Category Archives: Topical

Includes posts on physics, philosophy, sciences, quantitative finance, economics, environment etc.

Why the Speed of Light?

November 10, 2008 manoj

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?

November 9, 2008 manoj 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: 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

November 8, 2008 manoj

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.

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.

Environment, Quantitative Finance

An Economics Question

November 7, 2008 manoj 1 Comment

To all the MBA and Economics types out there, I have one simple question. For some of us to be wealthy, is it necessary to keep some others poor?

I asked an economists (or rather, an economics major) this question. I don’t quite remember her answer. It was a long time ago, and it was a party. May be I was drunk. I do remember her saying something about an ice cream factory in an isolated island. I guess the answer was that all of us could get richer at the same time. But I wonder now…

Inequality has become a feature of modern economy. May be it was a feature of ancient economies as well, and we probably never had it any better. But modern globalization has made each of us much more complicit in the inequality. Every dollar I put in my savings or retirement account ends up in some huge financial transaction somewhere, at times even adding to the food scarcity. Every time I pump gas or turn on a light, I add a bit to the cruel inequality we see around us.

Somehow, big corporations are emerging as the villains these days. This is strange because all little cogs in the corporate mega machine from stakeholders to customers (you and me) seem blameless decent folks. Perhaps the soulless, faceless entities that corporations are have taken a life of their own and started demanding their pound of flesh in terms of the grim inequalities that they seem to thrive on and we are forced to live with.

At least these were my thoughts when I was watching heartrending scenes of tiny emaciated Congolese children braving batons and stone walls for a paltry helping of high energy biscuits. Sitting in my air-conditioned room, voicing my righteous rage over their tragic plight, I wonder… Am I innocent of their misfortunes? Are you?

Articles and Essays, Physics, Science

Are Radio Sources and Gamma Ray Bursts Luminal Booms?

November 7, 2008 manoj 4 Comments

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.

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).

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.

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

October 21, 2008 manoj 2 Comments

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.

Books, Philosophy

Siddhartha by Hermann Hesse

October 18, 2008 manoj 3 Comments

I don’t get symbolism. Rather, I do get it, but I’m always skeptical that I may be getting something the author never intended. I think and analyze too much instead of just lightening up and enjoying what’s right in front of me. When it comes to reading, I’m a bit like those tourists (Japanese ones, if I may allow myself to stereotype) who keep clicking away at their digital cameras often missing the beauty and serenity of whatever it is that they are recording for posterity.

But, unlike the tourist, I can read the book again and again. Although I click as much the second time around and ponder as hard, some things do get through.

When I read Siddhartha, I asked myself if the names like Kamala and Kamaswami were random choices or signified something. After all, the first part “Kama” means something akin to worldliness or desire (greed or lust really, but not with so much negative connotation) in Sanskrit. Are Vasudeva and Givinda really gods as the name suggests?

But, I’m getting ahead of myself. Siddhartha is the life-story of a contemporary of Buddha — about 2500 years ago in India. Even as a young child, Siddhartha has urges to pursue a path that would eventually take him to salvation. As a Brahmin, he had already mastered the prayers and rituals. Leaving this path of piety (Bhaktiyoga), he joins a bunch of ascetics who see the way to salvation in austerity and penances (probably Hatayoga and Rajayoga). But Siddhartha soon tires of this path. He learns almost everything the ascetics had to teach him and realizes that even the oldest and wisest of them is no closer to salvation than he himself is. He then meets with the Buddha, but doesn’t think that he could “learn” the wisdom of the illustrious one. His path then undergoes a metamorphosis and takes a worldly turn (which is perhaps a rendition of Grahasthashrama or Karmayoga). He seeks to experience life through Kamala, the beautiful courtesan, and Kamaswamy the merchant. When at last he is fully immersed in the toxic excesses of the world, his drowning spirit calls out for liberation from it. He finally finds enlightenment and wisdom from the river that he had to cross back and forth in his journeys between the worlds of riches and wisdom.

For one who seeks symbolism, Siddhartha provides it aplenty.

