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The Arrow of Time

We are all aware of an intuitive "flow" of time from past to future. Not only do we feel this flow of time, but we also see it manifested in the behaviour of objects which change over time. Many objects seem to behave differently in the forward time direction when compared to the backward time direction. For example, we don't see a spilt glass of water jumping up and going back into the glass, we don't see a broken egg reforming itself. These effects all add to the impression that there is some sort of "forward direction" in the time dimension. This directionality is called the Arrow of Time.

However, this "arrow of time" is something of a mystery to physicists because, at the microscopic level, all fundamental physical processes appear to be time-reversible (we'll consider this later). Also, as shown on the Time and the Block Universe page, our universe appears to have a spacetime structure in which all of time is laid-out in a "block universe", i.e., there is no actual "flow" of time, no movement of a "now" point.

So on this page we will investigate the cause of this mysterious "Arrow of Time".


Entropy can be considered the amount of disorder in a system. For example, a car that has rusted could be said to have a greater entropy value than a new car: bits of the car may have fallen off, the paint may be flaking. Basically, the molecules of the car have become more disordered over time: entropy has increased.

As has just been just discussed, all microscopic processes appear to be time-reversible. The question of why we see an "arrow of time" in macroscopic processes has therefore presented physics with a long-standing conundrum. For this reason, much attention has focussed on the fact that the entropy of a closed system increases with time, i.e., a system will gradually become more disordered with time. Eventually the system (gas in a closed container, for example) will reach a state when all its molecules are completely randomly orientated. This state is called thermal equilibrium. The rule that entropy increases with time is called the second law of thermodynamics.

The reason for this increase in entropy can be seen from a purely probabilistic argument: a system will have many more possible disordered states than ordered states, so a system which changes state randomly will most likely move to a more disordered state. It's really just a matter of likelihood. For this reason, the second "law" of thermodynamics is not really a "law" at all, certainly not an unbreakable law on the same basis as other physical laws - it is a statistical principle. In fact, it might be possible for a room full of randomly-distributed particles to re-order itself quite by chance so that all the particles end up in one corner of the room - it would just be incredibly unlikely!

While the second "law" of thermodynamics is "just" a statistical principle, it is a mightily powerful statistical principle! This is because the basis of the second law - that "disorder will increase" - seems so obvious, and seems to appeal to a fundamental, platonic principle of mathematics. For this reason, the second law manages to appear even more fundamental and unbreakable than the other physical laws, some of which (for example, the amount of electric charge on an electron) seem rather arbitrary in comparison. This fundamental strength of the second law is described well by the astrophysicist Sir Arthur Eddington:

"If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can offer you no hope; there is nothing for it but to collapse in deepest humiliation."
- Sir Arthur Eddington

One of the most inexplicable features of the early universe is that it had an incredibly low value of entropy. This value of entropy was so low that even now - 13 billion years later - we still find ourselves living in a world of relatively low entropy. As a result, many of the objects we surround ourselves with have low entropy: new cars, and perfect unbroken eggs in egg cups. And these objects are basically falling apart around us as they inevitably move to higher entropy states: cars rust, eggs fall on the floor and break. Hence, the increase in entropy in our ordered world is one reason why we detect an apparent "arrow of time".

But change of entropy is fundamentally time-symmetrical!!

However, this is a good time to clear-up a very widely-held misconception about the change of entropy: that change of entropy is in some way fundamentally time-asymmetric, that entropy change behaves fundamentally differently in the forward time direction to the backward time direction. This is absolutely not the case. In the general case, entropy increases in the backward time direction in just the same way as it increases in the forward time direction: change of entropy is symmetrical with time. (However, a very small minority of physicists might still believe change of entropy is time-asymmetric - see my comments at the bottom of this discussion with the notoriously tetchy physicist Luboš Motl here).

The probabilistic basis of the second law of thermodynamics simply says that a system will have many more possible disordered states than ordered states, so a system which changes state randomly will most likely move to a more disordered state. This seems very clear and obvious - such a simple statement is never going to be the cause of something so mysterious as fundamental time-asymmetry. Indeed, this change to a more disordered state is just as applicable in the reverse time direction as in the forward time direction: it's just a change of state, independent of time.

But what about the second law of thermodynamics which states that "entropy increases with time"? This seems to imply a fundamental time-asymmetry to entropy. But we have to realise that the second law only applies to special-case systems: objects with low entropy, the sort of objects we generally encounter in everyday life (rusting cars, etc.). In fact, if we consider general-case objects (i.e., objects in thermal equilibrium), objects which have never been arranged into any sort of order, then their entropy is at a maximum already so their entropy can only decrease with time - completely at odds with the second law!

This generally-held misconception that change of entropy is fundamentally time-asymmetrical is revealed by the Loschmidt paradox. The Loschmidt paradox considers the apparently fundamental time-asymmetry of entropy implied by the second law and states that this is at odds with the known time symmetry of fundamental processes. It is only when we realise that the second law is frequently badly stated and hence contains unstated assumptions (which have been just considered) that the Loschmidt paradox is resolved. (Wikipedia describes this resolution of the paradox, showing how one of the key assumptions of Boltzmann's version of the second law of thermodynamics was flawed - see here).

But if change of entropy is time-symmetric, why do we see the entropy of the universe as only increasing? Roger Penrose considers this question in his book The Road to Reality. Penrose considers what we might expect to happen if we trace the entropy of the universe back in time from the state it is in now. If change of entropy is really time-symmetrical, then we should expect to see entropy increasing as we trace the universe into the past, just as we will see entropy increasing into the future. But we know, in fact, that the universe had a lower entropy in the past: i.e., the entropy of the universe actually reduces in the past. So where does this asymmetry come from?

As Roger Penrose goes on to reveal, the time-asymmetry of change of entropy within the universe is explained by the extraordinarily low entropy of the universe at its origin:

Basically, the low-entropy past of the universe "fixes" the experiment. If we want to get a symmetrical answer then we have to be careful to conduct a symmetrical experiment. Rather than starting with a special-case low entropy universe, we have to imagine a universe which started in thermal equilibrium and has reached its current state unaided, purely by chance:

After that low-entropy point is reached, we then see entropy starting to increase according to the second law. But the key thing is that if we trace the entropy of the universe back in time past the low-entropy point we now see that symmetry that Roger Penrose sought. Hence, change of entropy is fundamentally symmetrical.

In fact, throughout this discussion on the arrow of time we will find that the arrow of time is caused by the time-symmetric second law of thermodynamics, together with the very special, low-entropy initial conditions of the universe.

(This discussion on time-symmetric entropy change is based on an example by J. Richard Gott in his book Time Travel in Einstein's Universe in which the role of the universe is played by an ice cube - see here. The ice cube example is considered in detail in Chapter 6 of Brian Greene's book The Fabric of the Cosmos.)


We all have a very strong feeling of a directionality of time, which has a flow in a forwards direction. As Michael Lockwood says in his book The Labyrinth of Time: "We regard the forward direction in time, in stark contrast to the backward direction, as the direction in which causality is permitted to operate. Causes, we assume, can precede their effects, but cannot follow them."

But we have just seen how physical processes appear to be time-symmetrical, with no distinction between the forward and backward directions. So where does that leave causality? As Michael Lockwood again says about the passage of time: "We find no hint of this in the formalism of Newtonian physics. Not only is there no explicit reference to a passage or flow of time; there is not even any reference to cause and effect. Indeed, there is not even any directionality".

"But", you might protest, "surely causality works in only one direction: forwards in time? I kick a football - the football doesn't kick me." Well, let's consider the example immediately below of forward causality. We see a snooker cue coming in from the left, hitting the white ball, which then causes the white ball to hit the red ball:

However, if you shoot a movie of that sequence, and then play it backwards, it still makes perfect physical sense. As you can see below, we then have the red ball coming in from the right, hitting the white ball, which then causes the white ball to hit the cue backwards. So, because of the symmetry of the laws of physics, this process of causality - which we thought only applied to the forward direction of time - in fact applies equally to the backward direction of time as well:

The reason why we don't see causality happening in the backward direction is purely because of a bias in our psychological systems: something about the complexity of our psychological system (our brains!) causes our thought processes to work only in the forward direction of time (this will be considered below). The great advantage of recording the sequence on a movie and then playing the movie backwards (to reveal the time symmetry of causality) is that a movie camera works in a much more simple fashion than our brains and thus has no such psychological bias in the forward direction: it works in exactly the same way forward as backward.

So if causality is time-symmetrical, we could in fact think of our current situations are being caused by time-reversed future events as much as by past events! For example, as I sit here by my desk in work this morning, I could consider my position as being caused by me being in my apartment this evening, and driving my car from there backward in time, backward down the road the work, to put me in work this morning! It's a bit brain-bending, but it's equally valid as saying "I got up this morning, and drove forwards to work". It seems strange, but that's only because of our psychological bias. The movie of my complete day at work would tell the correct (time-reversible) story.

The Quantum Mechanical Arrow of Time

As has just been explained, almost all known physical principles (from Newtonian mechanics through to Einstein's relativity) have a completely symmetric treatment of past and future. Nowhere in any of these equations is there anything which distinguishes a forward direction of time from a backward direction of time. The exception to this rule appears to be quantum mechanics. On the page on The Quantum Casino it was explained how, when we make a measurement of a quantum observable, there is a "collapse of the wavefunction" in which a probability wave collapses to generate a single observed value from a range of possible values. This process appears to work in the forward time direction only, i.e., it is irreversible.

An explanation for this apparent "collapse of the wavefunction" is presented in detail on the page on Quantum Decoherence, so I don't want to repeat it here. Suffice to say that the coherent phase relationships of the interference terms are destroyed when a particle interacts with the environment. The dissipation of these terms into the wider environment can be interpreted in terms of increasing entropy (again, see the section on "Decoherence and Entropy" on the Quantum Decoherence page for full details). Quantum decoherence can then be understood as a thermodynamic process: after decoherence, the process is said to be thermodynamically irreversible.

