Is the Arrow of Time Driven by Probability and Entropy?

[keepit]

Is the arrow of time explained by probability - i mean do we go forward in tiome because there are more possibilities in the forward direction than there are to go directly back to the exact position we can from.

 

[Simon Bridge]

Technically, we time heads in the direction of increased entropy because there are more opportunities to be disordered than ordered.

But there have been papers which try to show movement backwards in time since, in that direction, there has been a "wavefunction collapse". They have a tendency to assume what they are trying to explain.

For your thinking - this would translate to many possible ways to go forwards in time and only one for going backwards - for every particle in your body. But the way to start thinking sensibly about this is to consider how you would know that a particle has come from the future or not? What would a reverse-time event look like?

 

[jarekd]

The fundamental equations of physics, from GRT to QFT, are Lagrangian mechanics: have time or CPT symmetry. One of formulations is the principle of least action - among all possibilities, physics chooses 4D scenario (path in classical mechanics, shape of spacetime in GRT, history of field configurations in field theory) which optimizes the action. So from Lagrangian mechanics perspective, we can imagine spacetime as 4D jello - the situation in the current moment is kind of equilibrium between past and future.

From the other side, we have effective theories like thermodynamics operating on statistics. It obviously emphasizes some time direction - breaks the symmetry of more fundamental theories.
So fundamental equations are symmetric, while the solution breaks symmetry - like a perfectly flat infinite water surface, to which we throw a stone.
To find the reason for our asymmetry: the 2nd law of thermodynamics, remind that Big Bang was spatially well localized and so had low entropy - so it created our entropy gradient and started all our reason->result chains ...

 

[keepit]

i suppose a reverse time event wouldn't change anything in the past or in the future at least in this physical universe.

 

[jarekd]

i suppose a reverse time event wouldn't change anything in the past or in the future at least in this physical universe.

GRT theoretically allows for non-timeorientable spacetime solutions (using wormoholes glued like in Klein bottle or slowly rotating black holes - sources: http://iopscience.iop.org/0264-9381/19/17/308/ ) - it means that there would exist a loop with this kind of configuration of light cones:
http://dl.dropboxusercontent.com/u/12405967/loop.jpg
I completely don't see these solutions realistic, but they are great thought experiment to feel the symmetry - theoretically they would allow to reverse direction of causality.
So if a rocket would make such a trip and returned back to Earth, e.g. a mug inside would still break to increase entropy ... but from our time perspective it would be pieces getting into a mug ...
Our mugs "break forward", because we can only make mugs from in Big Bang->..->humans-> ..->mug reason-result chain.

More standard experiments with reversed causality are e.g. Wheeler's experiment or delayed choice quantum erasure.

 

[Simon Bridge]

GRT theoretically allows for non-timeorientable spacetime solutions (using wormoholes glued like in Klein bottle or slowly rotating black holes ... it means that there would exist a loop with this kind of configuration of light cones...

... saying that the Einstein field equations have a solution of a certain kind is not the same say saying that such solutions are physically possible. GRT allows negative energy and imaginary mass too.

QM and causality is nice and tricky though. In effect, "the arrow of time" could be considered another name for causality.

among all possibilities, physics chooses 4D scenario (path in classical mechanics, shape of spacetime in GRT, history of field configurations in field theory) which maximizes the action.

(my emph.) I thought the principle was "least action"?

i suppose a reverse time event wouldn't change anything in the past or in the future at least in this physical universe.

What you are saying is that you cannot tell an allowed time reversed event from an event that is not time reversed? If so, then it makes no difference to the way we do physics - the distinction being one of semantic interest alone.

You can certainly tell the difference between a reversed and forward movie though can't you?

There is no end of stuff written on quantum causality. It's an area where abstract ideas in philosophy turn out to have consequences in physics. Overall I think it is still a work in progress.

The short answer to your question would be: "nobody knows but smart people are working on it".

 

[jarekd]

... saying that the Einstein field equations have a solution of a certain kind is not the same say saying that such solutions are physically possible. GRT allows negative energy and imaginary mass too.

Indeed the freedom of GRT solutions is huge and we should be very careful about interpreting them as realistic. For example the collapse of neutron star to black hole requires that density in the center reaches infinity to start forming the event horizon ... what requires that baryons are indestructible, what not necessarily have to be true as the baryon number can vary e.g. in hypothetical baryogenesis or Hawking radiation (thread).

