Paradoxes of Time and Space

Complexity: 
Hard


Imagine that man travels into outer space on a rocket at near the speed of light and then returns to earth. According to Einstein’s theory of relativity, the man will find he has not aged as much as his identical twin brother who stayed home. Time will have passed more slowly on the rapidly moving rocket than on the slow-moving earth. This disparity in the passage of time is often called time dilation.

This story of the twins is called the twin paradox, since it runs contrary to our expectations. Yet a simple diagram can easily show how it works.

The key to understanding the aging of the twins is Einstein’s postulate that no matter how fast a person is traveling, if he measures the speed of a beam of light it will always be the same. In principle, then, we could make a clock by having a beam of light bounce back and forth between two mirrors mounted in frames at a fixed distance from one another. Since light always goes at the same speed, the time a pulse of light takes to make one complete bounce from one mirror to the other and back will always be the same. So we can measure the passage of time by counting complete bounces.

In the graph, distance is plotted on the horizontal axis and the passage of time on the vertical. Two stationary mirrors leave parallel vertical lines as time passes. A pulse of light bouncing back and forth between the two mirrors leaves a zig-zag path, and in this diagram we can count 10 complete bounces.

The pair of lines moving right and then left in a V-shape represents the movement of a pair of mirrors that travel first to the right and then to the left. The zig-zag line between these two V-shaped lines represents the path of a light pulse bouncing between the two moving mirrors. We can count nearly 7 complete bounces in this case. This means that while an observer standing next to the stationary mirrors experiences that 10 units of time have passed, an observer traveling with the moving mirrors experiences only 7 units of time.

This shows how the twin paradox works. The striking thing about it is that even though the zigs and zags of the light trapped between the moving mirrors seem unequal, an observer moving with the mirrors will see them to be the same. For this to be possible, both space and time on a moving object must transform in a strange way.

Note, by the way, that the horizontal spacing between the two moving mirrors is shown to be smaller than the spacing between the two stationary mirrors. This is an example of how space transforms with motion. According to Einstein’s theory, a moving object will shrink in length by a certain percentage along its line of motion.

Apart from time dilation caused by motion, Einstein also discussed time dilation caused by gravitation. Imagine a beam of light moving up from the surface of the earth. According to the laws of physics, the light must lose energy as it climbs against the pull of gravity. The frequency of a beam of light is proportional to its energy. So as the light climbs upward, its frequency drops.

Now suppose the light is coming from the face of a clock situated on the earth’s surface, and that a person in outer space is using this light to see the clock. A person on earth can observe that for every second ticked off by the clock, the light will vibrate through a certain number of cycles. The person observing the clock from outer space will also see that the light vibrates through this many cycles in the time the second hand ticks off one second.

For the observer in outer space, however, the light has a lower frequency than on earth. So he’ll see the earth clock running slower than his own clock. Relative to the observer in space, time on earth must be passing more slowly. Calculations show that for a person in outer space, time on the earth’s surface would seem to pass only slightly more slowly. But time on a planet with an extremely strong gravitational field would pass very slowly indeed.

According to the theory of relativity, an object with a strong enough gravitational field will be surrounded by an imaginary sphere called the event horizon. As Joe Smith, say at 1:00 P. M. by his own watch, approaches the object in his space ship and passes the event horizon, he won’t notice anything unusual. But to an observer watching from a distance, as Joe approaches the event horizon, he will seem to slow down. He will never quite get there, and his watch will never quite reach 1:00 P. M. As the light coming from Joe grows to longer and longer wavelengths, Joe will fade out and gradually become invisible. Objects with such event horizons are known as black holes.

These examples show that modern physics allows for remarkable transformations of space and time. And apparently, similar ideas are found in Vedic literature.

We find an example in the story of a king named Kakudmi, who was able to travel to the world of Brahma and experience Brahma’s scale of time. Here is the story, as related in the Srimad-Bhagavatam:

Taking his own daughter, Revati, Kakudmi went to Lord Brahma in Brahmaloka, which is transcendental to the three modes of material nature, and inquired about a husband for her. When Kakudmi arrived there, Lord Brahma was engaged in hearing musical performances by the Gandharvas and had not a moment to talk with him. Therefore Kakudmi waited, and at the end of the musical performances he offered his obeisances to Lord Brahma and thus submitted his long-standing desire.
After hearing his words, Lord Brahma, who is most powerful, laughed loudly and said to Kakudmi, “O King, all those whom you may have decided within the core of your heart to accept as your son-in-law have passed away in the course of time. Twenty-seven catur-yugas have already passed. Those upon whom you may have decided are now gone, and so are their sons, grandsons, and other descendants. You cannot even hear about their names.” (Srimad-Bhagavatam 9.3.28-32)

One catur-yuga lasts 4,320,000 years. With this information, we can estimate the rate of time dilation on Brahmaloka. If the concert given by the Gandharvas took about one hour in Brahma’s time scale, then that hour must correspond to 27 times 4,320,000 earth years. It is interesting that this estimate closely matches one for time dilation in another story involving Brahma.

