What would a time machine look like?

I'm going to stop you right there...

 

Yes, actually. Massive objects can never be accelerated to the speed of light, for starters (see the many discussions here and elsewhere on special relativity for me on that). But also rather significantly, I assume, when you say "in a circle" you at least mean a closed loop in spacetime. Timelike loops are forbidden by causality in special and general relativity, meaning no time travel.

If you are interested in models of cosmology that allow for 'time travel' (and still, being good physics, preserve causality), then look into Godel universes or other topologically nontrivial spacetimes. This still does not allow for 'time machines' though, just a structure of spacetime that could, in theory, allow one travel 'backwards' in time. None of these models are actually viable for a universe with matter, really... and almost all relativist throw out any spacetime that allows for those closed timelike loops like you want, for being unphysical (and very unlike the universe we perceive).

 

I'm moving forward in time right now, using this device:

 

Hahaha, I read the original post as moving backwards in time. Yes, a time machine to move forward in time can look... pretty much like whatever you want lol

 

No, no, you are still very incorrect if you mean 'travel into the future faster than you would be doing otherwise'.

 

It doesn't need to be enclosed, if you don't mind the vacuum in space. If it accelerates you away and then back to the start point, you will have experienced less time, than the start point. So you would reach the future of the start point faster than waiting there.

 

1. Causality is a consequence of physical laws (in the regions of relatively flat spacetime), but not an axiom
2. AFAIK, closed timeloops do exist around kerr singularities
3. Causality can be preserved in the timelike loops (Novikov's principle)

 

Woah there fellas... you're barking up the wrong metaphor.

What Jax is referring to is a relativistic shuttle.

Head out to Sirius at .999c, turn around and come back at .999c and Earth will have aged significantly while you will have only aged a few years.

He is correct that, using a space ship to travel at near the speed of light in a loop, you would effectively travel into Earth's future.


Jax, you didn't have it wrong, it was just interpreted the wrong way - too many people thinking you were asking something other than what you were.


And the answer is: it would look like a spaceship capable of sustaining its occupants for a few years or decades, with an engine capable of accelerating continually up to relativistic speeds, and carrying a nigh-unlimited supply of fuel.


(Joe Haldeman used this in The Forever War, to have the heroine "wait" for centuries (Earth-time) while the hero "caught up with her").

 

According to GR, there is massive time dilation around super compact objects such as neutron stars and black holes, if you were to hover near the event horizon of a large static BH where the tidal forces were small, the outside universe would appear to speed up and technically, once you leave the BH's gravitational field, you would have travelled into the future.

But what about the ergoregion of a rotating black hole? Space is being dragged in the azimuth plane within this region faster than the speed of light and proper time according to Kerr metric which becomes zero at the static limit (the outer edge of the ergoregion) becomes negative between the static limit and event horizon, implying that maybe, if you entered the ergoregion and didn't fall into the black hole, you would travel faster than the speed of light relative to the outside universe, which, according to SR, seems to imply a different sort of time travel (i.e. into the past).

 

Wouldn't someone have already traveled back in time to show us what one looks like?

My guess would be: "Surprisingly similar to a DeLorean".

 

GR always reduced locally to SR for a freefalling observer (the equivalence principle), so nothing can ever travel faster than the speed of light in a local sense unless tachyons exist. The discussion of the ergosphere here suggests that when they say space is being dragged faster than the speed of light, they mean that even something moving at the speed of light in the direction opposite to the direction of rotation cannot mantain a fixed angle in whatever global coordinate system is normally used to describe rotating black holes. But I know physicists have analyzed the problem of where closed timelike curves (indicating backwards time travel) might occur, they definitely don't occur in the ergosphere although they could occur inside the inner event horizon if the Kerr solution is accurate (but the Kerr solution has questionable plausibility because there's infinite blueshift of infalling light on the boundary of the inner horizon). This is discussed briefly in the paragraph before section 3 (p. 12 of the PDF) of this paper by Kip Thorne:

 

In relativity objects don't really "travel" in either direction of time, they just have worldlines which represent their path through spacetime (similarly, if you draw a line or a curve on a piece of paper, it isn't really meaningful to ask if it's 'traveling up the page' or 'traveling down the page'). The idea of "backwards time travel" is represented by the idea of a worldline that actually curves around and intersects itself, like if you went back in time and shook hands with your younger self...this idea is known as a closed timelike curve, and although you can find theoretical examples of spacetimes that contain them, they all have features which make them questionable as spacetimes that could occur in reality (like the infinite energy on the boundary of the inner horizon of a rotating black hole, or the fact that the whole universe has to be rotating in the Godel metric), and there are also some arguments as to why a theory of quantum gravity (which it's thought that general relativity will turn out to be an approximation to) might remove these possibilities for closed timelike curves (for example see this article on how string theory, a popular candidate for a theory of quantum gravity, might eliminate closed timelike curves).

