Are paradoxes proofs of impossibility (time travel)?

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mosiajam
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Are paradoxes proofs of impossibility (time travel)?

Postby mosiajam » Fri Aug 27, 2010 4:05 pm UTC

Wikipedia wrote:Although time travel has been a common plot device in fiction since the 19th century, and one-way travel into the future is arguably possible given the phenomenon of time dilation based on velocity in the theory of special relativity (exemplified by the twin paradox), as well as gravitational time dilation in the theory of general relativity, it is currently unknown whether the laws of physics would allow backwards time travel.


I used to take it for fact that travel backwards in time was impossible, because this would create a paradox. In fact, my logic was this. If paradox, then fiction (I developed this idea to fix a lot of paradoxes popping up in books; the idea is that these paradoxes exist because the book makes a statement that could not possibly be true in the real world, such as: magic exists). So I took the idea of backwards time travel and I branded it as impossible.

Well, Wikipedia, which is usually well known for its clear and concise statements, obviously disagrees with me. So I was wondering, is there a property of logic (or something) that states that paradoxes are proofs of impossibility?

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Re: Are paradoxes proofs of impossibility (time travel)?

Postby gmalivuk » Sat Aug 28, 2010 12:10 am UTC

If time travel *necessarily* involved paradoxes, then yes, that would mean it was impossible. But there are many proposed formulations of time travel, and lots of them are free of paradox, and so there's no reason to declare those impossible out of hand.
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby mosiajam » Sat Aug 28, 2010 12:31 am UTC

gmalivuk wrote:If time travel *necessarily* involved paradoxes, then yes, that would mean it was impossible. But there are many proposed formulations of time travel, and lots of them are free of paradox, and so there's no reason to declare those impossible out of hand.


When we travel to another parallel universe that is exactly like ours but is x years behind, where supposed paradoxes are resolved by the "alternate universe" hypothesis, we're not traveling back in our universe's time, are we? We're essentially traveling to another formed universe that happens to have developed x years later than ours.

Also, on a random note, I think the idea of time travel necessitates spacetime movement, because my exact xyz coordinates in this universe is likely to be in complete vacuum in whatever time I travel to, since the Earth is not stationary (duhrrr?).

Also, my main concern is where the logical proof that paradoxes are proofs of impossibility is. It may sound like common sense, but I don't put too much stock in that stuff. Why? Zeno's paradoxes.

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Re: Are paradoxes proofs of impossibility (time travel)?

Postby gmalivuk » Sat Aug 28, 2010 12:51 am UTC

Well yeah, if you throw around the word "paradox" for things which are actually completely resolvable, then it doesn't mean something's impossible.
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby Goemon » Sat Aug 28, 2010 3:48 am UTC

Many people don't bother to look up the actual definition of the word "paradox" and might be startled to find out what it really means:

dictionary.com wrote:"a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth."



(Not that this has any real bearing on this topic.)
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby nash1429 » Sat Aug 28, 2010 4:26 am UTC

gmalivuk wrote:Well yeah, if you throw around the word "paradox" for things which are actually completely resolvable, then it doesn't mean something's impossible.


For example, Zeno's Paradoxes. Even if we don't have a resolution now we might have one later. Perhaps the OP should read up on general relativity.

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Re: Are paradoxes proofs of impossibility (time travel)?

Postby Blatm » Sat Aug 28, 2010 2:03 pm UTC

Goemon wrote:Many people don't bother to look up the actual definition of the word "paradox" and might be startled to find out what it really means:

dictionary.com wrote:"a statement or proposition that seems self-contradictory or absurd but in reality expresses a possible truth."



(Not that this has any real bearing on this topic.)


Paradox is a word that is going through puberty. Though I agree that the dictionary definition is useful and should be respected, a lot of people are using it to mean some sort of logical oxymoron. The problem is that definitions should be a reflection of use (in my opinion), so it would be detrimental to ignore the latter meaning. Now, it's fine to oppose some of these changes, but in this case, I can't think of a word that means what paradox is being used to mean. Ideally, we'd have two words for the two separate concepts, but, failing that, I think that it's worse to have no word for a concept than it is to have a word that can refer to two of them. Does anyone know a word for logical oxymora?

On topic: I tend to think the argument "x can't happen because it would break the universe" fairly unconvincing. The universe is a lot smarter than us, and it can pretty much do whatever it wants, because who is going to tell it not to? More practically, Futurama's episode dealing with time travel (where Fry kills his grandfather) did it pretty well.

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Re: Are paradoxes proofs of impossibility (time travel)?

