Whether we inquire or not, time will pass
Does time pass, or makes everything pass?
For empires bygone, it has been detrimental
But to seekers, it reveals truths fundamental
[BG 2.16]

This article describes a journey taken up by a professor and a few of his students. A ride on a bus from London to Oxford through the meadows and hills. A ride on dialogue on the nature of time through clocks, cosmology and civilizations. And a ride on time into the fundamental nature of the world and the self.

Scene

It was early morning. Prof. Gopinath and some students were on a bus from London to Oxford. Buses in the early morning were not crowded, so they could get the front seat on the upper deck. As the bus started plying from Victoria station, Karan looked out of the large front window and saw the clock tower in front of his face. Karan looked awestruck by the large clock tower.

Subal: What is Time?

Karan: Seven fourteen a.m.

Subal: (cheekily) I mean, what is TIME?

While Karan looked perplexed, Subal turned to Prof. Gopinath, sitting on the next seat, with an inviting gesture.

Professor: Indeed, this clock tower reminds us of the days of yore. Civilisations have evolved, and so have clocks. Whether it is temple bells, sundials, mechanical clocks or electronic watches, timekeeping has been a key activity of humanity.

Ravi: Whether it is a class, an exam, or an Olympic race, precise time measurement is essential. Businesses bill their clients based on time. Computers run their applications synchronously with clocks. Life seems impossible without a clock.

Neeti: Even without an external clock, we seem to have an inherent mechanism to keep time. When I listen to music, even a slight deviation of beats from their timing makes it sound disorderly.

Ravi: But, if done expertly, the deviation of beats may even beautify the music more.

Neeti: Certainly, our ears are very sensitive to time in music.

Karan was intrigued and saw this as an excellent opportunity for a rigorous discussion with the professor.

Karan: Would you like to say what TIME is?

Professor: Sure. Why don’t you start with your perspective?

Experiencing Time

Karan: I think it is a subjective experience; it depends on our state of mind. When we are enjoying, it passes quickly, and when we are in misery, it seems not to pass.

Professor: Surely, time has a subjective aspect, but let us discuss the objective concept of time.

Karan: It is one of the dimensions in the four-dimensional space-time. The arrow of time moves in one direction only.

Professor: The concept of four-dimensional Minkowski space is interesting.

Ravi: Could you please explain it to me?

Karan: The speed of light is found to be constant in all frames of reference. Suppose I am standing and see you quickly going past me on a bicycle. Now, if I start running along with you, I will perceive you going away slower. Technically, your speed of motion with respect to me changes with my speed of motion.

Ravi: Yes, from this bus, we can see the cars on the highway moving slowly with respect to us.

Karan: However, for light, this does not hold. The speed of light with respect to me is constant, irrespective of my speed of motion. This is called relativity. This effect profoundly impacts real-life measurements in fast-moving frames, e.g., satellites. To formulate this observation mathematically, Minkowski proposed a four-dimensional space with three space dimensions and a time dimension.

Professor: Well explained. But please think deeper and start from the first principles. From there, we can gradually build up to concepts like relativity. What is the most basic understanding of time?

Neeti: Time is a progression of events.

Professor: Could you think of some examples?

Neeti: Consider the wheel of the bus. It is in motion.

Professor: How do you experience motion?

Neeti: Motion is with respect to time.

Professor: But we have not defined time yet.

Neeti: The orientation of the wheel is changing.

Professor: How do you know the orientation?

Neeti: By seeing it?

Professor: Good. We can measure the orientation of a wheel in different ways - by seeing, touching, etc. And we observe the change in the orientation . Now, if I wish to record it, say, is this, then this, and so on, I need to write as a function of a quantity or variable, which we can call t. Hence, t is a variable and depends on it. So, we see the need for a variable to model change. This could be an objective understanding of time.

Neeti: OK. Experiences are changing, and we wish to write equations to model relations between these observed quantities. There is a need for an independent variable as a function of which these quantities are changing. This variable can be called time.

Measuring Time

Professor: Whenever we have a variable, we wish to quantify it. How do we quantify time?

Karan: With a clock?

Professor: (smiling) Start from the first principles. You have to make a clock yourself.

Ravi: We can do it with the help of the sun.

Professor: Good. We measure something by comparing it with something standard. For example, we take a ruler as a standard to measure distance, say how far Ravi is from me. I measure the distance in terms of how many units of that ruler make up that distance. Now how would you make a ruler for time?

Ravi: Day and night can make that ruler. We find periodicity in day and night - one occurs after the other, and the cycle continues. We can use it to quantify time. Each cycle of day-night can be used as a unit.

Professor: Yes. This implicitly assumes that a unit, i.e., the time difference between two consecutive days, is constant. In other words, it is not that the time difference between today and tomorrow is the same as that between tomorrow and day-after-tomorrow. The second assumption is that we can exactly call two events to be simultaneous. E.g., consider a baby is born and the sun is exactly overhead — simultaneously. After 5 days, when the sun is overhead again, the baby is 5 days old.

Karan: The trajectory of sun also changes over the year. In summer, it is high up in the sky, and in winter, it is lower.

Professor: Good. These movements have been well studied and used for making sundials. Using these, sundials can also tell the time of the year, apart from telling the time of the day.

Niti: We can use the sun to make a calendar. Likewise, phases of moon can also be used as a standard, as in a lunar calendar.

Professor: Sure. The movement of moon is also periodic like sun.