Continuing our snooker analogy, the "collapse of the wavefunction" is like a snooker break-off shot. Imagine each ball represents an interference term of the quantum state. Before the shot, (before we make a quantum observation), we see low entropy - everything is nicely ordered. All the interference terms are coherent, and capable of producing interference patterns.
After the shot, the system of balls represents a system with greatly-increased entropy (disorder). This is what happens when we make a quantum observation: interference terms dissipate into the "heat bath" environment, and all coherence is lost in the confused mess. The situation is now one of thermal irreversibility: it is extremely unlikely the original ordered situation could re-form itself. We therefore only see the collapse of the wavefunction operating the forward time direction (for the same reason we don't see broken eggs mending themselves).

So once again the underlying physical principles appear to be time symmetric, with no fundamental preference for either the forward or backward time direction. The apparent arrow of time produced by the "collapse of the wavefunction" is once again shown to be a result of increasing entropy. As Andreas Albrecht explains in his paper Cosmic Inflation and the Arrow of Time (when considering decoherence in the double-slit experiment): "A double-slit electron striking a photographic plate is only a good quantum measurement to the extent that the photographic plate is well constructed, and has a very low probability of re-emitting the electron in the coherent 'double slit' state. Good photographic plates are possible because of the thermodynamic arrow of time: the electron striking the plate puts the internal degrees of freedom of the plate into a higher entropy state, which is essentially impossible to reverse. Furthermore, different electron positions on the plate become entangled with different states of the internal degrees of freedom, so there is essentially no interference between positions of the electron. From this point of view, the quantum mechanical arrow of time is none other than the thermodynamic arrow of time."

Why can't we remember the future?

If physical processes all appear to be time-reversible at a fundamental level, we might ask the question "Why can't we remember the future?" After all, we can remember the past, and physics seems to make no distinction between past, present, and future. So why don't we already have prior knowledge of what is going to happen in the future?

In order to answer this question, we shall consider the reasoning of James Hartle which is based around the radiative arrow of time:

The Radiative Arrow of Time

In his paper The Physics of "Now", James Hartle makes the point that the reason we can't remember the future is because we have not yet received any information about future events. This thinking is based on the idea of a "light cone", the shape of which is defined by the speed of light:

At first glance, this might seem a very straightforward explanation of why we are unable to remember the future: it takes time for a light ray (photons) carrying information to reach us from a distant event. Basically, in the future we will have more information about distant events than we have at present. It is hard to imagine a situation in which light behaves differently - it would appear that light will always take time to travel from a point A to a point B:

This principle - that light will always take time, travelling forwards in time between two points - is called the radiative arrow of time (also known as the electromagnetic arrow of time). But this apparently clear-cut principle is not as clear-cut as it first appears. It turns out that the "world line" of the photon is the same for a photon travelling forwards in time from point A to B as it is for a photon travelling backward in time from point B to point A:

The world line of a photon (position of the photon at any given point in time) is the same for a photon going forwards in time from point A to point B as it is for a photon going backward in time from point B to point A.

In fact, if we temporarily forget about the little arrows on the world lines (which indicate "cause" and "effect") then we see that the world lines of both the forward and backward photons are precisely identical:

With the little arrows removed from the world lines, the paths of the photons going backward and forward in time are shown to be identical.

This principle is clearly illustrated by a Feynman diagram of particle interactions which can be rotated at will, showing particle interactions work exactly the same backward in time as forward in time:

It makes no sense to talk about the entropy of a single photon (entropy is a statistical property of a large group of particles), so a single photon has no arrow of time. However, we do not receive our information about distant events in the form of single photons. Rather, it appears we receive information in the form of light rays which are composed of billions of photons (bosons are quite happy to congregate in the same state, and gather together in a cooperative fashion to create light rays). For this reason, studies of the radiative arrow of time have concentrated on studying the Maxwell electromagnetic field equations which treats light as a field with a wave nature (rather than considering the path of individual particles).

It is often quoted that Maxwell's electromagnetic field equations are time-reversible and so allow for advanced (backward-in-time) waves as well as retarded (forward-in-time) waves. However, in practice it is much easier to produce a retarded wave than an advanced wave, and this reveals the limitations of Maxwell's equations as a full description of the behaviour of light. We need to combine Maxwell's equations with something else in order to derive a radiative arrow of time.

James Hartle attempts to use Maxwell's equations to deduce the radiative arrow of time in Appendix A of his aforementioned paper The Physics of "Now" which is called The Cosmological Origin of Time's Arrow. His approach (based on principles described in H. Dieter Zeh's book The Physical Basis for the Direction of Time) combines the time-symmetric Maxwell's equations with the time-asymmetric boundary conditions of the universe as a whole (he considers the asymmetrical total amount of electromagnetic radiation). The approach suggests that because there were no free electromagnetic fields at the start of the universe, but there are fields in the future, those fields must all be caused by retarded waves that have their sources in the past. However, I don't see how the radiative arrow of time can depend on the total of electromagnetic fields in the universe in this way. There's no equivalent of the second law of thermodynamics (increasing entropy) for electromagnetic fields. The total of electromagnetic field in an isolated system does not tend to increase (as is the case with entropy). The radiative arrow of time must surely depend on the increasing sum total of entropy in the universe, not the total of electromagnetic field. Surely the radiative arrow of time must have the same cause as the thermodynamic arrow of time.

At the beginning of the last century, Walter Ritz proposed that only retarded (forward-in-time) waves were physically possible (i.e., the process was fundamentally time-asymmetric). In 1908 and 1909 he had a famous argument with Einstein over this matter, as Einstein believed the process was fundamentally symmetric and could be explained by thermodynamic arguments (see here). It turns out that it is easier to create a light ray in the forward time direction as the behaviour of the billions of photons as they are produced (by an ordered source such as a light bulb) and scattered (when they reach a target) can be understood in turns of increasing entropy: "This arrow has been reversed in carefully-worked experiments which have created convergent waves, so this arrow probably follows from the thermodynamic arrow in that meeting the conditions to produce a convergent wave requires more order than the conditions for a radiative wave. Put differently, the probability for initial conditions that produce a convergent wave is much lower than the probability for initial conditions that produce a radiative wave. In fact, normally a radiative wave increases entropy, while a convergent wave decreases it." (see the Wikipedia article on the Arrow of Time). Hence, the reason we do not see convergent, advanced waves can be explained in terms of entropy.

When I turn on an electric light, for example, the photons leave the bulb in a relatively ordered form. The photons then radiate away from the bulb, redistributing themselves around the room (i.e., a radiative wave), creating a state of greater disorder - increased entropy. As Andreas Albrecht explains in his paper Cosmic Inflation and the Arrow of Time: "The complete absence of the time-reverse of radiation absorption is understood to be one feature of the thermodynamic arrow of time in our world. A hillside absorbing an evening news broadcast is entering a higher entropy state, and the entropy would have to decrease for any of the troublesome time-reversed cases to take place. So in the end, the radiation arrow of time is none other than the thermodynamic arrow of time."

Could it be possible to remember the future?

If we consider the hypothetical situation in which we have found a way to circumvent the limitations imposed by the radiative arrow of time, it is interesting to ask if it could ever be possible to remember the future. And, if so, what would our "memories" by like?

In this respect, the Scottish philosopher Donald Mackay suggested an interesting "thought experiment". Mackay wondered if it could ever be possible to predict how someone will behave in the future, and, if so, what would be the consequences for human free will. If we had complete knowledge of the current state of a person's brain, would we be able to accurately predict a person's actions in the short-term future? Basically, if we are able to predict how a person will behave - and the decisions they will make - in the future then human free will is shown to be a fallacy, an illusion.

However, Mackay suggested that it would be impossible to predict a person's future decisions if that predicted future was made known to the person. This is because the person could then choose to act in a different way from how you have told him he will behave. This is described by John D. Barrow in his book Impossibility: "Consider a person who is asked to choose between soup or salad for lunch. If we introduce a brain scientist who not only knows the complete state of this person's brain, but that of the entire universe as well at present, we could ask whether this scientist can infallibly announce what the choice of lunch will be. The answer is 'No'. The subject can always be stubborn, and adopt a strategy that says 'If you say that I will choose soup, then I will choose salad, and vice versa'. Under these conditions it is logically impossible for the scientist to predict infallibly what the person will choose if the scientist makes his prediction known."

So if a person gains access to knowledge about his future behaviour, it would appear that it becomes impossible to predict that future. But this knowledge about future behaviour is precisely what a person will gain if he is able to remember the future. So if a person is able to remember the future, he could then choose to act in a different way to how his memory of the future tells him he will act! There would appear to be a logical inconsistency here: if a person is able to remember the future, then those memories of the future instantly become unreliable. Therefore, it would appear to be impossible to "remember the future".

As an example, here's how Dilbert might behave if he could remember the future:

This logical inconsistency prohibiting you from remembering the future (based on Mackay's reasoning) arises because the following two statements cannot both be true:

  1. You can receive - or "remember" - information about events in the future.
  2. It is possible to change future events.

However, it might be possible to remember the future (the first of those two statements being true) if the second statement is, in fact, false. Indeed, if all of spacetime is laid-out as an unchanging four-dimensional "block universe" then the future is just as "set in stone" as the past.

Block Time

For more information about this, see this excellent Scientific American article by Paul Davies, or see the Time and the Block Universe page.

So now let's proceed on the basis that it is not possible to change future events - a scenario which contains no logical inconsistencies and thus allows us (at least in theory) to "remember the future". We can then ask what form these "memories of the future" might take.

In our everyday experience, our memories of the past seem set in stone, but we have no recollection of the future. It is this distinction, this lack of recollection of the future, that gives us the impression that the past is set in stone, but future events can be altered.

In our everyday experience, we can remember the past (memories which appear fixed - like photos in frames), but not the future. So it appears possible that future events can be altered.
The fact that we can remember the past - yet have no recollection of the future - is the reason why we feel the "flow" of time: we get a false impression that the "unreal" future has become the "real" past.
However, in a block universe the future is just as set in stone as the past, and our memories of the future would take exactly the same nature as our memories of the past: an unchanging future, set in stone.
If we were able to remember the future, we would find our memories of the future are also unalterable, just like our memories of the past.

Surprisingly, though, the idea that events are "fixed-in-time" and cannot be altered does not rule out the existence of "free will" (as some have suggested). When we think back to our past, we view those events as fixed and unalterable. However, we also remember moments in that fixed past when we made decisions, i.e., expressed our "free will". If we were able to remember our future then we would similarly remember future events when we make decisions, i.e., express our free will in the future. So the concept of a fixed block universe does not rule out the existence of free will. For more on this, see the section "Free Will in a Block Universe" on the Time and the Block Universe page.

