Mystery of Time Resolved?

After millennia of inquiry by most able scientists the concept of time still harbours mystery, which is the theme of these recent podcasts: 

• David Albert: A Masterclass on Time's Arrow
• What is Time? Stephen Wolfram's New Groundbreaking Theory

We all experience that time moves forward from a past over a now to a future, named as the Arrow of Time or 2nd Law of Thermodynamics. Why does our life always move forward to a new day, never rewind to yesterday? Why are our lives irreversible? 

In terms of physics the question can be formulated as follows:

• Why can a macroscopical system based on reversible microscopical physical laws, be irreversible? 

Ludwig Boltzmann took on the challenge in the late 19th century opening the door to modern physics and after much struggle came up with an explanation in terms of statistics as a form of statistical mechanics based on Newtonian mechanics augmented with the throw of a dice. Forward motion of time is here favoured by being more probable than backward motion thus showing an Arrow of Time, as discussed by David Albert.

Stephen Wolfram presents another explanation in terms of computational irreducibility.

My own explanation exposed in detail on this blog, connects to Wolfram's in the sense that physics as computation is given preference, rather than the conventional view based on exact laws of physics. The basic idea is:

1. A physical system changes from one state to a next state through a computational process, which has finite precision and so involves some destruction of information (chopping of decimals).
2. If the complexity of the system increases under repetition of the process, the loss of information will be so big that reversal of is impossible.
3. A prime example is the development of turbulence in laminar fluid flow, which is irreversible. The laminar state cannot be recovered from the turbulent.  

For a popular exposition of this idea see The Clock and the Arrow.

Two New Approaches to Understanding the Second Law

Stephen Wolfram has recently presented a new approach to understanding the 2nd Law of Thermodynamics based on (i) computational irreducibility and (ii) our nature as computationally bounded observers supplemented by the remark: 

• Other observers—or even our own future technology—might see things differently.

The 2nd Law is to Wolfram not a law of physics per se without observers, but something in the mind of human observers with all their limitations, which may not be shared by any form of observer. 

Myself I have over a long period of time been searching a different understanding based on (a) finite precision computation and (b) stability, as developed in detail in The Clock and the Arrow; A Brief Theory of Time and Computational Thermodynamics.

Here (a) connects to Wolfram by seeing the evolution in time of a physical system from one time instant to the next as a form of computational process, where forces at current state are evaluated and so form the dynamics over a small time step creating a new state.  

But (b) has no counterpart in Wolfram's understanding. The essence of stability is that it makes a distinction between a step (or sequence of steps) forward in time and a step (or sequence) backward in time, as an expression of the direction of time expressed in a difference between forward stability and backward stability.  

Here, forward stability means that a step forward in time is possible under finite precision computation (chopping of decimals), while keeping the coherence of the state. The next state thus does not critically depend on the number of decimals kept in the forward computation. The typical case is turbulent flow in e.g. a water fall, where gross features of the water fall are maintained under turbulent fluctuations. 

The essence is here the fluctuating nature of turbulence allowing forward in time computation of mean values under chopping of decimals. This connects to the ageing of a photo with small details being lost while main features remain,  like in Photoshop smoothing of a photo by averaging over local details corresponding to chopping decimals. 

On the other hand, backward in time computation corresponds to unsmoothing, which requires very high precision or simply is impossible. The decimals that have been chopped during forward computation/smoothing are lost and cannot be retrieved and so an original photo cannot be fully recreated/computed from a blurred one. 

Wolfram puts forward the limitations of an observer as an explanation of impossibility of time reversal. 

I seek an explanation in different stability aspects forward and backward in time of inherent physical nature the same for all observers. 

Your choice.

War Irreversibility and Direction of Time

There are physical processes which are reversible, like the clock pendulum swinging back and forth without stop, and there are processes which are irreversible, like starting a war ending in mutual large scale destruction without possibility of return. What is the difference? This connects to the previous post on a proof of the 2nd Law of thermodynamics as the main unresolved question of physics (modulo the resolution/proof suggested in Computational Thermodynamics).

The Clock and the Arrow: A Short Theory of Time seeks the reason why physical processes move forward in time, including all forms of life showing progress from birth to death, thus expressing irreversibility, as a combination of (i) finite precision computation and (ii) increasing tension/difference. 

Time reversal of smashing an egg is impossible because of lack of precision in a restoration/reconstruction process. This is different from the standard explanation based on statistical mechanics claiming that time moving forward is more likely than backward, which is not illuminating.

A basic model combines (i) convection, (ii) diffusion and (iii) reaction = production/destruction, into a system with competing processes of:

• increasing tension/difference: convection + production  
• decreasing tension/difference: diffusion + destruction. 

As an urgent example, a war is the (inevitable) consequence of an arms race a during pre-war phase building tension/difference until so large that any little spark sets (lack of precision) off an avalanche of  destruction. Here displacement of weapons into local accumulation building tension as an anabol process corresponds to convection (assembling Uranium 238 to an atomic bomb), and levelling everything to gravel (pressing the button) corresponds to diffusion/desstruction in a metabol process.

