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…

Columns, Physics, Quantitative Finance, The Wilmott Magazine

Chaos and Uncertainty

The last couple of months in finance industry can be summarized in two words — chaos and uncertainty. The aptness of this laconic description is all too evident. The sub-prime crisis where everybody lost, the dizzying commodity price movements, the pink slip syndrome, the spectacular bank busts and the gargantuan bail-outs all vouch for it.

The financial meltdown is such a rich topic with reasons and ramifications so overarching that all self-respecting columnists will be remiss to let it slide. After all, a columnist who keeps his opinions to himself is a columnist only in his imagination. I too will share my views on causes and effects of this turmoil that is sure to affect our lives more directly than anybody else’s, but perhaps in a future column.

The chaos and uncertainty I want to talk about are of different kind — the physics kind. The terms chaos and uncertainty have a different and specific meanings in physics. How those meanings apply to the world of finance is what this column is about.

Symmetries and Patterns

Physicists are a strange bunch. They seek and find symmetries and patterns where none exists. I remember once when our brilliant professor, Lee Smolin, described to us how the Earth could be considered a living organism. Using insightful arguments and precisely modulated articulation, Lee made a compelling case that the Earth, in fact, satisfied all the conditions of being an organism. The point in Lee’s view was not so much whether or the Earth was literally alive, but that thinking of it as an organism was a viable intellectual pattern. Once we represent the Earth in that model, we can use the patterns pertaining to organism to draw further predictions or conclusions.

Expanding on this pattern, I recently published a column presenting the global warming as a bout of fever caused by a virus (us humans) on this host organism. Don’t we plunder the raw material of our planet with the same abandon with which a virus usurps the genetic material of its host? In addition to fever, typical viral symptoms include sores and blisters as well. Looking at the cities and other eye sores that have replaced pristine forests and other natural landscapes, it is not hard to imagine that we are indeed inflicting fetid atrocities to our host Earth. Can’t we think of our city sewers and the polluted air as the stinking, oozing ulcers on its body?

While these analogies may sound farfetched, we have imported equally distant ideas from physics to mathematical finance. Why would stock prices behave anything like a random walk, unless we want to take Bush’s words (that “Wall Street got drunk”) literally? But seriously, Brownian motion has been a wildly successful model that we borrowed from physics. Again, once we accept that the pattern is similar between molecules getting bumped around and the equity price movements, the formidable mathematical machinery and physical intuitions available in one phenomenon can be brought to bear on the other.

Looking at the chaotic financial landscape now, I wonder if physics has other insights to offer so that we can duck and dodge as needed in the future. Of the many principles from physics, chaos seems such a natural concept to apply to the current situation. Are there lessons to be learned from chaos and nonlinear dynamics that we can make use of? May be it is Heisenberg’s uncertainty principle that holds new insights.

Perhaps I chose these concepts as a linguistic or emotional response to the baffling problems confronting us now, but let’s look at them any way. It is not like the powers that be have anything better to offer, is it?

Chaos Everywhere

In physics, chaos is generally described as our inability to predict the outcome of experiments with arbitrarily close initial conditions. For instance, try balancing your pencil on its tip. Clearly, you won’t be able to, and the pencil will land on your desktop. Now, note this line along which it falls, and repeat the experiment. Regardless of how closely you match the initial conditions (of how you hold and balance the pencil), the outcome (the line along which it falls) is pretty much random. Although this randomness may look natural to us — after all, we have been trying to balance pencils on their tips ever since we were four, if my son’s endeavours are anything to go by — it is indeed strange that we cannot bring the initial conditions close enough to be confident of the outcome.

Even stranger is the fact that similar randomness shows up in systems that are not quite as physical as pencils or experiments. Take, for instance, the socio-economic phenomenon of globalization, which I can describe as follows, admittedly with an incredible amount of over-simplification. Long time ago, we used to barter agricultural and dairy products with our neighbours — say, a few eggs for a litre (or was it pint?) of milk. Our self-interest ensured a certain level of honesty. We didn’t want to get beaten up for adding white paint to milk, for instance. These days, thanks to globalization, people don’t see their customers. A company buys milk from a farmer, adds god knows what, makes powder and other assorted chemicals in automated factories and ships them to New Zealand and Peru. The absence of a human face in the supply chain and in the flow of money results in increasingly unscrupulous behaviour.

Increasing chaos can be seen in the form of violently fluctuating concentrations of wealth and fortunes, increasing amplitudes and frequency of boom and bust cycles, exponential explosion in technological innovation and adaptation cycles, and the accelerated pace of paradigm shifts across all aspects of our lives.

It is one thing to say that things are getting chaotic, quite another matter to exploit that insight and do anything useful with it. I won’t pretend that I can predict the future even if (rather, especially if) I could. However, let me show you a possible approach using chaos.

One of the classic examples of chaos is the transition from a regular, laminar flow of a fluid to a chaotic, turbulent flow. For instance, when you open a faucet slowly, if you do it carefully, you can have a pretty nice continuous column of water, thicker near the top and stretched thinner near the bottom. The stretching force is gravity, and the cohesive forces are surface tension and inter-molecular forces. As you open the faucet still further, ripples begin to appear on the surface of the column which, at higher rates of flow, rip apart the column into complete chaos.

In a laminar flow, macroscopic forces tend to smooth out microscopic irregularities. Like gravity and surface tension in our faucet example, we have analogues of macroscopic forces in finance. The stretching force is probably greed, and the cohesive ones are efficient markets.

There is a rich mathematical framework available to describe chaos. Using this framework, I suspect one can predict the incidence and intensity of financial turmoils, though not their nature and causes. However, I am not sure such a prediction is useful. Imagine if I wrote two years ago that in 2008, there would be a financial crisis resulting in about one trillion dollar of losses. Even if people believed me, would it have helped?

Usefulness is one thing, but physicists and mathematicians derive pleasure also from useless titbits of knowledge. What is interesting about the faucet-flow example is this: if you follow the progress two water molecules starting off their careers pretty close to each other, in the laminar case, you will find that they end up pretty much next to each other. But once the flow turns turbulent, there is not telling where the molecules will end up. Similarly, in finance, suppose two banks start off roughly from the same position — say Bear Stearns and Lehman. Under normal, laminar conditions, their stock prices would track similar patterns. But during a financial turbulence, they end up in totally different recycle bins of history, as we have seen.

If whole financial institutions are tossed around into uncertain paths during chaotic times, imagine where two roughly similar employees might end up. In other words, don’t feel bad if you get a pink slip. There are forces well beyond your control at play here.

Uncertainty Principle in Quantitative Finance

The Heisenberg uncertainty principle is perhaps the second most popular theme from physics that has captured the public imagination. (The first one, of course, is Einstein’s E = mc2.) It says something seemingly straightforward — you can measure two complementary properties of a system only to a certain precision. For instance, if you try to figure out where an electron is (measure its position, that is) more and more precisely, its speed becomes progressively more uncertain (or, the momentum measurement becomes imprecise).

Quantitative finance has a natural counterpart to the uncertainty principle — risks and rewards. When you try to minimize the risks, the rewards themselves go down. If you hedge out all risks, you get only risk-free returns. Since risk is the same as the uncertainty in rewards, the risk-reward relation is not quite the same as the uncertainty principle (which, as described in the box, deals with complementary variables), but it is close enough to draw some parallels.

To link the quantum uncertainty principle to quantitative finance, let’s look at its interpretation as observation altering results. Does modelling affect how much money we can make out of a product? This is a trick question. The answer might look obvious at first glance. Of course, if we can understand and model a product perfectly, we can price it right and expect to reap healthy rewards. So, sure, modelling affects the risk-reward equation.

But, a model is only as good as its assumptions. And the most basic assumption in any model is that the market is efficient and liquid. The validity of this assumption (or lack thereof) is precisely what precipitated the current financial crisis. If our modelling effort actually changes the underlying assumptions (usually in terms of liquidity or market efficiency), we have to pay close attention to the quant equivalent of the uncertainty principle.

Look at it this way — a pyramid scheme is a perfectly valid money making model, but based on one unfortunate assumption on the infinite number of idiots at the bottom of the pyramid. (Coming to think of it, the underlying assumption in the sub-prime crisis, though more sophisticated, may not have been that different.) Similar pyramid assumptions can be seen in social security schemes, as well. We know that pyramid assumptions are incorrect. But at what point do they become incorrect enough for us to change the model?

There is an even more insidious assumption in using models — that we are the only ones who use them. In order to make a killing in a market, we always have to know a bit more than the rest of them. Once everybody starts using the same model, I think the returns will plummet to risk-free levels. Why else do you think we keep inventing more and more complex exotics?

Summing up…

The current financial crisis has been blamed on many things. One favourite theory has been that it was brought about by the greed in Wall Street — the so-called privatization of profits and socialization of losses. Incentive schemes skewed in such a way as to encourage risk taking and limit risk management must take at least part of the blame. A more tempered view regards the turmoil as a result of a risk management failure or a regulatory failure.

This column presents my personal view that the turmoil is the inevitable consequence of the interplay between opposing forces in financial markets — risk and rewards, speculation and regulation, risk taking and risk management and so on. To the extent that the risk appetite of a financial institute is implemented through a conflict between such opposing forces, these crises cannot be avoided. Worse, the intensity and frequency of similar meltdowns are going to increase as the volume of transactions increases. This is the inescapable conclusion from non-linear dynamics. After all, such turbulence has always existed in the real economy in the form cyclical booms and busts. In free market economies, selfishness and the inherent conflicts between selfish interests provide the stretching and cohesive forces, setting the stage for chaotic turbulence.