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Comments are now closed on this page.

Somehow it seems that we should be able to "remember the future" as an act of out will, or choice in the present. I see remembering the future as imagining it. The whole "secret" thing or law of attraction. What do I want to "be my life?", experiencing what I want by "remembering" it. Somehow imagination and memory seem intertwined. I just tend to believe that freewill and the future already existing could be compatible. As a Christian, I believe that God already knows the future, therefore knows everything we will do in our lifetimes. For us to visualize a desire as actual, could that be using our memory in reverse? I don't know if you can make any sense of this, but maybe it will stimulate your thinking. I would be curious to hear your response. I guess I'll have to revisit this sight to see if anyone has commented. - Francine, 17th February 2008
Hi Francine, thanks for your comment. Donald Mackay (who I mentioned in the text) was also a Christian and proposed his theory to prove that there was such a thing as free will. Basically, as I described above, Mackay suggested that it would be impossible to predict a person's future decisions if that predicted future was made known to the person. However, as I described, I think there's a flaw in Mackay's argument in that he assumes it might be possible to alter future events - something perhaps not possible in a block universe. This is covered very well in John D. Barrow's book "Impossibility" which I can recommend to you.

Here's another extract from "Impossibility" which you might find interesting: "Is it possible to pray for the past to be changed? Few Christian theologians would support this idea if the past was known to the person praying; but what if an event has occured about which the outcome is still unknown to you? Or what about an outcome, like an examination result, that has already been decided, but which has yet to be announced? In his book on miracles, C.S. Lewis, an influential popular writer on theological questions, sided with the idea tha it was rational to pray for events whose outcome had already been decided, because from a God's-eye perspective your future intercession could be an ingredient in the global events which may affect the outcome of the event being prayed for. Lewis was adopting what physicists call the 'block universe' picture of spacetime, in which the entire spacetime alread exists as a complete entity. He conceived of the whole of space and time as viewed externally by God, and so all prayers were known by God before they were made. This would permit free will to be retained together with a doctrine of God's omniscience. God's foreknowledge does not predestine our actions. Rather it is our actions that determine God's foreknowledge. We introduce these interesting theological questions to show that the questions of changing the past and making sense of the resulting coherence of the universe are not questions that lie solely in the realm of physics." - Andrew Thomas, 17th February 2008
This is a brilliant article- mind boggling
I definately believe that by praying we can ask God to change the past if that result is unkown to us. But am confused as to why this would only be possible if we dont know the outcome.
Any thoughts ?

Dr Walia - hardeep walia, 18th February 2008
Hardeep, the question of "why this would only be possible if we dont know the outcome" - I can see a kind of logic behind this conclusion in that if we knew the outcome already, and then that outcome changed, we would have an inconsistency in the system: an event which both occurred and didn't occur. At least if we didn't know the outcome then we wouldn't have that logical inconsistency in our heads. But could it be said that the other outcome happened, even though we were not aware of it? Basically, if we are not aware of the event, does it actually happen, does it have reality? That then introduces ideas of the observer somehow "creating reality" by their observation - ideas from quantum mechanics. Yeah, "mind-boggling", as you say! - Andrew Thomas, 18th February 2008
Thanks for the great insight and many questions and paradoxes raised here. I am not a very bright fellow, but I have always had the strange sense that all of history which includes my memories are being constantly rewritten so to speak. Our memory of time, space and reality could be changing constantly at the quantum level. What seems like fixed and solid memories may really have changed many times over in the past few seconds. It would explain a lot of things if this is the case. Parallel universes could be constantly forming and collapsing all the time. We may be praying for things that we think are future but are really neither past or future, but from God's perspective there is no "Arrow of Time."---just the eternal now.The cause and effect of all things could be operating completely outside our concept of time moving forward. It would explain Jesus comment,"With God all things are possible!" - Rodney <>, 29th April 2008
Nice comment Rodney - Michael, 2nd May 2008
I've been listening to CDs of Vishal Mangalwadi's 2007 lectures at the U of Minnessota: "Must The Sun Set On The West". He says that God is outside of the universe he created, so he is not bound by the logic, for instance, or time, space, and energy, as we know it. That's why we need to "see what is there" rather than figuring it out in our minds, and why we cannot "know" the future unless he tells us. - Addamstaft, 9th June 2008
About Temporal Communication. I believe this may be how I have seen the future before.

I know, crazy.. right? Well I have an IQ of 130, have not been abducted by aliens, and am not considered weird by my fellow man..haha

I had a dream that I hit my bosses truck with my car on the driver side back. Then I woke up and in the morning and my bosses son told me he hit my car with my bosses truck in the drivers side back. The damage looked just like the dream. It is statistically impossible that this was a coincidence--especially because I have had this type of thing about 6 times on big stuff and hundreds of times on small stuff. (it was reversed but that happens in dreams). It was so astonishing I didnt even get mad my car was hit.

I theorized that I was actually in touch with the John of my future. Up until now I have ever heard anyone mention that this is how the future is seen by some people in some cases. Its like I pick up stray thoughts from the future me every now and then.

Another time a friend told me someone robbed his house. I went home and I thought real hard for a minute to intentionally "see" who did it. The name I came up with was a person who was never known as a thief and I hadnt seen him in maybe a year. I didnt say anything.

Well, 2 weeks later my friend told me that guy did it. I turned white. I dont think I saw him rob the house--I recalled the future conversation of being told he did it. I dont actually know if he did it... I just know he thinks the guy did it.

The other possibility is God allows us to know things. As a christian I know he can do this--I just dont know if thats the case here.

Either way--it proves the future already exists. There simply is no other explanation. I know its easy for people who havnt had these experiences to say Im misreading this--but I'm perceptive enough to know its real.

The real question you ask is could I have changed the future? Well, the missing component in people's search for the answer is God. If there is someone Outside Time who is in control --all the problems go away. In other word--if we do see the future..we see it for a reason. So whether we see it to confirm there is a God--or to prevent us from flipping out when something bad happens--or to actually prevent something for some unknown purpose...its up to God who knows all possible outcomes.

Anyway..very cool website my friend. - John R, 5th July 2008
That's a coincidence, because I had a dream last week about perfect surfing waves outside my flat (I'm a keen surfer, and we hardly ever get perfect waves here). And the next evening we had perfect waves just like in my dream! It really was a bit weird. I do suspect dreams tap into the enormous potential of the unconscious human mind in a way which we don't yet understand. Your experiences seem to bear that out. - Andrew Thomas, 5th July 2008
Without bringing religion into it, every scientist should know about the very strong evidence that already exists for precognition, in dreams or otherwise, including many carefully controlled experiments. See for example Dean Radin's books "Entangled Minds" and "Conscious Universe" (both with many good references) or any of several peer-reviewed journals such as the Journal of the Parapsychological Assn, and the Journal of the American Society for Psychical Research. We *can* indeed "remember the future", but it is difficult exactly because of the increasing entropy argument given above. - Richard Shoup, 15th September 2008
Thanks very much for those references, Richard. - Andrew Thomas, 15th September 2008
Very interesting page … so we could have the basis to explain “Déjà vu” as well as “Human Intuition” : both phenomena could be interpreted as a malfunctioning (maybe intentionally left) in the process which prevents us to remember the future. - Gabriel, 29th September 2008
That's a good point, Gabriel. Yes, I suppose déjà vu could be thought of as "remembering the future" as you feel that your current situation is already in your memory. This implies that there was a point in the past when you could have "remembered the future". - Andrew Thomas, 29th September 2008
some times i see the future, i notice the the people have no meaning to me becaus i dont no them yet. iv seen places befor i got there and coversations befor thay happend usualy about 6 monthes befor thay happen but some times longer. like i sed thay dont stay with me becaus i haven atatched any importance to them yet. but thats why i read theas time articals becaus to me theres mort to it than a one directonal time if there is time at all. i belive in free will but i think there are serten steps we will all take along the way in life no matter what road we take. - DAN HILL, 2nd October 2008
For me the whole thing turns around WHY I have never seen an egg repair itself. If time can be considered symmetrical then such things should (on occasions) be observed. Similarly there would be conditions under which the oxygen could leave a rusty car and so that bright metal would re-appear. I could make a long list of such effects, none of which has EVER been seen to reverse, so where is the evidence that anything like that is even possible ? And if there is not or cannot be experimental evidence then sorry mate but the most that one could call the whole thing is a Conjecture, an interesting idea that may or may not represent the real world, but which cannot be taken as fact until it is verified. - mike, 3rd October 2008
Well, Mike, once I remember seeing a snooker break-off shot on television and when the balls came to rest they had gone back to precisely their original positions in a triangular shape. So it does happen sometimes. Yeah, we don't see it often - but that's the point: these "time-reversal" events are so unlikely that they basically **never** occur, which is why we only see an arrow of time in the **forward** time direction. - Andrew Thomas, 3rd October 2008
The very idea of entropy is misleading and contradictory. Thermal equilibrium is, itself, an ordered state. Though the reactions leading up to it may seem random and chaotic, to label them as such is to ignore the very result of what we call entropy: "the system will reach a state when all its molecules are completely randomly orientated." In essence, it reaches a state in which it becomes transfixed. To say each molecule is randomly orientated is to ignore the principle that "entropy is a statistical property of a large group of particles", and if all molecules are completely randomly orientated, then they are "adjusted or located in relation to surroundings or circumstances," or "having a specific orientation". If the definitively larger group of molecules has reached a fixed system in which all independent contributing particles are equally randomly active, then the theory of entropy states this system must break down. In essence, if the system is structured in any way, that structure must naturally seek the most random path away from its systematic order. Thus, if every particle is alone in randomness, then they will randomly aggregate. From that point, we witness what phenomenal things happen from the simple collection of space dust over periods of hundreds of millions of years. Eventually, and on a grand enough scale, (say, one the size of the unknown universe,) the sheer weight of possibilities, ad infinitum, dictates an environment of ever-increasing entropy that destroys its structure, all the while creating structure to destroy the potential system of complete molecular randomization. To behave in any other way is to defy the basic principle upon which entropy is defined. - Chad Parsons, 4th October 2008
Chad, I've read what you said a couple of times - not sure I completely understand it - but it is true that gravitational entropy seems to work in the opposite way to normal entropy (is that what you're saying?). I will quote Roger Penrose from his book "The Road to Reality": "Gravitation is somewhat confusing, in relation to entropy, because of its universally attractive nature. We are used to thinking about entropy in terms of an ordinary gas, where having the gas concentrated in small regions represents low entropy, and where in the the high entropy state of thermal equilibrium the gas is spread uniformly. But with gravity, things tend to be the other way about. A uniformly spread system of gravitating bodies would represent relatively *low* entropy, whereas *high* entropy is achieved when the gravitating bodies clump together". See - Andrew Thomas, 4th October 2008
No gods no masters only the start of the ends of our lives. The arrow of time is a trans-way to the end of eternity and all inside its abyss. - Eternal darkness, 5th October 2008
This is really neat because I have formulas for all this stuff in my head from meditation. I would agree that as a transdimensional circuits we can experience our future. You must be tuned or have already been switched on to break certain barriers but everyone is connected in this way. On the physical level this is the highest point we can achieve. With practice understanding the process of the arrow of time and other ideas you can at least ferry the seas of the fifth dimension and potentially open a space through the sixth to gain access to the seventh and leave all this to its extent. - Mu, 5th October 2008
A key to how much we misunderstand time is related to our perception of time. In a conscious state, we experience time a certain way but in a sub conscious state, time is very different. How is it that when you dream, while in REM sleep, the elapsed time may be 10-15 minutes, but you may remember in great detail events that would take hours or days of elapsed time in the conscious state to occur? This is a great mystery of time. It is possible that in each second of time, there is greater time available to us but because of our biased perceptions, we are unable to account for time except in the limited way we are taught. Remove the clocks and watches that society has put all around us, forcing us to regard time in a set pattern. Your experience of time will change dramatically if you allow your sub conscious to not be influenced by your conscious, which is too much influenced by "standard time". There is more to time than we are experiencing. You have only to dream to prove this out. This is my theory. - Kimberly Hunter, 5th October 2008
Just because the future and the past can be determined doesn't mean we don't have free will.
Of course we don't have free will beyond our physical bodies and born personalities. That's obvious.
There are a few factors we can't control that we are born with such as our levels of intelligence.
Free will exists beyond those factors. We have to come to terms with that fact in order not to go crazy.
Our consciousness is the bit of magic that separates time and slows it down so we can understand what is going on.
Think of a fly. It only has a 24-hour lifespan. Perhaps the fly, whose reflexes are extremely quick, experiences time very differently, so his life might seem to him like an entire year.
This is an interesting way to look at time, and I'd like to see a study on it. - Donald, 5th October 2008
The Only Reason For Time Is So That Everything Doesn't Happen At Once. - Baker, 6th October 2008
Good article, but all this is just theory, and theory in practice is completely different. The teachings of Kant/Schopenhauer makes far more sense. Time, space and causality are just pre-conditions of knowledge i.e.,these are necessary for the individual to acquire knowledge, so they are innate properties of the human brain. This is an unchanchable condition, considering that the human being must keep his brain all the time. If we have another brain, with different structure, then, maybe, we could dispense with time, space, and the laws of causality - the world would be quite different from what we see now. So the past is no more and the future is not yet. This leaves us with the present which is also flowing according with the a priori fuctions of the brain above mentioned. Now, as for the law of causality, Schopenhauer says "Therefore, in the whole course of the world, a mote in a sunbeam could never describe any line in its flight other than the one is has described, nor could a man ever act in any way different, from that in which he has acted. No truth is more certain than this, namely that all that happens, be it great or small, happens with complete necessity. Consequently, at every moment of time the whole state or condition of all things is firmly and accurately determined by the state or condition that has just preceded it; and so it is with the stream of time back to infinity and on to infinity...For the chain of causality with its universal strictness - than brazen bond of necessity and fate - produces every phenomenon irrevocably and unalterably, just as it is...."

