Wednesday, January 21, 2015

How Fast Does Brahma Move? Einstein, Brahma and Time Dilation

Please note the following blog is written neither to prove nor disprove a super natural force; it is merely to elicit the reader’s interest in the wide ranging implications of Einstein’s theory of special relativity. Even after 100 years, the true implications of his theories, which forms the foundation of modern physics, remain hard to grasp for even the highly educated. One reason is the lack of emphasis on post classical physics education even at secondary / higher school level. Educators appears to shun away from relativity and quantum mechanics due to the counter intuitive nature of these theories. It is however unfortunate that many people never had a chance to learn the beauty of these profound concepts, grander than almost any other attempt by humans to understand reality as it really is. So below is my humble attempt at making just a small aspect of relativity accessible.

Almost all of the physics we learn in school is classical physics, founding fathers of which were such eminent names in history like Galileo and Newton. This so called classical mechanics is very intuitive as well as an extremely accurate way of describing the world. However towards the end of 19th century, one peculiar phenomenon – how to explain the constant speed of light – was causing much debate in the physics community. According to classical under standing, the measured speed of light should be different for different speeds of the observer and its source. However, Maxwell's equations of electromagnetism the and subsequent Michelson-Morley experiment showed that this is not true. The speed of light was a constant, irrespective of the speed of the observer or the speed of the light source.

Let us do a "thought experiment" using a moving train to understand this dilemma. Of note, most of Einstein's breakthroughs came from these types of “thought experiments”. Unlike a real train, it is certainly easy to propel your "thought train" to near light speed if needed! So let us assume you are inside a very long train travelling at 70 km/hour; and assume you are running inside this long train at 10 km/hour; for an outside observer, your speed would be the combined speed of you and the train (80 km/sec). This is one of the bed rocks of classical mechanics, called "velocity addition” and a very intuitive principle to grasp. For an out side observer looking at a man running inside the moving train, the running man's speed is the combined speed of his running and that of the train. So far simple - right? 


Now assume a man is sitting at the back of the train and flashing a light to the front of the train; we know the speed of light (c) is 299,792,458 meter/second. (From now on I will just use "C" to denote this speed to make this blog look less number filled!) So the question is for an observer outside the train, will the speed of the flash light would look a little bit faster than "C" as we have to add the train's speed to "C"just as the running man's example above? As noted above and per classical physics (and to most people’s common sense understanding even now) the answer is yes – one has to add the speed of the train to the speed of light to get the perceived speed of light for the stationary observer outside the train. But as noted, Maxwell’s equations suggest that the speed of light is a constant irrespective of the speed of the observer or the speed of the light source. Let us assume for fun this is a “super duper rocket train” moving at half the speed of light (say 0.5 C). Then for the outside observer, should the speed of light be 1.5 C (C+0.5 C)? No - despite the enormous speed of the train, for the outside observer, the flash light inside the train would be still moving at the same constant speed C. How is this possible? As you can see this “lack of velocity addition of light” is a very counter intuitive problem. And though several brilliant scientists pondered over how to solve this puzzle, it took the imaginative Einstein to come up with the correct solution to explain why light speed will appear constant to all observers, irrespective of how fast they are moving relative to each other or how fast the light source is moving.

Again, the solution of this puzzle required more imagination and "thinking outside the box" than mere expertise in Math and Physics. Renowned Physicist and Einstein’s close friend Hendrik Lorentz came very close to solving this puzzle; similarly the French mathematician and philosopher Henry PoincarĂ© was also working on how to solve this riddle. But, though extremely brilliant they all were, they all were still working under the assumption, which most of us still carry as almost scared, that time is universal. Our intuition assumes time passes the same way for the man standing outside the train and the man inside the moving train. In the ordinary speeds we travel, this is indeed the way things appear. What sets Einstein’s genius apart was his ability to question even such a cherished and "common sense" belief like the immutability of time.

Now let us see how Einstein solved the above riddle on the speed of a flash light in a moving train. His “Eureka” moment was when he figured out what a measure of time - a "second" for example-  in the fast moving train is not the same as a "second" perceived by the stationary observer. In the above example of an imaginary train moving at half the speed of light, the light speed within the train would still appear to be C for an outside observer - because for him a “second” inside the train would be equal to a whole lot longer than a second outside! The faster the speed of the train, the longer the "second" inside the train would appear. So instead of the cherished Galilean velocity addition, the speed of light will appear the same to all observers. Until Einstein, space and time were the fixed background on which events plays out in the universe. This amazing intuition of Einstein was the first hint at understanding space and time not as a static background but a dynamic structure that can move, warp and most importantly can have different relative values for different observers! Most revolutionary of all these ideas is again the fact that there is no "universal clock" ticking way; time for you and me could pass at different rates if we are travelling at different speeds. This is not the "subjective" feeling of time passing fast or slow depending on how one's mood but an actual change in the rate at which time passes; where my "second" could be actually longer or shorter than your "second"! Of course these become obvious only at near light speeds, so we don't feel this in our every day life.

