Category Archives: Physics

Physics was my first love. This category contains the posts closest to my heart. Twenty years from now, if this blog survives, this category will probably hold my most enduring insights. And two hundred years from now, if I am remembered at all, it will be for these insights; not for the kind of person I am, the money I make, nor anything else. Only for my first and last love…

Articles and Essays, Books, Columns, Creative, Philosophy, Physics, Science, Topical

The Unreal Universe

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We know that our universe is a bit unreal. The stars we see in the night sky, for instance, are not really there. They may have moved or even died by the time we get to see them. It takes light time to travel from the distant stars and galaxies to reach us. We know of this delay. The sun that we see now is already eight minutes old by the time we see it, which is not a big deal. If we want to know what is going on at the sun right now, all we have to do is to wait for eight minutes. Nonetheless, we do have to “correct” for the delay in our perception due to the finite speed of light before we can trust what we see.

Now, this effect raises an interesting question — what is the “real” thing that we see? If seeing is believing, the stuff that we see should be the real thing. Then again, we know of the light travel time effect. So we should correct what we see before believing it. What then does “seeing” mean? When we say we see something, what do we really mean?

Seeing involves light, obviously. It is the finite (albeit very high) speed of light influences and distorts the way we see things, like the delay in seeing objects like stars. What is surprising (and seldom highlighted) is that when it comes to seeing moving objects, we cannot back-calculate the same way we take out the delay in seeing the sun. If we see a celestial body moving at an improbably high speed, we cannot figure out how fast and in what direction it is “really” moving without making further assumptions. One way of handling this difficulty is to ascribe the distortions in our perception to the fundamental properties of the arena of physics — space and time. Another course of action is to accept the disconnection between our perception and the underlying “reality” and deal with it in some way.

This disconnect between what we see and what is out there is not unknown to many philosophical schools of thought. Phenomenalism, for instance, holds the view that space and time are not objective realities. They are merely the medium of our perception. All the phenomena that happen in space and time are merely bundles of our perception. In other words, space and time are cognitive constructs arising from perception. Thus, all the physical properties that we ascribe to space and time can only apply to the phenomenal reality (the reality as we sense it). The noumenal reality (which holds the physical causes of our perception), by contrast, remains beyond our cognitive reach.

One, almost accidental, difficulty in redefining the effects of the finite speed of light as the properties of space and time is that any effect that we do understand gets instantly relegated to the realm of optical illusions. For instance, the eight-minute delay in seeing the sun, because we can readily understand it and disassociate it from our perception using simple arithmetic, is considered a mere optical illusion. However, the distortions in our perception of fast moving objects, although originating from the same source are considered a property of space and time because they are more complex. At some point, we have to come to terms with the fact that when it comes to seeing the universe, there is no such thing as an optical illusion, which is probably what Goethe pointed out when he said, “Optical illusion is optical truth.”

More about The Unreal UniverseThe distinction (or lack thereof) between optical illusion and truth is one of the oldest debates in philosophy. After all, it is about the distinction between knowledge and reality. Knowledge is considered our view about something that, in reality, is “actually the case.” In other words, knowledge is a reflection, or a mental image of something external. In this picture, the external reality goes through a process of becoming our knowledge, which includes perception, cognitive activities, and the exercise of pure reason. This is the picture that physics has come to accept. While acknowledging that our perception may be imperfect, physics assumes that we can get closer and closer to the external reality through increasingly finer experimentation, and, more importantly, through better theorization. The Special and General Theories of Relativity are examples of brilliant applications of this view of reality where simple physical principles are relentlessly pursued using the formidable machine of pure reason to their logically inevitable conclusions.

But there is another, competing view of knowledge and reality that has been around for a long time. This is the view that regards perceived reality as an internal cognitive representation of our sensory inputs. In this view, knowledge and perceived reality are both internal cognitive constructs, although we have come to think of them as separate. What is external is not the reality as we perceive it, but an unknowable entity giving rise to the physical causes behind sensory inputs. In this school of thought, we build our reality in two, often overlapping, steps. The first step consists of the process of sensing, and the second one is that of cognitive and logical reasoning. We can apply this view of reality and knowledge to science, but in order do so, we have to guess the nature of the absolute reality, unknowable as it is.

