After reading this hopefully, you should be slightly more confused than when you started reading this... hopefully.

So time travel? What is it really and is it possible? Well that's what I'm attempting to answer¹. It is not only a realm of science fiction and anoraks, but of scientists who wear anoraks. Anyway, happy trekking.

Paradoxes

A Paradox is simply an idea which is supposed to prove time travel is impossible. Like all good ideas² they can be gotten around with some higgery jiggery pokery.

The 'Grand father Paradox'

Lets start by killing your Grandfather! The 'Grandfather' paradox is one of the most famous paradoxes. If you went back in time and killed your grandfather you could not exist in the present in which you went through the time machine to kill your grandfather, so your grandfather is still alive. Ergo it's impossible to time travel. Of course it doesn't have to be your Grandfather... Grandmothers do fine.

Maybe the first mention of the Grandfather paradox is in René Barjavel's Le Voyageur Imprudent, of course it doesnt have to even be a relation, going back in time and driving your boot down on the head of the first fish to think that 'maybe, you know, call me crazy, but, you know, maybe there is some thing about this 'Land'. Hey lets get crazy and lose the gills!'

Cumulative Paradox

Another famous paradox is the Cumulative Paradox. Any self respecting time traveller is going to want to head to a very famous part of time, hey they paid their money and they are not going to be trudging around some Cretaceous swamp. So everyone wants to head to a famous one, lets say the crucifixion of Jesus of Nazareth. So the final result is that anyone present at the Crucifixion³ would suddenly find millions of time travelers from all periods of time in the future looking at it... possible taking pictures.

Anyway if time travel is/was/will be possible at any time, historians would have probably recorded thousands of people showing up suddenly on Omaha beach on D-Day, or even around the Twin Towers on 9/11.

Closed Loop Paradoxes

Oh there are hundreds of these. A closed loop is best described as events which only get started because someone comes from the future to initiate them. Maybe the most obvious⁴ is a theory on how we in the present would get a time machine. Someone from the future comes here⁵ and, I dunno, drops dead. We find the time machine, reverse engineer it to figure out how it works. Of course its from the future so we don't understand most of it, several hundred years later it forms the basis of the Very First time machine. A Closed Loop of Actuality occurs because they have now got to send a time machine back again so that past can reverse engineer it... again

Chronology Protection Conjecture

Sounds very confusing, actually isn't. Basically Stephen Hawking maintains that there is unknown Physical Laws which shut down any time machine. At the moment laws of Physics do not forbid time travel at all. They just make it extremely difficult. One theory about time travel involves the towing around of black holes very quickly... sadly this needs more energy than there is in the entire universe.

Zeno's Paradoxes

Zeno, like most ancient Greeks, decided to annoy everyone in the future by giving us a series of paradoxes which are so obviously untrue, but quite hard to disprove theorectically. The first one the 'Dichotomy' says that moving is impossible. Because where ever you have to go to you have to get half way there, and what ever the halfway is you have to get half way to that and so on into infinity. The second is Achilles versus the Tortoise in a race. Achilles, the Greek hero, can obviously run faster, but he starts a little behind. So when he reaches the spot where the Tortoise was the Tortoise has moved on a bit farther, so then Achilles reaches that spot, but that wiley Tortoise has moved on another bit, so Achilles has to ... onto infinity. So when ever he reaches the place where the Tortoise is, it's moved on a bit. His third paradox says that an arrow, when fired, cant move⁶. Time must be divided into successive instances and at each instance the arrow occupies a definite position, so it must be at rest, so it's not moving. The final, and most confusing, is his Moving Rows Paradox. Three bodies are level with each other and in the smallest instance of time one moves the smallest possible distance to the right, while the other moves the smallest possible distance to the left. Then those two bodies have moved apart by twice the smallest distance in the smallest instance of time. So when they were just the smallest distance apart, halfway to their final destinations, time changed by the half the smallest possible instant of time. This would be smaller than the smallest possible instant of time, which is mental.

Possibilities

You've read why we cant, now lets find out how we might. Traveling into the future is absolutely the easiest thing imaginable, every single person can do it: wait. It's getting back that's hard.

Another name for a time machine is a Closed Timeline Curve or CTC's. So we ask 'Can a CTC exist?'

In flat Minkowski⁷ space time... no. The future and past never intersect⁸. If you walk along a flat plane facing due north and you never head off in an angle of more than 45 degrees you cant cross your own path from the south.

But you can in other forms of spacetime. The first person to notice this was the famous mathematician of mathematical logic Kurt Godel, he discover the rotating spacetime, and that past and future intersect at every point. However observations tell use that the universe is not rotating.

However CTC's can exist on a rolled up Minokowski spacetime. A little bit difficult to explain how, so just take it for granted.

Enough with CTC's lets get to the real Time Machines⁹

Sorry folks but the following theories hinge on a future society being able to create black holes... so don't be expecting them anytime soon. A black hole however doesnt contain CTC's by itself, so no time travel. But the time reversal of a black hole is a white hole. A black hole has an event horizon from which no particle can escape, a white hole has one into which no particle may fall into, but from which particles may emerge from any minute. Its a possibility that time in a White hole may run backwards, it remains unchanged for aeon's and suddenly spews forth a star, causuality may run from future to past. So lets say you glue a black hole and a white hole together. The result is a ... tube. Matter can pass through the tube from one direction only though: into the black hole and out of the white hole. Now you stitch the ends into any flat spacetime, my universe, your universe the same universe, whatever. Now you have a ... wormhole. Which isn't a time machine but is a pretty cool short cut across huge distances. The distance between the two openings is quite short, but the distance across normal spacetime can be vast.

Right, you have a wormhole, now we use some cool science hocus pocus and bring into effect time dilation by zig zagging the black whole end so as to keep the speed just under lightspeed. Hey presto a time machine!

One problem though, you can only go back as far as when the time machine was made, no going back to hunt dinosaurs or anything.

Another problem is that after matter enters the hole can snap closed on it's 'tail', the so called 'Catflap effect'. But this can be easily fixed by rotating the black hole or using exotic matter... well it should be easy in a few hundred thousand years anyway.

Lightspeed

Most time machines are subject to lightspeed, 'cause when you go fast enough time stops. Other theories, other than the one above, would be easier to make, use and maintain but are restricted because of lightspeed. So lets just follow the Star Trek method and engage the warp drive.... Whoooosshh!!

But travelling faster than light is forbidden by special relativity... but not by general relativity. So everyone says "Matter cant travel faster than light, But space can." So someone decided to warp space around the Enterprise and send it out to fight space dragons or whatever.

Great! Problem solved!

No, lets say we engaged it to warp 2¹⁰, 10 times the speed of light. The wall of the bubble must be 10 to the root of minus 32. If the ship is about 200m long, we would need... 10 billion the mass of the known universe.

The bent matter machine

Lets say you bend space to make a wormhole using matter. Matter is curved space. Levi-Civita bent space using magnetism, which has energy, which is mass. Mallet decided to bend space using light, which has energy, so it can act like mass. So a ring of light could create a ring of time!

So you walk along this ring of time until you hit the right exit and get off, back in time. But making a ring of light requires huge energy... but what if you slow it down? Eh? But a Mallet Time Machine suffers in the same way as the wormhole one. You cannot go back further than the machines creation

So we've reached the end

So are time machines possible? Yes, but possible when is the real question.¹¹