 

Thank you, very interesting article.
But the summary is "we dont know yet" :)

 

A time machine would look like a double gimbaled gyroscope, spherical in shape, with a blond actress sitting in the middle. The gimbals are giant hoops, and as they spin around they make powerful wushing noises.

 

My machine, probably an earlier, (or later?) mode,l makes a gnihsuw noise.

 

Hi JesseM

Thanks for the response. Are you saying that even though objects that enter a region where space is rotating faster than c, the object itself, relative to the outside universe, will never rotate faster than c and that space in the ergoregion 'rushes' past the object? The most influence being placed on the object is that it may approach a tangetial velocity of c (relative to infinity) as it reaches the horizon where the frame dragging rate increases to infinite.

Also, proper radial velocity for a Kerr black hole is expressed-

[tex]v=\frac{\sqrt{2Mr(r^2+a^2)}}{\rho^2}[/tex]

where

[tex]\rho^2=r^2+a^2cos^2\theta[/tex]

and [itex]M=Gm/c^2[/itex], [itex]a=J/mc[/itex]

which again implies that proper radial velocity increases over c relative to infinity not only outside the event horizon but outside the ergoregion. I have some idea of the difference between radial and 'proper' radial velocity but what exactly is going on here?

Regarding closed time-like curves, the reduced circumference [itex](\varpi)[/itex] in Kerr metric is expressed-

[tex]\varpi^2=\frac{\Sigma^2 sin^2\theta}{\rho^2}[/tex]

where

[tex]\Sigma^2=(r^2+a^2)^2-a^2\Delta sin^2\theta[/tex]

and [itex]\Delta= r^{2}+a^{2}-2Mr[/itex]

which doesn't deviate too much from the coordinate radius (r) until within the Cauchy horizon where it begins to diverge from r significantly and increase exponentially in close proximity of the ring singularity (where r=0 at the edge of the ring). This would give the impression that the reduced circumference would 'wrap round' the ring singularity, overlapping the original position. A simplistic view maybe but it does seem to suggest CTC's.

 

No, when I said things don't go faster than c, I referred specifically to a locally inertial frame--this is a term often used in discussions of the equivalence principle, it basically means you're zooming in on an infinitesimally small region of curved spacetime so the effects of curvature go to zero (at least to the first order). If you're comparing velocity in the ergosphere to velocity outside it then you're not dealing with a single local region, and the coordinate system you're using must be a non-inertial one. Even in flat SR spacetime, it's quite possible for things to travel faster than c in non-inertial coordinate systems, the light speed limit only applies to distance/time measured in the coordinates of an inertial frame.

I don't know how the conclusion of CTCs inside the inner horizon is reached, but I would caution against reading too much into any coordinate-dependent statements like this, there are plenty of examples in GR of things that look really weird in one coordinate system but turn out to just be coordinate artifacts with no physical significance. For example, in the case of a nonrotating black hole spacetime, if you use Schwarzschild coordinates then it takes an infinite amount of coordinate time for anything to reach the horizon so it was once thought there was some sort of singularity there, but later physicists understood that this effect disappeared if you used other coordinate systems on the same spacetime (like Kruskal-Szekeres coordinates), and that it takes only a finite proper time for an infalling observer to reach the horizon, so there is no physical singularity at the horizon. CTCs are a coordinate-independent notion--geodesics that wrap around and intersect themselves--so I don't think you can conclude anything about whether they exist in a given region just by looking at the peculiarities of how a particular choice of coordinate system behaves in that region (and the coordinate system you're talking about may be the most convenient one to use for a rotating black hole, but it isn't the only possible one).

 

This is one possible way time travel could work, although more often physicists who speculate about such things imagine that if time travel was possible, there would just be a single self-consistent time travel in which nothing could be "changed", and any influences a time traveler had on the past would have been part of history all along (for example, you might travel back and start the Great Fire of London, in which case it was always true that you were the one who started it even before you went back). The idea that history is constrained to be consistent is sometimes called the "Novikov self-consistency principle", you can read about it here:

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

It seems to me that while the "branching parallel universes" theory you mention doesn't give rise to any obvious paradoxes, there'd be a lot of ways in which the "rules" governing time travel would probably have to be sort of inelegant and arbitrary. A while ago I wrote up a few paragraphs on my problems with the idea, using the "Terminator" movie as an example (if you don't know the plot, all you need to know here is that in the movie's 2029 there's an evil computer called Skynet at war with humanity, it sends a 'terminator' robot back to 1984 to kill Sarah Connor, the future mother of John Connor, the leader of the human resistance in 2029; in response, John Connor sends back a soldier named Kyle Reese to stop the terminator in 1984).