When we looked at Quantum Mechanics, we talked about its various interpretations. The reason we have such interpretations, I said, is that QM deals with a reality that we have no access to, through our sensory and perceptual apparatuses. On the other hand, Special Relativity is about macro objects in motion, and we have no problem imagining such things. So why would we need to have an interpretation? The answer is a subtle one. Continue reading →
The speed of light being a constant sounds like a simple statement. But there is more to it, quite a bit more. Let’s look at what this constancy really means. At first glance, it says that if you are standing somewhere, and there is a ray of light going from your right to left, it has a speed c. And another ray of light going from left to right also has a speed c. So far, so good. Now let’s say you are in a rocket ship, as shown in the figure below, moving from right to left.
When we hear about Einstein and the special relativity (or the special theory of relativity, to use the real name), we think of the famous equation, and weird things like the twin paradox. While those things are all true and important, the problem SR tries to solve is a completely different one. It is an attempt to defend a basic principle in physics. Continue reading →
In this section, we will try to look at the historical origin of Quantum Mechanics, which is usually presented succinctly using scary looking mathematical formulas. The role of mathematics in physics, as Richard Feynman explains (in his lectures on QED given in Auckland, New Zealand in 1979, available on YouTube, but as poor quality recordings) is purely utilitarian. Continue reading →
جب ہم آنکھیں کھولیں اور کسی چیز کو دیکھیں,,en,ہم اس چیز کو دیکھ رہے ہیں,,en,اس سے زیادہ اور کیا بات ہوسکتی ہے,,en,ٹھیک ہے,,en,ہم کہتے ہیں کہ آپ اپنے کتے کو دیکھ رہے ہیں,,en,جو آپ دیکھ رہے ہیں وہ واقعتا آپ کا کتا ہے,,en,اگر آپ چاہیں,,en,آپ تک پہنچ سکتے ہیں اور اسے چھو سکتے ہیں,,en,یہ بھونکتا ہے,,en,اور آپ واف کو سن سکتے ہیں,,en,اگر اس سے تھوڑا بدبو آجائے,,en,آپ اسے خوشبو دے سکتے ہیں,,en,یہ سارے اضافی ادراکی اشارے آپ کے عقیدے کی تائید کرتے ہیں کہ جو آپ دیکھ رہے ہیں وہ آپ کا کتا ہے,,en,براہ راست,,en,کوئی سوال نہیں پوچھا,,en,اس بلاگ پر میرا کام سوالات پوچھنا ہے,,en,اور شکوک و شبہات ڈالیں,,en,دیکھنے اور چھونے سننے اور مہک سے تھوڑا مختلف معلوم ہوتا ہے,,en,آپ اپنے کتے کی چھال کو سختی سے نہیں سنتے,,en,آپ اس کی آواز سنتے ہیں,,en,آپ کو براہ راست اس کی خوشبو نہیں آتی ہے,,en,آپ کو خوشبو آتی ہے,,en,کیمیائی پگڈنڈی کتا ہوا میں چھوڑ گیا ہے,,en,سماعت اور مہک کے تین مقامات کے تصورات ہیں,,en, we see that damn thing. What could be more obvious than that, right? Let’s say you are looking at your dog. What you see is really your dog, because, if you want, you can reach out and touch it. It barks, and you can hear the woof. If it stinks a bit, you can smell it. All these extra perceptual clues corroborate your belief that what you are seeing is your dog. Directly. No questions asked.