This is the story of the brahma-vimohana-lila, or the bewilderment of Brahma by Krishna. Several thousand years ago, Krishna descended to the earth as an avatara and was playing as a young cowherd boy, tending calves in the forest of Vrindavana (south of present-day New Delhi). To test Krishna’s potency, Brahma used mystic power to steal Krishna’s calves and cowherd boy friends and hide them in suspended animation in a secluded place. He then went away for a year of earthly time to see what would happen.

Krishna responded to Brahma’s trick by expanding Himself into identical copies of the calves and boys. So, when Brahma returned, he saw Krishna playing with the boys and calves just as before. Brahma became bewildered. Checking the boys and calves he had hidden, he found they were indistinguishable from the ones playing with Krishna, and he couldn’t understand how this was possible. Finally Krishna revealed to Brahma that these latter boys and calves were identical with Himself, and He allowed Brahma to have a direct vision of the spiritual world.

Now, it turns out that even though Brahma was absent for one earth year, on his time scale only a moment had passed. The Sanskrit word used here for a moment of time is truti. (Srimad-Bhagavatam 10.13.40) There are various definitions of a truti, but the Vedic astronomy text called the Surya-siddhanta defines a truti to be 1of a second. If we accept this figure, then one year on earth corresponds to 13,750 of a second in the time of Brahma.

As I pointed out, King Kakudmi’s visit to Brahmaloka took 27 times 4,320,000 earth years. If we multiply this by 1we find that in Brahma’s time King Kakudmi’s visit lasted 3,456 seconds, or just under an hour. This is consistent with the story that the king had to wait for a musical performance to finish before having a brief conversation with Lord Brahma.

Although the time dilation involved in visits to Brahmaloka is extreme, such large time dilations do arise in the theories of modern physics. For example, suppose that instead of crossing the event horizon of a black hole, Joe Smith simply came close to the event horizon and then went back out into space to rejoin the person observing his journey. If he had come close enough to the event horizon, he would find that although his trip seemed short to him, millions of years had passed, and the observer had died long ago.

It is curious that according to the Srimad- Bhagavatam the physical universe is surrounded by a shell, and Brahmaloka is located very close to that shell. The Bhagavatam gives the diameter of this shell as 500 million yojanas, which, using the standard figure of 8 miles per yojana, comes out to 4 billion miles.

This seems extremely small. In a purport in the Chaitanya-charitamrita, however,Srila Prabhupada makes the following comment:

Srila Bhaktisiddhanta Sarasvati Thakura, one of the greatest astrologers of his time, gives information from Siddhanta Siromani that this universe measures 18,712,069,200,000,000 x 8 miles. This is the circumference of this universe. According to some, this is only half the circumference. (Chaitanya-charitamrita, Madhya-lila 21.84)

Assuming that what is meant is circumference, the diameter of the universe should be 5,956,200,000 million yojanas, considerably bigger than 500 million.

What is the meaning of these apparently contradictory figures? I don’t know for sure, but it’s interesting to consider that transformations of space may take place as one approaches the shell of the universe. The time dilation stories involving Brahmaloka show that transformations of time take place as one approaches the shell, and in the theory of relativity space and time tend to change together.

In the Mahabharata Narada Muni gives Maharaja Yudhishthira a description of the assembly hall of Lord Brahma on Brahmaloka. He emphasizes that the structure of this hall is impossible to describe, and this seems consistent with the idea that space in Brahmaloka may undergo transformations incomprehensible from our earthly standpoint. Here is his description of Brahma’s hall:

It is not possible to describe it as it really is, king of the people, for from instant to instant it has another indescribable appearance. I know neither its size nor its structure, Bharata, and never before have I seen such beauty. The hall is very comfortable, king, neither too cold nor too hot; when one enters it, one no longer is hungry, thirsty, or weary. It is as though it is made up of many different shapes, all very colorful and luminous. No pillars support it. It is eternal and knows of no decay. It is self-luminous beyond the moon and sun and the flame-crested fire.

If strange transformations of space do occur in the region of Brahmaloka, then it could be that different scales of distance may be appropriate for describing travel to that region.

Going beyond Brahmaloka, one comes to the shell of the universe, described in Vedic literature as a region of transition from the physical world to the spiritual world. Since the Bhagavatam regards space as we know it as a physical element (called akasha, or ether), the shell marks the end of distance measurements as we know them, even though the thickness of that shell is described in the Bhagavatam in terms of units of distance. This also suggests that different scales of distance and even different types of distance may be involved in Vedic cosmology.

The shell of the universe also marks the end of time as we know it. According to the Vedic literature, a liberated soul is able to cross the shell of the universe and enter the transcendental region of Vaikuntha, where material time does not exist. Compare this with the idea of Joe Smith’s journey through the event horizon of a black hole. Just as Joe passes into a region that, for observers outside the event horizon, is beyond time, the liberated soul passes into a region beyond the time of the physical universe. So in a sense the shell of the universe described in the Bhagavatam might be compared to the event horizon of a black hole.

These comparisons between concepts from the Bhagavatam and concepts from modern physics are crude at best and should be regarded only as metaphors. But they do indicate that some of the strange features of the universe as described in the Vedic literature may be no more “far out” than some of the ideas in accepted theories of modern physics.