5. Exposure to Physics

§5.1 This chapter contains the details that His Holiness blessed me with of His exposure, in 1941, to scientific studies of light, aspects of relativity, and elements of quantum mechanics. He vouchsafed this information (in Tamil) in the second half of July 1984 in ten sessions of about 15 minutes each; he was then camping at Kalady. He had told me on 4th February that year at Sondekoppa (near Bengaluru) that He would do so some time; at that time, while clarifying an issue, He had given the example of an electron not having any specific position prior to being detected somewhere, and I had silently wondered when He first heard or read of this. Some of the points of note about His Holiness in this chapter are:

1. His systematically guiding and spiritually uplifting in days a physicist named Murthi who approached him (in 1941) on learning that he had only a few months to live.

2. His dispelling Murthi’s discomfiture at being unable to offer Him anything worthy as a mark of deep gratitude and delighting him by providing him the opportunity to expound physics to Him for an hour a day for a week.

3. His innovatively setting up, in private, and fruitfully performing the double-slit experiment with the unrelated materials at hand to observe for himself the interference pattern that Murthi told him about.

4. His imagining experimental situations and reflecting deeply on persons in uniform motion and their measuring the same speed of light; surmising, in his own way, time dilation and length contraction; and forming a diagram to estimate time dilation. (When Murthi concluded his second day’s account by stating Einstein’s two postulates and that their implications were amazing, He felt inclined to think privately about what the implications might be.)

5. His posing apt questions and surmising points rightly about the topics that He was hearing of for the first time.

§5.2 His Holiness: Over 40 years ago, in 1941, a bachelor named Murthi came to Sringeri to request my Guru for initiation into a Kr̥ṣṇa-mantra, seek advice on how to meditate, and to pray for blessings that his mind may remain centred on Kr̥ṣṇa. Just some weeks earlier, it had been found and then confirmed that he was suffering from an incurable disease. Doctors told him that he could expect to live for only some months. He promptly quit his job and came to Sringeri. He wished to stay for ten days, then proceed to Brindavan, and live there centred on Kr̥ṣṇa till the end of his life. My Guru told him that I would initiate him into a mantra and teach him meditation, and wholeheartedly blessed him that by God’s grace his desire to remain dedicated to God would be fulfilled. Before he came to meet me, my Guru told me about him and directed me to initiate and guide him. As it happened, that very evening, my Guru became withdrawn and remained so for weeks.

His Holiness (continuing): While conversing with me, Murthi told me that this was the second time he was receiving the blessings of my Guru in person. He said, “After my college studies in physics, I became a teacher of science. A few years later, in 1938, I learnt that the senior Jagadguru was then in Bangalore (Bengaluru).

I travelled to Bangalore and had His darśana there. The reason for my proceeding to His presence was purely worldly. To upgrade my knowledge of physics, I wanted to spend a fortnight in Dhaka and another fortnight in Calcutta (Kolkata); the great physicists Satyendra Nath Bose¹, whom I was in awe of, and Megnad Saha², who too I admired greatly, were at Dhaka University and Calcutta University respectively. I knew that there was practically no chance that I, who was just an ordinary teacher of science in South India, did not have a single research paper to my credit, had no recommendation, and knew no one in Dhaka or Calcutta, would be able to spend time with them. I thought that my chances of interacting with them would brighten greatly if I had the darśana of the senior Jagadguru, about whose true greatness I had heard. As I felt too ashamed to state my purpose to Him, I just prostrated before Him and mentally prayed to Him for His blessings for my trip.

He kindly smiled at me and nodded. Shortly thereafter, I went to Dhaka and Calcutta. I was greatly surprised that at Dhaka, Bose, notwithstanding his stature and tight schedule, spared much time for me and treated me as if I had been his old student. I was able to freely interact with the scholars there and devote much time to reading. At Calcutta, again to my surprise, Saha gave me time. I was also able to have discussions with his students and engage extensively in study. All this was definitely nothing but a miracle wrought by the senior Jagadguru. Because of the powerful impact that His very presence had made on me in Bangalore and my experience of the power of His grace, when I learnt that I had only some months left, I strongly felt that I must have His darśana and seek His blessings, this time not for anything material but for firm devotion to God.”

The next morning, I initiated Murthi into a mantra. I then taught him prāṇāyāma and instructed him about meditation. I found him to be devoted and unworried. During his stay, he dedicatedly performed much japa every day and put forth his best to meditate for hours, while seated at the Janardana Temple. He made a point of updating me daily, and I duly guided him. In response to his fervent request, I spoke to him every afternoon about Kr̥ṣṇa’s glories and select teachings.

His Holiness (continuing): He was eager to offer me something prized to tangibly express his gratitude but felt ill at ease that he had nothing worthwhile to offer me. Assuaging him, I told him, “As you are versed in physics, you could tell me something about it daily.” He happily expounded it every afternoon for an hour. I can vividly recall his expositions. They were riveting.

§5.3 His Holiness (continuing): He started with light. He said that for some centuries, it was deemed to be a wave¹. Newton (Isaac Newton, 1643-1727) advanced the view that it consists of particles². Using sketches, Murthi described reflection³ and refraction⁴ and how Newton elucidated, in terms of his position, these two as also the separation of sunlight into seven colours. Murthi then said that a senior contemporary of Newton (Christiaan Huygens, 1629-1695) maintained that light is a wave and explicated this scientist’s idea about how light spreads by the formation of further waves and how reflection from a surface can be accounted for. Newton’s view prevailed over the other one for years. Having pointed this out, Murthi detailed an experiment performed at the start of the 19th century using a source of light, two slits⁵, and a screen. He highlighted how its result was incompatible with the position that light is made up of particles and how it demonstrated that light comprises waves.¹

Single slit

Screen

Colour filter

(The fine slits are

shown as wide)

Source of light

Double slit

Portrayal of alternating bright and dark regions on the screen

(Gradual variations in the intensities are not depicted)

Setup of the Double-slit Experiment (Not to Scale)

His Holiness (continuing): The portion of the screen that is midway between the pair of slits and, hence, equidistant from them is the brightest. On either side of the bright central band, there is a dark band followed by alternating bright and dark bands. All this disfavours the view that light consists of particles. On the other hand, it accords well with the position that light is in the form of waves. When Murthi spoke of light waves from two narrow slits adding up at a spot on the screen to form a bright band and neutralizing each other at an adjacent place to form a dark band, I was reminded of the reinforcement and the balancing out that I had once witnessed, well before my saṁnyāsa, of a pair of waves in water. My father had taken me with him to the lake (the Dharmambudhi Lake where the Kempegowda Bus Station in Bengaluru now stands) and was conversing there for long with some people. I sat down on the bank. Perhaps because it was noon and hot, there was no one using the lake nearby and the water appeared still. I playfully tapped the water rhythmically with my right hand. I beheld waves form and spread away from me, looking like parts of bigger and bigger circles. There were several dry leaves floating on the water. I noticed, with some surprise, that the leaves did not move away with the spreading waves; they simply moved up and down wherever they were. I then tapped the water with my left hand also, at the same rate. I saw another set of waves form and spread. Where the waves set off by my left hand crossed those started by my right hand, I saw something new. While some leaves moved up and down far more than earlier, some others between these did not appear to move at all. Recalling this, I asked Murthi if the formation of dark bands due to the light rays from the two slits counteracting one another was somewhat like two water waves offsetting one another at some places. He said this was so. He added that the scientist who described the double-slit experiment had himself spoken of the result of water waves meeting

and of the effect of light waves meeting being like this.¹ His Holiness (continuing): Murthi described one more experiment that favoured light’s being a wave. In it, light passed through a tiny hole was shone on a small, circular object. A spot² of light was seen in the centre of the object’s circular shadow on a screen. If light consists of particles that go straight, it could not have illumined that spot. Waves from the object’s surface can add up there.

His Holiness (continuing): That a spot lit by a beam of light could become dark when a second beam of light was also directed to that spot intrigued me and I wished to observe this. Hence, that night, in the privacy of my room, I performed the experiment with two slits in a rudimentary way with the materials available with me. In those days, torchlights powered by batteries were not available in Sringeri. I, however, had one that had been submitted to the Math weeks earlier by a devotee and passed on to me by my Guru. I decided to use it as the source of light for the experiment. Murthi had explained why the light of the sun or a candle needed to be passed through a tiny hole or a narrow slit before being made to fall on the double slits and why it was desirable to use light of one colour rather than white light, which is made up of seven colours. I had four (razor) blades that had been given to me by a devotee along with a tool kit some months after my saṁnyāsa (in 1931). He had told me that such (razor) blades were then produced only in America and by one company. I took the precautions suggested by him to prevent them rusting and checked them occasionally¹ but did not know what they were meant for. I decided to use them to form slits with very small width. I thought of forming a fine slit by positioning the straight, sharp edge of one blade very close to the straight, sharp edge of another blade. Six glass panes were lying unused in Sacchidananda Vilas for years. I had no idea when or why they had been procured, possibly by Srikantha Sastri. I carried them to my room that evening. They were all one foot by one foot in dimension and of the same thickness. Two were wholly red, two green and two colourless. I passed light from the torch through the red glass and what emerged from the glass and fell on a white paper held by me appeared to me to be just red light. I then placed the green glass after the red glass. When I did so, virtually no light fell on the paper. On observing this, I recognized that the red glass that I had was effectively allowing just red light to pass through, while my green glass was, for its part, duly disallowing the red light to pass. I decided to keep the red glass in front of the torch to obtain red light. Making measurements and using a magnifying glass, I carefully positioned two blades in the middle of the other face of the glass so as to form a fine slit. I then covered the rest of the surface with carbon paper. I confirmed that the light from the torch passed through the red glass and emerged from just the slit as a very thin ray of red light. I then took up a colourless glass pane and determined where I should position the two slits on it so that the thin red beam would be centred between them. To form the two slits with very small separation between them, I took a fine (gold) thread from the zari border of my clothing, fixed it tautly on the glass and placed the sharp edges of two blades very close to it, one on either side. I used carbon paper to cover up the colourless glass except for the portion where the two slits were. The glass panes were such that it was not difficult to ensure, with supports, that they remained vertical on a wooden plank on the floor, with the torch positioned next to the red glass at the right height. White paper fixed on the other colourless pane served as my screen. Setting up all this took me about half an hour.¹

His Holiness (continuing): I was doubtful if this crude setup would result in my seeing alternating bright and dark bands as described by Murthi. However, when I darkened the room, turned on the torch and adjusted the distance of the screen from the slits, I could make out a vertical red band of light on the paper screen; on either side of it, there was a dark band followed by a red band.¹ I then carefully blocked one of the pair of slits with a blade. When I did so, I was able to discern dim red illumination in a portion that had been dark when both the slits were open. I reopened the closed slit and noticed that the said portion appeared dark again. Having seen for myself a spot lit by a beam of light become dark when another beam of light also fell on that spot, I dismantled the entire setup and went to sleep.