Why is there a Vaishnava temple when Siddhartha decides to forgo the spiritual path for a world one? Is it a coincidence or is it an indication of the philosophical change from an Advaita line to a patently Dwaita line?
Is the name Siddhartha (same as that of the Buddha) a coincidence?
Does the bird in the cage represent a soul imprisoned in Samsara? If so, is its death a sad ending or a happy liberation?
The River of life that has to be crossed — is it Samsara itself? If so, is the ferryman a god who will help you cross it and reach the ultimate salvation? Why is it that Siddhartha has to cross it to reach the world of Kamala and Kamaswamy, and cross it back to his eventual enlightenment? Kamala also crosses the river to his side before passing on.
The affection for and the disillusionment in the little Siddhartha is the last chain of bondage (Mohamaya) that follows Siddhartha across the river. It is only after breaking that chain that Siddhartha is finally able to experience Nirvana — enlightenment and liberation. Is there a small moral hiding there?

One thing I noticed while reading many of these great works is that I can readily identify myself with the protagonist. I fancy that I have the simple greatness of Larry Darrell, and fear that I secretly possess the abominable baseness of Charles Strickland. I feel the indignant torture of Philip Carey or Jay Gatsby. And, sure, I experience the divine urges of Siddhartha. No matter how much of a stretch each of these comparisons may be. Admittedly, this self-identification may have its roots more in my vanity than any verisimilitude. Or is it the genius of these great writers who create characters so vivid and real that they talk directly to the naked primordial soul within us, stripped of our many layers of ego? In them, we see the distorted visions of our troubled souls, and in their words, we hear the echoes of our own unspoken impulses. Perhaps we are all the same deep within, part of the same shared consciousness.

One thing I re-learned from this book is that you cannot learn wisdom from someone else. (How is that for an oxymoron?) You can learn knowledge, information, data — yes. But wisdom — no. Wisdom is the assimilation of knowledge; it is the end product of your mind and soul working on whatever you find around you, be it the sensory data, cognitive constructs, knowledge and commonsense handed down from previous generations, or the concepts you create for yourself. It is so much a part of you that it is you yourself, which is why the word Buddha means Wisdom. The person Buddha and his wisdom are not two. How can you then communicate your wisdom? No wonder Siddhartha did not seek it from the Buddha.

Wisdom, according to Hermann Hesse, can come only from your own experiences, both sublime and prosaic.

Articles and Essays, Creative, Philosophy, Physics

Constraints of Perception and Cognition in Relativistic Physics

September 13, 2008 manoj

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:. 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.

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[24] M. Thulasidas, The perceptual effect (due to LTT) of a superluminal object appearing as two objects is best illustrated using an animation, which can be found at the author’s web site: http://www.TheUnrealUniverse.com/anim.html
[25] S. Jester, H.J. Roeser, K.Meisenheimer, and R.Perley, A&A 431, 477 (2005), astro-ph/0410520.
[26] T. Piran, International Journal of Modern Physics A 17, 2727 (2002).
[27] E.P. Mazets, S.V. Golenetskii, V.N. Ilyinskii, Y. A. Guryan, and R. L. Aptekar, Ap&SS 82, 261 (1982).
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[33] C. Whitney, Galilean Electrodynamics, Special Issues 3, Editor’s Essays, Winter 2005.

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Columns, Quantitative Finance, The Wilmott Magazine

Commodity Prices — Who’s Holding the Cards?

September 10, 2008 manoj 3 Comments

Economists have too many hands. On the one hand, they may declare something good. On the other hand, they may say, “Well, not so much.” Some of them may have even a third or fourth hand. My ex-boss, an economist himself, once remarked that he wished he could chop off some of these hands.

In the last couple of months, I plunged right into an ocean of economist hands as I sat down to do a minor research into this troubling phenomenon of skyrocketing food and commodity prices.

The first “hand” pointed out that the demand for food (and energy and commodities in general) has surged due to the increase in the population and changing consumption patterns in the emerging giants of Asia. The well-known demand and supply paradigm explains the price surge, it would seem. Is it as simple as that?