Of course, my job on this blog is to ask questions, and cast doubts. First of all, seeing and touching seem to be a bit different from hearing and smelling. You don’t strictly hear your dog bark, you hear its sound. Similarly, you don’t smell it directly, you smell the odor, the chemical trail the dog has left in the air. Hearing and smelling are three place perceptions — کتا آواز / بدبو پیدا کرتا ہے,,en,آواز / بدبو آپ کو سفر کرتی ہے,,en,آپ کو آواز / بدبو آرہی ہے,,en,لیکن دیکھ رہا ہے,,en,یا چھونے,,en,دو جگہ کی چیز ہے,,en,وہاں کا کتا,,en,اور آپ یہاں اسے براہ راست جانتے ہو,,en,ہم کیوں محسوس کرتے ہیں جب ہم کسی چیز کو دیکھتے یا چھاتے ہیں,,en,ہمیں براہ راست احساس ہے,,en,جو کچھ ہم دیکھتے ہیں اس کے ادراک سچائی پر اس یقین کو بولی حقیقت پسندی کہا جاتا ہے,,en,ہم یقینا جانتے ہیں کہ دیکھنے میں روشنی شامل ہوتی ہے,,en,تو چھونے والا ہے,,en,لیکن زیادہ پیچیدہ انداز میں,,en,ہم جو کچھ دیکھ رہے ہیں وہ روشنی کسی چیز اور اس طرح سے جھلکتی ہے,,en,کچھ سننے سے مختلف نہیں,,en,لیکن دیکھنے کے طریقہ کار کا یہ علم ہمارے فطری کو تبدیل نہیں کرتا ہے,,en,کامنینس نظریہ کہ جو ہم دیکھ رہے ہیں وہی وہاں سے باہر ہے,,en,دیکھ کر یقین ہے,,en,بولی ورژن سے نکالنا سائنسی حقیقت پسندی ہے,,en, the sound/odor travels to you, you perceive the sound/odor.
But seeing (or touching) is a two place thing — the dog there, and you here perceiving it directly. Why is that? Why do we feel that when we see or touch something, we sense it directly? This belief in the perceptual veracity of what we see is called naive realism. We of course know that seeing involves light (so does touching, but in a much more complicated way), what we are seeing is the light reflected off an object and so on. It is, in fact, no different from hearing something. But this knowledge of the mechanism of seeing doesn’t alter our natural, commonsense view that what we see is what is out there. Seeing is believing.
Extrapolated from the naive version is the scientific realism, جو یہ دعوی کرتا ہے کہ ہمارے سائنسی تصورات بھی حقیقی ہیں,,en,اگرچہ ہم انہیں براہ راست نہیں جان سکتے ہیں,,en,تو جوہری اصلی ہیں,,en,الیکٹران حقیقی ہیں,,en,کوارکس حقیقی ہیں,,en,ہمارے بیشتر بہتر سائنس دانوں نے حقیقت میں اس حقیقت کے بارے میں ہمارے خیال سے اس اضافی سفر کے بارے میں شکوک و شبہات کا اظہار کیا ہے,,en,شاید ان میں سے بہترین,,en,شبہ ہے کہ جگہ اور وقت بھی حقیقی نہیں ہوسکتے ہیں,,en,فین مین اور جیل مان,,en,الیکٹران اور کوارک پر نظریات تیار کرنے کے بعد,,en,انھوں نے اپنے خیالات کا اظہار کیا کہ الیکٹران اور کوارکس حقیقی اداروں کی بجائے ریاضی کی تعمیرات ہوسکتے ہیں,,en,البرٹ آئن اسٹائن آرکائیو,,en, eventhough we may not directly perceive them. So atoms are real. Electrons are real. Quarks are real. Most of our better scientists out there have been skeptical about this extraploation to our notion of what is real. Einstein, probably the best of them, suspected that even space and time might not be real. Feynman and Gell-Mann, after developing theories on electrons and quarks, expressed their view that electrons and quarks might be mathematical constructs rather than real entities.
What I am inviting you to do here is to go beyond the skepticism of Feynman and Gell-Mann, and delve into Einstein’s words — space and time are modes by which we think, not conditions in which we live. The sense of space is so real to us that we think of everything else as interactions taking place in the arena of space (and time). But space itself is the experience corresponding to the electrical signals generated by the light hitting your retina. It is a perceptual construct, much like the tonality of the sound you hear when air pressure waves hit your ear drums. Our adoption of naive realism results in our complete trust in the three dimensional space view. And since the world is created (in our brain as perceptual constructs) based on light, its speed becomes an all important constant in our world. And since speed mixes space and time, a better description is found in a four dimensional Minkowski geometry. But all these descriptions are based on perceptual experiences and therefore unreal in some sense.