As I have emphasized, I have brought this non-orientable spacetime solution only as a thought experiment - to feel the time symmetry of Lagrangian mechanics (indeed minimizing action).
The concrete solution we live in breaks this time symmetry in 2nd law of thermodynamics ... while inside such rocket which traveled through time-reversing loop, the properties of local solution: 2nd law and reason-result chains would be reversed.
From Lagrangian perspective, there is already found a concrete 4D solution minimizing action: making that all eventual causal loops are already fixed to self-consistent. This view on spacetime is called Einstein's block universe/ethernalism.

It is great thought experiment (and headache bringing :) ) to imagine interactions with with such rocket.
For example could such astronaut breath with our air? I think so as air is usually in time-symmetric thermodynamical equilibrium ...
But I wouldn't try eating in his position, as our meat would like to change into chicken from his time perspective ...

QM and causality is nice and tricky though. In effect, "the arrow of time" could be considered another name for causality.

While our intuition works in the past->future directions, fundamental physical theories are time/CPT symmetric, like Lagrangian or quantum mechanics (with unitary - reversible evolution). It indeed makes them nonintuitive/tricky.
Interpretation of quantum mechanics which it is based on this 4D nature of spacetime is called transactional interpretation.
For example we can easily see the strength of quantum computers this way, as they can not only fix states in the past (initialization), but also fix to having the same values in the future (measurements) in "selection" below:
https://dl.dropboxusercontent.com/u/12405967/fqcomp.jpg

 

[mikeph]

I don't buy this logical link going like "we go forward in time because ...". We go forward in time, fact, nobody knows why. As we go forward in time, systems exhibit the statistically reasonable tenancy to evolve towards higher entropy configurations. I've never read a good reason why entropy is a reason for us going in time, as if the 2nd law would ever not be true or time would evere stop and go backwards.

 

[jarekd]

mikeph, particle is not "going in time", it just is its (action minimizing) trajectory - 1D submanifold of spacetime.
Our "going forward in time" represents reason-result relation chains human world, brains are based on: that we operate on reason-result chains from Big Bang: through Earth creation, evolution, our development.
Big Bang is the anchor for all our reason->result chains. It also was spatially localized - low entropic. As entropy has tendency to grow, it also created the entropy gradient: our 2nd law of thermodynamics.

So as fundamental physics is time/CPT symmetric, could there be also such "anchor" in the future?
Let us assume for a moment cyclic Universe model - that the Universe will finally collapse gravitationally and "bounce" starting a new Big Bang ... and so on.
So this Big Bounce will be localized and so low entropic - will create 2nd law of thermodynamics, start reason->result chains for this succeeding Universe ...
But let us also look at it toward the past - gravitational collapse caused this low entropic state, so toward the past again entropy should grow. So such Big Bounce should be seen as two Big Bangs: one toward our future and one toward our past - starting Universe evolution in opposite direction.
We can imagine that Lagrangian mechanics chooses action minimizing history of Universe for two fixed points: our Big Bang and our Big Collapse. They destroy nearly all information and symmetry of Lagrangian mechanics would allow to switch them.
Unfortunately, if it would be true, there are trillions of years of thermal death between us, so we rather shouldn't expect any low entropic objects from our Big Collapse.

update: I have just started thread about entropy in the cyclic universe model: https://www.physicsforums.com/showthread.php?t=712374

ps. Great model to understand the asymmetry is Kac ring - black and white balls in a ring and there are some marked positions. Now in each step rotate all of them by one position, switching color of those which went through a marked position.
Natural statistical assumption ("Stoßzahlansatz"): that total proportion of colors corresponds to proportion before the marked positions, says it should tend to equal distribution of colors (maximal entropy) ... however, making two full rotations we get the initial setting - entropy has to finally start decreasing - here is nice paper about it.
We can prove e.g. Boltzmann H-theorem that in classical mechanics entropy always grows ... but making time symmetry of the system we would get opposite conclusion - contradiction. Such "theorems" for time symmetric evolution need to have some hidden extremely subtle assumption, called Stoßzahlansatz.

 

[Simon Bridge]

I don't buy this logical link going like "we go forward in time because ...". We go forward in time, fact, nobody knows why.

Yo probably don't buy this because the question is usually asked in a common-language sense - i.e. you have incompletely defined terms.

How do we know we are going forward in time? What does "going forward in time" even mean?

Concentrate on what you can measure, and how you measure it, for insights.
Note: physical laws do not care whether you "buy" them or not - that's the power of science. You'll find it useful when you make an intuitive expression like that to try to support it somehow. See how jaredkd offers support for his POV ?

