On Time

What is time?

This is perhaps the most clichéd way of writing an article on this topic. Unfortunately, it is the best start that I could think of. Regardless, it does seem to have a simple answer at first glance. Seemingly, the intuitive answer is – time is what allows changes to happen. Or at least something along those lines. In fact, this was what everyone thought about time until one brilliant man Albert Einstein came along and introduced General Relativity (Einstein is not the only one deserving credit, there are many other people without whom relativity would have never worked out – Minkowski, Lorentz, Schwarzschild and many more). General Relativity just knocked over all understanding of space and time that we had. Einstein used beautiful mathematics to show that gravity can be described geometrically by the curvature of a surface. The surface was a union of space and time. This was the first instance that our understanding of time was questioned.

It is not surprising that our notion of time is flawed. Our intuition was developed by men throwing spears and rocks. Our idea of reality was limited to and shaped by our ability to observe. Our perception of nature was developed by classical definiteness, not quantum fuzziness. Newton, when he single-handedly developed what we now call Classical Mechanics, used the notion of absolute space and absolute time. There were these ever constant entities called space and time. His formulation of physics also did not establish an upper bound on the speed limit. Infinite speeds were allowed.

The fact that the speed of light is a constant was hinted at by many physicists. There is an urban myth that there was a physicist who liked to play about with constants. Once, as he was shuffling about with the values of the permittivity of free space (a constant used in calculations related to electrical phenomena) and the permeability of free space (the constant used in calculations related to magnetic phenomena), he got the speed of light as the result of the computation. This should not be surprising as light is an electromagnetic wave. The fact that the speed of light is a constant was firmly established by the Michelson-Morley experiment. Ironically, that experiment was developed to show that light needed a medium, hypothesized as aether, to move it. Everyone expected to observe that the speed of light would vary based on the direction in which we make the measurement. However, the speed of light was measured to be the same in all directions. This gave Einstein the very basic ingredient that he needed – confirmation the speed of light is a constant. He assumed the speed of light in vacuum to be an absolute constant, something that cannot be exceeded even relatively. He made another assumption, the laws of physics apply in the same fashion in all directions (to put it slightly technically, the invariance of the laws of physics). Just with these assumptions, he shook the world.

The brilliance of Einstein lay in his unique ability to conduct gedankenexperiments (a physicist’s fancy way of saying thought experiment). And the best way to understand why space and time are not absolute, due to these two assumptions is to conduct one gedankenexperiment. Imagine a single photon propagating unhindered through the cosmos. Now consider yourself accelerating towards the photon. As you are accelerating you start noticing weird effects. Any other photon that is traveling towards you will take longer to reach you, even though they are all from the same starting point. An interesting note on photons, they are responsible for visual imagery. So, if a photon takes longer to reach you, that means that information itself takes longer to reach you. So, the faster you travel, the slower information will reach you and this will give the appearance of time slowing down. At the speed of light, time will appear to stop. And photon emitted after you have reached the speed of light will never reach you. The only photons that you will receive are the ones that reach you the moment you start traveling at the speed of light are the ones that hit you at that instant. So, you get no new information. It appears as though time has frozen for you. (This is to put to it intuitively, however, relativity tells us that time actually does not exist when one travels at the speed of light.) interestingly, if you were allowed to break the speed of light barrier, it would appear as though you were traveling back in time as you could now reach the photons that had already passed you by.

The conclusion that we draw from this is that we experience time due to information processing. Information is bounded by the speed of light. Therefore, our speeds will determine the passage of time. This was the first time the notion of absolute time was, not only questioned, but also annihilated. There is another gedankenexperiment that we can do that will cement this idea.

Consider a single photon between two perfectly reflecting mirrors, in vacuum. Perfectly reflecting means that the photon will not be absorbed into any of them. The speed of light in vacuum is a constant. So, the time interval between two reflections can be considered to be constant. So, this allows to accurately measure time. Now, set them in motion with some arbitrary velocity (lesser than the speed of light). For an observer in the mirror, he observes no difference. For another external observer who observes the moving mirrors in his frame of reference will see that the actual path between two reflections is not superimposing straight lines, but a series of continuous triangles. The distance that the external observer observes the light to travel is much more. Therefore, the observer will conclude that time will slow down for the moving observer.

This firmly established the fact that time is not absolute. It must be relative.

There are other questions related to the time that we must consider. Ones that will have a deeper impact. Let me put forth a question so basic that at first glance it seems to be a trivial one. Why is there only one direction of time? Physics has no answer to this. If you think about it, not a single law in physics talks about time changing. They only talk about changes that occur in intervals of time. In fact, there is only one law in physics that hints at a direction of time. The much famed second law of thermodynamics. In simple words, it says that a thermodynamical quantity that we call entropy (in layman terms, entropy is a measure of disorder) always increases. It can never decrease with time. This does not tell us why entropy or disorder in nature must increase, all that we know that is just does. There is another flaw in using this to talk about only one fixed direction of time. Entropy can remain constant. When entropy remains constant, we cannot say if time is constant or if time is actually increasing.

Classically, the notion of time having one direction cannot be concluded. Does Quantum Mechanics say anything about this? Turns out, no. Quantum Mechanics itself is built on the notion of absolute time. In fact, there is another thing in Quantum Mechanics that makes us question time. Every observable quantity in Quantum Mechanics is represented by a mathematical beast called an operator. An operator is actually a simple thing. Think about the wave function describing a quantum system as a dictionary. Then, the operator corresponds to a shortcut to find the word. Applying an operator on the wave function gives us the possible values of the chosen property that the quantum system can take. For example, on applying the momentum operator on the wave function will give us information about all the possible momentum states that the quantum system can exist in. Time is very much a measurable quantity. However, there is no corresponding operator that someone has managed to develop that can give us information about time.

This is not the only problem with our idea of time. Quantum Field Theory too has no answer for us. The final answer comes from our efforts to develop a Quantum Theory of Gravity. In the fundamental Equation of Quantum Gravity, the Wheeler De-Witt equation, time does not appear! Seemingly, time does not seem to exist in the most fundamental theory of nature. Is it possible to describe a theory of nature independent of time?

A brilliant physicist, Julian Barbour did exactly this. He asked if it was possible to develop a theory of the world that did not require time as a fundamental property. And he succeeded, to a large extent. In a time independent theory of the world, with time as an emergent phenomenon, he described changes and such as configurational changes. He developed the theory of Shape Dynamics. Now, as studies have gone deeper into Quantum Gravity and Shape Dynamics, we have come to the conclusion that time is not needed to describe nature at a fundamental level. Time does not necessarily have to exist.

We have come a long way from our ideas of absolute time. We first realized that time was relative and then the time is not a necessary condition for describing nature. This has definitely failed to answer the clichéd question that I mentioned at the beginning of this article.

Clearly, we experience time. We remember the past, we form memories in the present and we mostly cannot predict the future. The answer to the question why we experience time boils down to memories. It is our ability to form and retain memories that help us distinguish the past, present and the future. Memories are what forms our notion of time. This can be made more intuitive through a gedankenexperiment.

Consider an individual who is unable to form memories, i.e., he or she has absolutely no form of a short-term memory. The only thing that an individual is able to experience is the present. It is like a video-camera that is switched on but is not recording. The person cannot make any memories, therefore, cannot be aware of the existence of a past. Clearly, that individual will have no notion of time. The individual’s entire existence will be independent of the variable – time. What we call and experience as time is clearly a psychological phenomenon.


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