And more, time, as a precondition of the brain to acquire knowledge, also means that time travel is impossble, as time does not exist in itself, only in our brains.

All this is very interesting, and I guess we can grant what you said with a scientific status of a theory, which means, a full possibility of falsifiability, refutability and testability (Popper).


R.Dias - R. Dias, 7th October 2008
hesitate to write. I am neither a scholar nor a learned person, as you can tell from this letter. I have wanted to tell something that I do know to be true. Maybe you have an answer for it, if so please be so kind as to tell me. Or at least for a lark, take my word for this and try and find a formula for it. Ok here goes. You guys are wrong when you state the question and answer to “So why don't we already have prior knowledge of what is going to happen in the future?” The thing is that we do. Not in seeing with our physical eyes, but with what ever makes up our thoughts. Our dreams? Is that energy? If so Energy can travel forward easily. Please do not just dismiss this because of my lack off knowledge on the rest of this subject. You guys are looking in the wrong place. I am a normal Grandmother 58 in Kansas, I do not lie. I have had dreams of the future, my whole life. Not of my personal future but the happening of things going on around the planet. You maybe talking about physical happenings, items that we see in the future, like eggs breaking. I am telling you that if you would just think of energy or what ever makes up the human mine and thoughts when it dreams you could have a clue. You can say this does not happen , no not to every one as much as I, but I see the future when it comes to tragic, emotional things that happen out side my own small world in Kansas. Energy or thoughts of the mind moving forward bring back information that then happens day or months or even years later. Not vague things that could just happen to anyone but detailed events that there is no mistaking. Try adding that to your formulas…I am sure you have heard of others that say they can do this also. Just because it might not happen to you does not mean it is not true. Ok now you can laugh at me and my total lack of understanding, but you might be so kind as to tell me if this has been considered? Linda Katz - Linda Katz, 8th October 2008
Hi Linda. No one is dismissing anyone's ideas here. I think the human subconcious is a very powerful thing and can pick up on little signals without us being consciously aware of it (for example, picking up on other people's small facial emotions), and can effectively "predict the future" on the basis of conclusions made at the subconcious level. And these can then emerge in our dreams, when our subconcious takes control. Don't they say that 90% of our brain's processing power is in the subconcious? I see Richard Shoup has published some references on this topic in his comment above. - Andrew Thomas, 8th October 2008

I'm not sure I have a complete understanding of all of the inherant principles of this article, but here goes.

I belive that future memory is one's own ability to imagine possible occurences and judge cause and effect. It seems to me that we are aware of the future's potential, and are thus able to choose what consequences we desire before taking action. Future memory is something as yet unset, a priori. We make decisions based on our past observances and the resultant refinement of our sense of causality. As we change over time we gain some sort of momentum through our possible paths; some decisions more likely as they are repeatedly made. If one is made aware of their direction (as Dilbert questioning his breakfast), they are more likely to take an alternate path. Similar to a object traveling in one direction until bumping another. Ones life and circumstances make for the general direction that one will lead through their possible futures, but ones own free will judges how you traverse time. The past is set, like a snake following behind you, while the future is open.

I don't want to use the remaining 1799 characters, but I feel that I will get a poor grade if I do not... - James, 10th October 2008
Andrew, I do so appreciate the reply. I do understand the comment on how the human subconscious could pick up on little signals without me being consciously aware of it. I totally get that. Here is the thing though; I am not talking about any events that happen to me. I am talking about dreaming about the latest train wreck that was split length wise. My husband did not see how a train could possibly be cut lengthwise when I told him of my dream a few months ago. He knew from experience that it would happen some how. It happened three month later. Also the dream I had of the stair step little girls {only girls} in old fashion dresses being shot to death. That happens in three days later. {The Amish} Then of course 911 , the Oklahoma bombing, three senators dyeing in plan crashes in the space of one month, the Hyatt Regency walkway collapse, the plane downed when its wing touches the ground, also seeing the terrified sturdiest inside the plane in her uniform, deaths of people I know but have not seen in years. I had a dream three nights in a row about a women getting shot in the head at our annual gun show. The show has been going on for years with never a problem. Sure enough the woman was killed by accident from a loaded gun. I dream of fires in my home town before they happen. I dreamt of a certain slot machine in Harrah's that I am going to win big on. I find it {by an inside restaurant} and win over 10,000 dollars. I had never been to Harrah's before. My first dream that I can remember that came true was when I was 7 years old. In my 30's this gift or what ever scarred me to death. There was no internet at that time, and just a small town Kansas library in which to find information. My mom help me a lot she thought it was a wonderful gift. What I hate is that I can see the accidents, the faces, but I have no information where it is going to happen even though it is sometime just a few days from happening. I have a life of amazing coincident, things unbelievable. I have touched my girl friends hand and knew where her lost dog was, by a little movie of my own playing in side my head at the moment of touch. I have dreamt that there was going to be an electrocution of a child at the carnival that was coming to town later in the week. Four days later out local newspaper headlines, ‘Child electrocuted carnival' Thank God she survived after hospital admittance. I cannot call up some paranormal experience when I want to. It has to happen on its own time. I am telling you this because if you would just try and formulate some of your ideas using the idea, that you're subconscious can travel in to the future. With all you smart people out there you could change the equation that ties certain things together. I am not talking about the "General Theory of Everything" I know that the current idea that you can not see the future is wrong. My whole life has been on long unusual paranormal event. I don't see dead people that is not my gift. I dream things that will happen in the future. Things I have no way of preventing. Some gift? I could tell you hundreds of things but my point is, I am not reading faces or headlines. I believe if some one would actually say ok, I believe the future can be seen in dreams energy or thoughts and they can travel forward in time it might help formulate a new theory. I do realize this in not the topic you are talking about on this page. It is the closest subject I could find that this might fit into. Thanks for reading this, these are just a few samples of things dreamt over the years. Thanks again for being so kind as to answer me. Linda

- Linda Katz, 10th October 2008
Hi Linda, that was a fascinating post, thanks. Maybe Hollywood could make a film about you? However, I must warn you you will have serious trouble getting a scientist to take you at all seriously.

Before we start imagining any paranormal activity, I think we have to eliminate any possible normal explanations. Something which is very clear is that you seem to get regular dreams about disasters. So, if that's the case, then whenever ANY disaster happens you will be able to say "Oh, I had a dream about a disaster". You see? You must get plenty of dreams about disasters which NEVER come true. When that happens, does that make you doubt your ability? Or do you only selectively remember when your dreams come true?