Postby Robert'); DROP TABLE *; » Sat Aug 28, 2010 2:10 pm UTC

Blatm wrote:On topic: I tend to think the argument "x can't happen because it would break the universe" fairly unconvincing. The universe is a lot smarter than us, and it can pretty much do whatever it wants, because who is going to tell it not to? More practically, Futurama's episode dealing with time travel (where Fry kills his grandfather) did it pretty well.

I think the argument is generally "X can't happen because it would the mean the universe isn't consistent", and we've got to assume that it is consistent, or we can prove your mother's phone number.
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby doogly » Sat Aug 28, 2010 3:20 pm UTC

This is actually my day job!

Generally relativity says G = 8pi T. The 8pi isn't too important. G is curvature, and T is stress-energy-momentum-pressure tensor. (it has lots of components. so does G, but everything in G is called curvature).
A time machine is a certain path through space, back inside your own past light cone. Do these paths exist? That's a question about G. And there are no restrictions on the kinds of curvature allowed in general relativity. The fact that you don't like them is not a sufficient way to rule them out. You'd have to prove something about T - that known sources of matter can't produce such curvature.

Progress is slow but I am optimistic that time machines will be impossible in general relativity.
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby mosiajam » Sun Aug 29, 2010 1:44 pm UTC

doogly wrote:This is actually my day job!


Quite the day job.

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Re: Are paradoxes proofs of impossibility (time travel)?

Postby Technical Ben » Sun Aug 29, 2010 3:50 pm UTC

doogly wrote:... You'd have to prove something about T - that known sources of matter can't produce such curvature.

Progress is slow but I am optimistic that time machines will be impossible in general relativity.


It's a pity I don't win a million dollars for my proof then isn't it. I think I could wrap up a proof for "matter not exceeding the speed of light" in a few mins if needed. That would kind of keep it out of those curvatures. ;)
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby gmalivuk » Sun Aug 29, 2010 4:16 pm UTC

Um, no, it wouldn't. Faster-than-light travel is already precluded by relativity, but curvatures that would allow for time travel aren't.
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby Technical Ben » Sun Aug 29, 2010 6:09 pm UTC

Oh ok. That's what I get for trying to be clever. :( Sorry.
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby doogly » Sun Aug 29, 2010 7:10 pm UTC

mosiajam wrote:
doogly wrote:This is actually my day job!


Quite the day job.

Seriously, I'm living the fucking dream.

You can rule out these curvatures with a restriction to intuitively reasonable matter, like "the energy density is never negative," or even something weaker, like "the energy density averaged over a complete geodesic is never zero." But, reasonable though these things sound, quantum fields in curved space are fucking weird, so these conditions are actually really easy to give counterexamples to. So you have to find a condition that is weak enough to be true, but strong enough to be useful.
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby furyguitar » Sun Aug 29, 2010 8:00 pm UTC

I think one has to think about what time is in order to move forward with time travel. The following is not my original idea, but I can't for the life of me remember where I read (which pisses me off because I want to read it again):

So this scientist said that time is really an arrangement of matter. So to go back in time, all one would have to do is make sure that every single atom is back to where it was at the given time one is trying to go back to. That leads to fun thoughts like is one actually going back in time (like picturing a time line and just moving back on it) or is the time continually moving forward but you just recreated the past at this current time. I don't even know if what I just said makes sense...

The important thing, though, is that it appears to rearrange every single atom in the universe to be exactly they were 5 minutes ago sounds like it would require a lot of energy...

Has anyone heard this description of time before? Does anyone know who it is attributed to?

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Re: Are paradoxes proofs of impossibility (time travel)?

Postby hemhhr » Sun Aug 29, 2010 9:11 pm UTC

doogly wrote:This is actually my day job!

Generally relativity says G = 8pi T. The 8pi isn't too important. G is curvature, and T is stress-energy-momentum-pressure tensor. (it has lots of components. so does G, but everything in G is called curvature).
A time machine is a certain path through space, back inside your own past light cone. Do these paths exist? That's a question about G. And there are no restrictions on the kinds of curvature allowed in general relativity. The fact that you don't like them is not a sufficient way to rule them out. You'd have to prove something about T - that known sources of matter can't produce such curvature.

Progress is slow but I am optimistic that time machines will be impossible in general relativity.

