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I wonder if a time machine can be the cause of a bootstrap paradox?

Background: Let's say one day I found in my room a portable time machine. I use this machine to travel to the future, where I realize I am the person who placed the machine in my room. I then travel to the past to drop off the time machine and let my past self use it.

The time machine always travels with me. There is only one time machine.

Condition: Now let's say this time machine has critical components built of iron and, after many, many iterations, it rusts and falls out of order. At some point I won't be able to travel to the future ... but the time machine should be here, shouldn't it ?

Question: Is something wrong with my scenario, or could this happen? (If so, how is it possible (theoretically)?)

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    $\begingroup$ "After many many loops it rusts and then become out of order": how many streams of time are there in your world? "Let my past me use it": and thus multiple future yous accumulate in the past. $\endgroup$ – AlexP Jun 30 at 20:07
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    $\begingroup$ The problem with a loop like this, is that it has no beginning, and it has no end. The time machine will behave as though it is infinitely old at all moments within the loop, and will experience maximum entropy. $\endgroup$ – Arkenstein XII Jun 30 at 20:11
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    $\begingroup$ Bootstrap paradoxes usually assume a completely fixed timeline, are you imagining a universe where it is in principle possible to "change" the past, or are you just asking how this type of paradox could possibly work in a fixed timeline given the natural tendency of metal to rust? If the latter, in normal physics there is always a finite probability that entropy-decreasing thermodynamic fluctuations happen, maybe one would have to happen in your scenario. Or since the technology of a machine that was never built is kind of arbitrary, you could assume self-repair abilities like living beings. $\endgroup$ – Hypnosifl Jun 30 at 20:23
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    $\begingroup$ @ArkensteinXII, or it should be made of unobtainium and completely unchangeable and eternal. $\endgroup$ – user28434 Jul 1 at 11:15
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    $\begingroup$ @user28434 It could, but the OP has specifically stated that it is made of iron. $\endgroup$ – Arkenstein XII Jul 1 at 19:59
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The paradox only occurs if you assume a single timeline. In which case it is pretty much identical to the 'grandfather paradox'. In the left fig. below, if there is a single timeline then there is a single 'time-path' for you (red line) - that doesn't in itself produce a paradox, but the time-machine also only has a single path (blue line) which by definition must be closed. So the time machine would age further in each loop and result in your paradox - unless time travel itself somehow reverses entropy in the machine in which case you could arm-wave yourself out of the paradox.

If you accept a multiverse-like multiple history situation, things are a little more complicated but there is no paradox. On the right below, some initial you (red line) gets access to a time machine, travels forwards and then backwards. On arrival at the end of the backwards step the timeline splits. The original timeline continues (in which you disappeared, reappeared in the future and then disappeared again forever). An alternate you (orange line) now repeats your journey in a first alternative universe,. This can be repeated numerous times until eventually (with the yellow-line you) the time-machine breaks and yellow you, the time machine, and your green-you alternative spend their lives all together in a final alternative. Note that the blue line is open , not closed, so the machine can obey the normal laws of entropy.

There is still a potential paradox in answering where the time machine came from in the first place. But a non-paradoxical solution would be that in some 'first' time-line, someone invents the time machine, then someone travels with it back in time and in a 'first' alternative timeline, stops that person from inventing it, so no 'other' time machine appears in any of the observed timelines.
enter image description here

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    $\begingroup$ You can get away with closed loop bootstrap paradoxes if you’re very careful about exactly what it is you’re bootstrapping. Digital messages from the future carried into the future and sent to the past with no genesis but themselves are valid if there’s no possibility of the message being edited, for example. $\endgroup$ – Joe Bloggs Jul 1 at 17:23
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There is a thought experiment out there that says that time travel is impossible; not because of the physics, but because of what we do with it.

Basically it goes like this. If time travel is possible, we'll use it to change the past. Eventually, we'll change the past to one in which it is impossible to create or use time travel. Hence, time travel is impossible.

