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Essay Abstract

In our everyday lives we have the sense that time flows inexorably from the past into the future; that time has a definite direction; and that the arrow of time points towards a future of greater entropy and disorder. But in the microscopic world of atoms and molecules the direction of time is indeterminate and ambiguous.

Author Bio

Gavin Crooks is divisional fellow in Physical Biosciences at Lawrence Berkeley National Laboratory. He obtained his Ph.D. from the University of California, Berkeley. His current research interests include the thermodynamics of molecular machines and solar energy capture. http://threeplusone.com

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Hello Gavin!

Thanks for the essay!

Consider a Hydrogen atom that emits a photon. The photon propagates as a spherically-symmetric wavefront of probability expanding at c, never to return (or not very likely). This seems to define an arrow of time at the atomic level, for radiation exists at the atomic level, and thus the radiative arrow of time manifests itself at the atomic level.

Best & thanks,

Dr. E (The Real McCoy)

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Huw Price discusses this issue in his great book "Time's Arrow and Archimedes' Point", chapter 3. The radiative arrow is due to time-asymmetric boundary conditions, and ultimately reduces to the thermodynamic arrow.

12 days later
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Dear Dr. Crooks,

May I try to answer the question in the title of your essay.

In your essay "Whither Time's Arrow?", you wrote: "Neither Newtonian mechanics, special or general relativity, quantum mechanics, nor quantum field theory picks a preferred direction in time, anymore than these theories picks out a preferred direction in space."

The apparent "expansion" of space due to the so-called 'dark energy from empty space' (L. Krauss, reference available upon request) does not pick up any preferred direction in space either, simply because this "direction" is omnipresent -- there is no direction in which space does NOT expand. The latter is ultimately needed as a reference direction w.r.t.w. we could discover another, preferred direction of space expansion.

Notice that such task is banned in GR by default, because it would require that GR determines the evolution of the lapse function and shift vector, along the "arrow" of the spacetime foliation. But as the lapse and the shift are gauge functions, any convertion into some Dirac observables would inevitably expose an *observable* absolute reference frame, and the ether will come back.

Hence many people at this Forum claim that we should "forget" time, but somehow avoid the driving force of the cosmological time arrow, and also the drastic contradiction between the predictions of their theories and all astronomical evidence of the cosmological time. As Thomas Thiemann acknowledged in astro-ph/0607380 v1:

"Why is it that the FRW equations describe the physical time evolution which is actually observed for instance through red shift experiments, of physical, that is observable, quantities such as the scale parameter?

"The puzzle here is that these observed quantities are mathematically described by functions on the phase space which do not Poisson commute with the constraints! Hence they are not gauge invariant and therefore should not be observable in obvious contradiction to reality."

In shorth, to answer the question posed in the title of your essay, the direction of time arrow is the one in which the amount of dynamic dark energy (DDE) is increasing -- the more time elapses along the cosmological time arrow, the more DDE we wind up with.

I tried to explain this paradoxical situation to my teenage daughter as follows: Suppose you accelerate a car, but the fuel gauge shows that you're actually gaining more fuel by accelerating the car. That's the ultimate 'free lunch' provided by DDE, only physicists cannot explain it.

A penny for your thoughts! It may be worth of billions, since we're talking about the cleanest and truly unlimited energy source.

Regards,

Dimi Chakalov

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Dimi Chakalov:

The issues you raise have to do with the cosmological origin of the arrow of time. On the other hand, the central topic of the essay is the other end of the scale, small systems and short times, where the ambiguity in time's arrow has quantitative consequences for modern, non-equilibrium thermodynamics. For molecular scale systems the origin of the large scale time-asymmetry of the universe is immaterial, although the consequences of time-asymmetry are vast.

GEC

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Gavin:

The issues I raised are indeed related to the cosmological origin of the arrow of time. Bottom line here is the quantum vacuum as the prime candidate for Einstein's cosmological constant proposal from February 1917. Hence "the other end of the scale", as you put it, is automatically involved.

I wonder how you would comment on my answer to the question posed in the title of your essay.

Dimi

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Dear Dr. Crooks,

In your essay, you explain very well the arrow of time. The arguments and the experiments presented show that the time's arrow is local, depends on scale, and its "length" can be almost zero or negative, being thus neither fundamental nor absolute. Congratulations for the well-written essay.