Another example is the transition from laminar fluid flow with diffusion no longer strong enough to control tension/difference created by convection into turbulent flow with small scale motion turned into heat in turbulent diffusion. 

Irreversibility with a direction of time is here expressed by the fact that an anabol process as a construction process requiring precision, is slow (brick by brick building a house or letter by letter writing a book), while a metabol process like burning a book can be quick because coarse precision is enough. The reason unburning of a book is impossible is that the fine precision required cannot be met in finite time. 

The ocurrence of irreversibility is an inevitable consequence of increasing tension from convection + production creating increasingly sharp differences, which ultimately have to be broken down in some form of destructive Reset.  In the Green Reset the Industrial Society built by fossil fuel over a period of 100 years creating increasing inequality will have to be destroyed into a New Fossil-Free Society of equality, according to Agenda 2030.   

  

Destruction of human civilisation in a nuclear power exchange is a matter of minutes, does not require precision bombing and is irreversible. 

Life is irreversible because the anabol process of building a living organism cell by cell with finite precision is slow, while the metabol process required to sustain growth is quick and so cannot be reversed with finite precision. 

Bergson and Deleuze on Duration of Time (and Irreversibility)

                                                             Duration of thinking.

                                                             Duration of smoking.

Both Bergson and Delueze say something essential about time by stressing the concept of duration or "thickness of the present" as a transformer changing past into future. To Bergson and Deleuze change is thus a fundamental aspect of time, and maybe time can simply be identified with change.

Deleuze makes a distinction between a more simple elementary concept of time represented by the Greek god Aion as the simple tick of a clock in linear progression with an infinitely thin present tick as an infinitely thin cut between past and future, and a more complete concept of time represented by Chronos as the duration transforming past to present. One of Bergson's masterpieces is Duration and Simultaneity.

Chronos thus represents the continuity of a phenomenon or being under change, where the past is transformed into present into future in a continuous change which loads the present with history, and which then gives time a direction. Aion represents discontinuous time without history and direction with every tick the same.

We understand that Chronos gives a fuller picture of time than Aion, which is the view of Einstein with his space-time events without history which has created so much confusion and misunderstanding.

Chronos concept of time is present in the generic mathematical model of a time-dependent problem as an intial value problem of the form: Find a function $u(t)$ of a real variable $t$ named time, such that

• $\frac{du}{dt} = f(u)$ for $t > 0$ 
• $u(0) = 0$ 

where $f(v)$ is a given function of a vector-valued real variable $v$. Here the differential equation in time-discretized form expresses the transformation of the state $u(t)$ from one time instant $t$ to the next $t + dt$ with the length of the Chronos duration equal to the time step $dt > 0$, carrying along (some of) the history of previous states, in an update of the form $u(t+dt) = u(t) + f(u(t))dt$ with $u(t)$ carrying the history and $f(u(t))dt$ the change.

With the duration of the present equal to the time step, we understand that the length of the duration of the present is not given once and for all, but like the time step can be smaller or bigger depending on the precision of time resolution of an underlying continuous evolution in time we may choose, and like the time step is never zero.

The irreversibility of certain processes as time evolution of $u(t)$, then is expressed in the initial value problem as stability in forward/increasing time and instability in reverse backward/decreasing time. The reversibility or irreversibility of certain processes is thus determined by stability aspects with actual physical processes being represented by intial value problems which are stable in forward time, and irreversible physical procesess being represented by intial value problems which are unstable in backward time and thus not realizable as physical processes.

The 2nd law of Thermodynamics as the law of irreversibility of certain physical processes thus can be based on stability which is a physical property, instead of probability which is unphysical and has ruined modern physics.

It is more illuminating to give evidence of irreversibility as physicsl break-down or blow-up of unstable processes, than to say following Boltzmann that natural processes have a tendency to move from improbable to probable states (rather than the opposite), which is an empty tautological statement.

PS1 Concerning simultaneity, which is so important to Einstein, one may say that physics does not care about this concept, because in physics things happen locally and if two particles collide they do it at the same time. It would be ridiculous to report as a curious fact of a new physics that you met a person in a certain street corner at 1.00 pm once during a day according to your clock, while the person you met insisted that he/she met you once at 2.00 pm according to his/her clock the same day at the same street corner.

This would not be accepted as evidence of new physics, only as evidence that at least one of the clocks was off time. Right?   And yes, Einstein's physics is at most epistemology but not real physics, according to Lorentz.

PS2 Concerning time as change, one may identify time with motion as change of position, of the Earth, of the arms of a clock or with propagation of light. The basic question is then to answer how motion is possible as a solution of Zeno's Paradox of the arrow which at each moment is still and yet moves or changes position. A resolution is presented in posts on Zeno's paradox.

PS3 Bricmont and Sokal as Fashionable Nonsense accuses Deleuze and Guattari of using mathematical language in imprecise way in philosophical texts, which may be more or less meaningful, but forgets that Einstein in a scientific physics text is even more imprecise which is not meaningful. 

Konrad Zuse on The World as Clock with Finite Precision

                                      Konrad Zuse pondering if physics is digital? If so, time has a direction.