Physics has always been a source of talent and ideas for quantitative finance, much like mathematics provides a rich toolkit to physics. In his book, Dreams of a Final Theory, Nobel Prize winning physicist Steven Weinberg marvels at the uncanny ability of mathematics to anticipate physics needs. Similarly, quants may marvel at the ability of physics to come up with phenomena and principles that can be directly applied to our field. To me, it looks like the repertoire of physics holds a few more gems that we can employ and exploit.

Box: Heisenberg’s Uncertainty Principle

Where does this famous principle come from? It is considered a question beyond the realms of physics. Before we can ask the question, we have to examine what the principle really says. Here are a few possible interpretations:

  • Position and momentum of a particle are intrinsically interconnected. As we measure the momentum more accurately, the particle kind of “spreads out,” as George Gamow’s character, Mr. Tompkins, puts it. In other words, it is just one of those things; the way the world works.
  • When we measure the position, we disturb the momentum. Our measurement probes are “too fat,” as it were. As we increase the position accuracy (by shining light of shorter wavelengths, for instance), we disturb the momentum more and more (because shorter wavelength light has higher energy/momentum).
  • Closely related to this interpretation is a view that the uncertainty principle is a perceptual limit.
  • We can also think of the uncertainly principle as a cognitive limit if we consider that a future theory might surpass such limits.

The first view is currently popular and is related to the so-called Copenhagen interpretation of quantum mechanics. Let’s ignore it for it is not too open to discussions.

The second interpretation is generally understood as an experimental difficulty. But if the notion of the experimental setup is expanded to include the inevitable human observer, we arrive at the third view of perceptual limitation. In this view, it is actually possible to “derive” the uncertainty principle, based on how human perception works.

Let’s assume that we are using a beam of light of wavelength lambda to observe the particle. The precision in the position we can hope to achieve is of the order of lambda. In other words, Delta x approx lambda. In quantum mechanics, the momentum of each photon in the light beam is inversely proportional to the wavelength. At least one photon is reflected by the particle so that we can see it. So, by the classical conservation law, the momentum of the particle has to change by at least this amount(approx constant/lambda) from what it was before the measurement. Thus, through perceptual arguments, we get something similar to the Heisenberg uncertainty principle

Delta x.Delta p approx constant

We can make this argument more rigorous, and get an estimate of the value of the constant. The resolution of a microscope is given by the empirical formula 0.61lambda/NA, where NA is the numerical aperture, which has a maximum value of one. Thus, the best spatial resolution is 0.61lambda. Each photon in the light beam has a momentum 2pihbar/lambda, which is the uncertainty in the particle momentum. So we get Delta x.Delta p approx 4hbar, approximately an order of magnitude bigger than the quantum mechanical limit.

Through more rigorous statistical arguments, related to the spatial resolution and the expected momentum transferred, it may possible to derive the Heisenberg uncertainty principle through this line of reasoning.

If we consider the philosophical view that our reality is a cognitive model of our perceptual stimuli (which is the only view that makes sense to me), my fourth interpretation of the uncertainty principle being a cognitive limitation also holds a bit of water.
About the Author

The author is a scientist from the European Organization for Nuclear Research (CERN), who currently works as a senior quantitative professional at Standard Chartered in Singapore. More information about the author can be found at his blog: http//www.Thulasidas.com. The views expressed in this column are only his personal views, which have not been influenced by considerations of the firm’s business or client relationships.

Philosophy, Physics, Science

Why the Speed of Light?

What is so special about light that its speed should figure in the basic structure of space and time and our reality? This is the question that has nagged many scientists ever since Albert Einstein published On the Electrodynamics of Moving Bodies about 100 years ago.

In order to understand the specialness of light in our space and time, we need to study how we perceive the world around us and how reality is created in our brains. We perceive our world using our senses. The sensory signals that our senses collect are then relayed to our brains. The brain creates a cognitive model, a representation of the sensory inputs, and presents it to our conscious awareness as reality. Our visual reality consists of space much like our auditory world is made up of sounds.

Just as sounds are a perceptual experience rather than a fundamental property of the physical reality, space also is an experience, or a cognitive representation of the visual inputs, not a fundamental aspect of “the world” our senses are trying to sense.

Space and time together form what physics considers the basis of reality. The only way we can understand the limitations in our reality is by studying the limitations in our senses themselves.

At a fundamental level, how do our senses work? Our sense of sight operates using light, and the fundamental interaction involved in sight falls in the electromagnetic (EM) category because light (or photon) is the intermediary of EM interactions. The exclusivity of EM interaction is not limited to our the long range sense of sight; all the short range senses (touch, taste, smell and hearing) are also EM in nature. To understand the limitations of our perception of space, we need not highlight the EM nature of all our senses. Space is, by and large, the result of our sight sense. But it is worthwhile to keep in mind that we would have no sensing, and indeed no reality, in the absence of EM interactions.

Like our senses, all our technological extensions to our senses (such as radio telescopes, electron microscopes, redshift measurements and even gravitational lensing) use EM interactions exclusively to measure our universe. Thus, we cannot escape the basic constraints of our perception even when we use modern instruments. The Hubble telescope may see a billion light years farther than our naked eyes, but what it sees is still a billion years older than what our eyes see. Our perceived reality, whether built upon direct sensory inputs or technologically enhanced, is a subset of electromagnetic particles and interactions only. It is a projection of EM particles and interactions into our sensory and cognitive space, a possibly imperfect projection.

This statement about the exclusivity of EM interactions in our perceived reality is often met with a bit of skepticism, mainly due to a misconception that we can sense gravity directly. This confusion arises because our bodies are subject to gravity. There is a fine distinction between “being subject to” and “being able to sense” gravitational force.

This difference is illustrated by a simple thought experiment: Imagine a human subject placed in front of an object made entirely of cosmological dark matter. There is no other visible matter anywhere the subject can see it. Given that the dark matter exerts gravitational force on the subject, will he be able to sense its presence? He will be pulled toward it, but how will he know that he is being pulled or that he is moving? He can possibly design some mechanical contraption to detect the gravity of the dark matter object. But then he will be sensing the effect of gravity on some matter using EM interactions. For instance, he may be able to see his unexplained acceleration (effect of gravity on his body, which is EM matter) with respect to reference objects such as stars. But the sensing part here (seeing the stars) involves EM interactions.

It is impossible to design any mechanical contraption to detect gravity that is devoid of EM matter. The gravity sensing in our ears again measures the effect of gravity on EM matter. In the absence of EM interaction, it is impossible to sense gravity, or anything else for that matter.

Electromagnetic interactions are responsible for our sensory inputs. Sensory perception leads to our brain’s representation that we call reality. Any limitation in this chain leads to a corresponding limitation in our sense of reality. One limitation in the chain from senses to reality is the finite speed of photon, which is the gauge boson of our senses. The finite speed of the sense modality influences and distorts our perception of motion, space and time. Because these distortions are perceived as a part of our reality itself, the root cause of the distortion becomes a fundamental property of our reality. This is how the speed of light becomes such an important constant in our space time. The sanctity of light is respected only in our perceived reality.

If we trust the imperfect perception and try to describe what we sense at cosmological scales, we end up with views of the world such as the big bang theory in modern cosmology and the general and special theories of relativity. These theories are not wrong, and the purpose of this book is not to prove them wrong, just to point out that they are descriptions of a perceived reality. They do not describe the physical causes behind the sensory inputs. The physical causes belong to an absolute reality beyond our senses.

The distinction between the absolute reality and our perception of it can be further developed and applied to certain specific astrophysical and cosmological phenomena. When it comes to the physics that happens well beyond our sensory ranges, we really have to take into account the role that our perception and cognition play in seeing them. The universe as we see it is only a cognitive model created out of the photons falling on our retina or on the photo sensors of the Hubble telescope. Because of the finite speed of the information carrier (namely photons), our perception is distorted in such a way as to give us the impression that space and time obey special relativity. They do, but space and time are not the absolute reality. They are only a part of the unreal universe that is our perception of an unknowable reality.

[This again is an edited excerpt from my book, The Unreal Universe.]

Debates, Philosophy, Physics

What is Space?

5 Comments

This sounds like a strange question. We all know what space is, it is all around us. When we open our eyes, we see it. If seeing is believing, then the question “What is space?” indeed is a strange one.

To be fair, we don’t actually see space. We see only objects which we assume are in space. Rather, we define space as whatever it is that holds or contains the objects. It is the arena where objects do their thing, the backdrop of our experience. In other words, experience presupposes space and time, and provides the basis for the worldview behind the currently popular interpretations of scientific theories.

Although not obvious, this definition (or assumption or understanding) of space comes with a philosophical baggage — that of realism. The realist’s view is predominant in the current understanding of Einstien’s theories as well. But Einstein himself may not have embraced realism blindly. Why else would he say:

In order to break away from the grip of realism, we have to approach the question tangentially. One way to do it is by studying the neuroscience and cognitive basis of sight, which after all provides the strongest evidence to the realness of space. Space, by and large, is the experience associated with sight. Another way is to examine experiential correlates of other senses: What is sound?

When we hear something, what we hear is, naturally, sound. We experience a tone, an intensity and a time variation that tell us a lot about who is talking, what is breaking and so on. But even after stripping off all the extra richness added to the experience by our brain, the most basic experience is still a “sound.” We all know what it is, but we cannot explain it in terms more basic than that.