I know the description above is highly circular — I talked about space being a mental construct created by light traveling through, get this, space. And when I speak of its speed, naturally, I’m talking about distance in space divided by time, and positing as the basis for the space-time mixing. This circularity makes my description less than clear and convincing. But the difficulty goes deeper than that. You see, all we have is this cognitive construct of space and time. We can describe objects and events only in terms of these constructs even when we know that they are only cognitive representations of sensory signals. Our language doesn’t go beyond that. Well, it does, but then we will be talking the language, for instance, of Advaita, calling the constructs Maya and the causes behind them Brahman, which stays unknowable. Or, we will be using some other parallel descriptions. These descriptions may be profound, wise and accurate. But ultimately, they are also useless.
But if philosophy is your thing, the discussions of cognitive constructs and unknown causations are not at all useless. Philosophy of physics happens to be my thing, and so I ask myself — what if I assume the unknown physical causes exist in a world similar to our perceptual construct? I could then propagate the causes through the process of perception and figure out what the construct should look like. I know, it sounds a bit complex, but it is something that we do all the time. We know, for instance, that the stars that we see in the night sky are not really there — we are seeing them the way they were a few (or a few million or billion) years ago because the light from them takes a long time to reach us. Physicists also know that the perceived motion of celestial objects also need to be corrected for these light-travel-time effects.
In fact, Einstein used the light travel time effects as the basis for deriving his special theory of relativity. He then stipulated that space and time behave the way we perceive them, derived using the said light-travel-time effects. This, of course, is based on his deep understanding that space and time are “the modes by which we think,” but also based on the assumption that the the causes behind the modes also are similar to the modes themselves. This depth of thinking is lost on the lesser scientists that came after him. The distinction between the modes of thinking and their causation is also lost, so that space and time have become entities that obey strange rules. Like bent spoons.
Richard Feynman used to employ the game of chess as a metaphor for the pursuit of physics. Physicists are like uninitiated spectators at a chess match, and they are trying figure out the rules of the game. (He also used sex, but that’s another story.) They observe the moves and try figure out the rules that govern them. Most of the easy ones are soon discovered, but the infrequent and complex ones (such as castling, to use Feynman’s example) are harder to decipher. The chess board is the universe and the players are presumably the Gods. So when Albert Einstein’s said that he wanted to know God’s thoughts, and that the rest were details, he probably meant he wanted to know the rules and the strategies based on them. Not the actual pattern on the board at any point in time, which was a mere detail.
A remarkable Indian writer and thinker, O. V. Vijayan, also used the metaphor of a chess game to describe the armed strife between India and her sibling neighbor. He said that our too countries were mere pawns in a grand chess game between giant players of the cold war. The players have stopped playing at some point, but the pawns still fight on. What made it eerie (in a Dr. Strangelove sort of way) is the fact that the pawns had huge armies and nuclear weapons. When I first read this article by O. V. Vijayan, his clarity of perspective impressed me tremendously because I knew how difficult it was to see these things even-handedly without the advantage of being outside the country — the media and their public relations tricks make it very difficult, if not impossible. It is all very obvious from the outside, but it takes a genius to see it from within. But O. V. Vijayan’s genius had impressed me even before that, and I have a short story and a thought snippet by him translated and posted on this blog.
Chess is a good metaphor for almost everything in life, with its clear and unbending rules. But it is not the rules themselves that I want to focus on; it is the topology or the pattern that the rules generate. Even before we start a game, we know that there will be an outcome — it is going to be a win, loss or a draw. 1-0, 0-1 or 0.5-0.5. How the game will evolve and who will win is all unknown, but that it will evolve from an opening of four neat rows through a messy mid game and a clear endgame is pretty much given. The topology is pre-ordained by the rules of the game.
A similar set of rules and a consequent topology exists in the corporate world as well. That is the topic of the next post.
