Re: time-space Why the paradoxes of time? (CONFUSED)

[jose]

I think this might be a very simple question, but I found no info on the net or in my chicken head...

I've read M Kaku and Hawkings, and they write about a lot of paradoxes if time travel was possible (killing your parents, rewriting history, etc etc)

I might be overlooking something, but if we travel thru time, there would be NO earth.. the Earth has moved throughout space, AND throughout time... So if we travel back iin time, there won't be ANY Earth...

My picture is this:
If Mark and Lisa have a date at 12:00 at the park, but Marks gets stucked in traffic, and gets there 6 hours left, the very impatient Lisa would have already left.. She is ~somewhere~ else..

Likewise if we travel back in time, everything would be ~sometime~ else, even if we're in the same "place", the Earth is at a different "time"...

Thanks for the help.

 

[dicerandom]

I think that in reaching this conclusion you're assuming some sort of 'universal time,' or at least a universal simultenaity.

Picture a 3d box, the vertical axis being time. Let's align the box such that the Earth is along the central vertical of the box, if I let time move forward I will see the Earth move up towards the top if the box.

If I understand you correctly, you're saying that if someone who was on the Earth when it was near the top of the box were to time travel back to the bottom of the box they would find that there is no earth, since the Earth is now at the top of the box.

It's a nice idea, I like it, but I don't think it'll work. In relativity we are mostly concerned with what are called events, an example of an event would be a light pulse going off or an object reaching a particular point. We can think of the Earth as being a whole series of events, every moment in time there is an event of "the Earth is here", so that if we look at the whole collection of events the Earth sweeps out a vertical tube in our box. So I think you could actually think of the Earth as being a sort of four dimensional tube structure. At any given time when you look at the Earth it's spherical, but that's because you're only looking at a three dimensional cross section of its true four dimensional structure.

 

[JesseM]

I think that in reaching this conclusion you're assuming some sort of 'universal time,' or at least a universal simultenaity.

Picture a 3d box, the vertical axis being time. Let's align the box such that the Earth is along the central vertical of the box, if I let time move forward I will see the Earth move up towards the top if the box.

If I understand you correctly, you're saying that if someone who was on the Earth when it was near the top of the box were to time travel back to the bottom of the box they would find that there is no earth, since the Earth is now at the top of the box.

This seems really confusing--why would the Earth move forward in time if you move back in time? I think he was just talking about the fact that the Earth is moving around the sun in its orbit, so if you assume some sort of absolute space and say that time travel means traveling through time without traveling through space, then the Earth would have been in a different position in absolute space in the past.

There are a few assumptions here that would be wrong according to modern physics. The first is the assumption of absolute space, the idea that there's a single point in space in the past that's at "the same place" as where I am in the present--in reality, different reference frames have different definitions of what the same point in space is at different times. For example, if I'm driving by you at 50 mph, in your rest frame you'd say that an hour ago the car was 50 miles behind the point in space it is now, but in my rest frame I'd say that an hour ago the car was in exactly the same position it is now, since in my rest frame the car is standing still while you are the one moving at 50 mph. So there's no single position in the past that's at "the same position I am now", this depends on which reference frame you use, and all reference frames are equally good according to modern physics.

The other wrong assumption is that time travel would just involve disappearing from one time and reappearing in another, the way it usually works in science fiction movies like Back to the Future or the Terminator. But all the proposals for how time travel might be possible according to general relativity involve continuous paths with no sudden breaks, like traveling through a wormhole in such a way that you can enter one mouth in the present and exit the other mouth in the past. Obviously in this case, where you exit is simply a matter of where the two wormhole mouths are placed, if both are traveling along with the Earth than you can enter and exit next to the earth. But in any case, even if you traveled to the past and found yourself far from the Earth in space, as long as your distance from the Earth in light-years was smaller than the amount of time in years you had traveled into the past, there would always be the potential to race back to Earth in a rocket and arrive before you departed, so the potential for "grandfather paradox" type situations would still be there.