The ramifications of these two different philosophical stances described above are tremendous. Since modern physics has embraced a non-phenomenalistic view of space and time, it finds itself at odds with that branch of philosophy. This chasm between philosophy and physics has grown to such a degree that the Nobel prize winning physicist, Steven Weinberg, wondered (in his book “Dreams of a Final Theory”) why the contribution from philosophy to physics have been so surprisingly small. It also prompts philosophers to make statements like, “Whether ‘noumenal reality causes phenomenal reality’ or whether ‘noumenal reality is independent of our sensing it’ or whether ‘we sense noumenal reality,’ the problem remains that the concept of noumenal reality is a totally redundant concept for the analysis of science.”

From the perspective of cognitive neuroscience, everything we see, sense, feel and think is the result of the neuronal interconnections in our brain and the tiny electrical signals in them. This view must be right. What else is there? All our thoughts and worries, knowledge and beliefs, ego and reality, life and death — everything is merely neuronal firings in the one and half kilograms of gooey, grey material that we call our brain. There is nothing else. Nothing!

In fact, this view of reality in neuroscience is an exact echo of phenomenalism, which considers everything a bundle of perception or mental constructs. Space and time are also cognitive constructs in our brain, like everything else. They are mental pictures our brains concoct out of the sensory inputs that our senses receive. Generated from our sensory perception and fabricated by our cognitive process, the space-time continuum is the arena of physics. Of all our senses, sight is by far the dominant one. The sensory input to sight is light. In a space created by the brain out of the light falling on our retinas (or on the photo sensors of the Hubble telescope), is it a surprise that nothing can travel faster than light?

This philosophical stance is the basis of my book, The Unreal Universe, which explores the common threads binding physics and philosophy. Such philosophical musings usually get a bad rap from us physicists. To physicists, philosophy is an entirely different field, another silo of knowledge, which holds no relevance to their endeavors. We need to change this belief and appreciate the overlap among different knowledge silos. It is in this overlap that we can expect to find great breakthroughs in human thought.

The twist to this story of light and reality is that we seem to have known all this for a long time. Classical philosophical schools seem to have thought along lines very similar to Einstein’s reasonings. The role of light in creating our reality or universe is at the heart of Western religious thinking. A universe devoid of light is not simply a world where you have switched off the lights. It is indeed a universe devoid of itself, a universe that doesn’t exist. It is in this context that we have to understand the wisdom behind the statement that “the earth was without form, and void” until God caused light to be, by saying “Let there be light.”

The Quran also says, “Allah is the light of the heavens and the earth,” which is mirrored in one of the ancient Hindu writings: “Lead me from darkness to light, lead me from the unreal to the real.” The role of light in taking us from the unreal void (the nothingness) to a reality was indeed understood for a long, long time. Is it possible that the ancient saints and prophets knew things that we are only now beginning to uncover with all our supposed advances in knowledge?

I know I may be rushing in where angels fear to tread, for reinterpreting the scriptures is a dangerous game. Such alien interpretations are seldom welcome in the theological circles. But I seek refuge in the fact that I am looking for concurrence in the metaphysical views of spiritual philosophies, without diminishing their mystical and theological value.

The parallels between the noumenal-phenomenal distinction in phenomenalism and the Brahman-Maya distinction in Advaita are hard to ignore. This time-tested wisdom on the nature of reality from the repertoire of spirituality is now being reinvented in modern neuroscience, which treats reality as a cognitive representation created by the brain. The brain uses the sensory inputs, memory, consciousness, and even language as ingredients in concocting our sense of reality. This view of reality, however, is something physics is yet to come to terms with. But to the extent that its arena (space and time) is a part of reality, physics is not immune to philosophy.

As we push the boundaries of our knowledge further and further, we are beginning to discover hitherto unsuspected and often surprising interconnections between different branches of human efforts. In the final analysis, how can the diverse domains of our knowledge be independent of each other when all our knowledge resides in our brain? Knowledge is a cognitive representation of our experiences. But then, so is reality; it is a cognitive representation of our sensory inputs. It is a fallacy to think that knowledge is our internal representation of an external reality, and therefore distinct from it. Knowledge and reality are both internal cognitive constructs, although we have come to think of them as separate.