Starting from his miraculous year of 1905, Einstein has dominated physics with his astonishing insights on space and time, and on mass and gravity. True, there have been other physicists who, with their own brilliance, have shaped and moved modern physics in directions that even Einstein couldn’t have foreseen; and I don’t mean to trivialize neither their intellectual achievements nor our giant leaps in physics and technology. But all of modern physics, even the bizarre reality of quantum mechanics, which Einstein himself couldn’t quite come to terms with, is built on his insights. It is on his shoulders that those who came after him stood for over a century now.
One of the brighter ones among those who came after Einstein cautioned us to guard against our blind faith in the infallibility of old masters. Taking my cue from that insight, I, for one, think that Einstein’s century is behind us now. I know, coming from a non-practicing physicist, who sold his soul to the finance industry, this declaration sounds crazy. Delusional even. But I do have my reasons to see Einstein’s ideas go.
Let’s start with this picture of a dot flying along a straight line (on the ceiling, so to speak). You are standing at the centre of the line in the bottom (on the floor, that is). If the dot was moving faster than light, how would you see it? Well, you wouldn’t see anything at all until the first ray of light from the dot reaches you. As the animation shows, the first ray will reach you when the dot is somewhere almost directly above you. The next rays you would see actually come from two different points in the line of flight of the dot — one before the first point, and one after. Thus, the way you would see it is, incredible as it may seem to you at first, as one dot appearing out of nowhere and then splitting and moving rather symmetrically away from that point. (It is just that the dot is flying so fast that by the time you get to see it, it is already gone past you, and the rays from both behind and ahead reach you at the same instant in time.Hope that statement makes it clearer, rather than more confusing.).
Why did I start with this animation of how the illusion of a symmetric object can happen? Well, we see a lot of active symmetric structures in the universe. For instance, look at this picture of Cygnus A. There is a “core” from which seem to emanate “features” that float away to the “lobes.” Doesn’t it look remarkably similar to what we would see based on the animation above? There are other examples in which some feature points or knots seem to move away from the core where they first appear at. We could come up with a clever model based on superluminality and how it would create illusionary symmetric objects in the heavens. We could, but nobody would believe us — because of Einstein. I know this — I tried to get my old physicist friends to consider this model. The response is always some variant of this, “Interesting, but it cannot work. It violates Lorentz invariance, doesn’t it?” LV being physics talk for Einstein’s insistence that nothing should go faster than light. Now that neutrinos can violate LV, why not me?
Of course, if it was only a qualitative agreement between symmetric shapes and superluminal celestial objects, my physics friends are right in ignoring me. There is much more. The lobes in Cygnus A, for instance, emit radiation in the radio frequency range. In fact, the sky as seen from a radio telescope looks materially different from what we see from an optical telescope. I could show that the spectral evolution of the radiation from this superluminal object fitted nicely with AGNs and another class of astrophysical phenomena, hitherto considered unrelated, called gamma ray bursts. In fact, I managed to publish this model a while ago under the title, “Are Radio Sources and Gamma Ray Bursts Luminal Booms?“.
You see, I need superluminality. Einstein being wrong is a pre-requisite of my being right. So it is the most respected scientist ever vs. yours faithfully, a blogger of the unreal kind. You do the math. 🙂
Such long odds, however, have never discouraged me, and I always rush in where the wiser angels fear to tread. So let me point out a couple of inconsistencies in SR. The derivation of the theory starts off by pointing out the effects of light travel time in time measurements. And later on in the theory, the distortions due to light travel time effects become part of the properties of space and time. (In fact, light travel time effects will make it impossible to have a superluminal dot on a ceiling, as in my animation above — not even a virtual one, where you take a laser pointer and turn it fast enough that the laser dot on the ceiling would move faster than light. It won’t.) But, as the theory is understood and practiced now, the light travel time effects are to be applied on top of the space and time distortions (which were due to the light travel time effects to begin with)! Physicists turn a blind eye to this glaring inconstancy because SR “works” — as I made very clear in my previous post in this series.