§5.4 His Holiness (continuing): On the second day of his exposition, Murthi started with the measurement of the speed of light. He said that for many centuries it was supposed that the speed of light was infinite and that it reached anywhere instantaneously. Thereafter, in the 17ᵗʰ century, an experiment was performed to determine the speed of light. A person stood on a hill with a covered lamp and a second person on another hill about a mile away. The first person uncovered his lamp. As soon as the other person perceived the light, he exposed his lamp and the first person noted when he saw it. The time interval between the first person opening his lamp and seeing the light from the other lamp was presumed to be the time taken by light to travel from the first hill to the second and then from the second hill to the first.¹ As soon as Murthi told me about the procedure, I voiced my misgiving. I told him that people cannot react instantaneously, and so, there would be a temporal gap between the second person perceiving the light from the first lamp and uncovering his lamp. In view of our unavoidable reaction time, the experiment cannot be reliable even if light were to take as much as a tenth of a second to travel the mile from one hill to the other, and there is no question of light being expected to require even a tenth of a second to cover the mile. After all, at sunrise, we are able to see light all over the sky without our being able to discern any time for the light to spread. Murthi agreed and communicated that this experiment did not result in the ascertainment of any finite speed of light.

His Holiness (continuing): Murthi then described an interesting astronomical study that showed that the speed of light is finite. He said that in the 17ᵗʰ century, several moons of Jupiter¹ were identified, and it was ascertained that the moon closest to Jupiter goes around it once in about 42 hours. This moon is called ‘Io’². Murthi said that it becomes hidden from the earth each time it goes behind Jupiter in the course of its orbit³ around the planet. Therefore, as seen from the earth, an eclipse of Io occurs repeatedly. A scientist (Ole Rømer) recorded the timings of the eclipses over a period of several years. He found that the interval between eclipses decreases as the earth moves nearer Jupiter and increases as the earth moves away from Jupiter.⁴ He understood that this is because the speed of light is finite and light takes less and less time to reach the earth as the earth moves closer and closer to Jupiter and more and more time to reach the earth as the earth moves farther and farther from Jupiter. On the basis of his data and the then accepted size of the earth’s orbit⁵, another scientist (Christiaan Huygens) computed the speed of light to be around 132,000 miles per second. Murthi pointed out that the correct

speed is about 186,300 miles per second.¹ His Holiness (continuing): He then conveyed that the first earth-based scientific experiment that yielded a finite speed of light was conducted only over 150 years later, in the middle of the 19ᵗʰ century.² Describing this experiment, Murthi said that the setup comprised a source of light, a rotating wheel with many teeth and a mirror that was located five miles away. A bright flash of light passed through the gap between two successive teeth of the wheel, went to the distant mirror, and returned. If, by the time the light returned, the rotating wheel turned to the extent that the next gap between the teeth took the place of the previous gap, the returning light encountered no obstruction and passed through. On the other hand, if the wheel did not turn this much, the returning light encountered a tooth and was obstructed. The speed of the wheel was increased till the returning light was able to pass through. The time taken for the light to go outwards for five miles and return was then equal to that taken for one gap of the turning wheel to take the place of the earlier one. As the size of the teeth, the number of teeth, speed of rotation, and the distance travelled by the light were known, the speed of light could be computed. Murthi said that the speed of light reported (in 1849) on the basis of this experiment is only about five percent more than its actual speed.

His Holiness (continuing): He then described another earth-based experiment that, he said, had been done 15 years earlier (that is, in 1926) and gave an accurate value for light’s speed.¹ First, the distance between two mountains, which was about 22 miles, was carefully measured such that any inaccuracy was less than one inch. A very powerful flash of light was produced in the research centre on the first mountain by the use of several generators. The flash was so bright that it was capable of even lighting up the sky between the mountains. The light was precisely directed to one face of an eight-faced mirror. Reflected from that face of the mirror, it travelled to a mirror on the second mountain 22 miles away and returned from there. The returning light fell on another face of the octagonal mirror and entered a viewing device. This experiment was then performed with the octagonal mirror rotating. If, by the time the light went outwards and returned, the mirror turned such that a face was in the right position to direct the light to the viewing device, the flash was seen through that device. On the other hand, if the rotating octagonal mirror was in any other position when the light returned, the light did not pass into the viewing device. Much data was gathered by doing the experiment again and again, for two years, with the mirror being rotated in a controlled manner, at various speeds. The speed of light was worked out based on the to and fro distance travelled by the light and the speed of rotation of the octagonal mirror that resulted in the returning light passing into the viewing unit.

His Holiness (continuing): I asked him how long light takes to come to the earth from the moon, from the sun, from the brightest star that we see, Mr̥ga-vyāḍha (Sirius or Dog Star), and from the Dhruva-nakṣatra (Pole Star). He stated that the moon is about 240,000 miles from us, and light takes about one and a quarter seconds to cover this distance.¹ The sun is about 93 million miles away, and light takes about eight and a quarter minutes to arrive from there.² He said that in a year, light covers about six trillion miles¹. It takes about eight years to come here from Mr̥ga-vyādha (Sirius)² and a few hundred years to reach us from the Dhruva-nakṣatra (Pole Star).³ He added that on a clear night, we can see stars from which light arrives after well over a thousand years. Recapitulating the times mentioned by him, I asked him whether, in view of the finite speed of light and the great distances involved, scientists hold that we see the moon only as it was one and a quarter seconds earlier, the sun as it was eight and quarter minutes earlier, Mr̥ga-vyādha (Sirius) as it was about eight years earlier, the Dhruva-nakṣatra (Pole Star) as it was a few hundred years earlier, and several stars as they were well over a thousand years earlier. His answer was that such is the case and that scientists maintain that when we look up at the sky at night, we see what was there at various times in the past, with what is more and more distant seen here now as it was further and further in the past.

His Holiness (continuing): He then pointed out that the light that we get from the sun, the moon, the stars and terrestrial sources like oil lamps; the heat that we obtain from the sun and from fire here; radio signals; and X-rays are all waves of the same kind, with just different wavelengths¹. Electricity and magnetism² were, he said, once thought of as distinct phenomena. The discovery that a current in a wire can make an iron piece a magnet and that a moving magnet can give rise to current in a wire led to the realisation that the two are not disparate. Years earlier, soon after I first went to Bangalore by car from Sringeri (in 1936), I asked an engineer how a car’s engine functions. In the course of his explanation, he touched upon how electricity is produced and used in a car. This led me to ask him and learn how electricity is generated at Shivasamudram³. I thus knew that electricity and magnetism are related.

Murthi said that light, heat, X-rays, etc. are waves with two constituents: An oscillating electric field⁴ and an associated, oscillating magnetic field. These stimulate one another. Like water moving up and down and a wave spreading sideways, the light wave travels in a direction that is perpendicular to these⁵.

§5.5 His Holiness (continuing): Murthi said that about 300 years before, an Italian scientist (Galileo) had, while making the case that the earth rotates and also goes around the sun, pointed out through an example that a person moving at a constant velocity does not sense that he is in motion. A person is in the lower part of a big ship. Regardless of whether the ship is motionless or moving straight at any constant speed without any shake, he does not find any difference in how water falls drop by drop from a container into a bowl. He does not notice any change in how the smoke of burning incense rises up. He does not find changes in how an object tossed by him in different directions moves.¹ His Holiness (continuing): Having described the Italian scientist’s ship-related example, Murthi mentioned that in keeping with this, Einstein posited that the laws of physics are the same for every observer² in uniform motion. He further posited that the velocity³ of light in empty space is the same for all observers. Saying just that the implications of these two postulates⁴ are astonishing, he concluded his second day’s account.

His Holiness (continuing): Since Murthi had said that the implications were astounding, I decided to spend some time thinking about them. I first considered the example of the person in the ship. Prior to travelling straight at some constant speed, the ship would have started from rest and gradually picked up speed till that uniform speed was reached. During this time, he would have sensed a little tug and discerned that he was moving. However, the states to be considered are only those of the ship being stationary with respect to the shore and being in uniform motion with respect to it. Hence, I imagined that the man enters the lower part of the ship when it is near the shore, does not, obviously, sense any motion, does some experiments, and falls asleep. By the time he gets up, the ship is moving straight, at a uniform speed. After getting up too, he does not sense any motion. He continues with his experiments. He observes, for instance, that the water drops look like before, fall vertically as before, and also take the same time as before to fall the one foot from the container above to the bowl below¹. This means that the laws of nature, or at least those that are relevant to the results of his studies, operate in the same way after he gets up (that is, when the ship is moving straight at a uniform speed with respect to the shore) as they did before he fell asleep (when the ship was not moving with respect to the shore). Hence, after getting up, he discerns that he is not in motion not merely because he feels no jerks but also since his studies show that everything is as it had been before he fell asleep (when the ship remained stationary near the shore).