Your antiquating time machine paradox is really just a less complex version of this. The loop is infinite. The durability of your time machine is not. The Laws of Entropy state that this loop has to eventually fail because eventually the machine fails. While the Ship of Theseus model can help, the problem is that every time you consume a resource in the past to fix the machine, you're also making a minor change to the past that could (eventually) accumulate to a future which precludes the use of the time machine. Even if you only use parts in the future, or the latest point in your loop, eventually the supply of those parts has to run out also. All things considered, this is not an infinitely tenable scenario.

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    $\begingroup$ What you call a thought experiment in your paragraphs one & two is an argument formulated by the SF writer Larry Niven. It also is known as Niven's Law. The argument is a reductio ad absurdum, and like most reductio ad absurdum is probably false. It is wholly dependent on the models' nature of time and type of time travel that occurs within it. It demands time can be rewritten. My own suspicion is this model of time travel will only restrict the use of time travel not make it impossible. Time machines are ingenious exercises in logic. $\endgroup$ – a4android Jul 1 at 5:11
  • $\begingroup$ My favorite example of "what we do with it" is Killing Young Hitler¹. If a time machine exists, someone will want to use it to kill Hitler before he rose to power, perhaps by shooting him during WWI (with period-correct bullets) when his death would be assumed to have been caused by enemy fire. But if Hitler never rose to power, no one would want to go back to kill him, which means he'd be alive to rise to power, which means someone would want to kill him... ¹Young Hitler is older than Baby Hitler, and if a WWI combatant, there wouldn't be the moral issue attached to killing the latter. $\endgroup$ – Monty Harder Jul 1 at 15:19
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The Bootstrap Paradox is a theoretical paradox of time travel that occurs when an object or piece of information sent back in time becomes trapped within an infinite cause-effect loop in which the item no longer has a discernible point of origin, and is said to be “uncaused” or “self-created”. It is also known as an Ontological Paradox, in reference to ontology, a branch of metaphysics dealing with the study of being and existence. (Source)

Can the time machine be a necessary component of the bootstrap paradox? sure! A really good example is, IMO, the machine in the movie Primer (2004). Does your scenario describe a viable bootstrap paradox? Maybe.

All bootstrap paradoxes focusing on an object have one basic problem: the object never seems to get old. This is because the explanation of the paradox is, IMO, inadequate. Note that the quote above states, "...trapped within an infinite cause-effect loop..." This is NOT a requirement for a bootstrap paradox. In fact, it's almost never the case than an infinite loop exists (at least I've never heard of one where it had to exist, or could even be assumed to exist).

Why? Let's look at your scenario. you-before-first-use finds the machine and uses it, causing you to become future-you. Future-you travels back in time to place the machine. And there's the problem. Future-you watches you-before-first-use use the machine ... and then lives out the rest of his/her life in comfort and profit (having sold the rights to your autobiography). The loop only occurs once. The only way it could occur an infinite number of times is for future-you to always be the one who uses the machine the first time.

Curiously, neither example used in the source I quote above represents an infinite loop, even though the article believes they do. In Heinlein’s short story “All You Zombies” (1959), the protagonist travels back in time to impregnate his/her former self, becoming his/her own parent. OK, the person who traveled back in time didn't disappear. The linearity of time for the traveler is unique with a single loop. It can only be thought of as happening over-and-over if you ignore the future of that aspect of the protagonist (who most likely lived a long and happy life...)

The example of Somewhere in Time (1980) involves a pocket watch. But, once again, the loop only can occur once unless you assume that when Christopher Reeves traveled back in time he somehow merged with his future self.

It's easier to answer the question by asserting a single loop — but then you wouldn't have a question.

Since the loop can only occur once in your scenario, there's no issue with the iron components becoming rusted and failing.

What would it take to get infinite loops in my scenario?

Star Trek the Next Generation investigated two possible ways.

