We are all time travellers because we're all travelling into the future at the rate of one second per second. What's surprising is that some things are travelling into the future faster than that.

For example, moving clocks actually time travel into the future because they run slow, in accordance with Einstein's theory of special relativity. To be specific, a clock in a spacecraft orbiting the Earth at 30,000 km/h slows by one part in three billion, losing about 0.0034 seconds every 100 days compared to a similar clock on the Earth.

However, from the orbiting clock's perspective, the Earth clocks run slightly fast, and hence move relatively further into the future. Therefore, when the astronauts come back to Earth, they also come back to the future.

One hundredth of a second

This was the case with Vladimir Titov and Musa Manarov, who spent just under 366 days in the Mir Space Station during 1987 and 1988. On arriving back on Earth they had aged about 0.012 seconds less than their colleagues who stayed home. Hence they had time travelled about a hundredth of a second into Earth's future. Although they surely didn't notice this, they could easily have measured it with accurate clocks.

It's hard to get excited about a few milliseconds of time travel: so how about serious time travel? To travel two years into the Earth's future for each year of your time, you would have to travel at 87 per cent of the speed of light, or about 260,000 km/sec – more than 30,000 times faster than a space shuttle. Say you left on 1 January 2010 and came back one year later by your time, the date on Earth would be 1 January 2012. There's no doubt about that. Both the theory and the supporting experiments are rock solid.

Can we expect to do serious time travel in the foreseeable future? After all, you can buy a 10-day trip to the International Space Station for US$20 million (around A$22 million), which gives you a third of a millisecond of time travel into the future.

At 87 per cent of the speed of light, a 30,000 kg spacecraft has about three trillion gigajoules (GJ) of kinetic energy. Electricity costs at least A$10 per GJ, so that's roughly thirty trillion dollars worth of energy. To put this in perspective, the Australian Gross Domestic Product for 2006 was somewhat less than a trillion dollars. Furthermore, thirty trillion dollars would be just a fraction of the actual cost, which would also include research and development, manufacturing, and the inevitable inefficient conversion of electricity to kinetic energy.

Chronological paradox

Nevertheless, that's the easy kind of time travel, taught in detail to first year physics students at my university. What about travel into the past?

Unlike the future, the past is known. Hence, if you could travel into the past it seems you could change known facts, and produce facts that are both true and false, i.e. contradictions. For example, in the movie Back to the Future, Marty McFly prevents his parents from meeting in the way he knows they actually did. Consequently, his wallet photo of his family starts to fade. This is pure fiction: the real world could not sustain such contradictions. If Marty was present in the past, he did not prevent them meeting – that's a fact recorded by the photo in his wallet.

But this makes us feel uneasy – couldn't Marty have decided to prevent them meeting? Although the photo seems to prove that he didn't make that decision, isn't he free to 'change' his decision once he's travelled back in time? This is the ancient problem of whether free will can exist in a universe obeying laws – such as the laws of physics. Maybe it can, but not to the extent that it is free to will contradictions.

A world with travel into the past would obey different laws to the ones we have discovered so far. This fact tends to polarise views on time travel into the past. Some welcome new laws, others would like to avoid them at all costs. Finding a way to time travel into the past would be a landmark development in physics – it seems to me that also finding new laws would be entirely appropriate.

Just too weird

The simple resolution is that time travel into the past is physically impossible. However, the physics of general relativity is infested with this very concept. If you don't want it, you may have to pass a specific law of physics against it, as Stephen Hawking did with his "chronology protection conjecture" – just ruled it out because it's too weird.

One problem with this approach is that physics has developed by accepting weirdness – quantum mechanics for example – so we should be careful about excluding things just because they're radical.

In summary, time travel into the future is logically and physically possible, but not presently economically possible. Time travel into the past is logically possible, but may not be physically possible, and the economic cost is incalculable.

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