His Holiness (continuing): At this point, I happened to recall Bhagavatpāda’s illustration in the Bhagavadgītā-bhāṣya, “To a man in a moving boat, the stationary trees on the bank appear to move in the opposite direction.” With this in mind, I imagined that the man in the ship looks out through a tightly closable opening at a height and sees another ship nearby. That second ship is stationary (with respect to the shore). However, this person, who discerns that his ship is stationary, perceives the second ship as moving past him in the opposite direction. The speed at which he finds the second ship moving is the constant speed at which his own ship is moving (with respect to the shore). I then imagined that in the second ship there is a closable opening at the same level as in the first ship. Inside that ship, a person is watching water fall drop by drop, straight down from a vessel into a bowl kept a foot below. The person in the first ship is able to see what is happening inside the second ship when the openings of the ships pass one another. One watering plants from a pot while walking sees the water falling straight down, but the persons standing nearby see the water falling to the front in a curved path (His Holiness showed with His hand, a semi-parabolic path). Likewise, the person in the first ship sees the water drops in the second ship falling in a curved path into the bowl. On the basis of this observation, he confirms that the second ship is indeed moving. On the other hand, the person in the second ship sees the water drops fall vertically. He finds the first ship moving past his ship and observes that water drops are falling in a curved path in that ship. He confirms thereby that the first ship is indeed moving. I then conceived that the second ship is not stationary with respect to the shore. It is travelling without jerks at a uniform speed but in a direction opposite to that of the first ship. In this situation too, the person in the first ship discerns that his ship is stationary and that the second ship is the one that is moving. However, he sees the second ship as moving faster than he would have done had that ship been stationary. Further, he sees the falling water drops in the second ship taking a longer path than he would have observed had that ship been still. Similar to this is what the person in the second ship makes out with respect to the first ship.

His Holiness (continuing): As far as a person standing on the shore is concerned, he is not moving and these two ships are the ones that are moving. I imagined a person stationed on the sun, observing the earth and the man on the shore. While he finds himself to be stationary, he sees that the man on the shore is not at rest and that he is moving along with the earth. I thereafter imagined a person observing the sun and the earth from afar in space. I reasoned that he would see himself as stationary and would see the man on the sun not as stationary but as rotating with the sun. Furthermore, he would see the man on the shore as rotating with the earth and also moving with the earth, around the sun. My conception of a person on the sun observing the earth and another observing the sun and the earth from somewhere in space was fanciful. However, it helped me to extrapolate the example of the ship of the Italian scientist (Galileo) and appreciate that steady motion is something relative¹. After all, tacitly accepting the earth as our reference, all of us find ourselves to be stationary when we are standing. Though rotating with the earth, we do not sense this and, instead, see the sun rising in the east and setting in the west every day. Though hurtling through space, going around the sun in a year, we do not discern that we are moving and, on the contrary, note that the sun moves northwards for six months and southwards for six months.

His Holiness (continuing): I imagined that the moon has air and an ocean, as on the earth. There is a ship in the lunar ocean. A person in it is observing water drops falling from a vessel into a bowl kept a foot below. I reasoned that as the gravity¹ on the moon would be different from that on the earth, the falling of the water drops there would not be identical to that on the earth². Nonetheless, just like on the earth, there would be no difference between how the water falls when the ship proceeds straight at a uniform speed, without any shaking, and how it falls when the ship is stationary with respect to the shore there. Hence, just as on the earth, the person in the ship would, not only on account of not feeling any jerks but also on the basis of studies such as this, conclude that he is not in motion. A person on the shore there would discern that he is stationary and that the ship is moving. On the other hand, a person standing on the earth would see that person as moving with the moon. The person on the shore on the moon would, for his part, see the person on the earth not as stationary but as moving with the earth. Thinking in this fashion about the ship on the moon helped me to grasp further how steady motion can be indiscernible and how it is relative.

His Holiness (continuing): I then turned to Murthi’s statement that Einstein deemed that the speed of light in space is the same for all observers. I thought of a ship and a person within it conducting studies on the speed of light. The ship faces east and is stationary, near the shore. The person shines a light towards the front of the ship (that is, to the east) and, somehow, measures its speed accurately. Murthi had said that the speed of light is about 186,300 miles per second. Rather than recollect this again and again, I decided to think of the value as c in view of Murthi having stated that the true speed of light in space is denoted by c. The person finds the speed of his beam to be exactly c. For convenience, I deliberately chose to overlook the point that this beam is moving through air, while c is the speed of light moving in airless space. As light passed through air in some of the elegant experiments conducted to measure the speed of light, I presumed that the discrepancy between c and the speed of light in air is small¹. The person in the ship then shines light in the opposite direction (the west) and, once more, finds that its speed is c. He continues by directing light northwards, southwards, upwards, and downwards. Each time, he finds that its speed is c only. After this, he sleeps for some time. While he is asleep, the ship starts and picks up speed. By the time he wakes up, it is moving eastwards at a uniform speed, without any shake. Resuming his study, he directs a beam of light towards what he knows is the front of the ship (that is, towards the east) and measures its speed. He finds it to be exactly c. As he had done previously, he then directs a beam westwards, northwards, southwards, upwards, and downwards. Each time, he determines that its speed is exactly c. Thus, even by measuring the speed of light in different directions, he cannot identify that his ship is not stationary near the shore but is travelling at a uniform speed.

His Holiness (continuing): I then considered a man on the shore facing this ship that is steadily moving away from him at night. He points a light in the direction of the ship and measures its speed. He finds it to be exactly c. As this beam of light goes past the ship, the person in the ship observes it through his opening and measures its speed. He also finds its speed to be c, not c minus the uniform speed at which the ship is moving in the direction of the beam. I then thought of a second ship moving at some other uniform speed in a direction opposite to that of the first ship. A person in the interior of the second ship also notices the beam from the shore passing nearby and measures its speed. He finds this beam’s speed to be exactly c, not c plus the unchanging speed of the second ship, which is moving in a direction opposite to that of the beam. I acknowledged that every one of these measurements of the speed of the beam of light from the shore yields the same result because the speed of light is posited to be the same for all observers.

His Holiness (continuing): Since the person in the first ship measures the speed of the light from the shore to be exactly c even though the ship is moving away from the shore at some constant speed, I inferred that no matter how fast anyone may manage to travel at a uniform speed, one cannot overtake a beam of light. After all, regardless of whether the ship moves steadily at just one mile an hour or unrealistically fast at 100,000 miles per second, the person in it will find the ray of light from the shore going past the ship at a speed that is exactly c. His Holiness (continuing): Earlier, I had conceived that a person in a steadily moving ship is studying the fall of water in drops from a container into a bowl below. I had noted that while he finds the water drops falling straight down into the bowl, a person in a stationary second ship sees these drops falling in a curved path. In keeping with this, I conceived that the person in the steadily moving first ship is directing light downward and the person in the stationary second ship is seeing this. I noted that while the light is travelling straight down as observed by the person in the first ship, the person in the second ship sees it taking a straight, but slanting, path downward (His Holiness indicated the path by a movement of His hand). I understood that the second person would not find the light taking a curved path like a falling drop of water. This is because the speed of light is constant, while a drop of water falls with rising speed. I had visualized water drops falling a distance of one foot from the container above into the bowl below and recognized that the time taken for them to drop that one foot is the same regardless of whether the ship is stationary or moving at a uniform speed. In line with this, I imagined that the person in the first ship keeps a foot rule vertical, directs a beam downward from its initial mark, and records, using a watch, the time the ray takes to reach the final mark on the foot rule. I did realize that the speed of light is so great that even a second is many crore times greater than the time required by light to travel one foot.¹ Yet, I simply supposed that he is able to measure this time. As per his assessment, light travels straight down along the foot rule and therefore moves exactly one foot to reach the final mark from the initial mark. The time taken by the ray to reach the final mark and measured by him is, thus, that taken by it to travel one foot. He determines that the speed of that beam is exactly c.

The person in the second ship also measures the time taken by this very beam to travel from the initial to the final mark of that very foot rule. However, as discerned by him, while the light journeys from the initial mark, the foot rule moves sideways, along with the first ship. Even if the ship were to move as fast as a bullet, its speed would be negligible compared to the tremendous speed of light. Consequently, by the time light reaches the final mark, the foot rule would have practically not moved sideways. I imagined, therefore, that the ship is moving unrealistically fast, at half the speed of light. Due to the very swift sideways movement of the foot rule, the person in the second ship sees the beam of light travelling in a slanting path and, hence, covering more than a foot to reach the final mark. Still, like the man in the first ship, he also finds that the speed of that beam is c, for light’s speed is the same for all observers.

His Holiness (continuing): A point that struck me as significant was that though both the persons measure the time taken by the same beam to travel from the initial mark to the final mark of the same foot rule, they record different values. The time recorded by the person in the first ship (who sees the light as having travelled one foot) is less than that recorded by the one in the second ship (who sees that beam as having travelled more than one foot). Else, the two persons could not have arrived at the same value c for the speed of that beam. I conceived that on finishing his measurement, the person in the first ship writes it on a board and records that this is the time taken by light to go from the initial to the final mark of the foot rule. The writing on the board is seen by the person in the second ship. From it, he first comes to know that, like himself, the person on the first ship has measured the time taken by the beam to reach the final mark on the foot rule from the initial mark. He also notes that that person has recorded a shorter time than what he has determined. There being no reason for him to doubt that person’s meticulousness, he concludes that the watch used by that person is running slow.

His Holiness (continuing): If the first ship is stationary, he does not observe any sideways movement of the foot rule, finds the beam of light moving straight down from the initial to the final mark, and measures the same time for the light’s travel as that recorded on the board in the first ship. He does not conclude that the watch in the first ship is running slow. It is only when the first ship is moving relative to his that he decides that that watch is running slow. I proceeded to reason that, as found by him, the more the steady speed of the first ship, the more would be the sideways movement of the foot rule and, as a result, the more extended would be the path of light to reach the final mark from the initial mark. As a consequence of light having to travel further to reach the final mark and because the speed of light is the same for all observers, the more the first ship's steady speed, the more would be the time measured by him as compared to that measured and recorded on the board by the person in the first ship. His ascertainment, in the light of the measurements, of how slowly the watch in the first ship is running compared to his watch depends, thus, on the speed of the first ship with respect to his ship.