 

[dicerandom]

This seems really confusing--why would the Earth move forward in time if you move back in time? I think he was just talking about the fact that the Earth is moving around the sun in its orbit, so if you assume some sort of absolute space and say that time travel means traveling through time without traveling through space, then the Earth would have been in a different position in absolute space in the past.

Didn't occur to me as being a problem, I guess I figure that if you've mastered moving through time then moving through space as well should pose no great difficulty.

Edit: BTW, in my example the Earth didn't move forward in time when I moved back, it just stayed where it was.

 

[JesseM]

Edit: BTW, in my example the Earth didn't move forward in time when I moved back, it just stayed where it was.

Oh, I missed the fact that the Earth was already at the top of the box when you left--that makes more sense, maybe that is actually what jose was talking about.

 

[jose]

Actually my doubt is related with what dicerandom said, his analogy of the box is better than the park thingy...:P

Thanks for the explanation, however, I'm afraid that I still don't have the picture clear, even if the Earth is 4D... a 3D tube... shouldn't it move thru the "box"...

 

[JesseM]

Actually my doubt is related with what dicerandom said, his analogy of the box is better than the park thingy...:P

Thanks for the explanation, however, I'm afraid that I still don't have the picture clear, even if the Earth is 4D... a 3D tube... shouldn't it move thru the "box"...

There's no movement in 4D, everything is just frozen in place. As an analogy, imagine you had some pieces of string frozen in a block of ice, and then you sliced the block into a series of thin horizontal cross-sections, took a picture of each one, and used the pictures as frames in a movie. When you played the movie the cross-sections of the strings might appear to be moving around, but this would just be because the pieces of string were not all straight and vertical in the ice, so the cross-sections of a given string would be in different positions in different horizontal slices. Now just imagine the block of ice as spacetime, with time as the vertical dimension and space as the horizontal dimensions, so each horizontal slice represents space at a particular moment in time. The strings aren't moving within the block, there's only movement when you break up the 3D block into a series of 2D slices, and similarly the tubes corresponding to the Earth or the traveller aren't moving in 4D spacetime, it's only when you break it up into a series of 3D moments that you see movement.

 

[Whitestar]

There are a few assumptions here that would be wrong according to modern physics. The first is the assumption of absolute space, the idea that there's a single point in space in the past that's at "the same place" as where I am in the present--in reality, different reference frames have different definitions of what the same point in space is at different times. For example, if I'm driving by you at 50 mph, in your rest frame you'd say that an hour ago the car was 50 miles behind the point in space it is now, but in my rest frame I'd say that an hour ago the car was in exactly the same position it is now, since in my rest frame the car is standing still while you are the one moving at 50 mph. So there's no single position in the past that's at "the same position I am now", this depends on which reference frame you use, and all reference frames are equally good according to modern physics.

Exactly, it's all relative. :)

The other wrong assumption is that time travel would just involve disappearing from one time and reappearing in another, the way it usually works in science fiction movies like Back to the Future or the Terminator. But all the proposals for how time travel might be possible according to general relativity involve continuous paths with no sudden breaks, like traveling through a wormhole in such a way that you can enter one mouth in the present and exit the other mouth in the past. Obviously in this case, where you exit is simply a matter of where the two wormhole mouths are placed, if both are traveling along with the Earth than you can enter and exit next to the earth. But in any case, even if you traveled to the past and found yourself far from the Earth in space, as long as your distance from the Earth in light-years was smaller than the amount of time in years you had traveled into the past, there would always be the potential to race back to Earth in a rocket and arrive before you departed, so the potential for "grandfather paradox" type situations would still be there.

But which do you subscribe to: the self-consistent theory or the multiple timeline/parallel universes theory?

 

[JesseM]

But which do you subscribe to: the self-consistent theory or the multiple timeline/parallel universes theory?