Best regards,

Cristi Stoica

Flowing with a Frozen River

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Dear Dr. Gavin Crooks,

Thermodynamic entropy can never decrease. It is impossible for the exchange of energy it describes to reverse its direction. The definition of thermodynamic entropy is precise. It is defined under ideal conditions. It does not include any system for which any part can vary from its average temperature. We very closely approximate it by restricting the analysis to infinitesimal changes. The fact that these conditions cannot exist in the real world does not allow for loosening its definition. If it is given a notation for averaging, then it is not thermodynamic entropy. The new process may look similar, but it has become something different, something else. Thermodynamic entropy does not refer to a general process of achieving thermal equilibrium. Thermal equilibrium will eventually be achieved for other closed systems. Intervening conditions of disequilibrium do not affect the ultimate outcome. Yet, the kind of process they undergo is not the kind of process defined by thermodynamic entropy. Yes, in a system that is not in equilibrium, energy can flow in various directions at various points within the system. However, that kind of system is not telling us what thermodynamic entropy is telling us. It cannot tell us, location by location or instant by instant, about the direction of time. Thermodynamic entropy does tell us that its process, including our approximation of it using infinitesimals, moves forward as time moves forward.

Respectfully,

James Putnam

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Dear James Putnam,

Respectfully, in the microscopic realm entropy can both increase and decrease. This makes sense theoretically and has been observed experimentally. If you are used to thinking about entropy in terms of macroscopic thermodynamics, it takes some time to get used to the idea that entropy is statistical, fluctuates, and is not a property of equilibrium systems alone.

Gavin Crooks

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Dear Cristi Stoica,

You may also be interested in my recent PRL paper with Ed Feng, "Length of time's arrow". The FQXi essay attempts to give a basic introduction to relevant results in non-equilibrium, small system thermodynamics, but inevitable glosses over many details of the theory. The paper goes into much more depth.

http://threeplusone.com/pubs/fulltext/Feng2008a.pdf

Gavin Crooks

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Dimi Chakalov,

Cosmological questions are outside my domain of expertise (At present), so I choose not to speculate. Hypotheses non fingo.

Gavin Crooks

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Gavin:

I think "hypotheses non fingo" can hardly be justified, since your essay would then cover (at best) only 4 per cent from the stuff in the universe. As to the "cosmological questions", every time you contemplate about entropy in the microscopic realm, you are -- willingly or not -- implying the nature of time and its driving force. It's a package.

Have a nice white Christmas.

Dimi

3 years later
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Connections

The binding of existence

This is a story, built upon knowledge, intuition, and speculation. In the end, it is built upon some known theoretically successfully tested truths, and some unknowns conveyed in a formula that I consider trumps any objections - as we ponder the scope of existence. First we know of existence, by way of our self-awareness, coupled with scientific knowledge. Second by way of the unknowns i.e., "Infinity", that must incongruously play with us (self-aware-finite creatures), in some connected manner.

This Second irascibly indefinable thing called "Infinity", simply stumps our "finite" minds every time, when we attempt to figure out its mathematical infinities. As it must. As if it did not stump our efforts to understand it, it would become defined, and anything defined, is "Finite.". So we have an absolute conundrum that operates our existence. But we are still connected, in a union, both finite and infinite, through the known attributes we have scientifically tested to be true. As without "Infinity", there can be no "Finite." And remember Infinity, has no bounds, no time, no space, no beginning and no end.

This is plainly contrary to finite logic, but Infinity simply is contrary. Always has been. And always will be. But it is also the very milk of our very finite existences... We are Connected... Our actions matter, as I will soon explain - in summary.

INFINITY: Irascible and fundamentally a necessary fickle fact. An argument that no mathematics or thought equation can defend against... To challenge this premise is to supersede infinity's very nature. It will never ever happen.

Therefore we are circumscribed to live within, the physics - largely of Newtonian and Einstein's mathematics. I would caution to note: that these finite mathematics are subject to change that currently work fairly well for our finite existence as we mathematically calculate how to penetrate and maneuver the Stars, or add 2 plus 2 to equal 4. But they do not work to unravel Quantum Mechanics (in total), and the cache of oddities, such as "Superposition's", whereby subatomic particles are in several places at one time, until they are interrupted by measurement. Or do these current finite mathematics explain "Entanglement", which allows for two subatomic elements to be millions of miles apart, however if one changes its state of "spin" or "electrical" charge the other particle millions of miles away responds instantly. Yes, this violates the concept of the speed of light as the fasted method of action in the Universe.