His Holiness (continuing): The movement of the first ship relative to the second ship and the constancy of the speed of light are responsible for the person in the second ship construing that the watch in the first ship is running slow and not any defect in that watch. Therefore, even if the person in the second ship were to directly observe the running of the watch in the first ship and compare it with the running of his watch, he would still conclude that the former watch is running slowly. It was only at this point in my thinking that I realized that he would see not just the watch but also everything else in the interior of the first ship, with light the sole exception, functioning slowly. He would, for example, find that the person in that ship moves slothfully, closes and opens his eyes slowly, and even breathes sluggishly. He would find water drops falling slowly from the vessel above into the container below. Thus, as ascertained by him, the very course of time¹ would be slow there; the extent of slowing would depend upon the speed at which the first ship moves with respect to his ship.

His Holiness (continuing): I had earlier inferred that no matter what steady speed one manages to achieve, one cannot overtake a beam of light since, regardless of whether one travels steadily at one mile per hour or at 100,000 miles a second, a beam of light goes past one at the speed c. I presumed that only light and, maybe, what is akin to light can travel at exactly c and that none can reach this speed. I, nevertheless, thought of what might happen if the steady speed of the first ship were to be c. I readily concluded that from the perspective of the person in the second ship, the watch in the first ship would not be running at all. The person there would be completely motionless, without any sign of eye-movement, breath, or even a heartbeat. A water drop that is midway between the upper vessel and the container below would remain just suspended in space. In short, time would appear to have stopped there. I arrived at this conclusion by considering, from his perspective, the movement of the beam of light from the initial mark of the foot rule in the first ship. The foot rule moves with the ship and, accordingly, its final mark moves eastwards in a horizontal straight line at the speed c. At the start, the beam is one foot directly above the final mark. Hence, if the beam is to reach the moving final mark at some time, the beam has to cover a longer distance than that covered by the final mark in that time. However, the speed of the beam and that of the final mark are both exactly c. Hence, the beam can never reach the final mark. This would be the case even if it were initially one inch or one-thousandth of an inch above the final mark. Thus, as seen by him, the beam does not travel downwards at all and all it does is to travel eastwards at a speed of exactly c, keeping pace with the initial mark, which is also moving at the speed c. I then easily figured out that he, who finds light itself maintaining its position at the initial mark of the foot rule, would see the person and the water drop as motionless.

His Holiness (continuing): I surmised that though an object cannot, even in principle, reach the speed c, it could, conceivably, reach a uniform speed of almost c. If the speed of the first ship is almost c, he sees the beam moving not thoroughly horizontally but in a very slightly inclined path towards the final mark. He finds the watch, the person, and the drop of water there to be well-nigh but not completely motionless. There is no slowing of time when the first ship is stationary and only trifling slowing even when it travels at 100,000 miles per hour as even this very great speed is much less than a thousandth part of the speed of light. There is great slowing as the speed approaches that of light, with time almost stopping when the speed is almost that of light. I did not lose sight of the fact that while there is such slowing of time in the first ship as found by the person in the second ship, for the person in the first ship, everything there is normal only.

His Holiness (continuing): I proceeded to think about the relation between the speed of the first ship (with reference to the second ship) and the slowing of time there as found by the person in the second ship. I noted that as both the persons find the beam moving from the initial mark of the foot rule at the same speed c, therefore when the person in the first ship finds that it has moved one foot, the person in the second ship must, regardless of whatever the speed of the first ship is, also find that it has traversed one foot. The only difference is that if the first ship is stationary, both find that the beam has travelled one foot straight down from the initial mark, while if the first ship is moving at a uniform speed, the person in the second ship finds that the beam has moved one foot from the initial mark in a slanting, downward path. At this point, I realized that I could use a simple sketch to compute, for any speed of the first ship, the extent to which the flow of time is slowed down there, as assessed from the second ship.

His Holiness (continuing): {What His Holiness conveyed partly through words and partly through gestures is put fully in words in this paragraph.} I took two sheets of paper¹ and pasted them together so as to form a large sheet. In it, I marked a point to represent the initial mark of the foot rule in the first ship. With the aid of my foot rule, I drew a line one foot long, straight down from that point. This line represented the foot rule in the ship, with the bottom of that line corresponding to the final mark. I then drew a horizontal line one foot long from the initial point. Next, from the point, I drew a slanting line one foot long, between the vertical line and the horizontal line. I bore in mind that when the person in the first ship finds the beam at the bottom of the vertical line, the person in the second ship finds it at the end of the slanting line. I took my foot rule and measured the distance of the end of the slanting line from the vertical line. I did so as I recognized that this distance depended on the speed of the first ship. If the speed were one quarter that of light, the distance would be three inches; if the speed were half that of light, it would be six inches; if the speed were three fourths that of light, it would be nine inches, and so on. Then, I measured how far the end of the slanting line was from the horizontal line. I understood that this distance shows how slow the person in the second ship finds time flowing in the first ship. After all, this is the distance that the person in the second ship finds light to have travelled down the foot rule when the person in the first ship finds it at the final mark of the foot rule. If the distance is three inches, then, as discerned by the person in the second ship, the time in the first ship moves at one fourth that in his ship; if the distance is six inches, then he finds time in the first ship flowing at half that in his ship; if the distance is nine inches, he finds time passing at three fourths the rate in his ship, and so on. Accordingly, with one slanting line and two measurements, I found the extent of slowing for one speed. To relate other degrees of slowing with speeds, I systematically drew more slanting lines, with different slopes. From my two measurements on each of them, I ascertained that the extent of slowing does not vary uniformly with speed. It grows mildly at speeds that are much less than that of light and rises rapidly as the speed of the first ship comes closer and closer to that of light.

0 3" 6" 9" 12 inches

< 3"- Clock Speed 25%

(This is the rate at which

Ship 1's clock runs with

respect to Ship 2's clock,

as noted from Ship 2)

11.6" - Ship Speed 0.97c

("Ship Speed" refers to the speed

of Ship 1 relative to Ship 2)

Length of each slanting line - 12"

< 9" - Clock Speed 75%

7.94" - Ship Speed 0.66c

< 11.6" - Clock Speed 97%

12"

3" - Ship Speed 0.25c

Representation of Diagram Conceived By His Holiness

His Holiness (continuing): Recalling that as determined by the person in the first ship, his ship is stationary and the second ship is moving westward at a steady speed, I reasoned that he finds time to be running slow in the second ship to the very same extent that the person in that ship finds time to be running slow in the first ship. Each of the persons finds everything to be normal in his own ship. I recognized that if the speed of light is to be the same for both of them, the flow of time in a ship needs to be measured differently by them and so it is not as though one of them is right and the other wrong. I thought of the following analogy. A person is standing on the North Pole and another on the South Pole.¹ There is a mirror situated midway between them in space, and this moves with the earth, such that it appears stationary to both of them. Each of them is able to see, through a telescope, the reflection of the other in this mirror. As determined by the first person, while he is standing upright on the ground, the other is hanging upside down like a bat. The second person finds himself upright and the first one upside down. Because the earth is round, which direction is up is not the same for both of them, and so, it is not that one of them is right about what is up and the other wrong. Because the earth is rotating, at the very instant when it is noon in India, it is night in the United States, and neither the statement of one in India that it is day nor that of one in the United States that it is night is erroneous. As the speed of light is c for all observers, persons who are moving at a constant speed relative to one another ascertain the flow of time at even the same place dissimilarly with respect to their own clocks and, though distinct, their findings are valid.

His Holiness (continuing): I then thought of what would happen if the person in the first ship (who finds that the watch of the person in the second ship is running slowly) and the person in the second ship (who finds that the watch of the person in the first ship is running slowly) were to meet and compare the times shown by their watches. It was obvious that they can never meet as long as the first ship is moving at a uniform speed with respect to the second ship. For them to meet, the first ship that is moving eastwards at a steady speed would have to slow down, stop, start travelling westwards, and then slow down and stop next to the second ship. Murthi had mentioned only steady speed and the constancy of the speed of light and, in view of that, I had all along taken into account only uniform speed. I had no idea about what effects the slowing or speeding up of the first ship would have on the flow of time in it as ascertained by the one in the second ship. Nonetheless, I figured that any effect of the first ship starting and accelerating¹ to reach a steady speed cannot depend on how long the ship travels thereafter at the uniform speed. Likewise, any effect of the ship slowing down to a stop from its uniform speed cannot depend on how long the ship had been moving earlier at the uniform speed. I presumed, therefore, that if the acceleration and the deceleration¹ were to last for a very much shorter time than the journey at a constant speed, then, as ascertained from the stationary second ship, the travel of the first ship would be essentially at the uniform speed. I initially thought of proceeding further by assuming that the first ship accelerates from rest to the uniform speed instantaneously and also that it later decelerates from the uniform speed to a stop instantaneously. However, I then pictured what looked to me to be an equivalent scenario, but one that did not require instantaneous attainment of the uniform speed and instantaneous halting.

His Holiness (continuing): I supposed that a person on the shore enters the first ship and that it accelerates to the uniform speed in some time. While moving at the uniform speed, it comes alongside the still second ship. When the first ship does so, the person in it starts a stopwatch². As the stopwatch starts, the person in the second ship notes the time in his watch. He also compares the running of the stopwatch and his watch. The time noted by him is 1 p.m., and the first ship’s uniform speed is such that he finds that the stopwatch is running at half the rate of his watch.¹ The person in the first ship determines, for his part, that the watch in the second ship is running at half the rate of his stopwatch. The first ship continues its journey at the uniform speed and passes another stationary ship. The watch in this third ship runs at the same rate as and shows the same time as the watch in the second ship. After all, this third ship is not moving with respect to the second ship. When the first ship is alongside the third ship, the person in it stops his stopwatch. The person in the third ship observes this and notes the time in his watch. It is 3 p.m. He then ascertains that another watch in the first ship is running at half the rate of his watch. Meanwhile, the person in the first ship finds that the watch in the third ship is running at half the speed of his watch. The first ship starts slowing down and comes to a stop.

