The Arrow of Time explained

- Why does time always runs forward? Is time travel possible?

  by Ronald Koster, version 1.0, 2001-01-12

  Spanish translation (courtesy of Laura Mancini)
  Hungarian translation (courtesy of Elana Pavlet)


Keywords: arrow of time, time, time travel, entropy, second law of thermodynamics

Summary

Time in the universe always runs forward, never backwards. That is what is called 'The Arrow of Time'. The second law of thermodynamics is a result of the Arrow of Time and the laws of probability. This can be deduced as follows (in mathematical notation):

("Causality" OR "Modesty Principle") ⇒ "Travelling backwards in time is impossibe"
⇒ "Time in the universe can never be observed to be running backwards" = A

(A AND "What can never be observed does not exist" ⇒ "Time in the universe can never run backwards"
⇔ "Time in the universe always runs forward" = B

(B AND "Laws of probability") ⇒ "Entropy of the universe increases with time"

Time always runs forward in the entire Universe

In our universe we observe that time always runs forward. Since Einstein's Theory of Relativity we know there is no such thing as absolute time in the universe. Time runs at different rates in the universe, slower near massive objects and at different rates in frames with high velocity with respect to each other. But we do know time runs forward everywhere. Probably the best way we can verify this is via the second law of thermodynamics, which states:

The entropy of a system increases with time.

This is in fact the definition of the second law of thermodynamics. This law is a direct result of: This and the definition of the second law implicates the only way for entropy to decrease in a system is, since the laws of probability are strictly mathematical and therefore beyond dispute, when time in the systems runs backwards. Such a proces in which entropy decreases has never been observerd on Earth or anywhere else in the universe. That is why we believe time runs forward everywhere in the universe. But it is possible to find a theoretical explanation, or deduction, for 'the arorow of time' as well. Here's the explanation.

Why Time Travel is impossible

In science fiction time travel is a popular subject. But one can consider time travel in a more science fact way as well. Let us consider a box which we can use for time travelling. Time inside this box runs at a different rate as time observed outside the box in an inertial frame. This inertial frame is of arbitray large size. We choose it to span the entire or at least a very large part of the universe.

Travelling into the future using this box is, in theory, easy. Relativity teaches us that when the box travels at great speed (near the speed of light), time aboard the box will run slower than time in the inertial frame. Another way of achieving this is by placing the box in the nabourhood of a very massive object, like a neutron star or a black hole. An inhabitant of this box, which we will call the observer form now on, thus travels to the future. This describes how we ca use this box as a time machine to travel into the future.

Travelling backwards in time using this box is a more difficult matter. This would require time inside the box to run in the reverse direction as time outside in the inertial frame. There are at least two reasons why this is not possible. Each of them in itself forbids this. Those two reasons are the 'Causality paradox' and the 'Modesty principle'.

Causality Paradox

Suppose a person travels back in time to the time his father had no children yet. He then kills his father. There is nothing that we know of that forbids him doing so. However, this leads to a causality paradox. If he kills his father before he had any children, how could he have been born, and if he had not been born how could he have travelled back in time and kill his father etc. The only way to solve this paradox is by stating that appearently travelling backwards in time is not possible.

Modesty Principle

The modesty principle is the principle that nothing small can affect the entire universe. It is unlikely a small scale system will affect the entire universe. It is conceivable a star can significantly affect another star, but not an entire galaxy. In same way a space craft can affect another craft of comparable size, but not a star, etc. When travelling backwards in time is possible with our box described above that would mean the following.

When the observer is in the box during his travel, time in his box continues to go forward, but time outside in the inertial frame wil run backwards. And not vise verse, because then the observer would grow younger and travel to the future. The inertial frame we mentioned is in principle of infinite size, that is it spans the entire universe or at least a very large part of it. In some way when the observer is in his box during his travel backwards in time, his box affects the entire universe in such a way that time runs backwards in it. The small scale box affects the entire universe. This is highly unlikely. Yet again another paradox. The only way to solve this paradox is by stating that obviously travelling backwards in time using the box is not possible.

Conclusion: Time in the Universe always runs forward

Hence we find no observer can ever travel back in time. This is equivalent to stating no oberserver can ever observe time running backwards in the universe. And no 'observer can ever observe it', is equivalent to 'it can never happen'. Using the principle that non-observable things are non-exsisting things. Thus, time in the universe can never run backwards. This is the explanation of the Arrow of Time!

PS. Note that the causality and modesty principles do not forbid us from building a device which can make time run backwards in an isolated (small scale) piece of space. The above deduction only explains the Arrow of Time of the entire universe. Such a device would cause the entropy of the isoloated space to decrease! However, the entropy of the entire universe would still increase during that proces, since in the universe time would still be running forward. Thus the entropy increase in the world outside the isolated piece of space would be greater than the entropy decrease in the piece of space.