Now let’s look at the sensory signal responsible for hearing. As we know, these are pressure waves in the air that are created by a vibrating body making compressions and depressions in the air around it. Much like the ripples in a pond, these pressure waves propagate in almost all directions. They are picked up by our ears. By a clever mechanism, the ears perform a spectral analysis and send electric signals, which roughly correspond to the frequency spectrum of the waves, to our brain. Note that, so far, we have a vibrating body, bunching and spreading of air molecules, and an electric signal that contains information about the pattern of the air molecules. We do not have sound yet.

The experience of sound is the magic our brain performs. It translates the electrical signal encoding the air pressure wave patterns to a representation of tonality and richness of sound. Sound is not the intrinsic property of a vibrating body or a falling tree, it is the way our brain chooses to represent the vibrations or, more precisely, the electrical signal encoding the spectrum of the pressure waves.

Doesn’t it make sense to call sound an internal cognitive representation of our auditory sensory inputs? If you agree, then reality itself is our internal representation of our sensory inputs. This notion is actually much more profound that it first appears. If sound is representation, so is smell. So is space.

Figure
Figure: Illustration of the process of brain’s representation of sensory inputs. Odors are a representation of the chemical compositions and concentration levels our nose senses. Sounds are a mapping of the air pressure waves produced by a vibrating object. In sight, our representation is space, and possibly time. However, we do not know what it is the representation of.

We can examine it and fully understand sound because of one remarkable fact — we have a more powerful sense, namely our sight. Sight enables us to understand the sensory signals of hearing and compare them to our sensory experience. In effect, sight enables us to make a model describing what sound is.

Why is it that we do not know the physical cause behind space? After all, we know of the causes behind the experiences of smell, sound, etc. The reason for our inability to see beyond the visual reality is in the hierarchy of senses, best illustrated using an example. Let’s consider a small explosion, like a firecracker going off. When we experience this explosion, we will see the flash, hear the report, smell the burning chemicals and feel the heat, if we are close enough.

The qualia of these experiences are attributed to the same physical event — the explosion, the physics of which is well understood. Now, let’s see if we can fool the senses into having the same experiences, in the absence of a real explosion. The heat and the smell are fairly easy to reproduce. The experience of the sound can also be created using, for instance, a high-end home theater system. How do we recreate the experience of the sight of the explosion? A home theater experience is a poor reproduction of the real thing.

In principle at least, we can think of futuristic scenarios such as the holideck in Star Trek, where the experience of the sight can be recreated. But at the point where sight is also recreated, is there a difference between the real experience of the explosion and the holideck simulation? The blurring of the sense of reality when the sight experience is simulated indicates that sight is our most powerful sense, and we have no access to causes beyond our visual reality.

Visual perception is the basis of our sense of reality. All other senses provide corroborating or complementing perceptions to the visual reality.

[This post has borrowed quite a bit from my book.]

Articles and Essays, Philosophy, Physics, Science, Unpublished

Light Travel Time Effects and Cosmological Features

This unpublished article is a sequel to my earlier paper (also posted here as “Are Radio Sources and Gamma Ray Bursts Luminal Booms?“). This blog version contains the abstract, introduction and conclusions. The full version of the article is available as a PDF file.

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Abstract

Light travel time effects (LTT) are an optical manifestation of the finite speed of light. They can also be considered perceptual constraints to the cognitive picture of space and time. Based on this interpretation of LTT effects, we recently presented a new hypothetical model for the temporal and spatial variation of the spectrum of Gamma Ray Bursts (GRB) and radio sources. In this article, we take the analysis further and show that LTT effects can provide a good framework to describe such cosmological features as the redshift observation of an expanding universe, and the cosmic microwave background radiation. The unification of these seemingly distinct phenomena at vastly different length and time scales, along with its conceptual simplicity, can be regarded as indicators of the curious usefulness of this framework, if not its validity.

Introduction

The finite speed of light plays an important part in how we perceive distance and speed. This fact should hardly come as a surprise because we do know that things are not as we see them. The sun that we see, for instance, is already eight minutes old by the time we see it. This delay is trivial; if we want to know what is going on at the sun now, all we have to do is to wait for eight minutes. We, nonetheless, have to “correct” for this distortion in our perception due to the finite speed of light before we can trust what we see.

What is surprising (and seldom highlighted) is that when it comes to sensing motion, 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 of motion 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.

Exploring the second option, we assume an underlying reality that gives rise to our perceived picture. We further model this underlying reality as obeying classical mechanics, and work out our perceived picture through the apparatus of perception. In other words, we do not attribute the manifestations of the finite speed of light to the properties of the underlying reality. Instead, we work out our perceived picture that this model predicts and verify whether the properties we do observe can originate from this perceptual constraint.

Space, the objects in it, and their motion are, by and large, the product of optical perception. One tends to take it for granted that perception arises from reality as one perceives it. In this article, we take the position that what we perceive is an incomplete or distorted picture of an underlying reality. Further, we are trying out classical mechanics for the the underlying reality (for which we use terms like absolute, noumenal or physical reality) that does cause our perception to see if it fits with our perceived picture (which we may refer to as sensed or phenomenal reality).

Note that we are not implying that the manifestations of perception are mere delusions. They are not; they are indeed part of our sensed reality because reality is an end result of perception. This insight may be behind Goethe’s famous statement, “Optical illusion is optical truth.”

We applied this line of thinking to a physics problem recently. We looked at the spectral evolution of a GRB and found it to be remarkably similar to that in a sonic boom. Using this fact, we presented a model for GRB as our perception of a “luminal” boom, with the understanding that it is our perceived picture of reality that obeys Lorentz invariance and our model for the underlying reality (causing the perceived picture) may violate relativistic physics. The striking agreement between the model and the observed features, however, extended beyond GRBs to symmetric radio sources, which can also be regarded as perceptual effects of hypothetical luminal booms.

In this article, we look at other implications of the model. We start with the similarities between the light travel time (LTT) effects and the coordinate transformation in Special Relativity (SR). These similarities are hardly surprising because SR is derived partly based on LTT effects. We then propose an interpretation of SR as a formalization of LTT effects and study a few observed cosmological phenomena in the light of this interpretation.

Similarities between Light Travel Time Effects and SR

Special relativity seeks a linear coordinate transformation between coordinate systems in motion with respect to each other. We can trace the origin of linearity to a hidden assumption on the nature of space and time built into SR, as stated by Einstein: “In the first place it is clear that the equations must be linear on account of the properties of homogeneity which we attribute to space and time.” Because of this assumption of linearity, the original derivation of the transformation equations ignores the asymmetry between approaching and receding objects. Both approaching and receding objects can be described by two coordinate systems that are always receding from each other. For instance, if a system K is moving with respect to another system k along the positive X axis of k, then an object at rest in K at a positive x is receding while another object at a negative x is approaching an observer at the origin of k.

The coordinate transformation in Einstein’s original paper is derived, in part, a manifestation of the light travel time (LTT) effects and the consequence of imposing the constancy of light speed in all inertial frames. This is most obvious in the first thought experiment, where observers moving with a rod find their clocks not synchronized due to the difference in light travel times along the length of the rod. However, in the current interpretation of SR, the coordinate transformation is considered a basic property of space and time.

One difficulty that arises from this interpretation of SR is that the definition of the relative velocity between the two inertial frames becomes ambiguous. If it is the velocity of the moving frame as measured by the observer, then the observed superluminal motion in radio jets starting from the core region becomes a violation of SR. If it is a velocity that we have to deduce by considering LT effects, then we have to employ the extra ad-hoc assumption that superluminality is forbidden. These difficulties suggest that it may be better to disentangle the light travel time effects from the rest of SR.

In this section, we will consider space and time as a part of the cognitive model created by the brain, and argue that special relativity applies to the cognitive model. The absolute reality (of which the SR-like space-time is our perception) does not have to obey the restrictions of SR. In particular, objects are not restricted to subluminal speeds, but they may appear to us as though they are restricted to subluminal speeds in our perception of space and time. If we disentangle LTT effects from the rest of SR, we can understand a wide array of phenomena, as we shall see in this article.

Unlike SR, considerations based on LTT effects result in intrinsically different set of transformation laws for objects approaching an observer and those receding from him. More generally, the transformation depends on the angle between the velocity of the object and the observer’s line of sight. Since the transformation equations based on LTT effects treat approaching and receding objects asymmetrically, they provide a natural solution to the twin paradox, for instance.

Conclusions

Because space and time are a part of a reality created out of light inputs to our eyes, some of their properties are manifestations of LTT effects, especially on our perception of motion. The absolute, physical reality presumably generating the light inputs does not have to obey the properties we ascribe to our perceived space and time.

We showed that LTT effects are qualitatively identical to those of SR, noting that SR only considers frames of reference receding from each other. This similarity is not surprising because the coordinate transformation in SR is derived based partly on LTT effects, and partly on the assumption that light travels at the same speed with respect to all inertial frames. In treating it as a manifestation of LTT, we did not address the primary motivation of SR, which is a covariant formulation of Maxwell’s equations. It may be possible to disentangle the covariance of electrodynamics from the coordinate transformation, although it is not attempted in this article.