Ship 1 (Next to Ship 2) (Next to Ship 3) (Stops)

❶>accelerates>❶>uniform speed>❶>decelerates> ❶

Stopwatch started Stopwatch stopped

❷ ❸

Ship 2 (stationary) Ship 3 (stationary)

Ship 1 next to Ship 2 at 1 p.m. Ship 1 next to Ship 3 at 3 p.m.

Representation of the First Ship’s Outward Journey

His Holiness (continuing): Immediately after that, it starts moving in the opposite direction and accelerates till it reaches the uniform speed. While moving at the uniform speed, it comes to the side of the third ship. As the first ship does so, the person in it restarts his stopwatch. The person within the stationary third ship observes this and notes the time shown by his watch when the stopwatch restarts. It is 3:30 p.m. He finds that the stopwatch and the other watch in the first ship are running at half the rate of his watch. On the other hand, the person in the first ship finds that the watch in the third ship is running at half the rate of his watch. The first ship advances smoothly at just its uniform speed. When it comes alongside the second ship, the person in the first ship stops his stopwatch. The person in the second ship notes the time shown by his watch when the stopwatch stops. It is 5:30 p.m. He then finds that the other watch in the first ship is running at half the speed of his watch. As for the person in the first ship, he finds the watch in the second ship running at half the rate of his watch. The first ship then begins to decelerate and stops at the place near the shore where it started its journey.

(Stops) (Next to Ship 2) (Next to Ship 3) Ship 1

❶<decelerates<❶<uniform speed<❶<accelerates<❶

Stopwatch stopped Stopwatch restarted

❷ ❸

Ship 2 (stationary) Ship 3 (stationary)

Ship 1 alongside at 5:30 p.m. Ship 1 alongside at 3:30 p.m.

Representation of the First Ship’s Return Journey

His Holiness (continuing): Afterwards, the person of the third ship comes to the second ship and reports his measurements to the person there. From the initial time of 1 p.m. noted by the person of the second ship (when the first ship was passing it for the first time) and the time of 3 p.m. noted by the person of the third ship (when the first ship was passing it for the first time), they ascertain that the duration of the first ship’s forward journey at the uniform speed from alongside the second ship to the side of the third ship was two hours. Next, from the time of 3:30 p.m. noted by the person of the third ship (when the first ship was going past it on the way back) and the final time of 5:30 p.m. recorded by the person of the second ship (when the first ship was alongside it on the way back), they note that the duration of the first ship’s return journey at the steady speed was also two hours. They, therefore, conclude that the total time of the first ship’s travel at the uniform speed from alongside the second ship to the third ship and back was four hours, as per their watches. They recognize that the duration of travel at the uniform speed as measured from the first ship is that recorded by the stopwatch there. During the first ship’s forward as well as return journeys, they found the stopwatch and the other watch in the first ship running at half the rate of their watches. Thus, they expect the stopwatch to show the passage of just two hours, as against the four hours as per their watches.

His Holiness (continuing): The person on the first ship subsequently comes to the second ship bringing his stopwatch with him. He started his stopwatch when his ship was passing the second ship at the uniform speed and stopped it when his ship was beside the third ship. The times recorded by him for the start and end of his forward journey thus exclude the periods of acceleration and deceleration. It is as though the first ship instantaneously attained the uniform speed when next to the second ship, travelled to the third ship at just the uniform speed, and stopped suddenly. On the return journey, he restarted the stopwatch when the first ship was next to the third ship and finally stopped it when the ship was back next to the second ship. The periods of acceleration and deceleration were excluded in this case also. Consequently, the total time recorded by his stopwatch is that of his forward and return journeys at just the uniform speed between the second and third ships. For him, what his stopwatch finally shows is the actual duration of the full journey at the uniform speed. However, on his outward as well as return journeys, he found the watches of the second and third ships to be running at half the rate of his stopwatch and other watch. He thus expects the time of travel arrived at on the basis of the watches of these ships to be just half that registered by his stopwatch.

His Holiness (continuing): I came to the conclusion that they must find that while the duration of the first ship’s travel at the uniform speed from alongside the second ship to the side of the third ship and back is four hours as ascertained from the second and third ships, the duration as determined from the first ship and recorded by the stopwatch is only two hours. The reasoning that led me to this conclusion was as follows. If the first ship had just continued to travel eastwards at the uniform speed, the person in it would have been on the same footing as the person in the second ship. This is because, even in the light of experiments, he would have concluded that he is stationary, exactly like the person in the second ship. Also, he would have found the second ship to be travelling to the west at the uniform speed just like the person in the second ship would have found the first ship to be moving to the east at the uniform speed. His assessment of the flow of time in the second ship would then have been truly equivalent to the assessment of the flow of time in the first ship by the person in the second ship. However, the present situation is different. It is his ship that reverses the direction of travel and comes back to the side of the second ship. Regardless of whether, in order to change direction, his ship decelerates to a stop slowly or swiftly or, quite unrealistically, does so instantaneously, he cannot but experience being pushed eastwards and know that his ship has not been stationary. Similarly, when his ship accelerates in the opposite direction to reach the uniform speed, he cannot but know from the experience of being pushed eastwards that his ship is moving. Apart from his experience, an accelerometer¹ on the ship shows the slowing down and speeding up. None of this occurs on the second ship. Thus, in the present case, as the first ship does not just travel at the uniform speed in one direction, but changes direction and returns to the side of the second ship, the person in it is not on the same footing as the person on the second ship. Hence, while his stopwatch correctly records the duration of his ship’s journey at the uniform speed, his assumption that the duration determined by the persons of the second and third ships on the basis of their watches must be half that shown by his stopwatch is incorrect.

As regards the persons on the second and third ships, not only is their determination of the duration of the first ship’s travel on the basis of their watches correct, so is their assessment that the stopwatch in the first ship must show half this time.

His Holiness (continuing): Till this point, I had just used the example of the ship of the Italian scientist (Galileo) as the basis for all my analysis. I had not seen a big ship till then. Further, though I knew that even if one were to travel at only a thousandth of the speed of light, one would still go completely round the earth in a few minutes itself, I had, for facilitating my analysis, fancied that a ship travels for two hours at a speed near that of light. Hence, I continued my reflection about the implication of the constancy of the speed of light by considering not a big ship but what I was quite familiar with. Further, I decided to assume, for convenience, that the speed of light is just a few miles an hour. In keeping with this, I considered entities moving at less than this speed.

His Holiness (continuing): When young, on many days, after a swim in the river (Tunga), I placed my legs in the padmāsana, lay down on my back in the water, and, looking up at the sky, allowed myself to float freely downstream for some time. As long as I was carried by the current in a straight line, I did not discern that I was moving. It was only where the river took a turn that I sensed a pull. I also noticed that if, while being steadily carried downstream in a straight line, I arched my neck and looked at the water a little beyond my head, the water appeared still. One day, the sky was overcast. After the bend at some distance from the Sandhya-mandapa, I kept going with the flow, without any sensation of movement, till I had almost traversed the length of Sringeri. Only when I happened to look sideways at the riverbank, I realized that I had come far. I then swam back to the Sandhya-mandapa. In view of this experience, I chose to consider a person floating downstream in a river on his back instead of a person in a ship travelling on the ocean.

His Holiness (continuing): One day, when I was floating downstream on my back and seeing the river beyond my head, I noticed a small bird flying a little above the water and heading straight towards me. It went over me, flying just a few inches above my face, chest, and feet. I do not know why it flew this way and that was the only time I saw a bird do so. Remembering this, I imagined a person floating downstream at two miles an hour and a bird flying in the opposite direction at the same speed. Instead of the stationary ships that I had thought of earlier, I assumed that three persons are crouching in the waist-deep water of the river, in a line. I supposed that the first person is positioned half a mile up the river with respect to the second person and that the third person is half a mile downstream with respect to the second person. The three, who are not moving with respect to one another, have watches that are running at the same rate and are showing the same time. I imagined that the swimmer who is floating downstream on his back has a watch and a stopwatch with him.

His Holiness (continuing): While the first person finds the swimmer floating downstream at two miles an hour, the swimmer discerns that he is still and that it is the first person who is moving in his direction at two miles an hour. Just when the swimmer is beside him, the first person notes that the time shown by his watch is 5 p.m. As for the swimmer, he starts his stopwatch.

Meanwhile, the bird flies past the third person who is positioned a mile downstream. The time of the bird passing him is noted by the third person to be 5 p.m. He also determines that the bird is flying a little above the water at two miles per hour.

His Holiness (continuing): Freely floating downstream, the swimmer moves from next to the first person to beside the second person, who is stationed half a mile downstream. The second person ascertains the time in his watch when the swimmer is next to him and also the speed of the swimmer. He finds the time to be 5:15 p.m. and the speed of the swimmer to be two miles per hour. The swimmer, for his part, stops his stopwatch. Exactly when the swimmer comes next to the second person, that is, at 5:15 p.m. as per the second person’s watch, the bird too arrives there. The second person, like the third, finds that it is moving at two miles per hour.

