A capricious instant of time - part 1

A capricious instant of time - part 1

Fractal instants of time

Abstract

A fractal is a mathematical set that exhibits a repeating pattern that displays at every scale. If the replication is exactly the same at every scale we are left with a self-similar pattern. For some time I have been working towards constructing a framework within which a tick of a clock (an instant of time) might be contained in a self-similar style of a fractal. It's genesis in the quantum realm and emerging into the large scale universe as a perception of time. The fractal's dimensionality is utilized as temporal content in the same manner that fractal scales by some non-integer exponent.

This article serves as the basic background in the various slates on the meaning of time whilst Part II provides a more detailed look at time as treated by the use of fractals.

It will never be today again

There are many approaches toward understanding the phenomenon of time. We perceive time as past present and future. We think of time flowing like a river - swift, unyielding; there is no holding it back. The passage of time seems very concrete - the past, the present, aging. Surely the process of time is very real.

Time is one of the most common Nouns in the english language. We are ruled by time, and it waits for no one. Time, Einstein once said is the only reason why everything doesn't happen at once. And from those days of carefree innocence and pleasure, Dr. Seuss asks, how did it get so late so soon? It’s night before its afternoon. December is here before its June. My goodness how time has flown; how did it get so late so soon?

The beautiful story told with poignant simplicity of a six-year-old boy, Rob in Randolph Stow’s Australian novel; Merry-Go-Round in the Sea captures an innocence; uncluttered by erudition that only a child can posses.  He followed, crunching the big dry leaves. He was thinking of time and change, of how, one morning when he must have been quite small, he had discovered time, lying in the grass with his eyes closed against the sun. He was counting to himself'. He counted up to sixty, and thought: That is a minute. Then he thought: It will never be that minute again. It will never be today again.

When we measure the speed of a car, we are just comparing its motion to the motion of the hands of a clock and also indirectly to the fractional motion of the Sun across the sky. We seem to be measuring speed with something abstract called time; we are actually just comparing a known motion such as the Sun with an unknown motion of the car. Time is a way of describing different kinds of motions. But as we shall see, these processes could be compared directly without making reference to time. Time may have no independent existence - it may be just a common unit of motion making the world that is filled with motion easier to describe.

There seems to be a difference between time and the phenomena on which time is projected. Time can be spoken of only in relation to phenomena susceptible to change, and thus transitory and impermanent. If there is no process of change, then can one conceive of time in the first place, an independent time without relation to any other?

But still, time is a familiar comrade. We have lived with it and under its spell our whole life; it’s been a predictable if not an irksome passenger. We’ve never known of a time without it. We conceive the past as being immutably fixed, and the future as undefined and nebulous. As time passes, the moment that was once the present becomes part of the past; and part of the future, in turn, becomes the new present. In this way time is said to pass, with a distinct present moment "moving" forward into the future and leaving the past behind.

And yet, as natural as time may seem, our intuitive endorsement isn’t reflected in modern physics. Time is actually a difficult subject; perhaps one of the most difficult. Einstein was first to notice cracks in time. His special theory of relativity showed that time and length are not as absolute as everyday experience would suggest: Moving clocks run slower, and moving objects are shorter. Here, the concept of simultaneity is not universal and observers in different frames of reference can have different perceptions of whether a given pair of events happened at the same time or at different times.

Even worse, distorted space and time influence the way material objects behave. And there is no single special present but that all moments are equally real. The equations of physics don’t tell us which events are occurring right now. The present moment does not exist in them, and therefore neither does the flow of time. 

Within this intuitive understanding of time is the philosophy of presentism - only the present exists. It does not travel forward through an environment of time, moving from a real point in the past and toward a real point in the future. Instead, the present simply changes. The past and future do not exist and are only concepts used to describe the real, isolated, and changing present.

Enlightenment

Sir Isaac Newton founded classical mechanics on the view that space is distinct from body and that time passes uniformly without regard to whether anything happens in the world. For this reason he spoke of absolute space and absolute time, so as to distinguish these entities from the various ways by which we measure them. From antiquity into the eighteenth century, contrary views, which denied that space and time are real entities, maintained that the world is necessarily a material plenum. Concerning space, they held that the idea of empty space is a conceptual impossibility. 

Space is nothing but an abstraction we use to compare different arrangements of the bodies constituting the plenum. Concerning time, they insisted, there can be no lapse of time without change occurring somewhere. Time is merely a measure of cycles of change within the world.

Eternalism

Einstein would often say "people like us who believe in physics know that the distinction between the past the present and the future is only a stubbornly persistent illusion." In Einstein’s universe, sometimes called the block universe, the past, present and future co-exist superimposed in different dimensions. This ontological nature of time of time which dates back at least to the Cambridge philosopher J. M. E. McTaggart's B-Theory of time, first published in The Unreality of Time in 1908. If we pursue this thinking to its logical limits we could argue that dinosaurs are still alive and roaming the Earth in other time dimensions; so are multiple copies of the whole universe and us as well. 