But it was a fascinating post. - Andrew Thomas, 10th October 2008
I have read that the as entropy increases, so do the amount of correlations, so that the total Shannon information remains constant. This was the (rather hand-wavy) argument for how we only remember the past - that our brains are essentially evolving new patterns to correlate more closely with the external world (as we learn), so our perceptual arrow of time is in the same direction as the thermodynamic one. That is, we can only know new things as entropy increases. I wonder what you think of that argument?

Regardless, if we make a few assumptions;

1, the perceptual arrow is equivalent to the thermodynamic arrow

2, the number of possible states of the system increases as the universe expands

and if we consider a kind of overall "wavefunction" for the universe which is "determined" by its boundary conditions - it seems to me that the expansion of the universe is the only possibility. In other words, we can only ever perceive the universe as expanding, as the thermodynamic arrow (and hence our perceptual arrow) will only ever point from small universe to large universe.

If we were living in a contracting universe, entropy would be decreasing, but correlations would also be decreasing, and we would be remembering the future - i.e. a contracting universe would look like it was expanding to us. Indeed, the concept of expansion/ contraction is an illusory one which only arises, as you put it, due to our psychology.

Well, that's my theory anyway - I'd like to hear what you think. - John C, 11th October 2008
Well, John C, I think you make an interesting point about information not being lost when we take particle correlations into account. Yes, the **positions** of the particles becomes more disordered, but once we consider the particle "correlations" (essentially, the particle **velocities**) then we are always capable of winding things backwards to find out how they **used** to be. So no information is actually lost once we consider particle velocities as well as positions. I'd be very interested to know where you read that, please.

The next point you make about the expanding universe is pretty much the point I make in the main article: the initial conditions of the universe determine the arrows of time. And, yes, the perceptual arrow of time is one of those arrows. Basically, human evolution is lined-up with the arrow of time of the whole universe, and so our journey from birth to death (and the increase of our knowledge, and memories) also lines-up with that cosmic arrow of time, on the basis of the initial conditions of the universe. So, yes, I'd say you were correct on all counts.

But I'm not convinced that what you propose is particularly novel - to my mind it just seems a rephrasing of the principles in the main text. Thanks, though. Nice comment. - Andrew Thomas, 11th October 2008
Good article, by the way! Forgot to say that in my post.

Where I found the argument about correlations in the brain was just on wikipedia:

near the bottom of the section. Also:

The reason I thought my theory (that we could only ever perceive an expanding universe) might have been novel is that whenever I have read about the arrow of time, it seems that most cosmologists believe that entropy would still increase in a contracting universe. So, if we were living in a closed universe where it expands, stops then begins to contract, entropy would continue to increase throughout, and we would be able to observe it contracting (like your entropy graphs above).

My thought was that the entropic arrow might be absolutely determined by universal expansion. I have no idea if there is any evidence for that!

As an aside, what are your thoughts on the universe having a conservation of information law, and perhaps a constant total information (perhaps just for the observable universe)? Certainly, it seems that there's some agreement now that black holes do not destroy information. It might be interesting to speculate on what a future universe might be like, with higher entropy but also higher correlations between its components.

Apologies if you've addressed that elsewhere on the site, I just came across this page via Stumble, but will be exploring the other articles when I get the chance! - John C, 11th October 2008
Hi John, thanks very much for those useful links. I think my description of why information is not lost was quite accurate.

After having a think about it, I now find your suggestion about the perceptual arrow of time, and how we could only ever perceive an expanding universe to be quite intriguing. I think it actually strikes at the very heart of the question of whether we are living in an expanding or contracting universe right now! After all, with "nothing outside the universe", i.e., no external time reference axes, there is no absolute directional reference axis for time for you to say "the universe is expanding" rather than "the universe is contracting" - one is obviously just the reverse of the other, and with no external time reference axis how could you possibly prefer one statement over the other?

All you could ever say would be to refer to your psychological arrow of time, and to treat that as your "forward time reference". But that psychological arrow of time is always going to align itself from a low entropy universe state to a high entropy universe state. So it's not really satisfactory to define the forward time direction on that basis because you are then always going to be defining the forward time direction as the direction in which entropy increases. It means our current justification for saying "The universe is expanding" is based on nothing more than saying "a larger universe has a larger entropy, a smaller universe has a smaller entropy". Any universe which satisifies that statement could be said to be "expanding". But there's nothing in that statement which describes the change in the size of the universe with respect to any external "time axis". So that seems a very unsatisfactory description of any "expanding universe" to my mind. I don't see how we can possibly say we live in an expanding universe on that basis.

So you can't ever really say "The universe is expanding" rather than "The universe is contracting". It's just not valid to make that distinction, because you would be implicitly using the psychological arrow of time to provide your forward time direction, and that arrow of time is intimately related to the expansion of the universe in an incestuous manner which results in a circular definition. I think you reveal the absurdity of that situation when you realise that if the universe operates in such a way that a larger universe always has a larger entropy then we would always perceive the universe as expanding! There could be no such thing as a contracting universe!

Great comment - well done! - Andrew Thomas, 11th October 2008
Andrew - yes, that's exactly the point I was trying to get across; thanks for elucidating it a lot better than I did! In this case, our psychological view of time can make us ask ill-posed questions without realising (such as "is the universe expanding or contracting?", which doesn't really make sense in a block universe way of thinking). I suspect there are many similar such questions floating around, mostly of a philosophical bent (e.g. the old favourite question of free will), that give people headaches trying to resolve!

Been reading your page on the mathematical universe - fascinating stuff. And the comments! Look forward to reading your "information" page in the future. - John Cruickshank, 12th October 2008
I'd like to make the following objections to John Cruickshank's previous comment: Is it meaningful to talk of an "expanding universe"?

1. Even in a contracting universe the entropy is increasing!
2. An "internal" time or time arrow can be defined: the cosmic time (e.g. in the FRW metric)
3. Cosmic time does not reverse sign when the cosmic scale factor a(t) begins to decrease in the contracting phase
4. The psychological arrow of time depends on the entropy arrow but not on the cosmological arrow which is considered autonomous resp. fundamental.

So I conclude that it is meaningful to speak of an expanding (or contracting) universe. - Rene, 13th October 2008
Hi Rene, no, sorry, I can't agree. "Cosmic time" is an invention of humans - we define it as time since the Big Bang in the "forward" time direction. But WE decide what is the forward time direction - there is no great big clock in the universe which tells us cosmic time. We decide to align cosmic time with our psychological arrow of time.

And this ties in with the alignment of the "cosmological arrow of time". Yes, as you say, the cosmological arrow of time is DEFINED (by humans) to align itself with the expansion of the universe since the Big Bang. Wikipedia explains it well "if this arrow of time is related to the other arrows of time, then the future is BY DEFINITION the direction towards which the universe becomes bigger. Thus, the universe expands - rather than shrinks - by definition." That's the key words there - "by definition" - that's humans who have provided the definition of the direction. They could have *defined* the cosmological arrow to go in the opposite direction - back towards the Big Bang - but they chose to define it in the same direction as the psychological arrow of time (because it seemed more sensible, I guess). But again, it has all come back to the direction of the psychological arrow of time being the key factor.

Thanks very much for your excellent comment. I have wondered about this question myself several times before. - Andrew Thomas, 13th October 2008
This site is wonderful. As a retired engineer, I have been reading the pages in the order you have posted them and have learned a great deal. Thank you.

I am also confused by John Cruickshank's comment that it is not meaningful to talk about an expanding universe. Maybe you can help me understand.

Certainly I "sense" time, but I do not sense the expansion of the universe. My psychological view of time seems to be a phenomenon controlled by the electrochemical behavior of my neurons, but universal expansion is caused by gravitational and, perhaps, dark energy forces, i.e. they're like apples and oranges.

The reason I say "the universe is expanding" is the well known red shift in the spectral lines from distant galaxies. If the universe contains enough mass-energy, this expansion will reverse. Intelligent beings in the distant future may observe a blue shift and say "the universe is contracting" (probably not in English). As Rene pointed out above, even in a contracting universe the entropy is increasing, i.e. these future beings will have to deal with rust and splatter. So, it seems to me and contrary to your and John Cruickshank's reasoning, these future beings will be living in a smaller universe with larger entropy.

I know that most recent experimental data indicate that the expansion will continue at an accelerating rate. However, it wasn't that long ago that many scientists felt contraction was a possibility. Regardless, I do not see how gravitational effects that indirectly cause the spectral shift would also alter the thermodynamic arrow of time. I read that Einstein was surprised to learn about the red shift because it indicated that the cosmological constant in general relativity may have been a mere fudge factor; I doubt he would have found a blue shift any more or less surprising. - Tom Hoffman, 14th October 2008
Hi Tom, thanks for that. I actually agree with every single thing you say. However, I was making a more fundamental point about what we actually mean when we say "The universe is expanding".

Yes, if the universe starts contracting then we would see it as contracting, which is basically the point of your posting. I absolutely agree on all of that.

John Cruickshank and myself were just making a more fundamental point about how we have to be careful when we making statements such as "the universe is expanding" which appear intuitively correct, but in fact place far too much emphasis on our psychological feeling.

I actually think you hit the nail on the head when you say that the expansion of the universe (due to dark energy, or whatever) and the psychological arrow of time are two ENTIRELY different things. So we are saying something about the behaviour of the universe ("it is expanding") on the basis of something totally unrelated to that - our "feeling" about it. Now to me that sounds like a very dubious approach - describing the behaviour of stars and galaxies on the basis of the behaviour of the neurons in my head. For example, if one day they produce a drug you can take which reverses your feeling about the psychological arrow of time, would that mean the universe starts contracting?! Of course not, but that's how it would feel to you, and by your definition, the universe actually IS CONTRACTING if that happens! So that reveals what a dubious definition it was in the first place. Taking a drug should never result in the expansion of the universe going into reverse!

So the only conclusion John and I came to is that you really shouldn't talk glibly about the expansion of the universe, by simply saying "the universe is expanding". It would be better to say something like "according to my personal definition of the forward direction of the arrow of time, the universe is expanding."