Personally my guess is that in quantum gravity, time travel will turn out to be impossible...there seem to be hints of this in both semiclassical gravity and string theory, see here and here.

 

[MeJennifer]

I have a hard time seeing any paradoxes with CTCs. Classically what happens after an event is fully determined by the causal structure of spacetime, e.g. an incomming lightcone.

 

[JesseM]

I have a hard time seeing any paradoxes with CTCs. Classically what happens after an event is fully determined by the causal structure of spacetime, e.g. an incomming lightcone.

In spacetimes with CTCs the causal structure is a little more complicated since some event A can lie in both the past and future light cone of some other event B. And there can be situations where there are multiple self-consistent outcomes even if you fix the conditions outside the Cauchy horizon where CTCs can occur...see the discussion in the Novikov self-consistency principle article from wikipedia:

Among the coauthors of this 1990 paper were Kip Thorne, Michael Morris, and Ulvi Yurtsever, who in 1988 has stirred up renewed interest in the subject of time travel in general relativity with their paper Wormholes, time machines, and the weak energy condition,[2] which showed that a new general relativity solution known as a traversable wormhole could lead to closed timelike curves, and unlike previous CTC-containing solutions it did not require unrealistic conditions for the universe as a whole. After discussions with another coauthor of the 1990 paper, John Friedman, they convinced themselves that time travel need not lead to unresolvable paradoxes, regardless of what type of object was sent through the wormhole.[3]

In response, another physicist named Joseph Polchinski sent them a letter in which he argued that one could avoid questions of free will by considering a potentially paradoxical situation involving a billiard ball sent through a wormhole which sends it back in time. In this scenario, the ball is fired into a wormhole at an angle such that, if it continues along that path, it will exit the wormhole in the past at just the right angle to collide with its earlier self, thereby knocking it off course and preventing it from entering the wormhole in the first place. Thorne deemed this problem "Polchinski's paradox".[4]

After considering the problem, two students at Caltech (where Thorne taught), Fernando Echeverria and Gunnar Klinkhammer, were able to find a solution beginning with the original billiard ball trajectory proposed by Polchinski which managed to avoid any inconsistencies. In this situation, the billiard ball emerges from the future at a different angle than the one used to generate the paradox, and delivers its younger self a glancing blow instead of knocking it completely away from the wormhole, a blow which changes its trajectory in just the right way so that it will travel back in time with the angle required to deliver its younger self this glancing blow. Echeverria and Klinkhammer actually found that there was more than one self-consistent solution, with slightly different angles for the glancing blow in each case. Later analysis by Thorne and Robert Forward showed that for certain initial trajectories of the billiard ball, there could actually be an infinite number of self-consistent solutions.[5]

Echeverria, Klinkhammer and Thorne published a paper discussing these results in 1991;[6] in addition, they reported that they had tried to see if they could find any initial conditions for the billiard ball for which there were no self-consistent extensions, but were unable to do so. Thus it is plausible that there exist self-consistent extensions for every possible initial trajectory, although this has not been proven.[7] It should be noted, though, that this only applies to initial conditions which are outside of the chronology-violating region of spacetime,[8] which is bounded by a Cauchy horizon.[9] This could mean that the Novikov self-consistency principle does not actually place any constraints on systems outside of the region of spacetime where time travel is possible, only inside it.

Even if self-consistent extensions can be found for arbitrary initial conditions outside the cauchy horizon, the finding that there can be multiple distinct self-consistent extensions for the same initial condition—indeed, Echeverria et al. found an infinite number of consistent extensions for every initial trajectory they analyzed[7]—can be seen as problematic, since classically there seems to be no way to decide which extension the laws of physics will choose. To get around this difficulty, Thorne and Klinkhammer analyzed the billiard ball scenario using quantum mechanics,[10] performing a quantum-mechanical sum over histories (path integral) using only the consistent extensions, and found that this resulted in a well-defined probability for each consistent extension.