Time is laid out in a kind of time-scape similar to a landscape; future and past already exists and there cannot be a free will. Einstein believed that free will was just an illusion, and that awareness of this lack kept him from taking himself and others too seriously. Even though Einstein played a prominent role in the early development of quantum mechanics; as a determinist, he felt that the world is a structured and rigid manifold where effects follows cause and all things should be predictable, given the right information.

The Lord is subtle but not malicious

If time-scape is already laid out then what causes us to move through this time-scape? How does our consciousness move across time? What makes it move and why can’t we willfully move it anywhere anytime?

Time hasn’t sat idle over the last 100 years – a period that has seen the rise of quantum mechanics, cosmology and particle physics, among other fields. These have fundamentally changed our understanding of space, time and matter – perhaps even going as far as shedding light on the meaning of reality itself.

As already mentioned quantum mechanics didn’t agree with Einstein’s sensibilities. His refusal to accept the quantum mechanics revolution as complete reflected his desire to see developed a model for the underlying causes from which these apparent random statistical methods resulted. He was often quoted defending his unyielding stubbornness; invoking a kind of a God whose authority has little room for random or statistical quantum fluctuations. At one point and after reiterating his prediction that God “does not play dice," or "The Lord is subtle but not malicious" Bohr counters with "Einstein, stop telling God what to do." 

Niels Bohr was of course the Danish physicist who along with Werner Heisenberg, Max Born and others made the initial important contributions to the overall understanding of quantum mechanics. Simply put, quantum mechanics is the study of matter and radiation at an atomic level. But it is also a theory that challenges our imagination. It seems to violate some fundamental principles of classical physics, principles that eventually have become a part of western common sense since the rise of the modern worldview in the Renaissance. 

In the realm of quantum mechanics, observing something actually influences the physical processes taking place. The moment at which a measurement takes place is the moment at which the randomness lying at the heart of quantum reality expresses itself. Light waves act like particles and particles act like waves. Matter can go from one spot to another without moving through the intervening space. Information moves instantly across vast distances through what is called quantum entanglement. A phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated. In fact, in quantum mechanics we discover that the entire universe is actually a series of probabilities. The notion of time, not surprisingly doesn’t escape the nuttiness of quantum mechanics either. 

Hiatus

It is thought that time may be a by-product or side effect of some other, more fundamental process of reality. Recently, reports of quantum experiments are said to reveal how time emergences from entanglement. Back in the mid-1960s, a breakthrough by physicists John Wheeler and Bryce DeWitt allowed the successful integration of  previously incompatible ideas; that of the large scale features of the universe with the very small as described by quantum mechanics. But there was a catch. The realization that time played no role whatsoever in this formulation. In effect, it says that nothing ever happens in the universe. A conundrum called “the problem of time.”

In 1983, the theorists Don Page and William Wootters came up with a novel solution building on the exotic property in which two quantum particles share the same existence, even though they are physically separated. Their idea was that the way a pair of entangled particles evolves is a kind of clock that can be used to measure change. But the results depend on how the observation is made. 

One way to do this is to compare the change in the entangled particles with an external clock that is entirely independent of the universe. This is equivalent to God-like observer outside the universe measuring the evolution of the particles using an external clock. In this case, Page and Wootters showed that the particles would appear entirely unchanging, that time would not exist in this scenario.

But there is another way to do it that gives a different result. This is for an observer inside the universe to compare the evolution of the particles with the rest of the universe. In this case, the internal observer would see a change and this difference in the evolution of entangled particles compared with everything else is an important a measure of time. This is an elegant and powerful idea. It suggests that time is an emergent phenomenon that comes about because of the nature of entanglement. And it exists only for observers inside the universe. Any God-like observer outside sees a static, unchanging universe, just as the Wheeler-DeWitt formulations predict.

Space is over rated

But of course, none of this is straight forward. Quite an intentionally provocative comment caught my ear when the Caltech physicist Sean Carroll spoke at the 2011 FQXi conference, Setting Time Aright.” Carroll, typical in his casual and light hearted demeanor spares no time lurching into his talk with the words “I like time; I think time is important, so I want to say that space is totally over rated where time is under appreciated.”

According to Carroll a lot of people are trying to get rid of the notion of time. He draws a contrast between time and the approximated nature of space as found useful in certain circumstances; such as the obvious manifestation in quantum mechanics. We mistakenly imagine a particle to have a wave function that is a factor of space and time - a wave throughout space. In actual fact the wave function in quantum mechanics is not a function of space at all, rather a function of a configuration space. We don’t have the situation where a single wave function exists for every particle; instead there is a wave function for the entire universe - it is a function of what configuration the universe could be in. Space looks different in quantum mechanics where time looks the same. Time is there only once – it’s not a different time for every particle in the universe but a different space for every particle in the universe. 

Fractal instants of time

A fractal is a mathematical set that exhibits a repeating pattern that displays at every scale. If the replication is exactly the same at every scale we are left with a self-similar pattern. For some time, I have been exploring how a clock tick (an instant) might be self-similar at scales arising within the quantum realm and manifesting itself as part and parcel perception of reality. The fractal's dimensionality is utilized as temporal content in the same manner that fractal scales by some non-integer exponent.