Stationary ❶<-0.5 mile->❷<-0.5mile->❸ Persons Swimmer Ⓢ>>Ⓢ>>>>>>>Ⓢ>>>

<<<Ⓑ<<<<<<<Ⓑ<<<<<Ⓑ Bird

Person 1: Swimmer passes at 5 p.m., moving eastward at 2 mph

Person 2: Swimmer passes at 5:15 p.m., moving eastward at 2 mph

Person 3: Bird passes at 5 p.m., moving westward at 2 mph

Person 2: Bird passes at 5:15 p.m., moving westward at 2 mph

Swimmer starts a stopwatch as Person 1 passes him and stops it

as Person 2 passes him

Three Unmoving Persons, Swimmer and Bird

His Holiness (continuing): The still, second person finds the swimmer approaching him from one side at two miles per hour and the bird approaching him from the opposite side at two miles per hour. At this stage, I supposed that the speed of light is two and a half miles per hour. Accordingly, the second person finds the bird moving towards him at 80 percent of the speed of light. I then considered the speed of the bird as determined by the swimmer. I realized that though he is moving in one direction at two miles per hour and the bird is moving in the opposite direction at two miles per hour, he cannot find it approaching him at four miles per hour. Else, from his perspective, the bird would be moving at a speed greater than that of light. I imagined that a flash of light emanated earlier from the bird’s head. I reasoned that the swimmer must observe the light as approaching him at two and a half miles per hour, for the speed of light is the same for all observers. If he were to find the bird approaching him at four miles per hour, he would find the bird overtaking the flash of light. This cannot be. Therefore, I concluded that the swimmer must find the bird to be approaching him, not at four miles per hour but at some speed less than two and a half miles per hour, which I had taken to be the speed of light¹. I surmised that if the bird were stationary like the three persons, the swimmer would find it moving towards him, like the persons, at two miles per hour. On the other hand, even if he were moving downstream at almost two and a half miles per hour and the bird were flying in the opposite direction at almost two and a half miles per hour, he would find it approaching him only at nearly two and a half miles per hour, the assumed speed of light, and not at nearly five miles per hour. I comprehended that this is a consequence of the speed of light being the same for all observers and not due to any erroneous assessment of the swimmer.

His Holiness (continuing): I conceived that the first person subsequently walks up to the second person. They confirm that their watches show the same time and run at the same rate. When the swimmer was next to the first person, the time as per the latter’s watch was 5 p.m. and when the swimmer was beside the second person, the latter’s watch showed 5:15 p.m. Hence, the first and second persons conclude that the swimmer took 15 minutes to cover the half-a-mile distance between them. The swimmer started his stopwatch when the first person was at his side and stopped it when the second person was beside him. For him, the time interval between the first person going past him and the second person coming beside him is that recorded by his stopwatch. Because the swimmer moved past the first and second persons at

80 percent of my assumed speed of light, both of them found the swimmer’s watch running much slower than their own watches. The swimmer, for his part, found the first and second persons moving towards him at 80 percent of my assumed speed of light and, hence, found the watches of the first and second persons running much slower than his. I conceived that upon coming to a bend in the river and feeling a tug, the swimmer realized that he had not been still but had been floating downstream. He turned, swam up the river, and joined the first and second persons. I gave thought to whether his stopwatch records the same time as that arrived at by the first and second persons or a greater or a lesser time. The swimmer was the one who decelerated from his uniform speed, reversed his direction of travel, and joined the second person. In view of this, I concluded, just as I had done earlier with regard to the stopwatch of the first ship, that the time recorded by the swimmer’s stopwatch must be less than that determined by the first and second persons on the basis of their watches. That is, it must be less than 15 minutes.¹ His Holiness (continuing): At this juncture, it struck me that the distance between the first and second persons made out by the swimmer as he freely floated downstream must also be less than that discerned by the first and second persons. As ascertained by the first and second persons, the distance between them was half a mile, and the swimmer moved at two miles an hour for 15 minutes to reach the second person. On the other hand, as determined by the swimmer, the second person advanced towards him at two miles per hour and reached him in less than 15 minutes after the first person had done so. Therefore, for him, the distance between the first and second persons is less than half a mile. I understood that if the speed of light is the same for all observers, not only the passage of time, but also distances may be ascertained differently by two persons moving uniformly with respect to one another, and their findings, though different, are valid.

His Holiness (continuing): As I told you, at the close of his talk on the second day, Murthi mentioned two postulates of Einstein and stated that their implications were amazing. It was because my curiosity was aroused about what the startling implications might be that I cogitated as I have described to you. I discontinued my reflection when I found that about two hours had passed. This was the first time I had pondered on such a topic and unhesitatingly recognized that most or all of my conclusions might be erroneous.

His Holiness (continuing): Over the next two days, Murthi expounded Einstein’s two postulates and what follows from them. I was pleasantly surprised to find that none of my conclusions were discordant with what he pointed out. From his account, I became acquainted with several implications that I had partially or wholly missed. For instance, I understood that the shrinking of lengths occurs in just the direction of motion. With the aid of an example, he made known that while two events may occur simultaneously to a person, those very events may occur at different times to another, who is moving at a uniform speed relative to the first. Murthi mentioned that a person may find one of two events occurring first, while another may find the other event occurring first. I asked him if such could be the case even if the two events were causally related. I had in mind the oddity of one of the two persons first seeing an arrow hit a target and later seeing it being shot. He said that when cause and effect are involved, none would find a reversal of the sequence of cause and effect. He explained how this is ensured by the speed of light being the same for all observers and one’s speed being less than that of light. I asked him, “Suppose there is a lamp and a screen far away. A rod is moved in front of the lamp at almost the speed of light. The rod’s shadow on the screen covers a much larger distance than the rod and, so, moves faster than light. How does such exceeding of the speed of light impact Einstein’s postulates and their implications?” He clarified why such cases are not relevant.

His Holiness (continuing): Murthi thereafter explained a formula relating the extent to which time slows down and speed. A portion¹ of it involved two squares² and a square root³. He had computed the extent of slowing for several speeds based on the formula, written down the values on a sheet, and brought it with him for me. I later compared, in private, these values with what I had arrived at by making two measurements with a foot rule on each slanting line in my diagram. Though the accuracy of my measurements was limited, I found that my results were quite close to those provided by Murthi.⁴ He also pointed out how the formula can be used to compute the extent to which distance shrinks in the direction of motion, for different speeds. I noted that for any speed, the extent to which distance shrinks is the same as that by which time slows down.

His Holiness (continuing): He presented an example involving a pair of twins. One of them leaves the earth in a vehicle that travels at a speed close to that of light. He returns after one year, as ascertained by him. As determined by the twin on earth, several years have passed. When the two meet, they find that this twin has aged more than the twin who left the earth and returned.¹ The closer the speed of the latter’s vehicle to that of light, the more the difference in their aging.

Murthi added that the total length of the journey as determined by the twin who went in the vehicle is less than the length of his journey as ascertained by the twin who remained on earth.

His Holiness (continuing): I asked him, “Suppose one of the twins travels towards the sun at so very close to the speed of light that, as determined by the twin on earth, his watch is well-nigh still. Then, as found by the twin who travels, the distance to the sun will not be crores of miles but will be almost zero and his time of travel will also be almost zero. Am I correct?” He said that I was.

His Holiness (continuing): This led me to think, “Then, for light itself, the distance traversed to reach the earth from the moon, the sun, the Pole Star or anywhere else in the cosmos is zero and the time of travel too is zero.” I then realized that I had ignored a pertinent distinction between the case of light and that of the twin. While the twin travels at well-nigh the speed of light with respect to the earth or his destination, he is stationary with reference to his vehicle. A watch that does not move relative to him can determine the duration of his travel. Likewise, a means to measure distance can have him as a point of reference. However, there is nothing with respect to which light is at rest. Else, there would arise the contradiction of light being stationary with respect to something and simultaneously moving with respect to that itself at the speed c, since its speed is c for all observers. Hence, while the passage of time for the twin and the distance of something from him can be measured, this is impossible in the case of light. Thus, while it can be found through measurements that the distance to the destination and time of travel are almost zero for the twin, it is impossible to establish, likewise, that distance and time of travel are zero for light. I briefly conveyed to Murthi what I had surmised about time and distance with respect to light in order to know what all I might have got wrong. He did not object to what I told him.

His Holiness (continuing): Murthi familiarized me with the concepts of ‘mass’ and ‘momentum’¹ and pointed out that a major implication of the speed of light being the same for all observers is that mass and energy² are equivalent. He described a simple equation³ between the mass of an object that is at rest with respect to an observer and its energy; this involved the speed of light. He provided the example of a copper ball that is carefully weighed. It is heated and then weighed again. It weighs a wee bit more than before. As it cools, its weight decreases. Finally, it weighs the same as it did at the start. Likewise, less force is needed to accelerate it when it is cool than when it is hot. Thus, though no copper is added or removed, the ball’s mass changes in keeping with the energy that is absorbed or given up by it.

His Holiness (continuing): I asked him, “There is a box made of mirrors. It has a small closable hole on one side. The box is weighed. A powerful beam of light is made to enter the box via the hole that is then closed.

The light inside keeps getting reflected in the box’s mirrors. The box is weighed again. Will it weigh more than before?” He said that it would but the difference would be minuscule. This is what I had supposed when conceiving the example and hence proceeded to pose my intended question, “Does the change imply that light has mass? As light is never at rest with respect to any observer, one cannot speak of any mass at rest for it. The equivalence that you described between mass and energy will thus not apply to it. Yet, the unmoving box with light in it has a greater mass than the same box without light in it. How?” He explained that what he had given is a special case of a general formula¹. This equates energy with mass and momentum. An object, such as the copper ball, that is at rest has mass but no momentum. As for light, it has no rest mass but has momentum, like a moving ball. The box’s weight rises because the light within it has momentum and, thus, energy. On account of the additional energy, the box weighs a little more than before just as it would if an unmoving object with minuscule mass were placed in it. Light’s momentum is proportional to its frequency². I then asked him, “Since light has momentum, does light striking a mirror push it?” He replied that it does, but the force is minute. All this was interesting.