One is like in Star Trek the Next Generation's Cause and Effect. The ship itself is thrown back in time to a starting point. When tracking the linear history of the ship, there is only one ship repeating the same loop in time over and over and over. The show creatively lets the crew in on the secret by providing means of "communicating" outside the loop. There are never, for example, two Picards. There's only ever one. In this case, nothing can age, and so your iron components would never fail. Said another way, time simply "resets" to the beginning of the loop.

The second is STNG's episode Time Squared. In this, a future Picard is thrown back into the past. But this episode cheats the question by never portraying an infinite loop. This is a good example because it shows what to do with the duplicates (Picard and the shuttle craft): they're destroyed in the explosion. So, although the episode does not show an infinite loop, one could be created if Picard took the same actions over and over.

But in your case, you-before-first-use always uses the machine. There's no way to create an infinite loop because you need future-you to always make the choice.

Conclusion

Which returns us to the above stated conclusion: your machine will never take more than one iteration and therefore the component will never wear out. If you figure out how to make iterations, it will either always result in a new machine or in the machine never aging.

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  • $\begingroup$ The question was about the machine itself, not the person riding it, no? Likewise when people talk about a closed time loop in Somewhere in Time they are talking about the watch, not Christopher Reeve's character. $\endgroup$ – Hypnosifl Jul 1 at 1:10
  • $\begingroup$ @Hypnosifl in this case, the object is the subject of the paradox, but everyone and everything is involved - unless you consider this a question about magic. If the people don't/can't age, neither can the machine. The paradox is described as the inability to determine the origin of the object, but that's not what the OP's asking about. He's asking about whether or not degradation can break the paradox. Considering he asked, "can this happen?" an answer like mine that advocates it cannot is suitable regardless of reason. $\endgroup$ – JBH Jul 1 at 1:13
  • $\begingroup$ Why should the machine's lack of age imply the people can't? See the diagram titled "single future closed loop" in Penguino's answer, there can be continued progressive aging along the red line, but any aging along the blue line has to reverse itself at some point before it meets itself and closes the loop. Every point on the blue line lies in both the past and future of every other point, but that's not true of the red line, where you can define a notion of proper time along it that continually goes forward from birth to death. $\endgroup$ – Hypnosifl Jul 1 at 1:30
  • $\begingroup$ @Hypnosifl, I explained my reasoning in my answer. You needn't like it or agree with it. Indeed, you could help the OP considerably by posting your own answer. $\endgroup$ – JBH Jul 1 at 2:18
  • $\begingroup$ I don't see any part of your answer that explains the reasoning behind your comment "If the people don't/can''t age, neither can the machine", that's all I was asking about in my last comment--unless I misunderstood and you didn't mean to imply that since the people age normally throughout the loop, that shows there is no longer a paradox about whether the machine ages in the loop (but if you didn't mean to imply that I don't see how your comments about the people would actually address the paradox about the machine). $\endgroup$ – Hypnosifl Jul 1 at 3:24
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"I use this machine to travel to the future, where I realize I am the person who placed the machine in my room. I then travel to the past to drop off the time machine and let my past self use it."

I am going to assume you mean that FutureYou created the time machine, then went back in time to give it to CurrentYou (PastYou from FutureYou's perspective). That is because the other reading, where you go to the future and then to the past to drop off the machine, doesn't make much sense. The good news is that we can still form a stable time loop given what you have said in the premise.

  • To start with, you wake up with a time machine in your room
  • Next, you travel to the future and learn that you created the time machine. This knowledge is the key to the stable loop
  • You go on merry adventures throughout time, until eventually a critical part of your time machine rusts through and the machine stops working

At this point your question is how can you have a time machine if you aren't able to go to the future with it? But we already know that you invented the machine in the future, and it is obviously true because how else would it have appeared in your bedroom? So the only logical solution is that....

You invent a time machine.

It might take years, or even decades. You might have to wait for new technology to be developed or existing ones to be refined. You will probably need to completely redesign and rebuild the entire machine from scratch (otherwise it would have been old and beat up when you first found it in your room).