I have recently discovered that the idea which I have pursued in different pieces of work, the idea to view physics as a Clock with Finite Precision, was expressed in 1969 by the German computer pioneer (and civil engineer) Konrad Zuse (who constructed the first working computer named Z3 in 1941) in the remarkable article Calculating Space on Digital Physics, starting out with the following experience which I share with Zuse:

• The work which follows stands somewhat outside the presently accepted method of approach, and it was for this reason rather difficult to find a publisher ready to undertake publication of such a work. 

Here are some highlights from Calculating Space, connecting in particular to my book The Clock and the Arrow: A Brief Theory of Time about the 2nd law of thermodynamics and the direction of time:

• It is obvious to us today that numerical calculations can be successfully employed in order to illuminate physical relationships. 
• To what extent are the realizations gained from study of calculable solutions useful when applied directly to the physical models? Is nature digital, analog or hybrid? And is there essentially any justification for asking such a question? 
• The examples of digitalization of fields and particles which have been preented are in their present unfinished form still far removed from being able to serve in the formulation of physical rules. Nevertheless, they give a rough impression of the possibilities for using the tools of the automaton theory to answer physical questions.
• The question to what extent it is possible to consider the entire universe as a finite automaton depends on the assumption which we make in relation to its dimensions. 
• An infinite information content is required for an unlimited spacetime element. It is practically impossible to simulate such a model with computers because of the necessity of infinite number of places required. 
• The sources of error are correspondingly great in the extremely large number of collisions between gas molecules, and these errors quickly lead to deviations from theoretical processes.
• This means that the better the causality rule is approximated in the reverse time direction, the more calculations we must be prepared to carry out in our model. This leads to the result that simulations of universal systems with causality functioning in both time directions belong to the category of “unsolvable” problems.
• Of course, it can be said that this is true only for calculating simulative models. But this result should encourage us to reconsider the matter. Are we justified in assuming a model of nature for which no calculable simulation is possible? 
• From this point of view, it appears that the frequently advanced argument of determination in both time directions should be fundamentally reexamined.
• But if Zuse didn’t hit upon the concept of universal computation (as Turing did), he was interested in another very deep question, the question of the nature of nature: “Is nature digital?” He tended toward an affirmative answer. (from Afterword)

Time Is Real

Not Even Wrong reports in Time Reborn that

• Lee Smolin’s new book, Time Reborn, is out today. For more about the ideas in the book, see video of a talk here, and an interview here.

The talk is summarized as follows:

• What is time? Is our perception of time passing an illusion which hides a deeper, timeless reality? Or is it real, indeed, the most real aspect of our experience of the world? Einstein said that "the distinction between past, present, and future is only a stubbornly persistent illusion," and many contemporary theorists agree that time emerges from a more fundamental timeless quantum universe. But, in recent cosmological speculation, this timeless picture of nature seems to have reached a dead end, populated by infinite numbers of imagined unobservable universes. 
• In his talk, Lee Smolin explains why he changed his mind about the nature of time. Like many fellow theorists, he used to believe time is an illusion, but he now embraces the view that time is real and everything else, including the laws of nature, evolves. Drawing from his new book, Time Reborn, Smolin explains how the great unsolved problems in physics and cosmology may be solved by adopting the view of a real time. then he will go beyond physics to explain how our view of time affects how we think of everything from our personal and family lives to how we face major problems such as climate change and economic crisis. In a world in which time is real, the future is open and there is an essential role for human agency and imagination in envisioning and shaping a good future.

This is in the line of my own ideas exposed in The Clock and the Arrow and Many-Minds Relativity.

Time is real, while the reality of the rest can be debated.

Confused Feynman on Direction of Time

                                             Feynman illustrating reversible mechanics.

Feynman thrills an audience of Cornell students by a lecture on the Distinction of Past and Future or  the Direction of Time and Irreversibility (Part 1, Part 2, Part 3, Part 4):

• If you drop a cup and it breaks, you can sit there a long time waiting for the pieces to come together and come back into your hands.
• We remember the past, we do not remember the future.
• Basic laws of physics are time-reversible, without distinction between past and future.
• Many ordinary phenomena based on reversible atomics are irreversible.  How come?
• It comes from the characteristic that if we start with an ordered system and have the irregularities of nature of bouncing then the thing goes one way.
• The thing goes from ordered to disordered.
• How did it get ordered in the first place?
• We have to add the hypothesis that the past was more organized than the present.

We hear Feynman present the standard explanation of the irreversibility of certain processes as an effect of irregularities destroying order, combined with a hypothesis that the past was more ordered than the present. 

But Feynman's explanation is not convincing, since the hypothesis of more ordered past is not explained, not even made plausible.

The interested reader finds a new approach to the irreversibility of systems based on reversible basic laws based on finite precision computation as realization of the irregularities hinted at by Feynman, developed in a setting directed to a general audience in The Clock and the Arrow: A Brief Theory of Time: 

Irreversibility is here explained as an effect of instability of certain processes combined with finite  precision computation: The smashed cup cannot be re-assembled because the required high degree of precision cannot be realized. Read and reflect!