The hypothesis that the number of possible states of every finite volume of space-time is finite.


Is the universe reversible?

Time reversal invariance

The laws of physics appear to be time reversal invariant under an operation involving inverting the parity and charge of all its elements.

This is true of both classical and quantum physics.

People seem to have a hard time accepting this symmetry for some reason.


Time reversal invariance is connected with determinism. The ability to run the universe backwards would strongly suggest that determinism is true - and this is perceived as unpalatable, due to the implied lack of free-will.

We can't experimentally reject determinism - so we can't reject time reversal invariance because of determinism.

The second law of thermodynamics

Physics on a large scale appears to exhibit irreversibility. This observation has been codified into a "law" - known as the second law of thermodynamics - which suggests that there is a fundamental time asymmetry.

In fact this is not an unbreakable law of physics, but rather a statistical rule - and such laws are common in reversible systems which lie near to ordered initial states.

Familiarity with the second law of thermodynamics appears to have led many people to believe that physics is irreversible. However it represents no evidence in that direction whatsoever - and physics is microscopically reversible - according to both Newtonian mechanics and quantum mechanics.

Wave function collapse

One of the arguments in favour of irreversibility invokes "wave function collapse" as a fundamentally irreversible process, which prevents the universe being run backwards. However nobody has ever seen a wave function collapse, and such a thing is not present in the equations of quantum physics.

Wave function collapse turns out to be a story - made up to explain how quantum systems could take specific values on observation. It introduces an almost mystical distinction between the observer and the observed - which apparently some 20th-century physicists found pleasing.

No theory explaining wave function collapse is necessary - wave functions never collapse - the whole idea is a fantasy, with no connection to real physics.

Quantum doo-dah

Another of the arguments in favour of irreversibility invokes "random quantum fluctuations" in order to claim that the universe is asymmetrical in time.

Supposedly, it is well-known that quantum physics has told us that randomness is a fundamental characteristic of the universe. Some sort of mixture of Heisenberg's uncertainty principle and Bell's theorem is supposed to rule out simple deterministic explanations of physics.

However, upon closer inspection, this too is simply befuddlement. The equations of quantum physics - like classical physics before it - are deterministic.

Heisenberg's uncertainty principle has nothing to do with randomness or determinism. It refers to the difficulty that embedded observers have in finding out what state any region of the universe is in. This limits their ability to predict the future - but says nothing about whether the dynamical system they are embedded in is reversible or not.

Bell's theorem was popularly billed as ruling out deterministic, local physical theories - but it simply doesn't do that - deterministic, local physical theories are still popular, and are not - in fact - prohibited by Bell's inequality at all.

So it appears that there's actually no evidence at all in favour of irreversibly from quantum theory.

Black holes

Some people (including Stephen Hawking) have conjectured that reversibility is violated by black holes. The idea is that information flows into a black hole, and not much comes out.

What does come out is Hawking radiation - which is supposed to be a senseless blur - independent of what went into the black hole.

Supposedly, no information or signal can escape from a black hole.

In an attempt to resolve the issue, some theorists have conjectured that - from the point of view of an observer in our universe - nothing ever goes into the black hole in the first place. Rather it seems to get slower and slower as it approaches the event horizon, without ever falling in. When the black hole evaporates all the information is still available, since - from the point of view of an observer - it never fell in in the first place.

All in all, this is a pretty obscure and esoteric objection to reversibility. It places the laboratory necessary to observe the phenomenon at a place where it is very difficult to build one - on the edge of a black hole - and seems to be mainly conjecture.


It does not appear to be necessary to hypothesize the existence of a genuine random number generator to explain the world as we see it.

Now, we can't exhaustively rule out the hypothesis that nature "plays dice" - any more than we can rule out any other hypothesis.

However, we can experimentally observe that the world is either exactly microscopically reversible - or very, very close to being exactly microscopically reversible - so close that no reliable experiment has ever suggested a violation of reversibility.

The laws of physics exhibit time reversal invariance - and always have done so. Consequently, it is of some interest to consider what the consequences of reversibility are, assuming that the universe really is reversible.

Consequences of reversibility

We can rule out certain physical phenomena as a consequence of accepting reversibility - and this assists us when formulating physical theories by providing a constraint.

Conservation of information

Reversibility is effectively the result of a law of conservation of information. In this context, "information" may be taken to refer to the knowledge of the state of the system which is necessary to recover earlier states from current ones.

Reversibility can then be seen as a consequence of the conjecture that no information is ever created or destroyed.

Behavior in finite, reversible systems is fundamentally cyclic in nature.

In general the state of a specified finite reversible system can be characterised by two numbers. One number indicates which cycle the state is on, and the second indicates how far into that cycle evolution has progressed. Both numbers can be considered as counting from the first item in the set - when they are ordered lexicographically.

The first number may be considered to be fixed for any working system - and so all that remains in order to specify a state within it is an offset which ranges from zero to the number of time-steps in the cycle.

Temporal inversion

Reversibility suggests that one way of viewing the two kinds of charge in the universe (positive and negative), is to think of some particles as moving backwards in time.

If the electron is viewed as moving forward in time, the positron can be considered as exactly the same particle moving backwards in time.

This was one of the keys to the quantum electrodynamics perspective - and Richard Feynman described it in his Nobel Prize lecture.

Hawking radiation

As an example of reversibility in action, we will consider the phenomenon of Hawking radiation - and will see that the existence of such radiation can be predicted simply from accepting finiteness and reversibility.

Consider a finite model of the universe. In such a universe, if black holes did not evaporate we would have a violation of the recurrence theorem - which is an immediate consequence of reversibility in conjunction with finiteness.

In a finite, reversible universe, anything that can be done must also be able to be undone - by continuing to run the system in the same direction - or else there would be no way to recover the initial state again.

From this we know that if things appear to disappear as they "fall into" black holes other things must be able to apparently emerge.

Conversely, if you hold that nothing can ever leave a black hole (by definition) you must also adhere to the notion that nothing ever falls into one either. All that would happen would be that as an object approaches the event horizon the slower it goes. Eventually the black hole evaporates - and the object never actually gets as far as puncturing the event horizon.

It can be argued that none of this applies to our universe - since we don't know if that is spatially finite or not.

Hawking radiation was apparently not predicted on the grounds of reversibility. Indeed Hawking himself sometimes seems to question the reversibility of the universe.

Similarly - on grounds of reversibility - one can predict that - if singularities ever form in the first place - there must also be a mechanism by which they can dissipate.

It's not clear whether such a result is of much use: it seems inevitable that GR will break down somewhere short of singularities - and quite possible that it will do so this side of the event horizon - in which case discussion of what happens on the very edge of black holes will be rather theoretical.

Tim Tyler | |