Unlike SR, LTT effects are asymmetric. This asymmetry provides a resolution to the twin paradox and an interpretation of the assumed causality violations associated with superluminality. Furthermore, the perception of superluminality is modulated by LTT effects, and explains gamma ray bursts and symmetric jets. As we showed in the article, perception of superluminal motion also holds an explanation for cosmological phenomena like the expansion of the universe and cosmic microwave background radiation. LTT effects should be considered as a fundamental constraint in our perception, and consequently in physics, rather than as a convenient explanation for isolated phenomena.

Given that our perception is filtered through LTT effects, we have to deconvolute them from our perceived reality in order to understand the nature of the absolute, physical reality. This deconvolution, however, results in multiple solutions. Thus, the absolute, physical reality is beyond our grasp, and any assumed properties of the absolute reality can only be validated through how well the resultant perceived reality agrees with our observations. In this article, we assumed that the underlying reality obeys our intuitively obvious classical mechanics and asked the question how such a reality would be perceived when filtered through light travel time effects. We demonstrated that this particular treatment could explain certain astrophysical and cosmological phenomena that we observe.

The coordinate transformation in SR can be viewed as a redefinition of space and time (or, more generally, reality) in order to accommodate the distortions in our perception of motion due to light travel time effects. One may be tempted to argue that SR applies to the “real” space and time, not our perception. This line of argument begs the question, what is real? Reality is only a cognitive model created in our brain starting from our sensory inputs, visual inputs being the most significant. Space itself is a part of this cognitive model. The properties of space are a mapping of the constraints of our perception.

The choice of accepting our perception as a true image of reality and redefining space and time as described in special relativity indeed amounts to a philosophical choice. The alternative presented in the article is inspired by the view in modern neuroscience that reality is a cognitive model in the brain based on our sensory inputs. Adopting this alternative reduces us to guessing the nature of the absolute reality and comparing its predicted projection to our real perception. It may simplify and elucidate some theories in physics and explain some puzzling phenomena in our universe. However, this option is yet another philosophical stance against the unknowable absolute reality.

Articles and Essays, Physics, Science

Are Radio Sources and Gamma Ray Bursts Luminal Booms?

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This article was published in the International Journal of Modern Physics D (IJMP–D) in 2007. It soon became the Top Accessed Article of the journal by Jan 2008.

Although it might seem like a hard core physics article, it is in fact an application of the philosophical insight permeating this blog and my book.

This blog version contains the abstract, introduction and conclusions. The full version of the article is available as a PDF file.

Journal Reference: IJMP-D Vol. 16, No. 6 (2007) pp. 983–1000.

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Abstract

The softening of the GRB afterglow bears remarkable similarities to the frequency evolution in a sonic boom. At the front end of the sonic boom cone, the frequency is infinite, much like a Gamma Ray Burst (GRB). Inside the cone, the frequency rapidly decreases to infrasonic ranges and the sound source appears at two places at the same time, mimicking the double-lobed radio sources. Although a “luminal” boom violates the Lorentz invariance and is therefore forbidden, it is tempting to work out the details and compare them with existing data. This temptation is further enhanced by the observed superluminality in the celestial objects associated with radio sources and some GRBs. In this article, we calculate the temporal and spatial variation of observed frequencies from a hypothetical luminal boom and show remarkable similarity between our calculations and current observations.

Introduction

A sonic boom is created when an object emitting sound passes through the medium faster than the speed of sound in that medium. As the object traverses the medium, the sound it emits creates a conical wavefront, as shown in Figure 1. The sound frequency at this wavefront is infinite because of the Doppler shift. The frequency behind the conical wavefront drops dramatically and soon reaches the infrasonic range. This frequency evolution is remarkably similar to afterglow evolution of a gamma ray burst (GRB).

Sonic Boom
Figure 1:. The frequency evolution of sound waves as a result of the Doppler effect in supersonic motion. The supersonic object S is moving along the arrow. The sound waves are “inverted” due to the motion, so that the waves emitted at two different points in the trajectory merge and reach the observer (at O) at the same time. When the wavefront hits the observer, the frequency is infinity. After that, the frequency rapidly decreases.

Gamma Ray Bursts are very brief, but intense flashes of \gamma rays in the sky, lasting from a few milliseconds to several minutes, and are currently believed to emanate from cataclysmic stellar collapses. The short flashes (the prompt emissions) are followed by an afterglow of progressively softer energies. Thus, the initial \gamma rays are promptly replaced by X-rays, light and even radio frequency waves. This softening of the spectrum has been known for quite some time, and was first described using a hypernova (fireball) model. In this model, a relativistically expanding fireball produces the \gamma emission, and the spectrum softens as the fireball cools down. The model calculates the energy released in the \gamma region as 10^ {53}—10^ {54} ergs in a few seconds. This energy output is similar to about 1000 times the total energy released by the sun over its entire lifetime.

More recently, an inverse decay of the peak energy with varying time constant has been used to empirically fit the observed time evolution of the peak energy using a collapsar model. According to this model, GRBs are produced when the energy of highly relativistic flows in stellar collapses are dissipated, with the resulting radiation jets angled properly with respect to our line of sight. The collapsar model estimates a lower energy output because the energy release is not isotropic, but concentrated along the jets. However, the rate of the collapsar events has to be corrected for the fraction of the solid angle within which the radiation jets can appear as GRBs. GRBs are observed roughly at the rate of once a day. Thus, the expected rate of the cataclysmic events powering the GRBs is of the order of 10^4—10^6 per day. Because of this inverse relationship between the rate and the estimated energy output, the total energy released per observed GRB remains the same.

If we think of a GRB as an effect similar to the sonic boom in supersonic motion, the assumed cataclysmic energy requirement becomes superfluous. Another feature of our perception of supersonic object is that we hear the sound source at two different location as the same time, as illustrated in Figure 2. This curious effect takes place because the sound waves emitted at two different points in the trajectory of the supersonic object reach the observer at the same instant in time. The end result of this effect is the perception of a symmetrically receding pair of sound sources, which, in the luminal world, is a good description of symmetric radio sources (Double Radio source Associated with Galactic Nucleus or DRAGN).

superluminality
Figure 2:. The object is flying from to A through and B at a constant supersonic speed. Imagine that the object emits sound during its travel. The sound emitted at the point (which is near the point of closest approach B) reaches the observer at O before the sound emitted earlier at . The instant when the sound at an earlier point reaches the observer, the sound emitted at a much later point A also reaches O. So, the sound emitted at A and reaches the observer at the same time, giving the impression that the object is at these two points at the same time. In other words, the observer hears two objects moving away from rather than one real object.

Radio Sources are typically symmetric and seem associated with galactic cores, currently considered manifestations of space-time singularities or neutron stars. Different classes of such objects associated with Active Galactic Nuclei (AGN) were found in the last fifty years. Figure 3 shows the radio galaxy Cygnus A, an example of such a radio source and one of the brightest radio objects. Many of its features are common to most extragalactic radio sources: the symmetric double lobes, an indication of a core, an appearance of jets feeding the lobes and the hotspots. Some researchers have reported more detailed kinematical features, such as the proper motion of the hotspots in the lobes.

Symmetric radio sources (galactic or extragalactic) and GRBs may appear to be completely distinct phenomena. However, their cores show a similar time evolution in the peak energy, but with vastly different time constants. The spectra of GRBs rapidly evolve from \gamma region to an optical or even RF afterglow, similar to the spectral evolution of the hotspots of a radio source as they move from the core to the lobes. Other similarities have begun to attract attention in the recent years.

This article explores the similarities between a hypothetical “luminal” boom and these two astrophysical phenomena, although such a luminal boom is forbidden by the Lorentz invariance. Treating GRB as a manifestation of a hypothetical luminal boom results in a model that unifies these two phenomena and makes detailed predictions of their kinematics.

CygA
Figure 3:.The radio jet and lobes in the hyperluminous radio galaxy Cygnus A. The hotspots in the two lobes, the core region and the jets are clearly visible. (Reproduced from an image courtesy of NRAO/AUI.)

Conclusions

In this article, we looked at the spatio-temporal evolution of a supersonic object (both in its position and the sound frequency we hear). We showed that it closely resembles GRBs and DRAGNs if we were to extend the calculations to light, although a luminal boom would necessitate superluminal motion and is therefore forbidden.

This difficulty notwithstanding, we presented a unified model for Gamma Ray Bursts and jet like radio sources based on bulk superluminal motion. We showed that a single superluminal object flying across our field of vision would appear to us as the symmetric separation of two objects from a fixed core. Using this fact as the model for symmetric jets and GRBs, we explained their kinematic features quantitatively. In particular, we showed that the angle of separation of the hotspots was parabolic in time, and the redshifts of the two hotspots were almost identical to each other. Even the fact that the spectra of the hotspots are in the radio frequency region is explained by assuming hyperluminal motion and the consequent redshift of the black body radiation of a typical star. The time evolution of the black body radiation of a superluminal object is completely consistent with the softening of the spectra observed in GRBs and radio sources. In addition, our model explains why there is significant blue shift at the core regions of radio sources, why radio sources seem to be associated with optical galaxies and why GRBs appear at random points with no advance indication of their impending appearance.

Although it does not address the energetics issues (the origin of superluminality), our model presents an intriguing option based on how we would perceive hypothetical superluminal motion. We presented a set of predictions and compared them to existing data from DRAGNs and GRBs. The features such as the blueness of the core, symmetry of the lobes, the transient \gamma and X-Ray bursts, the measured evolution of the spectra along the jet all find natural and simple explanations in this model as perceptual effects. Encouraged by this initial success, we may accept our model based on luminal boom as a working model for these astrophysical phenomena.