On the other hand, more and more food crops are being diverted into bio-fuel production. Is the bio-fuel demand the root cause? Bio-fuels are attractive because of the astronomical crude oil prices, which drive up the prices of everything. Is the recent OPEC windfall driving the price increases? What about the food subsidies in wealthy nations that skew the market in their favour?

Supply Side Difficulties

When explaining the food prices, one economic opinion puts the blame squarely on the supply side. It points an unwavering finger at the poor weather in food producing countries, and the panic measures imposed on the supply chain, such as export bans and smaller scale hoarding, that drive up the prices.

Looking at the bigger picture, let’s study oil as a proxy commodity and study its dynamics. Because of its effect on the rest of the economy, oil is indeed a good proxy.

In the case of oil, the dearth on the supply side is more structural, it is argued. The production capacity has stagnated over the last thirty years or so [1]. No infrastructural improvements have been made after the seventies. Indeed, new methodological improvements are expensive for all the easy methods have been fully exploited; all the low-hanging fruits have been picked, as it were.

The harder-to-reach “fruits” include deep sea explorations, crude oil from sand and, somewhat more tenuously, bio-fuels. The economic viability of these sources of oil depends on the oil price. Oil from sand, for instance, has an operating cost in the range of $20 to $25, as Shell’s CFO, Peter Voser is quoted as stating [2]. At $100 a barrel, oil from sand clearly becomes an economically viable source. Bio-fuels also are viable at high oil prices.

The huge investments involved in exploiting these new sources and their unpredictable economic viability exert strong upward pressure on oil prices, purely from the supply side, regardless of the demand situation. Once you invest a huge amount banking on a sustained high oil price, and then find that the oil market has softened below your viability level, you have to write off the investment, forcing losses and consequent price hikes.

With the high level of oil prices, investments are moving into infrastructure enhancements that will eventually ease the supply side crunch. But these fixes are slow in coming and are not going to ease the current dearth for about a decade. In other words, the high prices are here to stay. At least, so say the economists subscribing this supply side explanation of things.

Demand Spike

Although I personally find it hard to believe, people assure me that the exponential demand explosion in the emerging economies was completely unforeseen. My friend from a leading investment bank (who used to head their hybrids desk) told me that there was no way they could have anticipated this level of demand. I should probably shelve my scepticism and believe those in the know.

One thing I do know from personal experience is that the dynamics of a demand crash is different in emerging economies for a variety of reasons. First of all, identical movements in fuel prices have different impact in the overall spending pattern depending on the proportion they represent in the purchasing power of an average consumer. A 30% increase in the pump price, for instance, might mean a 5% reduction in the purchasing power to a US consumer, while it might mean 20% reduction for an Indian customer.

Besides, retail fuel prices in India are regulated and supported by government subsidies. Subsidies act as levies delaying the impact crude oil price movements. But when the crude oil prices rise beyond a certain point, the subsidies become untenable and the retail fuel prices surge upward, ushering in instant demand crash.

I came across another view of the skyrocketing oil prices in terms of the Middle-Eastern and American politics. The view was that the Saudi oil capacity is going to increase by about 10% soon and the prices will drop dramatically in the first quarter of 2009. It was argued that the drop will come as boost to the new American president, and the whole show is timed and stage-managed with a clear political motivation.

Speculation

All these different opinions make my head spin. In my untrained view, I always suspected that the speculation in commodities market might be the primary factor driving the prices up. I felt vindicated in my suspicions when I read a recent US senate testimony where a well-known hedge fund manager, Michael Masters [3], shed light on the financial labyrinth of futures transactions and regulatory loopholes through which enormous profits were generated in commodity speculation.

Since speculation is my preferred explanation for the energy and indeed other commodity price movements, I will go over some of the arguments in some detail. I hasten to state that the ideas express in this article are my own personal views (and perhaps those of Michael Masters [3] as well). They do not represent the market views of my employer, their affiliates, the Wilmott Magazine, or anybody else. Besides, some of these views are fairly half-baked and quite likely to be wrong, in which case I reserve the right to disown them and bequeath them to a friend of a friend. (Also, see the box on Biased Opinions).