Take a deep breath here – as it is truly counter intuitive. To recapture; what Maxwell’s equation proved and several subsequent experiments confirmed was the speed of light is an absolute constant in our universe. (Note this is not speed of “light” but of all electromagnetic waves whether we can see them or not). Einstein’s great insight was this can only be so if what we perceive as the passing of “time” depends on your velocity. This phenomenon – where a unit of time in a fast moving frame would appear longer to an outside observer – is called time dilatation. At the ordinary speeds we experience this is negligible. Even a rocket escaping earth’s gravity only has to travel above 11.2 km/sec which is such a puny speed when compared to light speed. However one can easily imagine when the time dilatation could be enormous as the examples below shows; where a minute in an imaginary rocket flying very near light speed could equal to even several years on earth! By the way these are all not idle speculation but time dilation and Einstein’s theories of special relativity have been experimentally verified. In fact, his famous formula E = mc2 is  derived directly from special relativity and as we all know, that sure does work, as most dramatically and destructively proven in Hiroshima and Nagasaki.


Interestingly enough, several old religious texts speak of time as relative. What humans perceive as a year may be a day for a “higher being”. Certain verses of Quran and Bible indicate where an angel could experience 1 day while humans will measure it as 50,000 years. The most extreme form of this time dilation I could find however is from Hindu mythology. More than most religions, Hindu mythology gives a very prominent role for time in its scriptures. Again note this is just as a fun exercise, purely to show how special relativity works, and has very little to do with super natural beings moving at close to light speeds! So here we go - how do we use Einstein’s time dilation equations to calculate the speed of Brahma? This is not as hard as it first appears; Hindu scriptures give specific directions on how long is a Brahma day. It is enormous! A Brahma day is also called Kalpa, is 12 hours of Brahma time, and is equal to 4.32 billion human years! After 12 hours of day, Brahma then sleeps for another 12 hours - kind of lazy for an almighty, if I may add!. So one full day of Brahma is two Kalpas or 8.64 billion human years or 3.06 Trillion human days! (Special thanks to my friend Anindya Sen for getting me up to speed on this aspect of Brahma!) Now that we know how big is the time dilation, we can easily calculate Brahma's speed. Below is the formula for calculating time dilation based on Einstein's special relativity:


So the only unknown variable in the above equation is V – the velocity at which an entity like Brahma should move so the time dilation equals when 1 Brahma day is equal to 3.06 trillion human days. Plugging the numbers we get Brahma's speed V has to be:

299792457.99999999999999999999839916026955444487163044482974 m/sec or 
99.999999999999999999999999999466017343756674783203 percent the speed of light. Now assume one wants to move an average human weighing say 70 kg to the speed of Brahma. How much energy would be needed? Einstein’s equations again help us figure this out quickly; it is M (Mass of the person who needs to be accelerated) x C2 x time dilation factor. So plugging the numbers above, if the rest mass of Brahma is 70 kg, the energy needed to attain the “Brahma” velocity noted above is a mind boggling 1925230456800000000000000000000000 Joules! Now this number is so huge it makes no sense; so just for comparison the annual global energy consumption is about 0.5 zettajoule (ZJ). 1 ZJ is equal to one sextillion (1021) joules. (Note the annual global energy consumption is almost 7 million times the energy released by the atomic bomb at Hiroshima; in another word, world consumes the energy equivalent of around 21,000 Hiroshima sized bombs every day!) But even thought the global energy consumption is enormous, the energy required to get to Brahma speed is a ginormous 1.93 Trillion zettajoules; or about the annual global energy output for the next 4 Trillion years! That is at least a 1000 times more than the expected life of our dear earth itself!

How about time dilation and potential for future space travel? What about the famous “Twin Paradox”? We are nowhere near even 1% of light speed but assume a future technology can propel our rockets to near light speed – what happens then? Assume our rocket can travel at 99% the speed of light and assume one of the twins became an astronaut and traveled in this rocket while the other remained on earth. To calculate her time dilation relative to her earthly twin; 1 - (0.99)2 = 0.02, the square root of this is 0.14, so the Time (Rocket) would be only 14% of Time (Earth). So if the twin left Earth at 99% the speed of light, visited a star system say 25 light years away and came back,  50 years would have passed on Earth, but the rocket twin would be only 7 years older by her biological clock! Two important things to note here: For the person in a rocket travelling at 99% speed of light, it does not "feel like" a star system 25 light years away take a little over 25 years to reach – it only takes about 3.5 years due to the effect of time dilation! Also note that for the astronaut, a day and a year would feel exactly as it would feel for the earthly twin. Only the passage of time between them is different. Are you getting a headache now? Won't blame you - as nothing is wired deeper in to our brain than the deep awareness that time should be the same for all - but trust Einstein- it is not! Time passes at different rate for different observers. Even our language fails to truly communicate this concept!