It has to be emphasized that perceptual effects can masquerade as apparent violations of traditional physics. An example of such an effect is the apparent superluminal motion, which was explained and anticipated within the context of the special theory of relativity even before it was actually observed. Although the observation of superluminal motion was the starting point behind the work presented in this article, it is by no means an indication of the validity of our model. The similarity between a sonic boom and a hypothetical luminal boom in spatio-temporal and spectral evolution is presented here as a curious, albeit probably unsound, foundation for our model.

One can, however, argue that the special theory of relativity (SR) does not deal with superluminality and, therefore, superluminal motion and luminal booms are not inconsistent with SR. As evidenced by the opening statements of Einstein’s original paper, the primary motivation for SR is a covariant formulation of Maxwell’s equations, which requires a coordinate transformation derived based partly on light travel time (LTT) effects, and partly on the assumption that light travels at the same speed with respect to all inertial frames. Despite this dependence on LTT, the LTT effects are currently assumed to apply on a space-time that obeys SR. SR is a redefinition of space and time (or, more generally, reality) in order to accommodate its two basic postulates. It may be that there is a deeper structure to space-time, of which SR is only our perception, filtered through the LTT effects. By treating them as an optical illusion to be applied on a space-time that obeys SR, we may be double counting them. We may avoid the double counting by disentangling the covariance of Maxwell’s equations from the coordinate transformations part of SR. Treating the LTT effects separately (without attributing their consequences to the basic nature of space and time), we can accommodate superluminality and obtain elegant explanations of the astrophysical phenomena described in this article. Our unified explanation for GRBs and symmetric radio sources, therefore, has implications as far reaching as our basic understanding of the nature of space and time.


Photo by NASA Goddard Photo and Video

Physics

The Big Bang Theory

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I am a physicist, but I don’t quite understand the Big Bang theory. Let me tell you why.

The Big Bang theory says that the whole universe started from a “singularity” — a single point. The first question then is, a single point where? It is not a single point “in space” because the whole space was a single point. The Discovery channel would put it fancifully that “the whole universe could fit in the palm of your hand,” which of course it could not. Your palm would also be a little palm inside the little universe in that single point.

The second question is, if the whole universe was inside one point, what about all the points around it? Physicists would advise you not to ask such stupid questions. Don’t feel bad, they have asked me to shut up as well. Some of them may kindly explain that the other points may be parallel universes. Others may say that there are no “other” points. They may point out (as Steven Weinberg does in The Dreams of a Final Theory) that there is nothing more to the north of the North Pole. I consider this analogy more of a semantic argument than a scientific one, but let’s buy this argument for now.

The next hurdle is that the singularity is in space-time — not merely in space. So before the Big Bang, there was no time. Sorry, there was no “before!” This is a concept that my five year old son has problems with. Again, the Big Bang cosmologist will point out that things do not necessarily have to continue backwards — you may think that whatever temperature something is at, you can always make it a little colder. But you cannot make it colder than absolute zero. True, true; but is temperature the same as time? Temperature is a measure of hotness, which is an aggregate of molecular speeds. And speed is distance traveled in unit time. Time again. Hmmm….

I am sure it is my lack of imagination or incompleteness of training that is preventing me from understanding and accepting this Big Bang concept. But even after buying the space-time singularity concept, other difficulties persist.

Firstly, if the whole universe is at one point at one time, one would naively expect it to make a super-massive black hole from which not even light can escape. Clearly then, the whole universe couldn’t have banged out of that point. But I’m sure there is a perfectly logical explanation why it can, just that I don’t know it yet. May be some of my readers will point it out to me?

Second, what’s with dark matter and dark energy? The Big Bang cosmology has to stretch itself a bit with the notion of dark energy to account for the large scale dynamics of the observed universe. Our universe is expanding (or so it appears) at an accelerating rate, which can only be accounted for by assuming that there is an invisible energy pushing the galaxies apart. Within the galaxies themselves, stars are moving around as though there is more mass than we can see. This is the so called dark matter. Although “dark” signifies invisible, to me, it sounds as though we are in the dark about what these beasts are!

The third trouble I have is the fact that the Big Bang cosmology violates special relativity (SR). This little concern of mine has been answered in many different ways:

  • One answer is that general relativity “trumps” SR — if there are conflicting predictions or directives from these two theories, I was advised to always trust GR.
  • Besides, SR applies only to local motion, like spaceships whizzing past each other. Non-local events do not have to obey SR. This makes me wonder how events know whether they are local or not. Well, that was bit tongue in cheek. I can kind of buy this argument (based on curvature of space-time perhaps becoming significant at large distances), although the non-scientific nature of local-ness makes me uneasy. (During the inflationary phase in the Big Bang theory, were things local or non-local?)
  • Third answer: In the case of the Big Bang, the space itself is expanding, hence no violation of SR. SR applies to motion through space. (Wonder if I could’ve used that line when I got pulled over on I-81. “Officer, I wasn’t speeding. Just that the space in between was expanding a little too fast!”)

Speaking of space expanding, it is supposed to be expanding only in between galaxies, not within them, apparently. I’m sure there is a perfectly logical explanation why, probably related to the proximity of masses or whatnot, but I’m not well-versed enough to understand it. In physics, disagreement and skepticism are always due to ignorance. But it is true that I have no idea what they mean when they say the space itself is expanding. If I stood in a region where the space was expanding, would I become bigger and would galaxies look smaller to me?

Note that it is necessary for space to expand only between galaxies. If it expanded everywhere, from subatomic to galactic scales, it would look as though nothing changed. Hardly satisfying because the distant galaxies do look as though they are flying off at great speeds.

I guess the real question is, what exactly is the difference between space expanding between two galaxies and the two galaxies merely moving away from each other?

One concept that I find bizarre is that singularity doesn’t necessarily mean single point in space. It was pointed out to me that the Big Bang could have been a spread out affair — thinking otherwise was merely my misconception, because I got confused by the similarity between the words “singularity” and single.

People present the Big Bang theory in physics pretty much like Evolution in biology, implying the same level of infallibility. But I feel that it is disingenuous to do that. To me, it looks as though the theory is so full of patchwork, such a mathematical collage to cook up something that is consistent with GR that it is hard to imagine that it corresponds to anything real (ignoring, for the moment, my favorite question — what is real?) But popular writers have embraced it. For instance, Ray Kurzweil and Richard Dawkins put it as a matter of fact in their books, lending it a credence that it perhaps doesn’t merit.

Articles and Essays, Creative, Philosophy, Physics

Constraints of Perception and Cognition in Relativistic Physics

This post is an abridged online version of my article that appears in Galilean Electrodynamics in November, 2008. [Ref: Galilean Electrodynamics, Vol. 19, No. 6, Nov/Dec 2008, pp: 103–117] ()

Cognitive neuroscience treats space and time as our brain’s representation of our sensory inputs. In this view, our perceptual reality is only a distant and convenient mapping of the physical processes causing the sensory inputs. Sound is a mapping of auditory inputs, and space is a representation of visual inputs. Any limitation in the chain of sensing has a specific manifestation on the cognitive representation that is our reality. One physical limitation of our visual sensing is the finite speed of light, which manifests itself as a basic property of our space-time. In this article, we look at the consequences of the limited speed of our perception, namely the speed of light, and show that they are remarkably similar to the coordinate transformation in special relativity. From this observation, and inspired by the notion that space is merely a cognitive model created out of light signal inputs, we examine the implications of treating special relativity theory as a formalism for describing the perceptual effects due to the finite speed of light. Using this framework, we show that we can unify and explain a wide array of seemingly unrelated astrophysical and cosmological phenomena. Once we identify the manifestations of the limitations in our perception and cognitive representation, we can understand the consequent constraints on our space and time, leading to a new understanding of astrophysics and cosmology.

Key words: cognitive neuroscience; reality; special relativity; light travel time effect; gamma rays bursts; cosmic microwave background radiation.

1. Introduction

Our reality is a mental picture that our brain creates, starting from our sensory inputs [1]. Although this cognitive map is often assumed to be a faithful image of the physical causes behind the sensing process, the causes themselves are entirely different from the perceptual experience of sensing. The difference between the cognitive representation and their physical causes is not immediately obvious when we consider our primary sense of sight. But, we can appreciate the difference by looking at the olfactory and auditory senses because we can use our cognitive model based on sight in order to understand the workings of the ‘lesser’ senses. Odors, which may appear to be a property of the air we breathe, are in fact our brain’s representation of the chemical signatures that our noses sense. Similarly, sound is not an intrinsic property of a vibrating body, but our brain’s mechanism to represent the pressure waves in the air that our ears sense. Table I shows the chain from the physical causes of the sensory input to the final reality as the brain creates it. Although the physical causes can be identified for the olfactory and auditory chains, they are not easily discerned for visual process. Since sight is the most powerful sense we possess, we are obliged to accept our brain’s representation of visual inputs as the fundamental reality.

While our visual reality provides an excellent framework for physical sciences, it is important to realize that the reality itself is a model with potential physical or physiological limitations and distortions. The tight integration between the physiology of perception and its representation in the brain was proven recently in a clever experiment using the tactile funneling illusion [2]. This illusion results in a single tactile sensation at the focal point at the center of a stimulus pattern even though no stimulation is applied at that site. In the experiment, the brain activation region corresponded to the focal point where the sensation was perceived, rather than the points where the stimuli were applied, proving that the brain registered perceptions, not the physical causes of the perceived reality. In other words, for the brain, there is no difference between applying the pattern of the stimuli and applying only one stimulus at the center of the pattern. The brain maps the sensory inputs to regions that correspond to their perception, rather than the regions that physiologically correspond to the sensory stimuli.