Another philosophical problem with the theory is that it is not testable. I know, I alluded to a large body of proof in its favor, but fundamentally, the special theory of relativity makes predictions about a uniformly moving frame of reference in the absence of gravity. There is no such thing. Even if there was, in order to verify the predictions (that a moving clock runs slower as in the twin paradox, for instance), you have to have acceleration somewhere in the verification process. Two clocks will have to come back to the same point to compare time. The moment you do that, at least one of the clocks has accelerated, and the proponents of the theory would say, “Ah, there is no problem here, the symmetry between the clocks is broken because of the acceleration.” People have argued back and forth about such thought experiments for an entire century, so I don’t want to get into it. I just want to point out that theory by itself is untestable, which should also mean that it is unprovable. Now that there is direct experimental evidence against the theory, may be people will take a closer look at these inconsistencies and decide that it is time to say bye-bye to Einstein.
Nothing would satisfy my anarchical mind more than to see the Special Theory of Relativity (SR) come tumbling down. In fact, I believe that there are compelling reasons to consider SR inaccurate, if not actually wrong, although the physics community would have none of that. I will list my misgivings vis-a-vis SR and present my case against it as the last post in this series, but in this one, I would like to explore why it is so difficult to toss SR out the window.
The special theory of relativity is an extremely well-tested theory. Despite my personal reservations about it, the body of proof for the validity of SR is really enormous and the theory has stood the test of time — at least so far. But it is the integration of SR into the rest of modern physics that makes it all but impossible to write it off as a failed theory. In experimental high energy physics, for instance, we compute the rest mass of a particle as its identifying statistical signature. The way it works is this: in order to discover a heavy particle, you first detect its daughter particles (decay products, that is), measure their energies and momenta, add them up (as “4-vectors”), and compute the invariant mass of the system as the modulus of the aggregate energy-momentum vector. In accordance with SR, the invariant mass is the rest mass of the parent particle. You do this for many thousands of times and make a distribution (a “histogram”) and detect any statistically significant excess at any mass. Such an excess is the signature of the parent particle at that mass.
Almost every one of the particles in the particle data book that we know and love is detected using some variant of this method. So the whole Standard Model of particle physics is built on SR. In fact, almost all of modern physics (physics of the 20th century) is built on it. On the theory side, in the thirties, Dirac derived a framework to describe electrons. It combined SR and quantum mechanics in an elegant framework and predicted the existence of positrons, which bore out later on. Although considered incomplete because of its lack of sound physical backdrop, this “second quantization” and its subsequent experimental verification can be rightly seen as evidence for the rightness of SR.
Feynman took it further and completed the quantum electrodynamics (QED), which has been the most rigorously tested theory ever. To digress a bit, Feynman was once being shown around at CERN, and the guide (probably a prominent physicist himself) was explaining the experiments, their objectives etc. Then the guide suddenly remembered who he was talking to; after all, most of the CERN experiments were based on Feynman’s QED. Embarrassed, he said, “Of course, Dr. Feynman, you know all this. These are all to verify your predictions.” Feynman quipped, “Why, you don’t trust me?!” To get back to my point and reiterate it, the whole edifice of the standard model of particle physics is built on top of SR. Its success alone is enough to make it impossible for modern physics to discard SR.
So, if you take away SR, you don’t have the Standard Model and QED, and you don’t know how accelerator experiments and nuclear bombs work. The fact that they do is proof enough for the validity of SR, because the alternative (that we managed to build all these things without really knowing how they work) is just too weird. It’s not just the exotic (nuclear weaponry and CERN experiments), but the mundane that should convince us. Fluorescent lighting, laser pointers, LED, computers, mobile phones, GPS navigators, iPads — in short, all of modern technology is, in some way, a confirmation of SR.
So the OPERA result on observed superluminalily has to be wrong. But I would like it to be right. And I will explain why in my next post. Why everything we accept as a verification of SR could be a case of mass delusion — almost literally. Stay tuned!