Now on a side note – some of you may have seen one of the best science fiction movies of 2014, “The Interstellar” which deals extensively with time dilatation. Unlike many science fiction movies, the science of “Interstellar” is quite well thought of. The movie had several consultants from the world of Physics including some of the world’s foremost experts on topics like relativistic time dilation, black holes and worm holes, most notably Kip Thorne, the famous Caltech physicist and close friend of Stephen Hawking. Let me take a short detour here to explain the time dilation shown in the movie; what we have so far described above is time dilation with increasing velocity; there is something else that also causes the same exact effect of time dilation and that is increasing gravity. As noted above the time dilation with increasing velocity is based on Special Theory of Relativity, which can be understood with some basic knowledge of mathematics. However the gravitational time dilation is based on Einstein’s General Theory of Relativity, an absolute “Mathematical Tour de force” and a much harder theory to grasp. While Einstein formulated his Special Theory of Relativity in a single year along with 4 other major breakthroughs (all in the same “Miracle Year of 1905"), his General Theory of Relativity took even Einstein over 10 years of hard work to come up with the final correct relativistic field equations. A true understanding of this requires deep knowledge in many fields of Mathematics, especially tensor calculus. Just looking at the Einstein's Field Equations of gravity gives me a head ache. Suffice is to say that time not only dilates with increasing speed but also with increasing gravity. 


Now does it all matter in real life? Yes indeed! If you ever used a GPS in your car or phone, believe it or not, these esoteric facts of time dilation becomes a major factor in accurately measuring your position. Why?  A GPS, whether in your car or the one made as part of your smart phone carries with it an atomic clock with an accuracy of 1 nanosecond (1 billionth of a second). A GPS receiver can determine your absolute position to within 5 to 10 meters, and to achieve this level of precision, the clock ticks from the GPS satellites must be known to an accuracy of 20-30 nanoseconds. However, because the satellites are experiencing a different level of gravity than a clock on the surface of earth and since they are constantly moving relative to observers on the Earth, effects predicted by both the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy. As the satellites are in motion relative to ground, Special Relativity predicts their clocks ticking more slowly - by about 7 microseconds per day; however as the satellites are experiencing less gravity than on ground level, and according to the General Relativity, clocks on satellites will be faster than identical clocks on the ground by 45 microseconds per day. The combination of these two relativistic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds (or 38,000 nanoseconds) per day! If these effects were not properly taken into account, errors in global positions would accumulate at a rate of about 10 kilometers each day! The whole system would be then worthless for navigation in a very short time, so the design of GPS system has to include these relativistic effects.

Now assume a conscious being, say a God consciousness if one is inclined to call it that - is moving at the speed of light? What happens to its time compared to a stationary observer? As you can see from the above equation on time dilation with speed that for such a being, when V=C, time dilation becomes infinite – i.e., time literally stops for any entity travelling at light speed (or when gravity increases to the level of a black hole). Assume a star you are looking at is 5 billion light years away; so the light left the star 5 billion years ago, and we are indeed seeing not only the distant star but also peering in to the very distant past; we are looking at the star as it was 5 billion years ago, before even our earth was formed! But assume the photon making up the light has a conscious awareness of the passing of time. Would it feel it left the star 5 billion years ago? NO! For the photon “time” has no meaning, and it left the star and reached the earth at the same exact instant as far it is concerned. Time dilation reaches infinity or time literally stops at light speed. Very hard to have an intuitive understanding of this but this truly revolutionary idea – that what we think of as this immutable force of time is just a relative quantity that can vary between different observers – is one of the many reasons why Einstein is called, well Einstein! Now what did Einstein himself think of time? He had a way with not only numbers but also with words, so let me end this blog with a direct quote from Einstein himself. This is from a letter he wrote on the death of Michele Besso, one of his dearest friends. In fact this letter was written only few weeks before his own death; one can see in this poignant words how Einstein himself thought about the passage of time: “Michele has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion."

Reference:


Albert Einstein: Physicist, Philosopher, Humanitarian by Professor Don Howard (The Great Courses)