Sense modality: Physical cause: Sensed signal: Brain’s model:
Olfactory Chemicals Chemical reactions Smells
Auditory Vibrations Pressure waves Sounds
Visual Unknown Light Space, time
reality

Table I: The brain’s representation of different sensory inputs. Odors are a representation of chemical compositions and concentration our nose senses. Sounds are a mapping of the air pressure waves produced by a vibrating object. In sight, we do not know the physical reality, our representation is space, and possibly time.

The neurological localization of different aspects of reality has been established in neuroscience by lesion studies. The perception of motion (and the consequent basis of our sense of time), for instance, is so localized that a tiny lesion can erase it completely. Cases of patients with such specific loss of a part of reality [1] illustrate the fact that our experience of reality, every aspect of it, is indeed a creation of the brain. Space and time are aspects of the cognitive representation in our brain.

Space is a perceptual experience much like sound. Comparisons between the auditory and visual modes of sensing can be useful in understanding the limitations of their representations in the brain. One limitation is the input ranges of the sensory organs. Ears are sensitive in the frequency range 20Hz-20kHz, and eyes are limited to the visible spectrum. Another limitation, which may exist in specific individuals, is an inadequate representation of the inputs. Such a limitation can lead to tone-deafness and color-blindness, for instance. The speed of the sense modality also introduces an effect, such as the time lag between seeing an event and hearing the corresponding sound. For visual perception, a consequence of the finite speed of light is called a Light Travel Time (LTT) effect. LLT offers one possible interpretation for the observed superluminal motion in certain celestial objects [3,4]: when an object approaches the observer at a shallow angle, it may appear to move much faster than reality [5] due to LTT.

Other consequences of the LTT effects in our perception are remarkably similar to the coordinate transformation of the special relativity theory (SRT). These consequences include an apparent contraction of a receding object along its direction of motion and a time dilation effect. Furthermore, a receding object can never appear to be going faster than the speed of light, even if its real speed is superluminal. While SRT does not explicitly forbid it, superluminality is understood to lead to time travel and the consequent violations of causality. An apparent violation of causality is one of the consequences of LTT, when the superluminal object is approaching the observer. All these LTT effects are remarkably similar to effects predicted by SRT, and are currently taken as ‘confirmation’ that space-time obeys SRT. But instead, space-time may have a deeper structure that, when filtered through LTT effects, results in our perception that space-time obeys SRT.

Once we accept the neuroscience view of reality as a representation of our sensory inputs, we can understand why the speed of light figures so prominently in our physical theories. The theories of physics are a description of reality. Reality is created out of the readings from our senses, especially our eyes. They work at the speed of light. Thus the sanctity accorded to the speed of light is a feature only of our reality, not the absolute, ultimate reality that our senses are striving to perceive. When it comes to physics that describes phenomena well beyond our sensory ranges, we really have to take into account the role that our perception and cognition play in seeing them. The Universe as we see it is only a cognitive model created out of the photons falling on our retina or on the photo-sensors of the Hubble telescope. Because of the finite speed of the information carrier (namely photons), our perception is distorted in such a way as to give us the impression that space and time obey SRT. They do, but space and time are not the absolute reality. “Space and time are modes by which we think and not conditions in which we live,” as Einstein himself put it. Treating our perceived reality as our brain’s representation of our visual inputs (filtered through the LTT effect), we will see that all the strange effects of the coordinate transformation in SRT can be understood as the manifestations of the finite speed of our senses in our space and time.

Furthermore, we will show that this line of thinking leads to natural explanations for two classes of astrophysical phenomena:

Gamma Ray Bursts, which are very brief, but intense flashes of \gamma rays, currently believed to emanate from cataclysmic stellar collapses, and Radio Sources, which are typically symmetric and seem associated with galactic cores, currently considered manifestations of space-time singularities or neutron stars. These two astrophysical phenomena appear distinct and unrelated, but they can be unified and explained using LTT effects. This article presents such a unified quantitative model. It will also show that the cognitive limitations to reality due to LTT effects can provide qualitative explanations for such cosmological features as the apparent expansion of the Universe and the Cosmic Microwave Background Radiation (CMBR). Both these phenomena can be understood as related to our perception of superluminal objects. It is the unification of these seemingly distinct phenomena at vastly different length and time scales, along with its conceptual simplicity, that we hold as the indicators of validity of this framework.

2. Similarities between LTT Effects & SRT

The coordinate transformation derived in Einstein’s original paper [6] is, in part, a manifestation of the LTT effects and the consequence of imposing the constancy of light speed in all inertial frames. This is most obvious in the first thought experiment, where observers moving with a rod find their clocks not synchronized due to the difference in LTT’s along the length of the rod. However, in the current interpretation of SRT, the coordinate transformation is considered a basic property of space and time. One difficulty that arises from this formulation is that the definition of the relative velocity between the two inertial frames becomes ambiguous. If it is the velocity of the moving frame as measured by the observer, then the observed superluminal motion in radio jets starting from the core region becomes a violation of SRT. If it is a velocity that we have to deduce by considering LTT effects, then we have to employ the extra ad-hoc assumption that superluminality is forbidden. These difficulties suggest that it may be better to disentangle the LTT effects from the rest of SRT. Although not attempted in this paper, the primary motivation for SRT, namely the covariance of Maxwell’s equations, may be accomplished even without attributing LTT effects to the properties of space and time.

In this Section, we will consider space and time as a part of the cognitive model created by the brain, and illustrate that SRT applies to the cognitive model. The absolute reality (of which the SRT-like space-time is our perception) does not have to obey the restrictions of SRT. In particular, objects are not restricted to subluminal speeds, even though they may appear to us as if they are restricted to subluminal speeds in our perception of space and time. If we disentangle LTT effects from the rest of SRT, we can understand a wide array of phenomena, as shown in this article.

SRT seeks a linear coordinate transformation between coordinate systems in motion with respect to each other. We can trace the origin of linearity to a hidden assumption on the nature of space and time built into SRT, as stated by Einstein [6]: “In the first place it is clear that the equations must be linear on account of the properties of homogeneity which we attribute to space and time.” Because of this assumption of linearity, the original derivation of the transformation equations ignores the asymmetry between approaching and receding objects and concentrates on receding objects. Both approaching and receding objects can be described by two coordinate systems that are always receding from each other. For instance, if a system K is moving with respect to another system k along the positive X axis of k, then an object at rest in K at a positive x is approaching an observer at the origin of k. Unlike SRT, considerations based on LTT effects result in intrinsically different set of transformation laws for objects approaching an observer and those receding from him. More generally, the transformation depends on the angle between the velocity of the object and the observer’s line of sight. Since the transformation equations based on LTT effects treat approaching and receding objects asymmetrically, they provide a natural solution to the twin paradox, for instance.

2.1 First Order Perceptual Effects

For approaching and receding objects, the relativistic effects are second order in speed \beta, and speed typically appears as \sqrt{1-\beta^2}. The LTT effects, on the other hand, are first order in speed. The first order effects have been studied in the last fifty years in terms of the appearance of a relativistically moving extended body [7-15]. It has also been suggested that the relativistic Doppler effect can be considered the geometric mean [16] of more basic calculations. The current belief is that the first order effects are an optical illusion to be taken out of our perception of reality. Once these effects are taken out or ‘deconvolved’ from the observations, the ‘real’ space and time are assumed to obey SRT. Note that this assumption is impossible to verify because the deconvolution is an ill-posed problem – there are multiple solutions to the absolute reality that all result in the same perceptual picture. Not all the solutions obey SRT.

The notion that it is the absolute reality that obeys SRT ushers in a deeper philosophical problem. This notion is tantamount to insisting that space and time are in fact ‘intuitions’ beyond sensory perception rather than a cognitive picture created by our brain out of the sensory inputs it receives. A formal critique of the Kantian intuitions of space and time is beyond the scope of this article. Here, we take the position that it is our observed or perceived reality that obeys SRT and explore where it leads us. In other words, we assume that SRT is nothing but a formalization of the perceptual effects. These effects are not first order in speed when the object is not directly approaching (or receding from) the observer, as we will see later. We will show in this article that a treatment of SRT as a perceptual effect will give us natural solution for astrophysical phenomena like gamma ray bursts and symmetric radio jets.

2.2 Perception of Speed

We first look at how the perception of motion is modulated by LTT effects. As remarked earlier, the transformation equations of SRT treat only objects receding from the observer. For this reason, we first consider a receding object, flying away from the observer at a speed \beta of the object depends on the real speed b (as shown in Appendix A.1):


\beta_O ,=, \frac{\beta}{1,+,\beta}            (1)
\lim_{\beta\to\infty} \beta_O ,=, 1           (2)

Thus, due to LTT effects, an infinite real velocity gets mapped to an apparent velocity \beta_O=1. In other words, no object can appear to travel faster than the speed of light, entirely consistent with SRT.