As Einstein called "Entanglement" Spooky, but none the less real. This seemingly violates the speed of light. But hold on, the Speed of Light travels, Entanglement implies "Connection". Or what is known as Local action.

Space is the key to this thought equation. Since space is "Infinite" to the "Finite" Observer. Space in this context is also in union with waves - as well as particles. However waves may connect all things instantly, just as waves may allow for "Superposition's."

The answer is simply that: This makes us both Local and Non-Local at the same time. Waves and or theoretical "Strings" perhaps in some union - connect our space and possibly time in ways we do not fully comprehend. If true, our infinite extended connections are observed from a finite realm only. It might be important to note here: That simply no distance is allowed in an Infinite realm, as infinity is immune to classification, therefore it is all things and no things at the same time. Make sense? It usually should not, as finite logic has a difficult time with this both intuitively and implicitly mathematically. Make sense yet?

Probably not, as this means that "Everything is Nothing and Nothing is Everything." Hence there are no real "infinites" to calculate in an Infinite realm. But this last statement is a clear oxymoron, as it should be, as infinity does not have mathematics or anything defined based in or of it. As this would imply a finite realm. It is simply infinite, and does not apply to our finite realm of mathematics.

Mathematics is purely the purview of the finite.

When I said there are really no infinities in the infinite realm. I meant it. But to us, within the finite realm or finite conscious state, as observers, Infinities are what - infinity, space and time are made of. Once again, the ultimate and infinite conundrum. However, how does this allow for the stuff of existence, such as "us", or cars, and trees and so on to exist? Well we do need infinity to have a finite realm, as I said.

That is the puzzle? That must never be answered technically, nor can it, again from a finite perspective or finite observer. This mind trap we are caught in trying to view infinity - would seem to drive one mad to think that Infinity, Space and Time have no beginning or an end.

But get use to it.

Infinity is indelible. Terms like "time" and "space" are non-words to describe Infinity correctly, as Infinity never had a beginning or an end. The space and time word terms we use within the realm of Infinities definition, or lack thereof, could not and do not exist. Unlike the finite world, which has an Alpha and Omega. (Dust to Dust, Evolution, and Space to move to, and a length of Time that life gives us to observe.

And - That is that...

We are here by way of connections of an indefinable Infinity, which has always been, and will always be. Make no mistake about it. This will provide us and others forever to give sentiency a journey to discover anew. New science from physics to health, coupled with new modes of life, new cultures to come. Save an Asteroid impacting the Earth, or a Super-Volcano taking us to our end of time as sentient beings. But others will arise, no doubt by way of times finite arrow.

The finite with a beginning and end is necessary, to find hope. Just imagine living for eternity without end. That proposition, would invoke a person to lose goals, have no new hopes, and actually impart a crazy madness of hopelessness. As you would be in the ultimate Trap, or Jail forever, if self-aware. What would be the point? One would ask themselves... And therefore, Life and Death, are necessary.

Dust to Dust and then perhaps? Take your best shot at a faithful guess! The options are many, the realities may be few. No one really knows. No one...

Plainly beyond us, the Infinite and Finite will ebb and flow, and new existences will arise through an endless connection to everything for all time...

Essential Points:

1. The Science is: That Infinity is incomprehensible to any complete understanding and, the Finite is limited to understanding all things, perhaps itself and certainly infinity. The connection between the finite and the infinite operate as if Everything is Nothing and Nothing is Everything... Have fun with that analogy! As for me, it holds true, as it confirms to me that cognitive logic eventually meets the illogic of Infinity. This lets us clearly know we will never actually know honestly and truthfully the great questions of life: As to know "ALL" or "Truth" would be to actually define a place and a time, which can only be finite. And that would defy the rules of Infinity, which cannot be technically ever defined. Otherwise it is no longer infinite; it would then become as a mere canvas with parameters. And Infinity is incomprehensible. End of Story - Yesterday, Today and Tomorrow... In other words Forever!

2. The Moral is: That Legacies matter. Build a good one. The Butterfly Effect is always on... And that is what really matters.

All the best in our journey's, Russ Otter

www.otterthink.blogspot.com

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