CERN has published news about some subatomic particles exceeding the speed of light, according to BBC and other sources. If confirmed true, this will remove the linchpin of modern physics — it is hard to overstate how revolutionary this discovery would be to our collective understanding of world we live in, from finest structure of matter to the time evolution of the cosmos. My own anarchical mind revels at the thought of all of modern physics getting rewritten, but I also have a much more personal stake in this story. I will get to it later in this series of posts. First, I want to describe the backdrop of thought that led to the notion that the speed of light could not be breached. The soundness of that scientific backdrop (if not the actual conclusion about the inviolability of light-speed) makes it very difficult to forgo the intellectual achievements of the past one hundred years in physics, which is what we will be doing once we confirm this result. In my second post, I will list what these intellectual achievements are, and how drastically their form will have to change. The scientists who discovered the speed violation, of course, understand this only too well, which is why they are practically begging the rest of the physics community to find a mistake in this discovery of theirs. As it often happens in physics, if you look for something hard enough, you are sure to find it — this is the experimental bias that all experimental physicists worth their salt are aware of and battle against. I hope a false negation doesn’t happen, for, as I will describe in my third post in this series, if confirmed, this speed violation is of tremendous personal importance to me.
The constancy (and the resultant inviolability) of the speed of light, of course, comes from Einstein’s Special Theory of Relativity, or SR. This theory is an extension of a simple idea. In fact, Einstein’s genius is in his ability to carry a simple idea to its logically inevitable, albeit counter-intuitive (to the point of being illogical!) conclusion. In the case of SR, he picks an idea so obvious — that the laws of physics should be independent of the state of motion. If you are in a train going at a constant speed, for instance, you can’t tell whether you are moving or not (if you close the windows, that is). The statement “You can’t tell” can be recast in physics as, “There is no experiment you can device to detect your state of motion.” This should be obvious, right? After all, if the laws kept changing every time you moved about, it is as good as having no laws at all.
Then came Maxwell. He wrote down the equations of electricity and magnetism, thereby elegantly unifying them. The equations state, using fancy vector notations, that a changing magnetic field will create an electric field, and a changing electric field will create a magnetic field, which is roughly how a car alternator and an electric motor work. These elegant equations have a wave solution.
The existence of a wave solution is no surprise, since a changing electric field generates a magnetic field, which in turn generates an electric field, which generates a magnetic filed and so on ad infinitum. What is surprising is the fact that the speed of propagation of this wave predicted by Maxwell’s equations is c, the speed of light. So it was natural to suppose that light was a form of electromagnetic radiation, which means that if you take a magnet and jiggle it fast enough, you will get light moving away from you at c – if we accept that light is indeed EM wave.
What is infinitely more fundamental is the question whether Maxwell’s equations are actually laws of physics. It is hard to argue that they aren’t. Then the follow-up question is whether these equations should obey the axiom that all laws of physics are supposed to obey — namely they should be independent of the state of motion. Again, hard to see why not. Then how do we modify Maxwell’s equations such that they are independent of motion? This is the project Einstein took on under the fancy name, “Covariant formulation of Maxwell’s equations,” and published the most famous physics article ever with an even fancier title, “On the Electrodynamics of Moving Bodies.” We now call it the Special Theory of Relativity, or SR.
To get a bit technical, Maxwell’s equations have the space derivatives of electric and magnetic fields relating to the time derivatives of charges and currents. In other words, space and time are related through the equations. And the wave solution to these equations with the propagation speed of c becomes a constraint on the properties of space and time. This is a simple philosophical look on SR, more than a physics analysis.
Einstein’s approach was to employ a series of thought experiments to establish that you needed a light signal to sync clocks and hypothesize that the speed of light had to be constant in all moving frames of reference. In other words, the speed of light is independent of the state of motion, as it has to be if Maxwell’s equations are to be laws of physics.
This aspect of the theory is supremely counter-intuitive, which is physics lingo to say something is hard to believe. In the case of the speed of light, you take a ray of light, run along with it at a high speed, and measure its speed, you still get c. Run against it and measure it — still c. To achieve this constancy, Einstein rewrote the equations of velocity addition and subtraction. On consequence of these rewritten equations is that nothing can go faster than light.
