something you previously discounted could work, alternate timelines. Imagine you send a poodle back, dead. In timeline t1 you had total universal energy "tue" x. In t2, t2=t1 only that now you've sent something extra into t2 from t1 and you now would have tue y where y>x. And t3 you have z, then t4 phi, then t5 omega, then t6 zeta. I don't think I see a contradiction (yet) if you're sending energy across spacetime or interdimensionally BUT the tue of the new world has more than the old. In all timelines however, that poodle is dead, apart from the first. And hence the cycle is broken in t2. You've just gone ahead and created an alternate timeline with more energy inside of it. That doesn't really make sense. So what if when you travel through time there is an exchange of entropy and energy in place of tardis, air and dead poodle. You would now have a different entropy(as induced by the change forced by hot air and Tardis) in t1(at least in pure physical order of microstates) but conserved energy in both timelines but different, noncyclic outcomes! Your future has influenced the past. And when we send the tardis back another exchange of entropy and energy occurs. Our past has now influenced change in the future too. However when we send the tardis back to the future(kek) are we sending it back to t1 or is it a new timeline t3? That's what's now boggling my mind.

Here's what I suggest. Our existence is actually an infinite series of timelines of existence in which all orders, entropy, orientations of matter, states differ, but tue stays the same throughout. When we travel through time, our reality shifts from tx to whatever tz is the exact combination of variables of the timeline we are travelling to. And when we travel back, it's not t1 anymore, but it is the same "reality" if that makes any sense. BUT the way we observe reality is continuous. So maybe when we create a new timeline the old one ceases to exist(thinking from your Berensteinstain Bears article) and our new existence is picked from the infinite series of timelines. And yes my theory is still based on causality and fate if not a little freer. But alas I'm not too well versed and I'm certain there are discrepancies and contradictions in my theory. On top of that it's 7am and I haven't slept yet so maybe I might sound like a complete fool. I'm thoroughly interested to hear your reply.

Unknown said...

I have a perdurantist outlook on existence if that adds anything.

Reece said...

I didn't really think about the issue of one experimenter going rogue. From one experimenter's point of view, the experiment will go like this:

Suppose that in my mad science laboratory, I have an insulated bowl of water which I call (1), a Stirling engine, and a TARDIS. When the experiment begins, a live puma jumps out of the TARDIS and mauls me to death. Nothing further happens.

It just raises a lot of questions. I suppose another experimenter's point of view would look like:

suppose that in my mad science laboratory, I have an insulated bowl of water which I call (1), a Stirling engine, and a TARDIS. When the experiment begins, another insulated bowl of water (2) is spit out of the TARDIS. The two bowls are then use as heat reservoirs for the Stirling engine (see video), which will use any heat difference between them to do useful work (which might be used to power a lightbulb). After this is done, the two bowls are in thermal equilibrium. The bowl we had at the beginning of the experiment (1) is now discarded, and a live puma is placed in the TARDIS and sent back in time to the beginning of the experiment.

Since there are presumably an infinite number of experimenters, what is it about the poor soul who gets mauled by the puma that sends the puma to him? What determines which timeline gets to move to which timeline?

Unknown said...

Well according to my suggestion he would move to a timeline in which he dies in that exact way in that exact moment. It falls into the infinite series of equally real timelines.

But if I were to look at your experiment, how can I fault it such that your theory might be invalidated?

Well, even if no net change occurred in the past from work, what's to say particles weren't moved, entropy didn't change(in terms of microstates of particles), etc. I feel there are too many factors to discount that. Furthermore, you're implying your experiment HAS to come from the mad scientist(s) who equilibrated bowls from higher heat temperatures. There must come a point where it is physically impossible for the mad scientist to equilibrate the bowls, what from lab equipment limitations or something, but for experimentation sake, he starts the experiment with the hottest bowl. Or, a mad scientist starts with a low temperature bowl i.e. 230K and heats it to 1300K then sends it back starting what appears to be an infinite regression process even though it had a beginning. Your theory for the sake of argument throws away what is allowed in physics to give a radical argument of infinite energy, which is impossible of course. Also, how would you explain all these scientists be ready to accept a bowl from the past. How did these scientists convene together to make this experiment possible? Well, one theory is they didn't and they can't because time travel is impossible, or that the scientist has faith in other timelines of him doing the exact same thing because he is sure they must exist.

Apparently my post was too long. I'll post a follow-up reply.

Unknown said...


However bizarre and unlikely it is, I think I do buy into time travel. The only thing is that it's not traversing time on a single line that is called your life. Rather, it is merely entering a new timeline which is part of an infinite series of timelines that all exist simultaneously and all are equally real. Now what is entering said timeline raises all sorts of questions. Maybe a soul perhaps? Maybe every timeline observes but some are linked to each other and converge and diverge at other times. But we can only know if we can ever travel back in time in reality.