The end result, then, is that after an object has followed this path, it is at an earlier time from the perspective of the rest of the universe.
So let's say I travel this path and murder my grandfather before he gives birth to my mother. I would expect that, from that moment on, my grandfather is dead. In other words, I caused change throughout a light cone.
If this kind of change can simply propagate forward in time like that, I would be exempt, right? Since I'm not in the light cone and I've destroyed the path that leads to me? I guess I'm imagining the change as this sort of moving thing that would need a way to find me, but I don't know how much basis in theory that metaphor has.

And yes this is on topic, I want to know how this conception of time travel runs into the paradoxes OP was talking about.

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Re: Are paradoxes proofs of impossibility (time travel)?

Postby Eternal Questionner » Sun Aug 29, 2010 9:29 pm UTC

furyguitar wrote:The important thing, though, is that it appears to rearrange every single atom in the universe to be exactly they were 5 minutes ago sounds like it would require a lot of energy...


I'm afraid I don't know where your source came from, but I can add this. Rearranging all the atoms of the universe as they where 5 mins ago, is completely impossible. As entropy always increases as we go forward in time, the universe of 5 mins ago must have had less entropy than the universe of today. And as the second law of thermodynamics states, entropy can never decrease in a closed system, the universe included. Thusly, to time travel in this way would be to violate the Second Law, at which point you have bigger problems on your hands.

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Re: Are paradoxes proofs of impossibility (time travel)?

Postby furyguitar » Sun Aug 29, 2010 9:32 pm UTC

Eternal Questionner wrote:
furyguitar wrote:The important thing, though, is that it appears to rearrange every single atom in the universe to be exactly they were 5 minutes ago sounds like it would require a lot of energy...


I'm afraid I don't know where your source came from, but I can add this. Rearranging all the atoms of the universe as they where 5 mins ago, is completely impossible. As entropy always increases as we go forward in time, the universe of 5 mins ago must have had less entropy than the universe of today. And as the second law of thermodynamics states, entropy can never decrease in a closed system, the universe included. Thusly, to time travel in this way would be to violate the Second Law, at which point you have bigger problems on your hands.

Excellent argument! It's funny that I can't even remember if the guy who wrote what I read was even saying it was possible or not, but that is how he viewed time - as an arrangement of atoms. It was in a magazine like Discover, Astronomy, Pop Sci, or something like that. Wish I still had it... If I ever find it, I will certainly put the information!

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Re: Are paradoxes proofs of impossibility (time travel)?

Postby Technical Ben » Mon Aug 30, 2010 3:27 pm UTC

hemhhr wrote:The end result, then, is that after an object has followed this path, it is at an earlier time from the perspective of the rest of the universe.
So let's say I travel this path and murder my grandfather before he gives birth to my mother. I would expect that, from that moment on, my grandfather is dead. In other words, I caused change throughout a light cone.
If this kind of change can simply propagate forward in time like that, I would be exempt, right? Since I'm not in the light cone and I've destroyed the path that leads to me? I guess I'm imagining the change as this sort of moving thing that would need a way to find me, but I don't know how much basis in theory that metaphor has.

And yes this is on topic, I want to know how this conception of time travel runs into the paradoxes OP was talking about.

[Highlight mine]
This is where time travel comes down to two possible ways of doing it. 1) Move the entire universe back to where it was. Or 2) Multi verses.
As I doubt anyone here can say we have the ability to "propagate" an effect to the rest of the universe to achieve 1. If there is a multi verse, or multiple universe moving in different directions then it might be possible. However, I hope you travel to a universe where they also breath oxygen, and not one where it's custard instead. As it would be a tasteful, but quick death.
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby mosiajam » Tue Aug 31, 2010 12:23 pm UTC

hemhhr wrote:
doogly wrote:This is actually my day job!

Generally relativity says G = 8pi T. The 8pi isn't too important. G is curvature, and T is stress-energy-momentum-pressure tensor. (it has lots of components. so does G, but everything in G is called curvature).
A time machine is a certain path through space, back inside your own past light cone. Do these paths exist? That's a question about G. And there are no restrictions on the kinds of curvature allowed in general relativity. The fact that you don't like them is not a sufficient way to rule them out. You'd have to prove something about T - that known sources of matter can't produce such curvature.

Progress is slow but I am optimistic that time machines will be impossible in general relativity.

The end result, then, is that after an object has followed this path, it is at an earlier time from the perspective of the rest of the universe.
So let's say I travel this path and murder my grandfather before he gives birth to my mother. I would expect that, from that moment on, my grandfather is dead. In other words, I caused change throughout a light cone.
If this kind of change can simply propagate forward in time like that, I would be exempt, right? Since I'm not in the light cone and I've destroyed the path that leads to me? I guess I'm imagining the change as this sort of moving thing that would need a way to find me, but I don't know how much basis in theory that metaphor has.