You might feel this is pedantic, but if we are really going to learn about the **fundamentals** of the universe then we have to be careful to leave all human baggage, and all human sensation, at the door.

Thanks a lot, Tom. - Andrew Thomas, 14th October 2008
Well that was futile. "Before we start imagining any paranormal activity". That's a Good one. I have kept a dream journal on and off for years. I do not dream of disasters on a regular basis. I am a voracious dreamer. I have the usual nonsense dream that every one does , about the their day, their life etc. A small explanation. The dreams I have, that then come true;
I have in the morning, in the first few moment when a person can still remember their dream before they fade from memory. With me , after remembering the dream , a totally different thought , unrelated to any previous thought pattern comes briefly into my mind . I then see a event in the future , that is going to happen. So I am awake for a few seconds after my dream, let's say, I am dreaming about horses. Then with no related thought what so ever , the event or disaster plays in my mind. I then know it will come true in a few day or months, Usually days. I tell my family and we wait for it to happen. When you say "I must warn you , you will have serious trouble getting a scientist to take you at all seriously."
Well no kidding , isn't that what your doing, isn't that what scientist do? Until finally someone brilliant goes beyond the accepted reality and makes a discovery. Try stepping out of the accepted Paradigm bias . Linda Katz So long - Linda Katz, 16th October 2008
Sorry, Linda, I didn't mean to insult you. I thought my questions were valid. From what you wrote, you appeared to have a succesion of dreams about disasters over a short time scale. Now, I don't think I can ever remember having a single dream about a disaster. So you do seem to have an unusual amount of those sort of dreams.

You said "I then know it will come true in a few day or months, Usually days." Sorry, Linda, but that's not totally convincing: if you have a dream about a plane crash then surely it's highly likely there's going to be a plane crash within a few months.

But I think I have an answer ...

If you could use your ability to make a **specific** prediction, ANY specific prediction whatsoever (for example, there will be a major plane crash in the US **tomorrow**) and it turned out to be accurate then the scientific community would be FORCED to treat your claims as credible.

So if you can make a specific prediction about the future, post it here. But it has to be quite specific. Then it's down in black and white with a clear date so we can test it. Seriously - give it a go. It doesn't matter if you get it wrong, but it would be brilliant if you get it right! It would take guts to do that, Linda, but you sound gutsy to me.

Your comments are always very welcome here, Linda. I don't want to lose you! I find this fascinating. - Andrew Thomas, 16th October 2008
Great article and discussions.
I had for years been comfortable with the psychological arrow of time to providing a forward time direction related to the expansion of the Universe and increasing Entropy.
However, the above gives me pause and brings up a problem with my understanding. Although entropy is increasing in our Universe, there are local areas of decreasing entropy(at expense of energy).
In such an environment--does the arrow of time reverse? - Ranon, 20th October 2008
Ranon, "Although entropy is increasing in our Universe, there are local areas of decreasing entropy". To be honest, I haven't heard about that. Thanks. - Andrew Thomas, 20th October 2008
An example is a growing living being.
delta G = Delta H - T delta S
describes the change in entropy which can be negative depending on the free energy etc and total energy and Temperature.
In other words, with the expenditure of energy things may become more ordered.

Within this pocket of decreasing Entropy, what happens to a fetus growing within the womb?
The "Arrow of Time" does not appear to reverse for a growing baby.

The problem of distinguishing system from surroundings may be rearing it's head here. - Ranon, 20th October 2008
Ranon, yes, you're absolutely correct in stressing the importance of isolating a system from its environment. You could, for example, reach into a box and reorganize the gas molecules into a more ordered state - hence apparently decreasing its entropy. The key thing to state is that entropy of a CLOSED system will always tend to increase. Thanks again. - Andrew Thomas, 20th October 2008
Thank you for the response.
I think that the question of whether there exists a "Closed" system in our Universe(Let alone other possible ones) is an open one.
BTW--I'm not too fond of the Multiverse theories - Ranon, 20th October 2008
I dont know if this have been mentioned in the comments, but it seems quite obvious that the thought experiment here regarding "knowing the future" is fundamentally flawed.

In determining the future, one have to know the current state of the universe and interpolate it forward in time using the laws of physics, but the act of informing the subject of the results of this interpolation changes the state of the universe, thus requireing a new interpolation and informing the subject again in an infinite loop.

But, still in total theory, no respect to practical problems, the experiment is probably flawed on an even more fundamental level regarding any abitary machinery's interference with the state of the universe, which it cannot take into its own iterative algorithms, no? - Kim Steien, 21st October 2008
Good point, Kim. Yes, quantum theory says we can never have a clockwork universe because we can never know the current state precisely, and also the universe proceeds on a random basis. This is the quantum mechanical arrow of time again. Yes, if the universe was clockwork then we could know the future. - Andrew Thomas, 21st October 2008
I am unsure of the correlation between the events and passage of time. I dropped a glass and it fell on the floor due to gravity and broke into pieces due to the impact. Now, even if a reversiblity was possible, where is the external force/energy to accumulate the pieces together, assemble the glass and push it back from the floor to my hand? If we apply the required external forces, put the pieces together, and push the glass back into my hand that wouldnt make it a reversal of time? It is still the present time. When i did some activities to drop and break the glass. I also need to do activities to put the glass back into my hand. How is it expected that glass may have the possibility to repair itself and how is it anyway connected with the passage of time? Am lost. - Deepak, 29th October 2008
Hi Deepak. When we drop a glass onto the floor and it breaks, energy is actually conserved throughout the process, so the energy at the end is actually the same as it is at the start. Let me explain: when we hold the glass in our hand it has potential energy. When we let go, that potential energy is converted to kinetic energy as the glass falls. When the glass breaks, the kinetic energy of the broken glass pieces gets transferred to motion of the air molecules around the glass which we hear as sound (the sound of breaking glass). So when we take the motion of air molecules into account, the energy at the end is the same as it is at the start.

Now, in theory we could just replay this sequence in reverse and it would all make sense (because the fundamental processes are reversible). So we could imagine the sound waves travelling backwards to converge at the glass, and the air molecules pressing against the pieces of broken glass to reform the glass! So it is possible for the glass to reform itself (in theory).

The only reason we don't see this happening in practice is because the glass molecules in the glass are highly-ordered, and systems tend to move to more disordered states. So it is just highly unlikely the glass will reform itself. Not impossible - just highly unlikely. - Andrew Thomas, 29th October 2008
I don't generally believe in theories such as this (or in infinite alternate universes) as I am more a believer of free will. I do, however, find it enjoyable to imagine such things as they promote lateral thinking etc.

What isn't quite explained in this article is quite how, for example, an egg breaking on the floor could go back in time and disobey gravity, afte all, if gravity went backwards, everything would float upwards. The truth is that, similar to you throwing a ball, gravity goes in exactly the same direction as it does forwards. The cause for the egg travelling upwards is that the pieces coming together cause the momentum for the movement. The energy for the movement of the shell comes from e.g. the air friction acting backwards. All the energy does is convert from one form to another so evenutally we can trace it all 'back' to the end of the universe.

On the note of asking God for the past to be changed, perhaps saying thank you is a way of asking. Theoretically, if we say thank you more, it means that we will do it more in future, and therefore there is a higher chance of something good happening. Just my thoughts...
- Mark, 6th November 2008
Mark, the energy needed to lift the shattered pieces of a broken eggshell equals exactly the the energy dismounted from the pieces as they hit the floor. It makes more sense if you think of the reverse process atom for atom. Akin, the reversal of humpty dumptys death is not just unlikely, its actually bloody unlikely :) - Kim Steien, 7th November 2008
i think. . . . This wonderfull bubbling pot of stew we call existence is the creation of man!. . . We are in fact living in a universe which itself is travelling backwards in time,but because we exist in it. . . Relatively Speaking!. . . . we dont notice this!. . . . Entropy will destroy everything,future humanity will find a way of reversing this flow,by existing in the opposite direction. . . . And if we are our own creators. . . . This loop. . . Seems to fit various models. . . . We a travelling in the opposite direction to god! We are God!. . . We are the alpha and the omega!.... - professor angus thwaite, 12th November 2008
How dramatic, Angus! - Andrew Thomas, 12th November 2008
I found your article somewhat strainous to follow but I got there. I believe entropy is the answer to why we feel an arrow of time because memories are simple chemical properties set in our mind and following time backwards would be a series of highly unlikely events in our brain releasing small amounts of energy back into our bodies and through the rods in our eyes and into the enviroment in exactly the way it enters our brain only in reverse. memory loss is equivelent to the first step however the energy created from the loss of the memory doesnt make it to the eye. i have tried to keep this simple, however im sure you understand. I think its important to remember that our brains work through a series of chemical reactions and nothing less scientific. This is especialy important when considering the effects of a principle is basic as the 2nd law of thermodynamics. thankyou for the thought prevoking article

- james davies, 18th January 2009
I'm sorry but your claims are ridiculous. the future is not set and you are a moron if you believe that it is. - Blythe, 19th February 2009
If I am a "moron" then so is Einstein, for according to Einstein: "People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion." - Andrew Thomas, 19th February 2009
Hi again, what are the tests done so far to test backward in test, at quantum or any level? - Wang, 16th May 2009
Well, in order to test the behaviour of physics backward in time we would have to reverse the direction of time, which we cannot do obviously! The only way we can effectively reverse the direction of time is to film something and then play the film backwards. For example, if you take a film of some balls hitting each other, and you reversed the direction of the film, the sequence would still look sensible. All the balls would be behaving correctly, bouncing off each other. In fact, you could not tell if the film was being played in the forwards or backwards direction. This would be an experiment to show physics works the same way in both the forward and backward time direction. - Andrew Thomas, 17th May 2009
Yes. Splendid stuff. However, it's a typical physicist's -- because physical -- view of The Way Things Are. Memory is dealt with, but not remembrance:

Remembrance to perception how allied;
What thin partitions sense from thought divide.

Alexander Pope

Too right. Isn't it plain, from all that is written above, that we can no longer pretend that the partition between brain and mind is something of which we need not -- because, for now, we cannot -- take account?

For all we know, the arrow of time may exist for the universe of the mind. Or, then again, it may not. It seems very doubtful indeed, for instance, that anything resembling the Second Law of Thermodynamics applied in a world without particulate states to which probability can necessarily be applied?