Physically, this apparent speed limit amounts to a mapping of c to \infty. This mapping is most obvious in its consequences. For instance, it takes an infinite amount of energy to accelerate an object to an apparent speed \beta_O=1 because, in reality, we are accelerating it to an infinite speed. This infinite energy requirement can also be viewed as the relativistic mass changing with speed, reaching \infty at \beta_O=1. Einstein explained this mapping as: “For velocities greater than that of light our deliberations become meaningless; we shall, however, find in what follows, that the velocity of light in our theory plays the part, physically, of an infinitely great velocity.” Thus, for objects receding from the observer, the effects of LTT are almost identical to the consequences of SRT, in terms of the perception of speed.

2.3 Time Dilation
Time Dilation
Figure 1
Figure 1:. Comparison between light travel time (LTT) effects and the predictions of the special theory of relativity (SR). The X-axis is the apparent speed and the Y-axis shows the relative time dilation or length contraction.

LTT effects influence the way time at the moving object is perceived. Imagine an object receding from the observer at a constant rate. As it moves away, the successive photons emitted by the object take longer and longer to reach the observer because they are emitted at farther and farther away. This travel time delay gives the observer the illusion that time is flowing slower for the moving object. It can be easily shown (see Appendix A.2) that the time interval observed \Delta t_O is related to the real time interval \Delta t as:


\frac{\Delta t_O}{\Delta t} ,=, \frac{1}{1-\beta_O}          (3)

for an object receding from the observer (\theta=\pi). This observed time dilation is plotted in Fig. 1, where it is compared to the time dilation predicted in SR. Note that the time dilation due to LTT has a bigger magnitude than the one predicted in SR. However, the variation is similar, with both time dilations tending to \infty as the observed speed tends to c.

2.4 Length Contraction

The length of an object in motion also appears different due to LTT effects. It can be shown (see Appendix A.3) that observed length d_O as:


\frac{d_O}{d} ,=, {1-\beta_O}           (4)

for an object receding from the observer with an apparent speed of \beta_O. This equation also is plotted in Fig. 1. Note again that the LTT effects are stronger than the ones predicted in SRT.

Fig. 1 illustrates that both time dilation and Lorentz contraction can be thought of as LTT effects. While the actual magnitudes of LTT effects are larger than what SRT predicts, their qualitative dependence on speed is almost identical. This similarity is not surprising because the coordinate transformation in SRT is partly based on LTT effects. If LTT effects are to be applied, as an optical illusion, on top of the consequences of SRT as currently believed, then the total observed length contraction and time dilation will be significantly more than the SRT predictions.

2.5 Doppler Shift
The rest of the article (the sections up to Conclusions) has been abridged and can be read in the PDF version.
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5 Conclusions

In this article, we started with an insight from cognitive neuroscience about the nature of reality. Reality is a convenient representation that our brain creates out of our sensory inputs. This representation, though convenient, is an incredibly distant experiential mapping of the actual physical causes that make up the inputs to our senses. Furthermore, limitations in the chain of sensing and perception map to measurable and predictable manifestations to the reality we perceive. One such fundamental constraint to our perceived reality is the speed of light, and the corresponding manifestations, LTT effects. Because space and time are a part of a reality created out of light inputs to our eyes, some of their properties are manifestations of LTT effects, especially on our perception of motion. The absolute, physical reality generating the light inputs does not obey the properties we ascribe to our perceived space and time. We showed that LTT effects are qualitatively identical to those of SRT, noting that SRT only considers frames of reference receding from each other. This similarity is not surprising because the coordinate transformation in SRT is derived based partly on LTT effects, and partly on the assumption that light travels at the same speed with respect to all inertial frames. In treating it as a manifestation of LTT, we did not address the primary motivation of SRT, which is a covariant formulation of Maxwell’s equations, as evidenced by the opening statements of Einstein’s original paper [6]. It may be possible to disentangle the covariance of electrodynamics from the coordinate transformation, although it is not attempted in this article.

Unlike SRT, LTT effects are asymmetric. This asymmetry provides a resolution to the twin paradox and an interpretation of the assumed causality violations associated with superluminality. Furthermore, the perception of superluminality is modulated by LTT effects, and explains g ray bursts and symmetric jets. As we showed in the article, perception of superluminal motion also holds an explanation for cosmological phenomena like the expansion of the Universe and cosmic microwave background radiation. LTT effects should be considered as a fundamental constraint in our perception, and consequently in physics, rather than as a convenient explanation for isolated phenomena. Given that our perception is filtered through LTT effects, we have to deconvolute them from our perceived reality in order to understand the nature of the absolute, physical reality. This deconvolution, however, results in multiple solutions. Thus, the absolute, physical reality is beyond our grasp, and any assumed properties of the absolute reality can only be validated through how well the resultant perceived reality agrees with our observations. In this article, we assumed that the absolute reality obeys our intuitively obvious classical mechanics and asked the question how such a reality would be perceived when filtered through LTT effects. We demonstrated that this particular treatment could explain certain astrophysical and cosmological phenomena that we observe. The distinction between the different notions of velocity, including the proper velocity and the Einsteinian velocity, was the subject matter of a recent issue of this journal [33].

The coordinate transformation in SRT should be viewed as a redefinition of space and time (or, more generally, reality) in order to accommodate the distortions in our perception of motion due to LTT effects. The absolute reality behind our perception is not subject to restrictions of SRT. One may be tempted to argue that SRT applies to the ‘real’ space and time, not our perception. This line of argument begs the question, what is real? Reality is nothing but a cognitive model created in our brain starting from our sensory inputs, visual inputs being the most significant. Space itself is a part of this cognitive model. The properties of space are a mapping of the constraints of our perception. We have no access to a reality beyond our perception. The choice of accepting our perception as a true image of reality and redefining space and time as described in SRT indeed amounts to a philosophical choice. The alternative presented in the article is prompted by the view in modern neuroscience that reality is a cognitive model in the brain based on our sensory inputs. Adopting this alternative reduces us to guessing the nature of the absolute reality and comparing its predicted projection to our real perception. It may simplify and elucidate some theories in physics and explain some puzzling phenomena in our Universe. However, this option is yet another philosophical stance against the unknowable absolute reality.

References

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Pages: 1 2
Articles and Essays, Philosophy, Physics, Unpublished

The Unreal Universe — Seeing Light in Science and Spirituality

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. This delay is due to the time it takes for light from the distant stars and galaxies to reach us. We know of this delay.

The same delay in seeing has a lesser known manifestation in the way we perceive moving objects. It distorts our perception such that something coming towards us would look as though it is coming in faster. Strange as it may sound, this effect has been observed in astrophysical studies. Some of the heavenly bodies do look as though they are moving several times the speed of light, while their “real” speed is probably a lot lower.

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

Light in Physics

Seeing involves light, obviously. The finite speed of light influences and distorts the way we see things. This fact should hardly come as a surprise because we do know that things are not as we see them. The sun that we see is already eight minutes old by the time we see it. This delay is not a big deal; if we want to know what is going on at the sun now, all we have to do is to wait for eight minutes. We, nonetheless, have to “correct” for the distortions in our perception due to the finite speed of light before we can trust what we see.

What is surprising (and seldom highlighted) is that when it comes to sensing motion, 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.

Einstein chose the first route. In his groundbreaking paper over a hundred years ago, he introduced the special theory of relativity, in which he attributed the manifestations of the finite speed of light to the fundamental properties of space and time. One core idea in special relativity (SR) is that the notion of simultaneity needs to be redefined because it takes some time for light from an event at a distant place to reach us, and we become aware of the event. The concept of “Now” doesn’t make much sense, as we saw, when we speak of an event happening in the sun, for instance. Simultaneity is relative.

Einstein defined simultaneity using the instants in time we detect the event. Detection, as he defined it, involves a round-trip travel of light similar to Radar detection. We send out light, and look at the reflection. If the reflected light from two events reaches us at the same instant, they are simultaneous.
Another way of defining simultaneity is using sensing — we can call two events simultaneous if the light from them reaches us at the same instant. In other words, we can use the light generated by the objects under observation rather than sending light to them and looking at the reflection.

This difference may sound like a hair-splitting technicality, but it does make an enormous difference in the predictions we can make. Einstein’s choice results in a mathematical picture that has many desirable properties, thereby making further development elegant.

The other possibility has an advantage when it comes to describing objects in motion because it corresponds better with how we measure them. We don’t use Radar to see the stars in motion; we merely sense the light (or other radiation) coming from them. But this choice of using a sensory paradigm, rather than Radar-like detection, to describe the universe results in a slightly uglier mathematical picture.

The mathematical difference spawns different philosophical stances, which in turn percolate to the understanding of our physical picture of reality. As an illustration, let us look at an example from astrophysics. Suppose we observe (through a radio telescope, for instance) two objects in the sky, roughly of the same shape and properties. The only thing we know for sure is that the radio waves from two different points in the sky reach the radio telescope at the same instant in time. We can guess that the waves started their journey quite a while ago.

For symmetric objects, if we assume (as we routinely do) that the waves started the journey roughly at the same instant in time, we end up with a picture of two “real” symmetric lobes more or less the way see them.

But there is different possibility that the waves originated from the same object (which is in motion) at two different instants in time, reaching the telescope at the same instant. This possibility explains some spectral and temporal properties of such symmetric radio sources, which is what I mathematically described in a recent physics article. Now, which of these two pictures should we take as real? Two symmetric objects as we see them or one object moving in such a way as to give us that impression? Does it really matter which one is “real”? Does “real” mean anything in this context?