Subal: There could be a limitation as places near the poles may see longer days and nights. In summer, there is hardly any night there.

Ravi: Still the position of sun changes periodically and one could use that to make a unit of time. During winter, one may rely on the position of moon or stars. Still, I agree there could be places where sun or moon are not visible at all, e.g., if the sky is covered with clouds.

Subal: How about hourglass? It has two equal-sized compartments, one over the other, connected via a small opening. Sand, or a fluid, is filled in the upper compartment, and it flows to the lower compartment in some time, which can serve as a unit of time. One can also have markings on the compartment to measure how much sand has flown.

Professor: While day-night can measure the time difference of the order of one day, what if we wish to measure smaller time differences — say, how long do I take to run from one end of the field to the other? The least count of day-night is of the order of a day, so I can’t use that. I need some method to measure the time durations of that order (running across a field).

Subal: While we can make two people start running simultaneously to find out who takes less time, if that option is not available, we have to compare with a third standard — such as an hourglass.

Professor: Could someone also point out the assumptions involved in using an hourglass?

Tina: The unit should remain the same always. The time taken by sand to flow down should be the same every time we repeat the process.

Subal: As the person starts running, the sand should fall simultaneously. This synchronisation may be a little imprecise.

Tina: That is certainly an issue for an Olympic race. (Laughter) A gunshot is used at the start, and a high-speed camera at the finish line. For the gunshot, the sound onset time can be precisely determined.

Karan: We can also use a pendulum to measure time. The time taken by the pendulum tip to go from one extreme to the other is constant (if the angle swept by it is small).

Professor: Nice to see so many ways to measure time. It seems we have nailed it.

Subal: Should we not be concerned about measuring time more universally? Measures like the sun and moon may work on Earth but will change for other planets. Even gravity changes from place to place, and hence, the time units defined by the pendulum and hourglass will change.

Professor: Nice point. There is a clear difficulty in communicating time across places as the units defined by these methods will change across places.

Ravi: The viscosity of sand in an hourglass changes with temperature and humidity. So one unit will pass quicker in summer than in rainy season. Based on this clock, a 60 years old in London would have lived longer than a 60 years old in Rajasthan desert. (Laughter)

Subal: Likewise, the pendulum will wear and tear with time.

Professor: Interesting. So we have found measures that are not invariant to place and time. The measure should be invariant to space and time, and reproducible everywhere.

Karan: Movements of the sun and moon are quite robust in that sense.

Professor: No doubt. They have been the basis of our calendars for ages.

Subal: They are reliable but not reproducible at places outside Earth. Other planets may have different durations of day and night.

Ravi: Also, the sun, moon, and Earth will not be the same forever. For, if their masses change, the lengths of day and night will change, too, as per Newton’s laws.

Professor: Then how do we measure time more robustly?

Karan: A clock?

Professor: You have to make a clock from first principles. There are no markets around you.

Karan: We can make a gear system that moves precisely.

Professor: How would you make it move at the same pace always?

Karan: We can use a motor or a spring system and adjust the gears so that all clocks are synchronised with respect to each other.

Neeti: This system may not be invariant to time. It is possible that all clocks are synchronised with respect to each other but drift with time, say because of wear and tear. To measure time precisely, I think we need something that oscillates on its own at the same rate always.

Karan: I have heard atomic clocks are very precise. International standards are defined using atomic clocks.

Neeti: Atoms do not undergo wear and tear.

Professor: Good. But I don't know the principle atomic clocks work on. Do you know?

Everyone shook their head.

Professor: No problem. I will read about it and let you know [1].

Time and Space

Karan: We discussed earlier that the speed of light is constant. So, light can also be used to measure time.

Professor: Certainly. Consider two mirrors facing each other at a fixed distance. A light pulse can bounce back and forth between them and be used as a measure of time.

Neeti: time = distance/speed. So, by fixing the distance d between the two mirrors, we can fix the time light takes to complete one return trip.

Professor: Now imagine this setup is mounted on a car with its mirrors parallel to the ground, and the car starts moving. For a person A sitting in the car, the light beam bounces vertically up and down, covering a distance d. But another person B, standing on the ground, sees the light going oblique, covering a distance longer than d. Hence, person B sees the clock moving slower or the unit of time being longer in the car. In this way, space and time are correlated.

Neeti: That means clocks tick at different rates in different moving frames.

Professor: This appears counterintuitive, but that is how nature is. We rest this discussion here, and let us see more perspectives on time.

to be continued…

References

[1] Atomic clocks work because of the precise frequency selectivity of Cesium atoms and precise vibration frequency of quartz crystals. If light or EM waves falling on a Cesium atom has the right frequency, the electrons in it get excited to higher energy states. Quartz crystal’s vibrations drive a light emitter’s frequency and Cesium atoms detect that frequency. If the quartz’s vibrations slow down, as detected by Cesium atoms, it is given a jolt to reinstate its vibrations.

[BG x.y]  Bhaktivedanta, A. C. (1972). Bhagavad-Gita as it is. Bhaktivedanta Book Trust. Chapter-x, text-y.

https://vedabase.io/en/library/bg/x/y/

[SB x.y.z]  Bhaktivedanta, A. C. (1974). Śrīmad Bhagavatam: with the original Sanskrit text, its Roman transliteration, synonyms, translations, and elaborate purports. Bhaktivedanta Book Trust. Canto-x, chapter-y, text-z.
https://vedabase.io/en/library/sb/x/y/z/

The readers are invited to send their perspectives on time in the comments below.