Recognizing and making use of the interconnections among the different domains of human endeavor may be the catalyst for the next breakthrough in our collective wisdom that we have been waiting for.

Philosophy, Physics

Ghost of Gravity

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It has been a while since my last post. I was reading Zen and the Art of Motorcycle Maintenance again just now, and came to the part where Pirsig compares scientific beliefs and superstitions. I thought I would paraphrase it and share it with my readers. But it is perhaps best to borrow his own words: “The laws of physics and of logic — the number system — the principle of algebraic substitution. These are ghosts. We just believe in them so thoroughly they seem real. For example, it seems completely natural to presume that gravitation and the law of gravitation existed before Isaac Newton. It would sound nutty to think that until the seventeenth century there was no gravity. So when did this law start? Has it always existed? What I’m driving at is the notion that before the beginning of the earth, before the sun and the stars were formed, before the primal generation of anything, the law of gravity existed. Sitting there, having no mass of its own, no energy of its own, not in anyone’s mind because there wasn’t anyone, not in space because there was no space either, not anywhere…this law of gravity still existed? If that law of gravity existed, I honestly don’t know what a thing has to do to be nonexistent. It seems to me that law of gravity has passed every test of nonexistence there is. You cannot think of a single attribute of nonexistence that that law of gravity didn’t have. Or a single scientific attribute of existence it did have. And yet it is still ‘common sense’ to believe that it existed.

“Well, I predict that if you think about it long enough you will find yourself going round and round and round and round until you finally reach only one possible, rational, intelligent conclusion. The law of gravity and gravity itself did not exist before Isaac Newton. No other conclusion makes sense. And what that means is that that law of gravity exists nowhere except in people’s heads! It’s a ghost! We are all of us very arrogant and conceited about running down other people’s ghosts but just as ignorant and barbaric and superstitious about our own.”

[This quote is from an online version of Zen and the Art of Motorcycle Maintenance.]

Philosophy, Physics, Science

Only a Matter of Time

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Although we speak of space and time in the same breath, they are quite different in many ways. Space is something we perceive all around us. We see it (rather, objects in it), we can move our hand through it, and we know that if our knee tries to occupy the same space as, say, the coffee table, it is going to hurt. In other words, we have sensory correlates to our notion of space, starting from our most precious sense of sight.

Time, on the other hand, has no direct sensory backing. And for this reason, it becomes quite difficult to get a grip over it. What is time? We sense it indirectly through change and motion. But it would be silly to define time using the concepts of change and motion, because they already include the notion of time. The definition would be cyclic.

Assuming, for now, that no definition is necessary, let’s try another perhaps more tractable issue. Where does this strong sense of time come from? I once postulated that it comes from our knowledge of our demise — that questionable gift that we all possess. All the time durations that we are aware of are measured against the yardstick of our lifespan, perhaps not always consciously. I now wonder if this postulate is firm enough, and further ruminations on this issue have convinced me that I am quite ignorant of these things and need more knowledge. Ah.. only if I had more time. 🙂

In any case, even this more restricted question of the origin of time doesn’t seem to be that tractable, after all. Physics has another deep problem with time. It has to do with the directionality. It cannot easily explain why time has a direction — an arrow, as it were. This arrow does not present itself in the fundamental laws governing physical interactions. All the laws in physics are time reversible. The laws of gravity, electromagnetism or quantum mechanics are all invariant with respect to a time reversal. That is to say, they look the same with time going forward or backward. So they give no clue as to why we experience the arrow of time.

Yet, we know that time, as we experience it, is directional. We can remember the past, but not the future. What we do now can affect the future, but not the past. If we play a video tape backwards, the sequence of events (like broken pieces of glass coming together to for a vase) will look funny to us. However, if we taped the motion of the planets in a solar system, or the electron cloud in an atom, and played it backward to a physicist, he would not find anything funny in the sequences because the physical laws are reversible.

Physics considers the arrow of time an emergent property of statistical collections. To illustrate this thermodynamic explanation of time, let’s consider an empty container where we place some dry ice. After some time, we expect to see a uniform distribution of carbon dioxide gas in the container. Once spread out, we do not expect the gas in the container to coagulate into solid dry ice, no matter how long we wait. The video of CO2 spreading uniformly in the container is a natural one. Played backward, the sequence of the CO2 gas in the container congealing to solid dry ice in a corner would not look natural to us because it violates our sense of the arrow of time.