But, you know that it is possible because you have already done it. After spending however many years on your time adventures you should be familiar enough with the machine to at least have a rough idea of the design of it, and what kind of technology it uses. Even if it is as high a level as "Important Part A was built by Technodyne Industries" and then waiting until that company is founded to see what they build. You can work out the details as you go.

The only thing this really requires is for the machine to break down sometime before you create it in the future, and within your life span. If you break down in the 1500s you are going to have a bad time, but if you break down 45 years before you create the time machine you will be golden.

There is a little bit of a bootstrap paradox as far as the design and functionality of the machine, but less than you may think. CurrentYou, who is using the time machine, can have only a very high level idea of how it works or what the design of it is. Obviously you will know what it looks like, but you won't know why. After the breakdown when you realize you need to rebuild the machine, you can learn more about the theory and reverse engineer your own design.

There would need to be some future information which would be right on the line of paradoxical (in my opinion), such as which parts to use and what things look like. But there is also an argument that that information is emergent from the machine itself. If a part is made by a specific company, and then that company comes out with that part in the future, that isn't inherently paradoxical. Knowing that you need their part for the time machine is a little questionable, but you can always say that what you learned while studying the theory drove you to use that part instead of just the knowledge that you used it.

The main hangup I think people have with these kinds of stable time loops is forgetting that you still have a personal, subjective timeline you have to follow. Just because you know what you will do in the future doesn't mean you know how you got to that point. If you ignore all of the time travel parts the story is that you find a machine and eventually manage to reverse engineer it. Nothing about that seems unreasonable.

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The time machine doesn't break down - its condition oscillates.

If there are multiple timelines, then you have no "obligation" to return the time machine. If you do it regardless (perhaps out of belief that you have to do it), then Penguino's answer covers what happens.

If there is only one timeline, then when you return the time machine to the past and when "past you" finds it, it will be in the exactly the same condition like when you found it. This is the only logical possibility since these two events are actually the same event.

Without time loops, entropy grows and unmaintained things get into worse condition over time, e.g. iron rusts. However, if there is a time loop, entropy can't grow the whole time, because it has to return to its previous value. But that's okay, because there is a non-zero probability that entropy will decrease, although said probability is usually absurdly small. But in a time loop, a decrease (or constancy) of entropy becomes mandatory.

The amount of rust on the time machine will also be periodic. If the time machine will rust at some periods of time, then it will also "un-rust" at some other periods of time. The same goes for the condition of any of its components.

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If you're looking for a way to do this, then Ship of Theseus is the way to go. That is, the Time Machine is made up of parts and the parts are gradually replaced alongside this time-travel cycle. Each part is replaceable, but despite that, the ship cannot be completely built from scratch for reason which aren't understood. Of course, this doesn't really help because any time loop (which puts physical objects in the past) generates entropy and these time loops are supposedly infinite, which means an infinite increase in entropy.

You're asking 'Is this possible if I don't replace it?' and the answer is 'No', but it's not 'No' because the machine rusts, it's 'No' because it's a self-fulfilling paradox. Time is linear, not circular, the time machine can't be there in the first place. Something cannot come from nothing.

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  • $\begingroup$ What do you mean by "these time loops are supposedly infinite"? Thinking in terms of spacetime as a fixed 4D structure (the block universe idea, see my comment here for another way to think about this perspective) there's just one loop, it's not as if there are multiple cycles of the loop where the entropy can be different in each cycle (not unless you posit what the site here calls "metatime") $\endgroup$ – Hypnosifl Jun 30 at 20:55
  • $\begingroup$ @Hypnosifl I mean infinite from a linear perspective on the time machine's part. $\endgroup$ – Halfthawed Jun 30 at 22:23
  • $\begingroup$ Doesn't the temporal "perspective" of a physical object depend on the assumption of some physical process that records change over time, like a clock or computer memory? In a fixed timeline there should be no such internal recording indicating multiple iterations of the loop. $\endgroup$ – Hypnosifl Jun 30 at 22:28

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