And yes this is on topic, I want to know how this conception of time travel runs into the paradoxes OP was talking about.


Stephen Hawking had a really interesting description of a certain something related to backwards time travel. Imagine I opened up a wormhole to the past a second ago. When the atmosphere in my reality enters the past's atmosphere, and then that enters its past's atmosphere, and so on and so forth, what I have is a feedback effect.

Hawking liked to think of it like microphone and speakers. At some point, when the feedback gets too severe, the system breaks down. So apparently having wormholes to the past is, in itself, bound to fail, even if it is possible.

Now, if you didn't die after murdering your grandfather, since you're not in the light cone, you aren't in the past of the original world anymore, since the events should effect everything relevant in its own world. You're in a world which happens to have developed exactly like the original, but is a bit late by the amount of years you supposedly traveled back in time. You murdered someone who resembles exactly your grandfather. However, this time, you're not a part of your world's future, yes?

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Re: Are paradoxes proofs of impossibility (time travel)?

Postby snowyowl » Tue Aug 31, 2010 3:20 pm UTC

Okay, since we've deviated into time travel, allow me to add my two bits.
There are two main models of time travel. Each one has several variations, but those variations are not particularly significant in the general scheme of things. If time travel is possible, then science fiction has come up with the following two types of universe that support it:
  • When you go back in time, the events you see while in the past do not necessarily tally with your memories, and you can change things easily. You are in an alternate universe; killing your grandfather is possible, and will have no effect on you, since he is not your grandfather, but someone who is exactly like him in every respect but one: he's in the wrong universe. You are not exactly changing the past, you are changing a different past.
  • When you go back in time, you literally cannot change the past. You have no free will. If you attempt to kill your grandfather, something will prevent you from doing so - it doesn't matter what. If your future self gives you a recording of your actions, you will always do exactly what the recording says, unless you discover that it has been altered before you received it. Your actions are always predetermined, and always have been.
To answer the OP: the word you are looking for is probably "contradiction", not "paradox". Contradictions are statements such as "2+2=5" which cannot be true, so anything which asserts a contradiction to be true is impossible.
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby Robert'); DROP TABLE *; » Tue Aug 31, 2010 5:35 pm UTC

mosiajam wrote:Stephen Hawking had a really interesting description of a certain something related to backwards time travel. Imagine I opened up a wormhole to the past a second ago. When the atmosphere in my reality enters the past's atmosphere, and then that enters its past's atmosphere, and so on and so forth, what I have is a feedback effect.

Hawking liked to think of it like microphone and speakers. At some point, when the feedback gets too severe, the system breaks down. So apparently having wormholes to the past is, in itself, bound to fail, even if it is possible.

Surely there is a limit to the amount of times you can go through the wormhole? If you have a wormhole with usable area x, and an object with area y, the object can only pass through the wormhole [imath]\lfloor{\frac{x}{y}}\rfloor[/imath] times maximum, otherwise it would collide with itself.
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby mosiajam » Tue Aug 31, 2010 6:43 pm UTC

Robert'); DROP TABLE *; wrote:Surely there is a limit to the amount of times you can go through the wormhole? If you have a wormhole with usable area x, and an object with area y, the object can only pass through the wormhole [imath]\lfloor{\frac{x}{y}}\rfloor[/imath] times maximum, otherwise it would collide with itself.

Wormholes are one way. However, since as soon as an air particle leaves a wormhole, another opens up a second later, and enters it again. Like a microphone and speaker, I don't think that the microphone could ever get overburdened with sound, except at the moment it blows up.

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Re: Are paradoxes proofs of impossibility (time travel)?

Postby frezik » Tue Aug 31, 2010 7:16 pm UTC

Wouldn't Paradoxes as Proofs be a form of Reductio ad absurdum? You start by assuming the opposite, but then show that you get a contradictory result from that axiom. For instance, you can prove that you can't (naively) use infinity as just another number by assuming you can, then try doing a little algebra that way:

1 + ∞ = ∞
1 + ∞ - ∞ = ∞ - ∞
1 = 0

Which is clearly absurd, so we must not be able to use infinity this way. If you have a true paradox (i.e., one that you can't resolve), and the universe is as consistent as we think it is (we've gotten pretty far assuming it is), then yes, Paradox as Proof should be valid.

Eternal Questionner wrote:
furyguitar wrote:The important thing, though, is that it appears to rearrange every single atom in the universe to be exactly they were 5 minutes ago sounds like it would require a lot of energy...