Masters points out that there is no real supply crunch. Unlike the Arab Oil Embargo time in 1973, there are no long lines at the gas pump. Food supplies are also healthy. So some new mechanism must be at work that drives up the commodity demand despite the price level.

Masters blames the institutional investors (pension funds, sovereign wealth funds, university endowments etc.) for the unreasonable demand on commodity futures. Since futures prices are the benchmark for actual physical commodities, this hoarding of the futures contracts immediately reflects in the physical spot prices and in the real economy. And as the prices climb, the investors smell blood and invest more heavily, stoking a deadly vicious cycle. Masters points out that the speculative position in petroleum is roughly the same as the increase in demand from China, debunking the popular notion that it is the demand spike from the emerging giants of Asia that is driving the oil price. Similarly, bio-fuel is not the driver in food prices — the speculators have stockpiled enough corn futures to power the entire US ethanol industry for a year.

Although quants are not terribly interested in the transient economic drivers of market dynamics or trading psychology, here is an interesting thought from Mike Master’s testimony. A typical commodity trader initiating a new trade is pretty much insensitive to the price of the underlying. He has, say, a billion dollars to “put to work,” and doesn’t care if the position he ends up holding has five million or ten million barrels of oil. He never intends to take delivery. This price-insensitivity amplifies his impact on the market, and the investor appetite for commodities increases as the prices go up.

Most trading positions are directional views, not merely on the spot price, but on volatility. In a world of long and short Vega positions, we cannot expect to get a full picture of trading pressures exerted on oil prices by studying the single dimension of spot. Is there a correlation between the oil prices and its price volatility?

Figure 1. Scatter-plot of WTI Spot prices in Dollar and its volatility. Although the plot shows random clusters at low spot levels, at price > $75 (highlighted in the purple box), there appears to be a structure with significant correlation.

Figure 1 shows a scatter plot of the WTI spot price vs. the annualized volatility from publicly available WTI spot prices data [4]. Note than my definition of volatility may be different from yours [5]. At first glance, there appears to be little correlation between the spot price and volatility. Indeed the computed correlation over all the data is about -0.3.

However, the highlighted part of the figure tells a different story. As the spot price climbed over $75 per barrel, the volatility started showing a remarkable correlation (of 0.7) with it. Was the trading activity responsible for the concerted move on both prices and volatility? That is my theory, and Michael Masters may agree.

Hidden Currency Theory

Here is a dangerous thought — could it be that traders are pricing oil in a currency other than the once mighty dollar? This thought is dangerous because international armed conflicts may have arisen out of precisely such ideas. But an intrepid columnist is expected to have a high level of controversy affinity, so here goes…

We keep hearing that the oil price is down on the back of a strong dollar. There is little doubt that the oil prices are highly correlated to the strength of the dollar in 2007 and 2008, as shown in Table 1. Let’s look at the oil prices in Euro, the challenging heavy-weight currency.

Figure 2. Time evolution of the WTI spot price in Dollar and Euro. The Euro price looks more stable.

At first sight, Figure 2 does appear to show that the price is more stable when viewed in Euro, as expected. But does it mean that the traders are secretly pricing their positions in Euro, while quoting in Dollar? Or is it just the natural tandem movement of the Euro and WTI spots?

If the hidden currency theory is to hold water, I would expect stability in the price levels when priced in that currency. But, more directly, I would naively expect less volatility when the price is expressed in the hidden currency.

Figure 3. WTI Volatilities measured in Dollar and Euro. They are nearly identical.

Figure 4. Scatter-plot of WTI volatilities in Dollar and Euro. The excess population above the dividing line of equal volatilities implies that the WTI spot is more volatile when measured in Euro.

Figure 3 shows the WTI volatilities in Dollar and Euro. They look pretty much identical, which is why I replotted them as a scatter-plot of one against the other in Figure 4. If the Dollar volatility is higher, we will find more points below the red line, which we don’t. So it should mean that the hidden currency theory is probably wrong [6].

A good thing too, for nobody would be tempted to bomb me back to the stone ages now.

Human Costs

The real reasons behind the food and commodity price crisis are likely to be a combination of all these economic factors. But the crisis itself is a silent tsunami sweeping the world, as the UN World Food Program puts it.