§5.6 His Holiness (continuing): Murthi then touched upon what he said relates to a general theory developed by Einstein. He began with an example. There is a closed compartment and a person is in it. It is far from the earth, in empty space. Irrespective of whether it is not moving or is moving at a uniform speed with respect to the earth, the person in it finds himself at rest and weightless. A ball tossed by him moves straight across the compartment, at a uniform speed. It does not head in a curve to the floor. Next, the compartment is close to the earth. It is falling freely, accelerating as it does so, like a stone dropped from a height. In this case too, the person in it finds himself stationary and weightless. A ball tossed by him moves straight, with no change in speed, just as it did earlier. He cannot differentiate by means of investigations whether his compartment is falling freely and accelerating, or is far away, in space, without any acceleration. Thus, during a free fall, the effect of gravity¹ is essentially nullified.

His Holiness (continuing): I asked him, “The force with which the compartment is drawn to the earth would be less when it is 100 miles from the earth than when it is one mile away. Hence, as the compartment falls from 100 miles to one mile, the person in it can know from the varying acceleration itself that he is falling. The example cannot, therefore, apply to a long, free fall towards the earth, the moon, or any such big mass. Is it that what is considered is a small portion of the drop over which the change in acceleration is negligible?” Murthi said that such is the case and that, in view of its relevance, he was about to mention this himself. Thinking of the moon going around the earth, I asked him, “Suppose the compartment orbits the earth at some distance. While its speed is uniform, its direction of motion keeps changing steadily on account of the earth’s gravity. When the compartment is in a free fall, while its direction of motion is uniform, its speed keeps increasing due to gravity. Are its orbiting the earth and its falling freely to the earth equivalent for the person within it?” Murthi replied that they are.

His Holiness (continuing): He proceeded, with another example. A closed compartment with a person in it is kept on the ground. He weighs himself. Then, he drops a ball and notes how it falls to the floor, accelerating as it does so. Every such gravity-related study confirms to him that he is on the earth. The compartment is now in space, far from the earth. It is accelerating at the same rate as does a ball when it is dropped on the earth. The person within it weighs himself. His weight is the same as it was on the earth. He drops a ball. It accelerates to the floor of the compartment exactly as it did on earth. As every such investigation yields the same result as on the earth, he cannot distinguish between being in the compartment when it rests on the earth and when it steadily accelerates far away, in space. Likewise, he cannot differentiate between being in the compartment on the moon and when it accelerates far away, in space, at the same rate as does a ball that is dropped on the moon. The upshot of all this is that steady acceleration and unchanged gravity at a place are equivalent.

His Holiness (continuing): Murthi proceeded to point out that gravity affects light as it does an object like a ball. He said that while the compartment accelerates far away from the earth, light enters it through a small hole three feet above its base. Were the compartment at rest, the person in it would see the ray go straight across the compartment and strike the opposite side three feet above the base. On the other hand, when the compartment is accelerating, he finds it curving downward and hitting the opposite side less than three feet above the floor. The effects of steady acceleration are equivalent to those of gravity. Thus, the ray would curve even if the compartment were at rest near a big mass. As he was speaking, I visualized the person in the accelerating compartment and the ray curving towards the floor, like a ball. I made out that where the light hits the opposite side depends not only on the steady acceleration but also on how fast the compartment is moving when the light enters it. If the cubicle were moving at a steady speed, the ray would have travelled in a slanting line. The more the speed, the more the slope. In the present case, the upward speed is rising steadily with time, and so, the later the beam enters the compartment, the lower will be the spot where it strikes the opposite side. The light’s curved path in the accelerating compartment, thus, depends on when the light enters, but the effect of constant gravity on light would not, presumably, keep growing with time. This impeded my fully grasping from the example that acceleration and gravity affect light in a comparable way. However, I promptly realized that while the ray would hit a lower spot if the initial speed were greater, the extent to which light deviates from a straight line depends on just the acceleration. The realization that the extent of curving depends on just the acceleration removed the difficulty in my appreciating the example.

I did not say anything to Murthi about this. However, I did ask him, “If gravity affects light as it does a ball, does the light emanating from a torch that is pointed upwards lose momentum as it proceeds upward, away from the earth? Likewise, does the momentum of a ray that moves closer to the earth rise as it does so? You had told me that light’s momentum is proportional to its frequency. In case the momentum of the beam decreases or rises as it moves away from or towards the earth, does its frequency also vary accordingly?” He said that light’s frequency changes due to gravity, but such change is minute in the case of the earth and was yet to be measured¹. He added that the downward shift in the frequencies of light leaving a star had been measured about 15 years before² (that is, in the 1920s).

His Holiness (continuing): He then said that a watch runs slower where the effect of gravity is more than where it is less. Thus, if a person standing on the moon were to view a watch on the earth, he would find it running slower than his watch. In keeping with this, a person on the earth would find the watch on the moon running faster than his own. I asked him, “Then, a watch far away in space must run faster than one on the earth. Even on the earth, a watch in Bangalore must run faster than one in Madras (which has nearly the same latitude but has a lower altitude). Also, in a single place itself, a watch on the roof of a house must run faster than one on the ground below. Is it not so?” He said that this was correct, but till then³ there was no means to measure such infinitesimal differences.

His Holiness (continuing): Murthi then told me about an interesting effect of mass on space-time¹. I knew from his exposition of the implications of Einstein’s two postulates that space and time are interrelated and that events can be regarded as located in space-time, rather than just in space or time.² This space-time has four dimensions³, three of space and one of time. He had said that far away from massive entities like the sun, it is flat and uniform. I had asked him if the flatness that he was referring to could be verified by any experimental means. He had said that it could be, in principle, and started by pointing out that the sum of the three angles of a triangle⁴ on a flat paper is 180 degrees. In the case of a triangle on a curved surface, such as that of a ball, the sum is different. I knew this.

Three points in a region of space are considered. A ray of light passes from the first to the second point, a second ray from the second to the third point, and another ray from the third to the first point. A triangle is thus formed by light, with the three points at its ends. If the sum of the angles of every such triangle in a region of space is 180 degrees, that space could be deemed flat. I do not know if he had conceived this test just then or had read about it somewhere. I found it ingenious but did recognize that it pertained to the flatness of just space. He had told me a definition of the distance between two points in flat space-time and that this distance is the same for all observers moving at uniform speeds relative to each other. Recapping some of what he had stated earlier about space-time, Murthi said that mass curves space-time. He stressed that light always takes the shortest path between two points in space-time. This path, he said, may even be curved. Where space-time is flat, such as far away from massive bodies like the sun, this is a straight line, and where space-time is curved, such as close to the sun, this shortest path is curved. He gave the example of a tiny ant walking straight ahead from a point to another on a flat sheet of paper and of that ant doing so on the surface of a big ball. Since it is tiny and the ball big, as it walks on the ball, it finds the surface flat and just walks straight ahead, like on the flat sheet. On the flat sheet, its path is a straight line and on the surface of the big ball, it is curved, but in both the cases, its path is the shortest between the points. He then pointed out that in flat space-time, a free object moves, like light, in a straight line, at a constant speed, taking the shortest path between two points. In the vicinity of a massive body, the path of this object becomes curved as it falls freely, accelerating towards that body. It may land on the massive body, or curve towards it but go past it, or finally end up orbiting it. In all the cases, its curved path is the shortest between points on it in the curved space-time. The earth is more massive than the moon and, hence, curves space-time more than the moon. A consequence of this is that a watch on the earth runs slower than a watch on the moon. He then said that Einstein had computed and predicted the amount by which the light from a distant star would bend as it passed by the sun and came to the earth. He added that this prediction was verified 22 years before (that is, in 1919) through measurements made during a total solar eclipse.

His Holiness (continuing): I asked him if scientists see empty space or time as some stretchable and bendable material like heated glass. His response was, “No.” My question was a prelude to my next ones, which were, “How then can any mass physically stretch and curve space and time and, hence, space-time? Is it that the curvature of space-time is basically a concept in terms of which the slowing of clocks, the curving of light and other effects near massive bodies are mathematically accounted for?” He replied that space-time itself is a concept. While space, per se, is intangible, its flatness and curvature have been defined mathematically and can be distinguished by measurements on objects in it.

§5.7 His Holiness (continuing): Thereafter, Murthi took up another topic; that of the electron. With the pertinent background, he apprised me about the discovery of the electron as a particle with a negative charge (by J. J. Thompson in 1897).¹ When I saw an oscilloscope for the first time many years later, I understood that the beam of electrons that produced a green glow in the front of its tube was the type of beam that had been investigated by the discoverer of the electron. Murthi then introduced me to the finding that illumination can cause the emission of electrons from a substance and to an experimental study of this phenomenon.² He said that when the illumination’s frequency is below a threshold, no electrons are emitted even if its intensity³ is high. Above the threshold, the speed of the electrons emitted rises as the frequency is increased. Change of intensity does not affect the speed of the electrons; what increases with the rise in intensity is the number of electrons emitted. These findings, he pointed out, cannot be accounted for if it is accepted that light is a wave and that an electron receives energy from it and becomes free. The reason that he mentioned was that the energy of a pure wave depends on its intensity and not on its frequency. Hence, the speed of the electrons should have depended on the illumination’s intensity and not on its frequency. He summed up that while the formation of bright and dark bands on a screen when light passes through a pair of slits shows that light is a wave, the observed dependence of the emission of electrons on the illumination’s frequency disfavours the view that light is a wave.