The apparent uniformity of CO2 in the container is due to the statistically significant quantity of dry ice we placed there. If we manage to put a small quantity, say five molecules of CO2, we can fully expect to see the congregation of the molecules in one location once in a while. Thus, the arrow of time manifests itself as a statistical or thermodynamic property. Although the directionality of time seems to emerge from reversible physical laws, its absence in the fundamental laws does look less than satisfactory philosophically.

Philosophy, Physics, Science

Half a Bucket of Water

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We all see and feel space, but what is it really? Space is one of those fundamental things that a philosopher may consider an “intuition.” When philosophers look at anything, they get a bit technical. Is space relational, as in, defined in terms of relations between objects? A relational entity is like your family — you have your parents, siblings, spouse, kids etc. forming what you consider your family. But your family itself is not a physical entity, but only a collection of relationships. Is space also something like that? Or is it more like a physical container where objects reside and do their thing?

You may consider the distinction between the two just another one of those philosophical hairsplittings, but it really is not. What space is, and even what kind of entity space is, has enormous implications in physics. For instance, if it is relational in nature, then in the absence of matter, there is no space. Much like in the absence of any family members, you have no family. On the other hand, if it is a container-like entity, the space exists even if you take away all matter, waiting for some matter to appear.

So what, you ask? Well, let’s take half a bucket of water and spin it around. Once the water within catches on, its surface will form a parabolic shape — you know, centrifugal force, gravity, surface tension and all that. Now, stop the bucket, and spin the whole universe around it instead. I know, it is more difficult. But imagine you are doing it. Will the water surface be parabolic? I think it will be, because there is not much difference between the bucket turning or the whole universe spinning around it.

Now, let’s imagine that we empty the universe. There is nothing but this half-full bucket. Now it spins around. What happens to the water surface? If space is relational, in the absence of the universe, there is no space outside the bucket and there is no way to know that it is spinning. Water surface should be flat. (In fact, it should be spherical, but ignore that for a second.) And if space is container-like, the spinning bucket should result in a parabolic surface.

Of course, we have no way of knowing which way it is going to be because we have no way of emptying the universe and spinning a bucket. But that doesn’t prevent us from guessing the nature of space and building theories based on it. Newton’s space is container-like, while at their heart, Einstein’s theories have a relational notion of space.

So, you see, philosophy does matter.

Books, Philosophy, Physics, Science

On Rationality and Delusions

This post started as a reply to M Cuffe’s comment on my post on The God Delusion. M Cuffe suggested that I’m merely asserting an individual’s right to be irrational, or ignorant. Yes, I am indeed saying that one has the right to be irrational. But that statement stems from something that I believe is deeper. It stems from what we mean by rationality, and why we think it is a good thing to be rational. I know it sounds “irrational,” but I’m talking about rationality as Persig talked about it in Zen and the Art of Motorcycle Maintenance.

Stepping back a bit, rationality is quintessentially a worldview. By rational, we mean things that seem normal to our commonsense. So the notion of a nuclear bomb moving or obliterating a mountain is rational, although we have never seen it. You believe it because it is consistent with your worldview. I believe it too, trust me. I was a nuclear physicist not too long ago. 🙂

And a god (or faith) moving mountains is clearly ludicrous to our rationality. I’m not asking people to give equal rational weight to faith and bomb moving mountains. I’m merely encouraging them to examine why they believe in one and not the other. Calling one more rational is just another way of saying that you choose to believe one more than the other. Why?

Thinking along those lines, I come to the conclusion that it is only a question of worldviews or belief systems. I personally subscribe to your worldview based on rationality as well, which is why I consider myself also an atheist (although one of my readers thought I was merely confused :-))

A god as an old man hiding behind the clouds is not consistent with our worldview. But it may have been a metaphor for something else. Let me explain. We have these abstract concepts of happiness, perfection, grief etc. Are these things real? Should we believe they exist? Such questions don’t make too much sense because these concepts are all in our minds. But then, what isn’t?