Increase in the food prices, though unpleasant, is not such a big deal for a large number of us. With our first world income, most of us spend about 20% of our salary on food. If it becomes 30% as a result of a 50% increase in the prices, we certainly won’t like it, but we won’t suffer that much. We may have to cut down on the taxi rides, or fine-dining, but it is not the end of our world.

If we are in the top 10% income bracket (as the readers of this magazine tend to be), we may not even notice the increase. The impact of the high food prices on our lifestyle will be minimal — say, a business-class holiday instead of a first-class one.

It is a different story near the bottom. If we earn less than $1000 a month, and we are forced to spend $750 instead of $500 on food, it may mean a choice between a bus ride and legging it. At that level, the increase in food prices does hurt us, and our choices become grim.

But there are people in this world who face a much harsher reality as the prices shoot up with no end in sight. Their choices are often as terrible as Sophie’s Choice. Which child goes to sleep hungry tonight? Medicine for the sick one or food for the rest?

We are all powerless against the juggernaut of market forces creating the food crisis. Although we cannot realistically change the course of this silent tsunami, let’s at least try not to exacerbate the situation through waste. Buy only what you will use, and use only what you need to. Even if we cannot help those who will invariably go hungry, let’s not insult them by throwing away what they will die yearning for. Hunger is a terrible thing. If you don’t believe me, try fasting for a day. Well, try it even if you do — for it may help someone somewhere.

Conclusions

Commodity speculation by institutional investors is one of the driving factors of this silent tsunami of rising food prices. Their trading strategies have been compared to virtual hoarding in the futures market, driving up real prices of physical commodities and profiting from it.

I don’t mean to portray institutional investors and commodity traders as criminal masterminds hiding behind their multiple monitors and hatching plots to swindle the world. The ones I have discussed with do agree on the need to curtail the potential abuse of the system by closing the regulatory loopholes and setting new accountability frameworks. However, we are still on the rising edge of this influx of institutional funds into this lucrative asset class. Perhaps the time is not ripe enough for robust regulations yet. Let us make a bit more money first!

Reference and Endnotes

[1] Jeffrey Currie et al. “The Revenge of the Old ‘Political’ Economy” Commodities (Goldman Sachs Commodities Research), March 14, 2008.
[2] Business Times, “Shell counts rising cost of squeezing oil from sand in Canada,” March 18, 2008. http://business.timesonline.co.uk/tol/business/article3572646.ece
[3] Testimony of Michael W. Masters (Managing Member / Portfolio Manager, Masters Capital Management, LLC) before the Committee on Homeland Security and Governmental Affairs. May 20, 2008. http://hsgac.senate.gov/public/_files/052008Masters.pdf
[4] Cushing, OK WTI Spot Price FOB (Dollars per Barrel) Data source: Energy Information Administration. http://tonto.eia.doe.gov/dnav/pet/hist/rwtcd.htm
[5] I define the WTI volatility on a particular day as the standard deviation of the spot price returns over 31 days around that day, annualized by the appropriate factor. Using standard notations, the volatility on a day t is defined as:
$sigma (t) = sqrt {frac{1}{{31}}sumlimits_{t - 15}^{t + 15} {left( {ln left[ {frac{{S(t)}}{{S(t - 1)}}} right] - mu } right)^2 frac{{252}}{{31}}} }$
[6] Given that the correlation between EUR/USD and WTI Spot is positive (in 2007 and 2008), the volatility, when measured in Euro, is expected to be smaller than the volatility in Dollar. The expected difference is tiny (about 0.3% absolute) because the EUR/USD volatility (defined as in [5]) is about 2%. The reason for the counter-intuitive finding in Figure 4 is probably in my definition of the volatility as in [5].
[7] Monwhea Jeng, “A selected history of expectation bias in physics,” American Journal of Physics, July 2006, Volume 74, Issue 7, pp. 578-583. http://arxiv.org/pdf/physics/0508199

Box: Biased Opinions

As an ex-experimental physicist, I am well aware of the effect of bias. Once you have a favoured view, you can never be free of bias. It is not that you actively misrepresent the data to push your view. But you tend to critically analyze the data points that do not match your view, and tend to be lenient on the ones that do.

