Our Struggles with Chronos

Is no rebellion possible against the tyranny of time?

Imagine yourself enclosed in a narrow cubi­cle in which you are hardly able to move. The very idea of such an imprisonment makes you feel suffocated. But you are imprisoned, even more exactly, in the present instant of time.

In spite of the fact that the present instant is in permanent motion towards the future, you are unable to free yourself from tight constraints of the present. You cannot go back to the past, because the past has already collapsed into nothingness; you cannot accelerate your run into the future, because the future still does not exist. You are living on the edge of the razor surrounded by the twofold abyss of void: the past and the future.

Ancient Greeks believed that old Chronos was the absolute ruler of “gods and people”. Is the tyranny of time an ontological neces­sity against which no rebellion is possible?

The first breach in Chronos’s iron power came from a quite unexpected side. Physics, the science of matter, was believed to be the most faithful enforcer in the service of Chronos; yet it was in physics that there appeared the first signs of rebellion. I leave my morning cup of coffee on the table to pick up a telephone call. After coming back, I find the coffee cold and undrinkable. There are strong reasons to believe that with this simple process the drama of time flow is connected. The process of cooling, or of energy dissipation, has been mathematically modelled by physicists and described as the process of “entropy increase”.

The law of nature stating that, when irreversible processes occur in isolated systems, the entropy increases was the first law of phy­sics that was sensitive to the direction of time or the “arrow of time”.

And here we meet the first conundrum. Cooling is a statistical process consisting of energy interchange between a great number of particles. If the arrow of time depends on such processes, it is meaningful only with respect to great aggregations of particles. You cannot do statistics on a single particle. Does this mean that a single particle does not experience the directional lapse of time?

The true troublemaker in the city of Chronos was Albert Einstein. In his Special Theory of Relativity, absolute time has been degraded (by the constant velocity of light) to the role of local indications of various clocks depending on their relative state of motion. The overthrowing of absolute time’s hegemony had manifold consequences: measuring rods behave differently in different reference frames, mass and energy are equivalent, there are events that cannot be causally related with each other. Although these effects are too tiny to be observed in everyday life, when in modern particle accelerators such as Cern – where one deals with velocities comparable to that of light – they dominate the scene, and one could do nothing without Einstein’s formulae.

Tyrants do not surrender easily. When Chronos noticed that he was losing, he decided to share his power with space. In 1908 Herman Minkowski formulated the Special Theory of Relativity in geometric terms. Time is relative but space-time is absolute, and Einstein’s Special Theory is nothing but the geometry of space-time.

Space-time does not “flow”, it exists “in one piece”. If so, it is perhaps our consciousness that, like a carriage wheel always touching the road at a single point, rolls along space-time and creates an illusion of a flowing time.

Only much later did Roger Penrose, by introducing the concept of bifurcating space-times, demonstrate that it is possible to reconcile the idea of becoming with the idea of space-time geometry.

In Einstein’s general theory of relativity, the modern theory of gravity, space-time remains absolute, but it can bend in manifold ways depending on the matter distribution throughout the universe. Space-time curvature strongly intervenes in the process of decomposing space-time into space and time separately. This fact can play various tricks with our sense of time. We would agree that a process evolving in time, as viewed by an observer (a historian), deserves the name of history. The transitional character of time can truly be regarded as an ontological foundation of history. But now it depends on the curved space-time geometry. The state of motion of a given historian changes the intimate relationship between the historian and the process being investigated, and it is this relationship that constitutes the history. This effect conspicuously manifests itself in regions in which space-time is strongly curved; for instance, around a ­massive star that has consumed its nuclear fuel and contracts under its own gravitational field.

When this process is viewed by an observer collapsing together with the star, its history is finite and it abruptly ends up in the black hole singularity. When the same process is viewed by an external observer, the history of the collapsing star lasts to infinity.

Relativity theory is a macroscopic theory, but if we want to penetrate the very roots of Chronos’s power we must reach the most fundamental layer of the world’s structure, the layer on which all physical forces are unified and universal gravity exhibits its quantum nature.

So far we have no such theory; we are only trying to tame this hypothetical layer with the help of various more or less speculative conceptions. The main obstacle is by no means the lack of clever ideas, but rather the painful deficiency of empirical indications. However, even our partial results show that, on our road to the final theory, old Chronos keeps for us a host of surprises.Why, for instance, does electromagnetic radiation propagate from its source to infinity and not vice-versa, while our well-established (and empirically tested) electromagnetic ­theory admits on equal footing both kinds of solution? What mechanism selects one kind rather than the other? Do we meet here another arrow of time? If so, what is its relationship with the entropic arrow of time?

Questions accumulate. Why does an electron know immediately about the result of a measurement made on another electron, even if the two are at two extremities of a galaxy? Why do elementary particles preserve their symmetries with respect to time reversal with the exception of the K0 meson, which seems to feel time’s intricacies better than other particles? Is the fact that anti-particles can be described as particles living in reversed time a mathematical trick or a symptom of deeper meaning?

Even if we have no answers to these perplexing questions, they are illuminating in some sense. The very fact that we ask them suggests that time is not a priori with respect to the universe but is somehow involved in the process of its becoming. This suggestion is strengthened by slowly accumulating indications that on the fundamental level there is no space and no time, at least in the usual sense, and that both space and time emerge from primordial symmetries only on higher levels of complexity.

Steven Weinberg and many physicists with him are dreaming Dreams of a Final Theory (his book describing the search for nature’s ultimate laws). Until we have a solid mathematical structure well rooted in trustworthy empirical results, the final theory will only be the subject of our dreams.

When we at last have this theory, will it end our struggling with Chronos? Life is a journey through time. As long as we live, let us have our dreams.

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