Let’s take perfection, for instance. Let’s say we assign some human form to it, so that we could explain it to a child or something. We then call it, say, the goddess of perfection or whatever. Over generations, for whatever reason, the notion of perfection disappears from our awareness, but the metaphor of the goddess remains. Now, to somebody who believes in the reality perfection, and therefore the existence of the goddess, it is not a delusion. In that belief system, in that context and worldview, it makes perfect sense. But in the absence of the abstract concept of perfection, the goddess becomes a delusion.

I believe that a large part of our collective wisdom is handed down in the form of such metaphors. Instead of dismissing them as delusions because their context is gone, we should perhaps try harder to rediscover the lost concepts. I also believe such metaphors exist in other fields that seem to work well. Take, for instance, the Qi concept in traditional Chinese medicine, the five elements (or three body types) in Ayurveda and so on. To the extent that traditional Chinese medicine and Ayurveda work, there has to be some knowledge buried in those practices. If we write off their basis merely because their metaphors are not consistent with our rationality, we may be writing off some potential sources of new or forgotten knowledge.

In addition, I believe that some of our smarter geniuses indeed see delusional metaphors in what we take to be supremely real.

Books, Philosophy, Physics, Science

Blind-Sight

In my post on A Plausible God, I cited blind-sight as an example of sensing that does not lead to conscious perception. This remarkable neurological syndrome illustrates the tight interconnection between our sense of reality and consciousness. Larry Weiscrantz and Alan Cowey discovered blind-sight at Oxford about 25 years ago.

Blindness can be physiological, when the physical eye is not functioning properly. Or it can be neurological, when the eye is fne but the visual signal processing is impaired. For example, if our right visual cortex is damaged, we are blind on the left side. When examining a patient with such a neurological blindness on one side, Weiscrantz shined a little spot of light on the patient’s blind side. Weiscrantz then asked the patient to point to it. The patient protested that he could not see it and could not possibly point to it. Weiscrantz asked him to try anyway. The patient then proceeded to point accurately to the spot of light that he could not consciously perceive.

After hundreds of trials, it became obvious that the patient could point correctly in ninety-nine percent of trials, even though he claimed on each trial that he was only guessing. How did the patient determine the location of an invisible object and point to it accurately? The neurological reason is that we all have two visual pathways. The new visual pathway goes through the visual cortex. The old, backup pathway runs through our brain stem to the superior colliculus.

The cause of our patient’s blindness was that his visual cortex was damaged, and it did not get the signals from one eye and its optic nerves. But the signals took the parallel route to the superior colliculus, using the old pathway. This rerouting allowed him to locate the object in space and guide his hand accurately to point to the invisible object. What this syndrome of blind-sight shows us is that only the new visual pathway leads to a conscious experience. While the old pathway is perfectly usable (for survival, for instance), it does not lead to a conscious experience of vision.

An interesting neurological condition, no doubt. But blind-sight is more than that. It is a rather confounding philosophical conundrum. The spot of light that the patient could see — was it real? Sure, we know it was real. But what if all of us were blind-sighted? If some of us started developing a semblance of awareness as a result of our blind-sight, would we believe them, or call them delusional? If there are senses that we can be unaware of, how sure can we be of the “sensed”? Or of our “delusions”?

This post is an edited version of section in The Unreal Universe. The information comes from The Emerging Mind: Reith Lectures on Neuroscience (BBC Radio, 2003) given by V. S. Ramachandran, the director of the Center for Brain and Cognition, San Diego, CA, USA. My book refers to several examples of physiological brain anomalies and their perceptual manifestation from this lecture series.

Books, Philosophy, Physics, Science

A Plausible God

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In my review of The God Delusion, I promised to post a plausible concept of God. By “a plausible concept,” I mean a concept that doesn’t violate the known principles of science, and should therefore be consistent with the so-called scientific worldview. Mind you, the plausibility of the concept says nothing about its veracity; but it may say something about it being a delusion.

Of all the sciences, physics seems to be the one most at odds with the God concept. Clearly, evolutionary biology is none too happy with it either, if Dawkins is anything to go by. But that analysis is for another post.

Let’s start by analyzing a physicist’s way of “proving” that there is no God. The argument usually goes something like this:

If there is a God who is capable of affecting me in any way, then there should be some force exerted by that God on me. There should be some interaction. Since the interaction is big enough to affect me, I should be able to use this particular interaction to “measure” the God-intensity. So far, I haven’t been able to measure any such God-related force. So either there is no God that affects me in any way, or there is a God that affects me through deviously disguised interactions so that whenever I try to measure the interaction, I’m always fooled. Now, you tell me what is more likely. By Occam’s Razor, the simplest explanation (that there is no God that can affect me) has the highest chance of being right.