For instance, suppose I do an experiment to measure a quantity that Richard Feynman predicted to be, say, 1.37. I repeat the experiment three times and get values 1.34, 1.30 and 1.21. The right thing to do is to report a measurement of 1.29 with an error of 0.06. But, knowing the Feynman prediction (and, more importantly, knowing who Feynman is), I would take a hard look at the 1.21 trial. If I find anything wrong with it (which I will, because no experiment is perfect), I might repeat it and possibly get a number closer to 1.37. It is biases of this kind that physicists try very hard to avoid. See [7] for an interesting study on biases in physics.

In this column, I do have a favoured view — that the main driver of the commodity price inflation is speculation. In order to avoid pushing my view and shaping my readers’ opinion, I state clearly that there is a potential of bias in this column. The view that I have chosen to favour has no special reason for being right. It is just one of the many “hands” popular among economists.

About the Author
The author is a scientist from the European Organization for Nuclear Research (CERN), who currently works as a senior quantitative developer at Standard Chartered in Singapore. 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. More information about the author can be found at his web site: http://www.Thulasidas.com.

Philosophy, Science

Genetics of Good and Evil

September 9, 2008 manoj

Good is something that would increase our collective chance of survival as a species. Evil is just the opposite. Certain things look good and noble to us precisely the same way healthy babies look cute to us. Our genes survived because we are the kind of people who would find our collective survival a noble thing, and wanton destruction of lives a cruel or evil thing.

The genetic explanation of good and evil above, though reasonable, may be a little too simplistic. Many morbid things are considered great or noble. Mindless brutality in wars, for instance, is thought of as a noble act of courage and sacrifice. Certain cruel social or cultural practices were once considered noble and are now considered abominable. Slavery, for instance, is one such custom that changed its moral color. The practice of slavery was condoned in some parts of the world while slave liberation was frowned upon, in an exact reversal of the current moral attitude.

Can we understand these apparent paradoxes in terms of our DNA replication algorithm? What exactly is the scope of the DNA replication algorithm? Obviously, it cannot be that a DNA wants (or is programmed) to replicate all DNAs. We would not be able to eat or survive in that case. Even the maxim “survival of the fittest” would not make any sense. Neither can it be that a DNA wants exact clones of itself. If that were true, it would not take a father and a mother to make a baby.

There is some behavioral evidence to suggest that DNA replication is optimized at sub-species or even intra-species level. A male lion, when he takes over a pride, kills or eats the cubs so that the lionesses of the pride have to mate with him. This behavior, however cruel and evil by our own genetic logic, makes sense to the male lion’s DNA replication program. His DNA is not interested in replicating the species DNA; it wants to replicate a DNA as close to itself as possible. Other examples of sub-species level optimization are easily found. Gorillas are fiercely territorial and protective of their groups. Their violent behavior in promoting their own specific DNA is in stark contrast to our perception of them as gentle giants.

Such blatant genetic motivations are mirrored in human beings as well; ethnic cleansing and racism are clear examples. We are also at least as territorial about our countries and homes as our gorilla cousins, as evidenced by the national boundaries and Immigration and Naturalization Services and so on. Even our more subtle socio-economic behavior can be traced back to a genetic sub-species level struggle for survival of our DNA.

This sub-species genetic division leads to the apparent paradox of the mixing of noble and the evil. Patriotism is noble; treason is evil. Spying for our country is bravery, while spying for some other country is clearly treason. Killing in a war is noble, but murdering a neighbor is clearly evil. A war for liberation is probably noble; a war for oil is not. Looking after our family is noble, but ignoring our own and looking after somebody else’s family is not that good.

Even though the actions and effects of each pair of these noble and evil deeds are roughly equivalent, their moral connotations are different. This paradoxical difference can be explained genetically by the notion that the DNA replication algorithm distinguishes between sub-species.

Ref: This post is an excerpt from my book, The Unreal Universe.

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Commodity Prices — Who’s Holding the Cards?

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Genetics of Good and Evil