I'm afraid I don't know where your source came from, but I can add this. Rearranging all the atoms of the universe as they where 5 mins ago, is completely impossible. As entropy always increases as we go forward in time, the universe of 5 mins ago must have had less entropy than the universe of today.


We can violate thermodynamics locally. Plan for a time machine:

1) Build a Dyson Sphere. Try not to use any of Jupiter's mass during construction.
2) Gather up power into a huge battery.
3) Use the power to revert the Earth's atomic state to where they were 5 minutes ago.
4) Dump the excess heat into Jupiter.

That takes care of thermodynamics. There's still the problem of the Heisenberg Uncertainty Principle, since we can't know everything about an atom's state. Ask Michael Okuda how the Heisenberg Compensator's work.
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby Robert'); DROP TABLE *; » Tue Aug 31, 2010 8:11 pm UTC

Ask Michael Okuda how the Heisenberg Compensator's work.

They have, he's said: "Very well, thank you."

However, since as soon as an air particle leaves a wormhole, another opens up a second later, and enters it again. Like a microphone and speaker, I don't think that the microphone could ever get overburdened with sound, except at the moment it blows up.

Yes, but then you have two air particles entering the wormhole. Eventually, after enough iterations, you end up the wormhole mouth filled with air particles.
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby mosiajam » Tue Aug 31, 2010 8:15 pm UTC

Robert'); DROP TABLE *; wrote:Yes, but then you have two air particles entering the wormhole. Eventually, after enough iterations, you end up the wormhole mouth filled with air particles.


I see your point. Now, though, it depends on the positioning of wormholes. I'm thinking not only of a wormhole through time, but also through space. Let's say the wormhole opens up to one second ago one centimeter away. Also, let's consider that wormholes aren't planes in 3D space. Let's say it manifests as a sphere.

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Re: Are paradoxes proofs of impossibility (time travel)?

Postby Robert'); DROP TABLE *; » Tue Aug 31, 2010 8:28 pm UTC

There would still be a limit to how much air could go through the wormhole, in total, so I don't think there's anything inherently paradoxical about it. (Though have fun doing the conservation of energy calculations if there's a potential difference.)
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby Technical Ben » Tue Aug 31, 2010 11:18 pm UTC

Robert'); DROP TABLE *; wrote:There would still be a limit to how much air could go through the wormhole, in total, so I don't think there's anything inherently paradoxical about it. (Though have fun doing the conservation of energy calculations if there's a potential difference.)


Didn't we have a similar problem when trying to calculate gravity through a worm hole (AFAIR in the "portal" thread somewhere)?
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby doogly » Tue Aug 31, 2010 11:24 pm UTC

There is no problem with calculating gravity in a wormhole. You have a wormhole metric, BAM! you have gravity.
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Re: Are paradoxes proofs of impossibility (time travel)?

Postby BlackSails » Wed Sep 01, 2010 2:30 am UTC

frezik wrote:That takes care of thermodynamics.


Not really.

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Re: Are paradoxes proofs of impossibility (time travel)?

Postby Dopefish » Wed Sep 01, 2010 5:44 am UTC

Eternal Questionner wrote:
furyguitar wrote:The important thing, though, is that it appears to rearrange every single atom in the universe to be exactly they were 5 minutes ago sounds like it would require a lot of energy...


I'm afraid I don't know where your source came from, but I can add this. Rearranging all the atoms of the universe as they where 5 mins ago, is completely impossible. As entropy always increases as we go forward in time, the universe of 5 mins ago must have had less entropy than the universe of today. And as the second law of thermodynamics states, entropy can never decrease in a closed system, the universe included. Thusly, to time travel in this way would be to violate the Second Law, at which point you have bigger problems on your hands.


Presumably our time traveller isn't affected by the rest of the universe being rearranged back to an earlier moment, otherwise they'd be back to the state they were in, with no memory of time travelling and the universe would be stuck on a continous loop. Most likely, the traveller consists of more mass/energy then whatever form their earlier self would've had, and so conservation of energy is already lost, and so the laws of thermodynamics could easily be lost too.

Also, I don't know how thoroughly the laws of thermodynamics have been proven, they could be laws in the same sense as Newton's laws. Accurate up to a point, but under certain circumstances, they don't apply.

As a late-at-night-and-I-shouldn't-be-posting thought, perhaps it's feasible that the time machine used in such a process basicly contains some sort of substance that can greatly increase it's own entropy to offset the universe's decrease. A great chaotic sponge of sorts, allowing time travel but still following thermodynamics.


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