We need a good deal more knowledge, here.

(And notice the word 'knowledge', which is not necessarily the same as 'information' and, I would personally contend, is actually a different commodity: knowledge is what information is converted into when it crosses the interface from the brain (where it may be handled exactly as it is handled in a computer) into the mind (where this is not the case) . . .
- Martin Woodhouse, 23rd May 2009
. . . . for instance:

"The reason why we don't see causality happening in the backward direction is purely because of a bias in our psychological systems: something about the complexity of our psychological system (our brains!) causes our thought processes to work only in the forward direction of time . . . .

Substitute the word "mind" for the word "brain", above, and the puzzle implied in the sentence
" . . . something . . . causes our thought processes to work only in the forward direction of time . . ." immediately vanishes; there is no reason to suppose that an immaterial system (my mind) is constrained in the same kind of way in which the physical system of my brain is constrained.

Once we are prepared to accept the distinction between mind and brain, and to agree that the mind is immaterial, we longer have any need to suppose that it acts according to any of the 'laws' which we have so carefully formulated over the history of physics . . .

On the other hand, the events which occur in the mind aren't randomly sequenced either, or we wouldn't be able to think or perceive at all. And whatever is not random is algorithmic, and we're entitled to believe that any algorithm can be discovered and described.

So the events of the immaterial mind are of a nature in which rules are available for discovery. It's just that we haven't made any great effort in the direction of discovering them yet, which is far from being the state of affairs in physics, the study of the material world.

It is, of course, very difficult to study mental events, since we can't use the experimental method to examine a system whose internal states are only accessible by the single person who is experiencing those mental events. So we can't rely on agreement between observers, at least not to the extent to which we rely upon it in scientific experimentation.

None the less, it's surely possible to construct some picture of the mental, immaterial world, as we have done with the world of nature?

We might start -- now that I think about it -- with a word which appears in your article, above: mental events are sequenced, and the word 'sequence' does imply some sort of 'time' axis, even if it's not wholly comparable with our use of the word in physics . . ? - Martin, 24th May 2009
Hi Martin, thanks for that, very interesting. You seem to be saying that the "mind" is not subject to the laws of physics: "Once we are prepared to accept the distinction between mind and brain, and to agree that the mind is immaterial, we longer have any need to suppose that it acts according to any of the 'laws' which we have so carefully formulated over the history of physics."

But surely the mind is not totally separate from the laws of physics. The speed at which we think, for example, is limited by the speed at which neurons can fire. And, as suggested in the text, the reason we cannot "remember the future" is at least partly due to the radiative arrow of time: information from the future has not yet reached us. So I can't agree with you on that point.

However, it IS true that the computational aspects of the brain are separate from the underlying hardware (in the same way that it doesn't matter on which computer you run your program). So in that sense the mind DOES have some separation from the physical world. This point is considered in the section "How Turing's Universal Computer applies to you" on the "Is the Universe a Computer?" page:

Thanks again. - Andrew Thomas, 25th May 2009
Nice site! Being a layperson, I hope I may ask some questions.

Troubling premise: entropy is symmetric in time.

Mr. Penrose suggests that a low-entropy genesis has "fixed" matters in such a way that we perceive an asymmetric progression of entropy. Yet, if entropy increases in any state change (e.g. shift in time), then that should hold from any arbitrary moment. If we trace back from now, we achieve a different result than if we trace forward from the proposed genesis. How is this contradiction explained?

Ignoring the problem of a low-entropy genesis, there's a more fundamental problem with symmetric entropy. If entropy increases as we move backwards or forwards in time, then any arbitrary point would be less entropic than a point instantly before or after it- that is, the point would be the bottom of the V in the graph. Call this point O and the more entropic points to either side O-1 and O+1. Let me choose a new arbitrary point. It too should be the bottom of its own V. I choose to set my second point to be O+1. By symmetry of entropy, now the points immediately before and after O+1 are more entropic than O+1. As a result O is more entropic than O+1. But I had just discovered that O+1 is more entropic than O. By transitive inequality, O is more entropic than O. How is this contradiction explained?

Thank you for your time! - M, 11th June 2009
Hi M, the problem you are describing is basically Loschmidt's Paradox which I discussed in the main text:'s_paradox

As we look backwards in time we find that the molecular velocities are not completely random: they are *correlated* so that if we reverse the velocities and trace the motions back far enough we will recreate the extremely low entropy condition of the Big Bang.

Change of entropy is only symmetrical in the general case - it's not symmetrical in, for example, the case of a glass bottle breaking when the bottle is already in the process of breaking. Then the bottle's past will be low entropy and it's future will be high entropy - just like our universe! - Andrew Thomas, 11th June 2009
Good article
remember though all universes exist and are equally real. The future IS set in stone, however, so are many other paths (in fact EVERY possible path) is set in stone. looking back, these events may seem to be the only possible events that could've happened but in reality I believe those are just the events we choose. - Stephen, 24th June 2009
Thanks very much for your comment, Stephen. You're basically describing David Deutsch's theory about how we have free will (basically, when you make a decision, you switch to a different universe). Here's a quote from New Scientist:

"Deutsch does not agree. In fact, he thinks it could make real choice possible. In classical physics, he says, there is no such thing as "if"; the future is determined absolutely by the past. So there can be no free will. In the multiverse, however, there are alternatives; the quantum possibilities really happen. Free will might have a sensible definition, Deutsch thinks, because the alternatives don't have to occur within equally large slices of the multiverse. "By making good choices, doing the right thing, we thicken the stack of universes in which versions of us live reasonable lives," he says. "When you succeed, all the copies of you who made the same decision succeed too. What you do for the better increases the portion of the ultiverse where good things happen."

Quote taken from: Taming the Multiverse

I don't actually agree with Deutsch. I think it is possible to have free will in a SINGLE universe. For more details, see my section "Free Will in a Block Universe" on the Block Universe page: - Andrew Thomas, 26th June 2009
Not only can we remember the future, but we can feel the joy or excitement as we do. This changes the past, which is the present at zero point for the symmetry equation. This means that remebering the future shifts the timeline, changing the environment from which our genes make choices on the proteins that make up our bodies. We shift ourselves to meet the future we already remembered. The idea is to not draw our own rays through the potential of all potentialities, but realize that remebering is listening, and not instructing. If you don't like what you see, then shift your weight in the now, and take another look. - Brooks Agnew, 27th June 2009
Andrew, my belief in Karma is simply that: a belief. I have no proof, but I didn't come to that conclusion easily, indeed I came to it kicking and screaming because from age birth to 37 (I'm 52 today) I believed in Free Will. I still want to, but for too many reasons to get into, Karma seems to have the edge. I'm not into "New Age" stuff btw which permeates California here in the US and apparently the Isle of Wight in your country.

In any event, have you read "The End of Time" by Julian Barbour, and if so, what do think of it? I was in my local bookstore last night and ran into it. Basically he says Time is an illusion, but the reviews of it are quite spotty, so I probably won't buy it. - Greg Sivco, 16th July 2009
Hi Greg, I have always found Julian Barbour desperately hard reading so I've tended to dodge his stuff - though everyone raves about him. I see he has just won the FQXi essay competition (with a paper that probably covers everything in his book): - Andrew Thomas, 16th July 2009
Thank you, Andrew, you confirmed my worst fears.

"Time" <=== What is it? I'd like to know, but I don't know, yet I take comfort in the fact that nobody else knows either, in spite of no shortage of opinion.

Hey, Andrew, I have a question. You have 13 wonderful pages on this your website. Is this the one that gets the most hits? - Greg Sivco, 17th July 2009
Hi Greg, yes, this page gets the most hits - it has had as many as 2,000+ hits in a single day. - Andrew Thomas, 17th July 2009
Help on my thought experiment. We know the further galaxy, the faster it runs apart from us.

Let's say there is a galaxy (assuming the laws of physics are the same there) running away from us at 99% of the speed of light. Let's say at the SAME time, the people in that galaxy doing the same thing with us on earth. The same thing can be: "start running an atomic clock". The people in that galaxy, according to General relativity, will know the atom clock on earth must run slower than theirs because the earth within milky way galaxy is speeding away at 99% light speed. We on earth will conclude the same that the atomic clock must run slower in the other galaxy speeding away from us at 99% light speed.

We can also imagine a judge in exact middle point from the two galaxies and tell each side to stop the atomic clock and measure the time at exact the same time (because the judge is at exact middle point, and each galaxy is speeding away from him at exact time maybe 49.5% of light speed).

So now my big puzzles, are the atomic clocks will measure same time? According to the General Relativity, each clock shall run slower against
the other clock. if the atomic clocks measure the same time, then the earth people passed the same time as the other galaxy people, although General Relativity tells the other galaxy people must pass time slower than us as they are moving at 99% of light speed.
- Wang, 19th July 2009
Hi Wang, this is just another form of the twin paradox:

In order to compare the times of the two clocks, they must both be decellearated and turned-around to be brought back to the judge. As that Wikipedia entry says: "Special relativity does not claim that all observers are equivalent, only that all observers at rest in inertial reference frames are equivalent. But the space ship jumps frames (accelerates) when it performs a U-turn."

When the clocks are moving apart, they appear to run slower, but when the clock is turned around and accelerated back to the other planet, it appears to run faster. The two effects cancel precisely (it is a perfectly symmetrical situation between the two planets) so the two clocks agree perfectly when they are brought before the judge. - Andrew Thomas, 19th July 2009
suppose the judge is at exact middle point, on straight line, of the two galaxies, departing from each other at close to light speed. The judge can beam a laser light to people at two galaxies to start/stop the atomic clock, and the people can beam back their pass of time to the judge. So in this way, there is no need to bring/move the clock from one galaxy to another.

I think judge will see the pass of times on the two galaxies are the same. But Relativity tells since the galaxies are departing from each other at close to light speed. Their pass of time is still the same?
- Wang, 20th July 2009
Hi Wang, yes, each planet wil see time on the other planet as passing more slowly, but they will also see the signal from the judge arriving at the distant planet later (because the distant planet is travelling away). So both clocks are seen to show the same time when they stop (the distant clock stops later, but it was running at a slower speed).