While this is a good argument (and one I used to make), it is built on a couple of implicit assumptions that are rather tricky to spot. The first assumption is that we cannot be affected by an interaction that we cannot sense. This assumption is not necessarily true.

Modern cosmology needs at least one other kind of interaction to account for dark matter and dark energy. Let’s call this unknown interaction the dark interaction. Even though we cannot sense the dark interaction, we are subject to it exactly as all other (known) matter is. The existence of this interaction beyond our senses is sufficient to break the physicist’s proof. A plausible God can affect us, without our being able to sense it, through dark interactions.

But that is not the end of the story. The physicist can still argue, “Fine, if we cannot sense this God, how would we know he exists? And why do so many people claim they can feel him?” This argument is based on the assumptions on conscious experience and sensing. The hidden assumptions in the physicist’s questions (again, not necessarily true) are:

  1. Sensing should lead to a conscious perception.
  2. All humans should have the same sense modality.

An example of sensing that does not lead to conscious perception is the syndrome of blind sight. (I will post more on it later). A patient suffering from blind sight can point to the light spot he cannot consciously see. Thus, sensing without conscious perception is possible. The second assumption that all men are created equal (in terms of sensory modality) does not have any a priori reason to be true. It is possible that some people may be able to sense the dark interaction (or some other kind of interaction that God chooses) without being conscious of it.

So it is possible to argue that there is a God that affects us through a hitherto unknown interaction. And that some 95% of us can sense this interaction, and the others are atheists. What this argument illustrates is the plausibility of God. More precisely, it demonstrates the consistency of a concept of God with physics. It is not meant to be a proof of the existence of God. And that is why, despite the plausibility of God, I am still an atheist.

In retrospect, this argument did not have to be so complicated. It boils down to saying that there are limits on our knowledge, and to what is knowable. There is plenty of room for God outside these limits. It is also a classic argument by those who believe in God — you don’t know everything, so how do you know there isn’t a God?

Columns, Corporate Life, Physics, Quantitative Finance, The Wilmott Magazine

Modeling the Models

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Mathematical finance is built on a couple of assumptions. The most fundamental of them is the one on market efficiency. It states that the market prices every asset fairly, and the prices contain all the information available in the market. In other words, you cannot glean any more information by doing any research or technical analysis, or indeed any modeling. If this assumption doesn’t pan out, then the quant edifice we build on top of it will crumble. Some may even say that it did crumble in 2008.

We know that this assumption is not quite right. If it was, there wouldn’t be any transient arbitrage opportunities. But even at a more fundamental level, the assumption has shaky justification. The reason that the market is efficient is that the practitioners take advantage of every little arbitrage opportunity. In other words, the markets are efficient because they are not so efficient at some transient level.

Mark Joshi, in his well-respected book, “The Concepts and Practice of Mathematical Finance,” points out that Warren Buffet made a bundle of money by refusing to accept the assumption of market efficiency. In fact, the weak form of market efficiency comes about because there are thousands of Buffet wannabes who keep their eyes glued to the ticker tapes, waiting for that elusive mispricing to show up.

Given that the quant careers, and literally trillions of dollars, are built on the strength of this assumption, we have to ask this fundamental question. Is it wise to trust this assumption? Are there limits to it?

Let’s take an analogy from physics. I have this glass of water on my desk now. Still water, in the absence of any turbulence, has a flat surface. We all know why – gravity and surface tension and all that. But we also know that the molecules in water are in random motion, in accordance with the same Brownian process that we readily adopted in our quant world. One possible random configuration is that half the molecules move, say, to the left, and the other half to the right (so that the net momentum is zero).

If that happens, the glass on my desk will break and it will make a terrible mess. But we haven’t heard of such spontaneous messes (from someone other than our kids, that is.)

The question then is, can we accept the assumption on the predictability of the surface of water although we know that the underlying motion is irregular and random? (I am trying to make a rather contrived analogy to the assumption on market efficiency despite the transient irregularities.) The answer is a definite yes. Of course, we take the flatness of liquid surfaces for granted in everything from the useless lift-pumps and siphons of our grade school physics books all the way to dams and hydro-electric projects.