His Holiness (continuing): Murthi then told me that Einstein explained the findings about the emission of electrons by proposing (in 1905) that light consists of discrete packets of energy. Such a particle of light came to be known as a ‘photon’¹. The energy of a photon is, as per Einstein, directly proportional to the frequency of the light. It is independent of the light’s intensity. Thus, a photon of red light has less energy than one of blue light, regardless of the intensities of the red and blue rays. An electron is emitted when a photon that has enough energy to free the electron transfers all its energy to that electron. Consequently, when the light’s frequency is below a threshold, no electron is emitted even if its intensity is great. At frequencies above the threshold, an electron receives more energy and emerges with greater speed. Different materials have different thresholds. When the light’s intensity is more, the number of photons is what is more, not their energy. Thus, when the light’s intensity is more, more electrons are emitted, not speedier ones. Murthi said that some years after Einstein published his theory, it was experimentally found (in 1915 by R. A. Millikan) that electrons are emitted from illuminated materials as predicted by Einstein. I asked him, “What becomes of the photon that transfers its energy completely to an electron?” He replied that it vanishes, having been fully absorbed by that electron. I then asked him, “Can an electron receive a part of the energy of a photon? If so, will there arise a photon that has just the remaining energy?” He said that such partial transfer of energy does occur in an interaction involving a photon with high energy and a nearly free electron. He added that the discovery and study of this distinct phenomenon¹ supported Einstein’s view that light comprises photons.

His Holiness (continuing): He thereafter informed me that scientists had come to regard light as possessing a dual nature; that of a wave and that of a particle. The wave-nature of light shows up in, for example, the formation of light and dark bands in the experiment with slits and its particle-nature in, for instance, the emission of electrons from an illumined material. I asked him if the two aspects can be observed at the same time and, if not, what determines which aspect is found when. He said that the prevailing scientific view was that the two are not observed together and that the set-up determines the aspect observed.

His Holiness (continuing): Murthi then told me that a French scientist (Louis de Broglie) proposed (in 1924) that just as light has two aspects, so does any particle. Every particle, such as an electron, is associated with a wave. The particle’s energy is directly proportional to the frequency of the wave. This is like the energy of a photon being, as per Einstein, directly proportional to the frequency of the light. Murthi then stated that a few years after the French scientist proposed that a particle, such as an electron, is associated with a wave, scientists¹ experimentally ascertained that electrons do behave as waves, like light passed through slits. He added that microscopes that rely upon the electron’s wave-aspect have, since the 1930s, been built and used to study minute objects.

His Holiness (continuing): He thereafter told me that a scientist (Erwin Schrödinger) formulated (in 1925 and reported in 1926) an equation that describes the wave of any particle². A rough analogy is an equation that describes a wave of water and gives the height of that wave at any location and time. For a particle such as an electron in an atom, the equation provides, for any location and time, a number with two parts (that is, a complex number).¹ A German researcher (Max Born) interpreted the square² of this (the absolute square of the complex number) as the probability³ of detecting the particle there at that time. When a measurement is made, an electron, for instance, is found at any one of its possible locations. I asked him, “What determines where the electron will be detected? Does its being detected somewhere imply that it was there prior to being detected?” He explained that the outcome of a measurement is random⁴, and the electron could very well have been detected elsewhere. All that can be specified is how probable it is that it will be observed somewhere. Prior to its being detected somewhere, an electron is not looked upon as having any specific location. He said that he had based his response on one scientific viewpoint (the Copenhagen Interpretation).

His Holiness (continuing): He then informed me that a German scientist (Werner Heisenberg) had arrived at the conclusion that the less the uncertainty in the position of a particle at any time, the greater is the uncertainty¹ in its momentum at that time; likewise, the less the uncertainty in its momentum, the more is the uncertainty in its position. By way of elucidation, he described an experiment that had been imagined by that scientist. A person wants to precisely measure the position and momentum of an electron. He sets up a powerful microscope and illumines the electron. The shorter the wavelength of the light, the sharper is the identification of the electron’s position. However, the less the wavelength, the more is the momentum of the photons. The higher the momentum of the photon that interacts with the electron, the greater is the change that it causes in the momentum of the electron. Thus, more precision in an electron’s position is only at the price of higher indefiniteness in its momentum.

His Holiness (continuing): I asked him, “You had said earlier that, before measurement, an electron has no specific location, and only the probability of its being detected at a place at some time can be known. The present example, however, seems to presume that an electron has some specific position and some specific momentum before it is illumined and that this position cannot be found without disturbing the momentum. Is the indefiniteness in an electron’s position and in its momentum only on account of the measurement-related disturbance¹, or is it intrinsic?” He mentioned that the scientist’s mentor (Neils Bohr) had clarified the example and the indefiniteness in an influential article² in a prestigious British journal and that he was basing his reply on it. Electrons, like light, behave as particles and as waves. Indefiniteness in an electron’s position and momentum is due to its having such dual aspects. Suppose an electron were to have, in its aspect as a wave, a specific wavelength, and frequency. Then, it would have a precise momentum. However, being a pure wave of unbounded length, its position would be totally indefinite. For there to be low indefiniteness in its position at any time, its wave must have a small extent. Such a wave-packet is obtainable by adding (sine) waves of different frequencies. Murthi explained this with some sketches. When the wave-packet has a small spread³, the indefiniteness in the electron’s position is correspondingly small, but, as this wave-packet is equivalent to a combination of (sine) waves of different frequencies, there is indefiniteness in the electron’s momentum. Murthi told me that the smaller the spread of the wave-packet, the more is the spread in the frequencies of the waves needed to give rise to this wave-packet. Thus, at a fundamental level itself, the less the spread in an electron’s position, the more is the spread in its momentum, and, likewise, the less the spread in its momentum, the more is the spread in its position.¹ He added that the scientist who first identified this relationship (Werner Heisenberg) also specified one between indefiniteness in energy and time. An electron that is in a stable state² in an atom may, such as when it absorbs a photon, shift to and briefly remain in an excited state³. The shorter it is in that excited state, the more is the indefiniteness in its energy.

His Holiness (continuing): Murthi then mentioned an intriguing phenomenon, which, he said, occurs since a particle such as an electron has a wave-aspect and the indefiniteness that he had spoken of. A marble that is on one side of a barrier cannot pass on to the other side unless it is moving energetically enough to be able to climb over the top of that barrier. However, in the case of an electron, there is a small probability that it will be detected on the other side of even an electrical barrier that it basically does not have the energy to surmount. This probability, he said, can be worked out by means of the electron’s wave-equation. The greater the width or height of the barrier, the less is the probability of the electron being detected on the other side. This phenomenon, he pointed out, would not have been possible if an electron were analogous to a marble.

His Holiness (continuing): Murthi then said that about a decade earlier, it was found (by Carl Anderson in 1932) that a ray of extremely high frequency (a gamma ray), whose photon has much energy, may create and give place to an electron and another particle. This particle is called a positron. While it has an electron’s mass, its charge is the opposite of that of an electron. Reminded of the equivalence of mass and energy that he had told me about earlier, I asked him, “If a photon can become fully replaced by an electron and a positron, can these two particles unite and give place to a photon that has their total energy?” He said that when an electron and a positron come together, not one, but two photons arise, each of which has half their total energy. These two photons fly off in opposite directions.¹

§5.8 His Holiness (continuing): He stopped here as I had told him at the start of his daily expositions of science to complete them in a week. Even as he was about to prostrate, I appreciatively told him that he presented the subject-matter cogently and that all the sessions were informative, thought-provoking, and engrossing.

His Holiness (continuing): In the middle of his stay in Sringeri, I taught him how to worship Kr̥ṣṇa mentally, and he practised this mānasa-pūjā thrice daily. On the day of his departure, he asked me whether he may, in addition to this, worship an image of Kr̥ṣṇa every day at Brindavan. On my assenting, He entreated me for an idol and instructions on worship. I fulfilled his request. On two earlier occasions and before leaving, he deeply expressed his gratitude and said, “This has been the most uplifting, meaningful, and joyful time of my life; but for God having kindly given me a terminal disease, I would have surely missed it.” By my Guru’s blessings and God’s grace, his fervent desire to spend his final months centred on Kr̥ṣna was consummated.¹

§5.9 A day after concluding His account of His exposure to physics (in 1941) from Murthi, His Holiness graced me with the following information at Kalady in July 1984.

His Holiness: The day after Murthi left Sringeri, I recalled that when an electron and positron come together, they disappear and are replaced by a pair of photons. Did this imply, I asked myself, if the electron-positron pair that existed earlier totally ceased to exist and if two photons that were non-existent earlier came into existence and if, consequently, the clear teaching of the scripture¹ that every effect has no existence other than as its material cause, just as an earthen pot has no existence apart from its cause, clay, that an effect is latent in its cause prior to its manifesting and that something cannot arise from what is non-existent is negatively impacted? To buttress the hypothetical problem, I recalled that a photon may be absorbed by an atom and, in terms of its electrons, that atom may pass from a stable to an excited state; though Murthi did not directly tell me this, I supposed that the atom in the excited state returns to its stable state not in a single step, emitting a photon, but in two steps, emitting two photons, the energy of each of which is different from that of the photon that was absorbed; another option that I envisaged on the basis of Murthi’s information that illumination can result in the emission of electrons from a substance was that upon the first photon being absorbed, an electron becomes free of the atom and does not emit any photon. I straightaway realized that all this was actually no problem at all for the teaching of the scripture about causality. From the viewpoint of the Śāstra, the electron-positron pair is not the material cause of the photons that arise; likewise, the absorbed photon is not the material cause of the photon or photons emitted when the atom returns to its stable state in one or in two steps nor is it the cause of the freed electron; the cause is energy, which is what is conserved in all the interactions and not the number of photons, electrons or positrons; it is what is on par with the clay of the scriptural example¹; just as clay is the material cause of the products of clay such as an earthen pot and an earthen jug and the pot is not, per se, the cause of the jug even if the pot be powdered and the jug fashioned thereafter, so too, it is energy that is the material cause of the photon, electron and positron and it is not the electron-positron pair that is the material cause of a pair of photons nor is a photon that excites an atom the cause of any emitted photon; just as we do not see pure clay as fully without any shape but see it with some form such as that of a lump, pure energy is not what is explicitly detected and it is energy manifest as a photon, electron or positron that is detected; just as apart from clay, no product of clay has any existence, a photon, electron or positron would, bereft of mass and momentum, be non-existent if it had zero energy.

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