The philosophical stance in implied in special relativity answers this question unequivocally. There is an unambiguous physical reality from which we get the two symmetric radio sources, although it takes a bit of mathematical work to get to it. The mathematics rules out the possibility of a single object moving in such a fashion as to mimic two objects. Essentially, what we see is what is out there.

On the other hand, if we define simultaneity using concurrent arrival of light, we will be forced to admit the exact opposite. What we see is pretty far from what is out there. We will confess that we cannot unambiguously decouple the distortions due to the constraints in perception (the finite speed of light being the constraint of interest here) from what we see. There are multiple physical realities that can result in the same perceptual picture. The only philosophical stance that makes sense is the one that disconnects the sensed reality and the causes behind what is being sensed.

This disconnect is not uncommon in 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.

The ramifications of the two different philosophical stances described above are tremendous. Since modern physics seems to embrace 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.”

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 readily understand it and disassociate 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.

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.”

The 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, as shown in the figure below.
Commonsense view of reality
In this picture, the black arrow represents the process of creating knowledge, which includes perception, cognitive activities, and the exercise of pure reason. This is the picture that physics has come to accept.
Alternate view of reality
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 formidable machine of pure reason to their logically inevitable conclusions.

But there is another, alternative 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, as illustrated below.

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 the illustration, the first arrow represents the process of sensing, and the second arrow represents the cognitive and logical reasoning steps. In order to apply this view of reality and knowledge, we have to guess the nature of the absolute reality, unknowable as it is. One possible candidate for the absolute reality is Newtonian mechanics, which gives a reasonable prediction for our perceived reality.

To summarize, when we try to handle the distortions due to perception, we have two options, or two possible philosophical stances. One is to accept the distortions as part of our space and time, as SR does. The other option is to assume that there is a “higher” reality distinct from our sensed reality, whose properties we can only conjecture. In other words, one option is to live with the distortion, while the other is to propose educated guesses for the higher reality. Neither of these options is particularly attractive. But the guessing path is similar to the view accepted in phenomenalism. It also leads naturally to how reality is viewed in cognitive neuroscience, which studies the biological mechanisms behind cognition.

In my view, the two options are not inherently distinct. The philosophical stance of SR can be thought of as coming from a deep understanding that space is merely a phenomenal construct. If the sense modality introduces distortions in the phenomenal picture, we may argue that one sensible way of handling it is to redefine the properties of the phenomenal reality.

Role of Light in Our Reality

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. 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 breakthroughs in human thought.

This philosophical grand-standing may sound presumptuous and the veiled self-admonition of physicists understandably unwelcome; but I am holding a trump card. Based on this philosophical stance, I have come up with a radically new model for two astrophysical phenomena, and published it in an article titled, “Are Radio Sources and Gamma Ray Bursts Luminal Booms?” in the well-known International Journal of Modern Physics D in June 2007. This article, which soon became one of the top accessed articles of the journal by Jan 2008, is a direct application of the view that the finite speed of light distorts the way we perceive motion. Because of these distortions, the way we see things is a far cry from the way they are.

We may be tempted to think that we can escape such perceptual constraints by using technological extensions to our senses such as radio telescopes, electron microscopes or spectroscopic speed measurements. After all, these instruments do not have “perception” per se and should be immune to the human weaknesses we suffer from. But these soulless instruments also measure our universe using information carriers limited to the speed of light. We, therefore, cannot escape the basic constraints of our perception even when we use modern instruments. In other words, the Hubble telescope may see a billion light years farther than our naked eyes, but what it sees is still a billion years older than what our eyes see.

Our reality, whether technologically enhanced or built upon direct sensory inputs, is the end result of our perceptual process. To the extent that our long range perception is based on light (and is therefore limited to its speed), we get only a distorted picture of the universe.

Light in Philosophy and Spirituality

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 thought experiment.

Once we appreciate the special place accorded to light in modern science, we have to ask ourselves how different our universe would have been in the absence of light. Of course, light is only a label we attach to a sensory experience. Therefore, to be more accurate, we have to ask a different question: if we did not have any senses that responded to what we call light, would that affect the form of the universe?

The immediate answer from any normal (that is, non-philosophical) person is that it is obvious. If everybody is blind, everybody is blind. But the existence of the universe is independent of whether we can see it or not. Is it though? What does it mean to say the universe exists if we cannot sense it? Ah… the age-old conundrum of the falling tree in a deserted forest. Remember, the universe is a cognitive construct or a mental representation of the light input to our eyes. It is not “out there,” but in the neurons of our brain, as everything else is. In the absence of light in our eyes, there is no input to be represented, ergo no universe.

If we had sensed the universe using modalities that operated at other speeds (echolocation, for instance), it is those speeds that would have figured in the fundamental properties of space and time. This is the inescapable conclusion from phenomenalism.

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 foreign 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 or 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 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 endeavour may be the catalyst for the next breakthrough in our collective wisdom that we have been waiting for.

Philosophy, Physics

Uncertainly Principle

1 Comment

The uncertainty principle is the second thing in physics that has captured the public imagination. (The first one is E=mc^2.) It says something seemingly straightforward — you can measure two complimentary properties of a system only to a certain precision. For instance, if you try to figure out where an electron is (measure its position, that is) more and more precisely, its speed becomes progressively more uncertain (or, the momentum measurement becomes imprecise).

Where does this principle come from? Before we can ask that question, we have to examine what the principle really says. Here are a few possible interpretations:

  1. Position and momentum of a particle are intrinsically interconnected. As we measure the momentum more accurately, the particle kind of “spreads out,” as George Gamow’s character, Mr. Tompkins, puts it. In other words, it is just one of those things; the way the world works.
  2. When we measure the position, we disturb the momentum. Our measurement probes are “too fat,” as it were. As we increase the position accuracy (by shining light of shorter wavelengths, for instance), we disturb the momentum more and more (because shorter wavelength light has higher energy/momentum).
  3. Closely related to this interpretation is a view that the uncertainty principle is a perceptual limit.
  4. We can also think of the uncertainly principle as a cognitive limit if we consider that a future theory might surpass such limits.

All right, the last two interpretations are my own, so we won’t discuss them in detail here.

The first view is currently popular and is related to the so-called Copenhagen interpretation of quantum mechanics. It is kind of like the closed statements of Hinduism — “Such is the nature of the Absolute,” for instance. Accurate, may be. But of little practical use. Let’s ignore it for it is not too open to discussions.

The second interpretation is generally understood as an experimental difficulty. But if the notion of the experimental setup is expanded to include the inevitable human observer, we arrive at the third view of perceptual limitation. In this view, it is actually possible to “derive” the uncertainty principle.

Let’s assume that we are using a beam of light of wavelength \lambda to observe the particle. The precision in the position we can hope to achieve is of the order of \lambda. In other words, \Delta x \approx \lambda. In quantum mechanics, the momentum of each photon in the light beam is inversely proportional to the wavelength. At least one photon is reflected by the particle so that we can see it. So, by the classical conservation law, the momentum of the particle has to change by at least \Delta p \approx constant\lambda from what it was before the measurement. Thus, through perceptual arguments, we get something similar to the Heisenberg uncertainty principle \Delta x \Delta p = constant.

We can make this argument more rigorous, and get an estimate of the value of the constant. The resolution of a microscope is given by the empirical formula 0.61\lambda/NA, where NA is the numerical aperture, which has a maximum value of one. Thus, the best spatial resolution is 0.61\lambda. Each photon in the light beam has a momentum 2\pi\hbar/\lambda, which is the uncertainty in the particle momentum. So we get \Delta x \Delta p = (0.61\lambda)(2\pi\hbar) \approx 4\hbar, approximately an order of magnitude bigger than the quantum mechanical limit. Through more rigorous statistical arguments, related to the spatial resolution and the expected momentum transferred, it may possible to derive the Heisenberg uncertainty principle through this line of reasoning.

If we consider the philosophical view that our reality is a cognitive model of our perceptual stimuli (which is the only view that makes sense to me), my fourth interpretation of the uncertainty principle being a cognitive limitation also holds a bit of water.

Reference

The latter part of this post is an excerpt from my book, The Unreal Universe.

Humor, Physics, Quotes

Sex and Physics — According to Feynman

Physics goes through an age of complacency once in a while. Complacency originates from a sense of completeness, a feeling that we have discovered everything there is to know, the path is clear and the methods well-understood.

Historically, these bouts of complacency are followed by rapid developments that revolutionize the way physics is done, showing us how wrong we have been. This humbling lesson of history is probably what prompted Feynman to say:

Such an age of complacency existed at the turn of the 19th century. Famous personas like Kelvin remarked that all that was left to do was to make more precise measurements. Michelson, who played a crucial role in the revolution to follow, was advised not to enter a “dead” field like physics.

Who would have thought that in less than a decade into the 20th century, we would complete change the way we think of space and time? Who in their right mind would say now that we will again change our notions of space and time? I do. Then again, nobody has ever accused me of a right mind!

Another revolution took place during the course of the last century — Quantum Mechanics, which did away with our notion of determinism and dealt a serious blow to the system-observer paradigm of physics. Similar revolutions will happen again. Let’s not hold on to our concepts as immutable; they are not. Let’s not think of our old masters as infallible, for they are not. As Feynman himself would point out, physics alone holds more examples of the fallibility of its old masters. And I feel that a complete revolution in thought is overdue now.

You might be wondering what all this has to do with sex. Well, I just thought sex would sell better. I was right, wasn’t I? I mean, you are still here!

Feynman also said,

Photo by “Caveman Chuck” Coker cc