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

(A

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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

- the laws of probabilty;
- time always runs forward.

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'.

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.

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.