So what am I quibbling about? Why do I harp on the possibility of uncertain foundations? I have two reasons. One is the question of scale. In our example of surface flatness vs. random motion, we looked at a very large collection, where, through the central limit theorem and statistical mechanics, we expect nothing but regular behavior. If I was studying, for instance, how an individual virus propagates through the blood stream, I shouldn’t make any assumptions on the regularity in the behavior of water molecules. This matter of scale applies to quantitative finance as well. Are we operating at the right scale to ignore the shakiness of the market efficiency assumption?

The second reason for mistrusting the pricing models is a far more insidious one. Let me see if I can present it rather dramatically using my example of the tumbler of water. Suppose we make a model for the flatness of the water surface, and the tiny ripples on it as perturbations or something. Then we proceed to use this model to extract tiny amounts of energy from the ripples.

The fact that we are using the model impacts the flatness or the nature of the ripples, affecting the underlying assumptions of the model. Now, imagine that a large number of people are using the same model to extract as much energy as they can from this glass of water. My hunch is that it will create large scale oscillations, perhaps generating configurations that do indeed break the glass and make a mess. Discounting the fact that this hunch has its root more in the financial mess that spontaneously materialized rather than any solid physics argument, we can still see that large fluctuations do indeed seem to increase the energy that can be extracted. Similarly, large fluctuations (and the black swans) may indeed be a side effect of modeling.

Creative, Philosophy, Physics, Quotes, Science

Change the Facts

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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.

World line of airplanesIn 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.

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The Big Bang Theory – Part II

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After reading a paper by Ashtekar on quantum gravity and thinking about it, I realized what my trouble with the Big Bang theory was. It is more on the fundamental assumptions than the details. I thought I would summarize my thoughts here, more for my own benefit than anybody else’s.

Classical theories (including SR and QM) treat space as continuous nothingness; hence the term space-time continuum. In this view, objects exist in continuous space and interact with each other in continuous time.

Although this notion of space time continuum is intuitively appealing, it is, at best, incomplete. Consider, for instance, a spinning body in empty space. It is expected to experience centrifugal force. Now imagine that the body is stationary and the whole space is rotating around it. Will it experience any centrifugal force?

It is hard to see why there would be any centrifugal force if space is empty nothingness.

GR introduced a paradigm shift by encoding gravity into space-time thereby making it dynamic in nature, rather than empty nothingness. Thus, mass gets enmeshed in space (and time), space becomes synonymous with the universe, and the spinning body question becomes easy to answer. Yes, it will experience centrifugal force if it is the universe that is rotating around it because it is equivalent to the body spinning. And, no, it won’t, if it is in just empty space. But “empty space” doesn’t exist. In the absence of mass, there is no space-time geometry.

So, naturally, before the Big Bang (if there was one), there couldn’t be any space, nor indeed could there be any “before.” Note, however, that the Ashtekar paper doesn’t clearly state why there had to be a big bang. The closest it gets is that the necessity of BB arises from the encoding of gravity in space-time in GR. Despite this encoding of gravity and thereby rendering space-time dynamic, GR still treats space-time as a smooth continuum — a flaw, according to Ashtekar, that QG will rectify.

Now, if we accept that the universe started out with a big bang (and from a small region), we have to account for quantum effects. Space-time has to be quantized and the only right way to do it would be through quantum gravity. Through QG, we expect to avoid the Big Bang singularity of GR, the same way QM solved the unbounded ground state energy problem in the hydrogen atom.

What I described above is what I understand to be the physical arguments behind modern cosmology. The rest is a mathematical edifice built on top of this physical (or indeed philosophical) foundation. If you have no strong views on the philosophical foundation (or if your views are consistent with it), you can accept BB with no difficulty. Unfortunately, I do have differing views.

My views revolve around the following questions.

These posts may sound like useless philosophical musings, but I do have some concrete (and in my opinion, important) results, listed below.

There is much more work to be done on this front. But for the next couple of years, with my new book contract and pressures from my quant career, I will not have enough time to study GR and cosmology with the seriousness they deserve. I hope to get back to them once the current phase of spreading myself too thin passes.