 

[mikeph]

Ok, I get what you mean. But I don't agree still that entropy is the reason there is a direction of time, because the contrapositive would be that if we saw eggs spontaneously unscrambling, we would deduce we were going backwards in time.

That's a physically possible situation, right? But it is statistically nonsensical. So we will never, whatever we physically observe, conclude that we're going backwards in time.

Given that the physical laws are invariant under a time reversal, surely we do not lose any generality by DEFINING 'forward in time' to be what we experience now. The resulting statistics would make sense whatever we define the direction of time to be, because eggs will always scramble and never unscramble.

 

[Simon Bridge]

Ok, I get what you mean. But I don't agree still that entropy is the reason there is a direction of time, because the contrapositive would be that if we saw eggs spontaneously unscrambling, we would deduce we were going backwards in time.

I sort-of agree there, which is why I was careful not to say that in post #2.

But you still need to say what you mean by "the direction of time".
You've put it in the direction of eggs scrambling ... but to know that unscrambling eggs is in the backwards direction, you must already have an idea of which is forwards.

Where does that come from?

See the problem?

We assign the label "past" to what we do for a reason.

Oh BTW: there's an awful lot written on this thing ... don't expect any final answers here.

 

[mic*]

Oh BTW: there's an awful lot written on this thing ... don't expect any final answers here.

That much is true Simon.

It is perplexing how we can speak of "spacetime" yet also speak of the "arrow of time"... Most physicists I have chatted to associate arrows with vector quantities. Most physicists I have chatted to say that the period which passes between a set of events (perhaps measured on an atomic clock) is not a vector.

 

[Simon Bridge]

It is perplexing how we can speak of "spacetime" yet also speak of the "arrow of time"...

I don't find it perplexing. These are different concepts.

Most physicists I have chatted to say that the period which passes between a set of events (perhaps measured on an atomic clock) is not a vector.

Meaningless. Not all arrows are vectors.

If you won't clarify your terms, you will remain confused.

 

[jarekd]

I really don't understand the problem?
We have only ways to create low entropic objects (like egg) from reason->result chain from our past, anchored in our Big Bang, so the only way for them to increase entropy is to do it toward our future (egg scramble).
However, if there would be a way to get low entropic objects from our future, like in rocket going through hypothetical time-reversing loop from #5 above, it would still have tendency to increase entropy, but this time it could be done only toward our past (from our time perspective, egg in such rocket would unscramble).

We see thermodynamics as something time asymmetric, but is it fundamentally so?
Let us get a bit deeper - to statistical mechanics: where is time asymmetry there?

They are a just general tools to work with our limited knowledge: so if we only know that given object is exactly in given position in given moment (low entropy), what is our knowledge about its position while going forward in time? ... while going backward in time?
In both cases we loose information while time difference increases - entropy of our (lack of) knowledge grows in both directions - there is no time asymmetry here.

Great intuition for thermodynamics in fundamentally symmetric systems is Kac ring I have mentioned in #9. There can be low entropic state, its entropy should grows while time goes forward ... but surprisingly, the deeper relations in the system makes that the entropy have to finally start growing and return to the initial state. Also looking backward in time from the initial low entropic state, entropy has to grow.
This model is great lesson to be very careful with statistical asymmetry of fundamentally symmetric systems like our CPT symmetric physics.

Thermodynamics says that entropy wants to grow - but it works in both time directions. It is just growing in randomness, loosing information.
However, different reasons can add tendency to getting to low entropic states. Like gravity "wanting" that everything is one place - localized, leading to low entropy of such hypothetical Big Collapse-Bang ... starting reason->result chains leading to our low entropic objects ...

 

[ZapperZ]

I'm surprised no one has made citations to some of the more popular articles published on this topic already.

Joel Lebowitz has a couple of related articles on this, one published in Physics Today quite a while back, and the other is a more updated version on Scholarpedia. I suggest we START with those, and also consider the level at which the OP can understand.

http://www.phys.unsw.edu.au/PHYS2060/readings/Boltzmanns%20entropy%20and%20times%20arrow%20-%20Joel%20Lebowitz.pdf

http://www.scholarpedia.org/article/Time's_arrow_and_Boltzmann's_entropy

Zz.

 

[Claude Bile]

Stephen Hawking in "A Brief History of Time" made a compelling argument that our perception of time must follow that of entropy due to how our brains create memory.

Yet microscopic processes appear to be time symmetric.

Ergo our perception of time flow may be dictated by our physiology (and the alignment of memory increase with entropy increase).

Claude.