This is my long-winded description of the context in which the speed violation measured at OPERA has to be seen. If the violation is confirmed, we have a few unpleasant choices to pick from:
Electrodynamics (Maxwell’s equations) is not invariant under motion.
Light is not really electromagnetic in nature.
SR is not the right covariant formulation of electrodynamics.
The first choice is patently unacceptable because it is tantamount to stating that electrodynamics is not physics. A moving motor (e.g., if you take your electric razor on a flight) would behave differently from a static one (you may not be able to shave). The second choice also is quite absurd. In addition to the numeric equality between the speed of the waves from Maxwell’s equations and the measured value of c, we do have other compelling reasons why we should believe that light is EM waves. Radio waves induce electric signals in an antenna, light knocks of electrons, microwaves can excite water molecules and cook food and so on.
The only real choice we are left with is the last one — which is to say SR is wrong. Why not discard SR? More reasons than a blog post can summarize, but I’ll try to summarize them any way in my next post.
There is beauty in truth, and truth in beauty. Where does this link between truth and beauty come from? Of course, beauty is subjective, and truth is objective — or so we are told. It may be that we have evolved in accordance with the beautiful Darwinian principles to see perfection in absolute truth.
The beauty and perfection I’m thinking about are of a different kind — those of ideas and concepts. At times, you may get an idea so perfect and beautiful that you know it has to be true. This conviction of truth arising from beauty may be what made Einstein declare:
But this conviction about the veracity of a theory based on its perfection is hardly enough. Einstein’s genius really is in his philosophical tenacity, his willingness to push the idea beyond what is considered logical.
Let’s take an example. Let’s say you are in a cruising airplane. If you close the windows and somehow block out the engine noise, it will be impossible for you to tell whether you are moving or not. This inability, when translated to physics jargon, becomes a principle stating, “Physical laws are independent of the state of motion of the experimental system.”
The physical laws Einstein chose to look at were Maxwell’s equations of electromagnetism, which had the speed of light appearing in them. For them to be independent of (or covariant with, to be more precise) motion, Einstein postulated that the speed of light had to be a constant regardless of whether you were going toward it or away from it.
Now, I don’t know if you find that postulate particularly beautiful. But Einstein did, and decided to push it through all its illogical consequences. For it to be true, space has to contract and time had to dilate, and nothing could go faster than light. Einstein said, well, so be it. That is the philosophical conviction and tenacity that I wanted to talk about — the kind that gave us Special Relativity about a one hundred years ago.
Want to get to General Relativity from here? Simple, just find another beautiful truth. Here is one… If you have gone to Magic Mountain, you would know that you are weightless during a free fall (best tried on an empty stomach). Free fall is acceleration at 9.8 m/s/s (or 32 ft/s/s), and it nullifies gravity. So gravity is the same as acceleration — voila, another beautiful principle.
In order to make use of this principle, Einstein perhaps thought of it in pictures. What does acceleration mean? It is how fast the speed of something is changing. And what is speed? Think of something moving in a straight line — our cruising airplane, for instance, and call the line of flight the X-axis. We can visualize its speed by thinking of a time T-axis at right angles with the X-axis so that at time = 0, the airplane is at x = 0. At time t, it is at a point x = v.t, if it is moving with a speed v. So a line in the X-T plane (called the world line) represents the motion of the airplane. A faster airplane would have a shallower world line. An accelerating airplane, therefore, will have a curved world line, running from the slow world line to the fast one.
So acceleration is curvature in space-time. And so is gravity, being nothing but acceleration. (I can see my physicist friends cringe a bit, but it is essentially true — just that you straighten the world-line calling it a geodesic and attribute the curvature to space-time instead.)
The exact nature of the curvature and how to compute it, though beautiful in their own right, are mere details, as Einstein himself would have put it. After all, he wanted to know God’s thoughts, not the details.