I feel like if we travel back in time and changed something, it may have no effect on the timeline we left because that timeline is its own and may not converge with the timeline we changed. Rather we would be part of a new timeline, that would seem exactly the way it was before but one or two things have changed, but make no mistake, it's not the same timeline. You have traversed time but you are no longer part of the timeline you just left. So in terms of the tardis, when sending things back in time, we are sending it back to a time that was predetermined to have a tardis send things back to it. And if that timeline sends something else back to YOUR timeline, it may not be your timeline, your timeline either will get nothing back, or will get something from a DIFFERENT timeline UNLESS that timeline converges(by that meaning exactly replicates) with the one that sent a bowl back to you. So when you ask What is it that makes this poor chap special so as to be dead by puma, it's that nothing makes him special. He existed as real-ly as you did. Only he received a puma in one of his many timelines. And what determines his movement from timeline to timeline? Convergence of timelines!

So the questions at this point you would have to ask are "What is time?", "What actually are we perceiving when we perceive time?". I have a radical thought : If I do partake in the "time is a dimension"(as per my 4D perdurantist view), then what's there to say that time and space are not single; individual in all realities conceivable? What if Past, Present and Future all exist together, have happened and have not happened yet. Some timelines diverge, converge and work together simultaneously, yet parallel, imagining each timeline as a 3D worm working in a straight line parallel to each other and there are connections between. Sometimes the come together, others the diverge and more than 2 can come together and more than 2 can diverge. And it does not need to be a 1:1 ratio for convergence and divergence, There for example could be 5 quintillion ways for timelines to converge exactly but only 3 trillion ways in which they can then diverge. Or, there could be 4 quadrillion ways they can converge and 7 septillion ways they diverge. Mind you, convergence and divergence occur on the slightest slightest difference. So much so as have the wrong quantum number assignment to a particle and they diverge.

That would mean that all connections between timelines are coincidences between each other and happen to converge, yet everything has already happened and so both timelines were destined to meet in the first place.

Unknown said...
This comment has been removed by the author.
Unknown said...

I believe I was a little unclear in my first rebuttal.

What I meant to say was: A hot bowl comes from the future, you place it in the Stirling engine. Temperature evens out. Hence energy is dissipated into the surroundings. Entropy increases. You send the new bowl back to the past to repeat the experiment at a lower temperature. However, entropy surely would not be conserved, even if dissipated entropy and energy from the future was transported back in replacement to keep energy conserved because the spatial dimensions of each particle would be completely different, at LEAST in the pure physical sense of 3D spatial and momentum microstates. So, time travel by this logically doesn't work....right?

That does not exclude alternate timelines altogether though.Time travel by entering different timelines does not have a logical contradiction(as far as I can see, though I am open to examples) and a 4D look at things does alleviate this matter from the problems at hand. It's not necessary that past you make the same decision, unless he is forever ruled by fate to carry out the same decision, which doesn't make sense if we attribute to the universe the quality of being able to be changed in different times(i.e. future self influences past self with hot bowl).

On a side note, I do like the experiment very much. It branches away just slightly, yet still tackles the problem of you making something for the future only for future you to come back and kill you. You give the time travel paradox a very original take.

dazzleworth said...

The whole idea of the grandfather's paradox is absurd. For one, time does not exist. In order for one to time travel, one must simply decrease entropy in the universe. There is no such thing as going back in time, like stepping on board a subway or aircraft and then going back to the point in the past. It simply doesn't happen. If you are able to travel to a point you weren't born, returning to that point means you simply won't exist. If you go back to a point you were one year old, you will end up a baby. You wouldn't be able to carry out his execution. You simply cant go back at your age as your are, and with your devices and commit murder. The process of time

What you could do best is however, before you press that button on the time machine is to specify a message or create the lower entropic conditions that would persuade your grandfather/mother not to get married or to go somewhere, or to do something/not do something that would prevent your birth. Remember that deceasing your entropy increases entropy somewhere else? But then again, its only signals you could send and you cannot guarantee that they would see and act on that information provided. However, there is a good chance that your message will cause your grandfather to have a change of heart. I mean, if you planned to to perform something, and had an uneasy feeling of some sort, you might just cancel or postpone your plans.

Its for this reason why precognition of the sixth sense may exist. You may have heard of stories where some people who have canceled or postponed their travel plans because of some intervention, before boarding their ill fated flight. So you see, this is real and may be indicative of the use of time travel, albeit a selected few (or perhaps used in conjunction of inter dimensional travel to parallel universes)

Unknown said...

this lowkey makes me think. for example, if alternate timelines do exist in conjunction with each other, do people ever really die? with an infinite amount of timelines, its reasonable to believe that the mad scientist indeed did die from the puma attack while surviving it in other timelines.