This is a classic example of simultaneity being relative: if you are on a planet the two clock-stopping events appear to happen at different times, but to the judge the two events appear to happen at the same time! - Andrew Thomas, 20th July 2009
Thanks very much, Andrew.

My question now is if the people in the above two galaxies, grow a tree (assuming all other conditions are the same for tree growth), instead of measuring the atomic clock, then what will happen?

According to Relativity, each galaxy will see time run slow in the other galaxy, so the tree in other galaxy will grow shorter.

The judge, at the exact straight line middle point, can send beam light signals (which will arrive at each galaxy same time) to each side to start grow the trees, to measure the tree heights, and the galaxies beam back the tree height info via light signals to the judge.

The judge will see the heights of the trees from the two galaxies are the same. The judge can even send such info to both sides, then both side shall be surprised to know the tree heights are the same, because according the Relativity, the tree in the other galaxy must grow shorter/slower!

My question is again, how come the trees can be both relatively shorter to each other (from views of one galaxy against the other galaxy), and being the same height at the same time (from the judge's view)? - Wang, 22nd July 2009
Hi Wang, a tree growing at a fixed rate is basically just another form of clock, so the situation here is exactly the same as it was with the clocks. As you say, each galaxy sees the tree in the other galaxy growing at a slower rate, but the judge will see them growing at the same rate. So you're totally correct about all that.

When the judge sends out his signal to tell the galaxies to measure their trees, if you are standing in one of the galaxies then the signal from the judge will appear to reach the other galaxy later than when you receive the signal (because the other galaxy is speeding away from you). So, even though the tree in the other galaxy appears to be growing slower it has more time to grow so will still be at the same height as your tree when it receives the judges signal. So both trees will register the same height. If you are standing in one galaxy, you will see the tree in the other galaxy be the same height as your tree when it receives the judges signal, even though it has appeared to grow slower, it will appear to have had more time to grow.

Like I say, this is all about relativity of simultaneity:

To the judge, the two signals appear to reach the trees at the same time. But to people in the galaxies, the two events happen at different times. - Andrew Thomas, 22nd July 2009
All this talk about Special and General Relativity is wonderful, even if Andrew's website is devoted to explaining Quantum Mechanics (the OTHER great 20th Century Innovation) to the "Intelligent Layman." However, there is another aspect of "Time" which, if proven can blow the whole "Dark Energy" issue out of the water. Click on the following link to see it:

I know nothing of that website by the way. Still, "Is Time Slowing Down?" on a cosmological scale seems quite important, especially when most mainstream Physics assumes Time moves at a constant rate. I have much to discuss on the issue, but let's see what Andrew has to say first. - Greg Sivco, 25th July 2009
Hi Greg, that was an interesting link, thanks. However, if "time itself" is slowing down - as Senovilla suggests - then I don't think that would alter any observed **lengths**, including the observed wavelength of light from distant galaxies. Hence, light from those galaxies would not appear red-shifted and the galaxies would therefore not appear to be accelerating away from us. So I do not believe Senovilla's theory accounts for the observed acceleration of the expansion of the universe.

I just posted about this on Physics Forums:

Thanks for all the great links you post, Greg. - Andrew Thomas, 25th July 2009
First, congratulations for giving us this fascinating website, and presenting some of the deepest questions in physics in such an accessible way. I'm going to mess things up a bit by getting slightly mathematical and presenting what I believe is an information-theoretic derivation and generalisation of Boltzmann's H-theorem. However, it's just a few lines of elementary algebra which, if understood properly, I believe resolves Loschmidt's paradox and clarifies the status of the 'molecular chaos' assumption, helping us to understand the nature of the 2nd law.

In information theory, the 'total correlation' of a set of variables is given as:

C(x_1,x_2,...) = Sum_i H(x_i) - H(x_1,x_2,...)

C is a measure of the extent to which the whole set of variables is correlated or shares information Now, C >= 0 always but when C = 0, the variables (x_i) are independent. This is the condition of molecular chaos. The terms on the right are entropies. H(x_1,x_2,...,x_n) is the JOINT entropy of the set of variables. It's crucial to realise that this quantity remains CONSTANT, for a time-reversible system. If you know the positions and velocities of all particles at time t=0, then you will know them all for all time: the volume of phase space does not change and therefore neither does the joint entropy (the information needed to specify the microstate exactly). So, dH(x_1,..,x_n)/dt = 0. By contrast, C tends to increase, as particles (more generally 'elements of the system') interact with one another and become more correlated, so dC/dt > 0. Hence, it mjst be true that the expected (or average) value of H(x_i) must increase: dH(x_i)/dt > 0 on average. This is essentially what Bolzmann showed but he assumed C = 0 to begin with. What it means is that the position and velocity of any given particle becomes more and more uncertain as information about it 'leaks' into the ensemble. Thus the ensemble of particles become evenly distributed in space and their velocities tend eventually to the maximum entropy Maxwell-Boltzmann distribution. What I've shown is that for any time-reversible system where dC/dt > 0, dH(x_i)/dt > 0 also (i.e. the 2nd Law must hold), which is a generalisation of the H-theorem. Note that an initial condition of C=0 is sufficient but not necessary to prove the theorem.

This derivation also clarifies the interesting role played by time-revesibility. Far from being paradoxical, it is almost a requirement for the 2nd Law. In dissipative (i.e. open) systems, neither time-reversibility nor the 2nd Law need hold, and the equation I presented immediately shows why.

So, in summary, it is the increase in correlations within closed systems which leads to the 2nd Law, and molecular chaos is not a necessary condition for the H-theorem. I also don't think the arrow of time requires the universe to have come from a low-entropy state. Eggs will never unbreak, so I'm with Lubos on that one. - Chris Whitrow, 14th August 2009
Addendum: I didn't deal with the objection that dC/dt > 0 is itself a time-asymmetric assumption (although less limiting than C = 0 at t = 0). I guess there's no easy answer to this, but it should be noted that it is equivalent to the second law (i.e. the implication goes both ways). If the 2nd Law is true, then dC/dt > 0 follows (which is not so for the molecular chaos assumption).

I think this points to the fact that the 2nd Law is really more to do with information processing than physics per se. It says that any PARTIAL description of a system becomes less certain as changes occur in the relations betwen the elemnets of the system. By 'partial description', I could mean one in terms of 'macrostates' (such as 'egg', 'omelette', etc.) OR simply a description of the position and velocity of a single molecule in a gas. A partial description is any which does not specify exactly the microstate. Applied to human beings, the 2nd law becomes a law of psychology and memory. There is indeed a 'time-reversed' equivalent of the 2nd law: namely that our memories and records of the past become more vague as we reach into the past.

I'm not sure if this really resolves the 'mystery' of the arrow of time. If anything, it tends to say: don't look for the answer in the laws of physics alone. - Chris Whitrow, 14th August 2009
Thanks for a great contribution, Chris.

In a nutshell, you're concentrating on the correlations between particles ("C tends to increase, as particles interact with one another and become more correlated") rather than concentrating on the increase in disorder (entropy) of the particles. Others have considered entropy from this informational viewpoint as well. For example, I can strongly recommend Seth Lloyd's book "Programming the Universe" which considers entropy change from the informational viewpoint, defining entropy as the information lost to random motion (in much the same way as your particles collide together, becoming correlated). To quote Lloyd: "Suppose an unknown bit of information interacts with a known bit of information. After the interaction, the first bit is still unknown, but now the second bit is unknown too. The unknown bit has infected the known bit, spreading the lack of knowledge, and increasing the entropy of the system". Lloyd called this process the "spread of ignorance" through a system (great phrase, I think).

But you're quite right in saying that none of this on its own explains the arrow of time - it doesn't explain your dC/dt > 0 time-asymmetic assumption. Play a movie in reverse - particles interact and get correlated just the same way in the backward time direction as they do in the forward time direction. So initial conditions clearly remain crucial. Sorry, but in order to explain the time asymmetry we still have to consider the initial condition of the universe - **that** is where the asymmetry comes from. Thanks again - very interesting. - Andrew Thomas, 14th August 2009
I still don't see what motivates the multiple balls on the table to coincidentally go a specific direction and then magically collect in a triangle. There is no "newtonian" force that motivates them in the reverse direction of time, nor is there rhyme nor reason to their coincidental direction, unless you also postulate that effect precedes cause. In other words if (and only if) effect precedes cause in the reverse direction of time, then the direction of the balls can be explained by the "attractive force" of the cause that will happen shortly. Otherwise, the balls have no motivation (resisting dirty joke here) and there is no way to explain their direction, motivation, or coincidental "ending" in a triangle. - MarkL, 20th September 2009
Mark, yes, you have hit the nail on the head when you say it is extremely unlikely the balls should "coincidentally" reform into the triangle shape. The laws of physics are time reversible so do not say that this could never happen, but it would be extremely unlikely. And that is precisely the reason we have an arrow of time: unlikely things rarely happen - entropy increases.

So at the start of the game, the balls are arranged into a very ordered pattern: a triangle. But as soon as the break-off shot is made, the balls become more disorded: entropy increases. But we don't see the balls forming a triangle again (entropy is very unlikely to decrease - not impossible, just unlikely). The laws of physics do not prohibit it, though - it is just highly unlikely. And *that* is the only reason why we see an arrow of time: the start of the universe had very low entropy, but has been getting more disordered ever since. - Andrew Thomas, 21st September 2009
Time is an abstract measure of energy change.
Like a meter stick measures delta distance (absolute -/+)."Time" measures energy change (absolute -/+). The future is only changed energy.
With either "measure" how does one determine the amount of change in any system? (absolutely).
There is no negative space meter stick either.

- Louis XIX, 28th September 2009
Would Libet's experiments which appear to demonstrate that our decisions are made before we become consciously aware of them lend support to the notion of remembering the future? - Edwin Griffiths, 3rd November 2009
That's very interesting, Edwin. I wasn't aware of the work of Libet. So our subconcious minds make the decision for us, and it's only later that we feel we are making the decision of our own volition? That has implications for the notion of free will.

Yes, as you suggest, if we could find a shortcut in the brain that tells us of the decision we are going to make *before* we make it then that is a form of "remembering the future" (and would put us in the same position as Dilbert in the main article). Thanks, Edwin. - Andrew Thomas, 3rd November 2009