Category Archives: Science

My thoughts on non-physics sciences — like evolutionary biology, cognitive neuroscience etc.

Books, Philosophy, Physics, Science

Blind-Sight

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

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

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

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

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

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

Books, Philosophy, Physics, Science

A Plausible God

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

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

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

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

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

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

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

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

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

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

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

Books, Creative, Philosophy, Science

The God Delusion

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I am an atheist. So I agree completely with all the arguments of The God Delusion. As a review of the book, that statement should be the end of it. But somehow the book gave me a strange feeling of dissatisfaction. You see, you may believe in God. Or you may not. Or you may actively believe that there is no God. I fall in this the last category. But I still know that it is only my belief, and that thought fills me with a humility that I feel Dawkins lacks.

Now, it is one thing to say that the concept of God is inconsistent with the worldview you have developed, perhaps with the help of science. The concept is indeed very inconsistent with my own personal worldview, which is why I am an atheist. But it is quite a different matter to discount the concept as a delusion. I believe that our knowledge is incomplete. And that there is plenty of room for a possible God to hide beyond the realms of our current knowledge. Does it mean that we should call our ignorance God and kneel before it? I don’t think so, but if somebody does, that is their prerogative.

You see, it is all a question of what your worldview is. And how much rigor and consistency you demand of it. So, what is a worldview? In my opinion, a worldview is the extension of your knowledge. We all have a certain amount of knowledge. We also have a lot of sensory data that comes in every moment that we have to process. We do most of this processing automatically, without conscious effort. But some of the higher level data and information that we encounter merit a closer analysis. How do we do it, given that we may not know much about it? We use our commonsense, our pre-conceived notions, the value systems our parents and teachers left in us and so on. One of these things that we use, or perhaps the totality of these things, is our worldview.

Let’s take an example. Douglas Adams tells us that dolphins are actually smarter than us and have regular inter-galactic communication. Well, we have no way of refuting this claim (which, of course, is only a joke). But our worldview tells us that it is unlikely to be true. And we don’t believe it — as though we know it is not true.

Another example, one that Bertram Russell once cited. Scripture tells us that faith can move mountains. Some people believe it. Science tells us that a nuclear blast can, well, move mountains. Some people believe that too. Note that most people haven’t directly witnessed either. But even for those who believe in the faith-mountain connection, nuclear energy moving mountains is far more plausible a belief. It is just a lot more consistent with our current worldview.

Now, just because God is a delusion according to Dawkins’s worldview (or mine, for that matter), should you buy it? Not unless it is inconsistent with yours as well. Worldviews are hard to change. So are our stances vis-a-vis God and science, when seen as belief-systems — as the movie Contact vividly illustrates. If you missed it, you should watch it. Repeatedly, if needed. It is a good movie anyway.

It is true what they say about a scientific worldview being inconsistent with any sensible notion of a god. But worldviews are a funny thing. Nothing prevents you from tolerating inconsistencies in your worldview. Although Dawkins goes to some length to absolve Einstein of this lack of consistency, the conventional wisdom is that he did believe in God. The truth of the matter is that our collective knowledge (even after adding Einstein’s massive contribution) is limited. There really is plenty of room beyond its limits for God (or eight million gods, if I were to believe my parents), as I will try to show in my next post.

That, however, is only the tip of the iceberg. Once we admit that there are limits to our knowledge, and to what is knowable, we will soon find ourselves staring at other delusions. What is the point it discounting a God delusion, while embracing a space-delusion? In a universe that is unreal, everything is a delusion, not just God. I know, you think it is just my sanity that is unreal, but I may convince you otherwise. In another post.

Columns, Corporate Life, Environment, Humor, Quantitative Finance, Science, The Wilmott Magazine, Work and Life

Talent and Intelligence

In the last post, I argued that how hard we work has nothing much to do with how much reward we should reap. After all, there are taxi drivers who work longer and harder, and even more unfortunate souls in the slums of India and other poor countries.

But, I am threading on real thin ice when I compare, however obliquely, senior executives to cabbies and slum dogs. They are (the executives, that is) clearly a lot more talented, which brings me to the famous talent argument for bonuses. What is this talent thing? Is it intelligence and articulation? I once met a taxi driver in Bangalore who was fluent in more than a dozen languages as disparate as English and Arabic. I discovered his hidden talent by accident when he cracked up at something my father said to me — a private joke in our vernacular, which I have seldom found a non-native speaker attempt. I couldn’t help thinking then — given another place and another time, this cabbie would have been a professor in linguistics or something. Talent may be a necessary condition for success (and bonus), but it certainly is not a sufficient one. Even among slum dogs, we might find ample talent, if the Oscar-winning movie is anything to go by. Although, the protagonist in the movie does make his million dollar bonus, but it was only fiction.

In real life, however, lucky accidents of circumstances play a more critical role than talent in putting us on the right side of the income divide. To me, it seems silly to claim a right to the rewards based on any perception of talent or intelligence. Heck, intelligence itself, however we define it, is nothing but a happy genetic accident.

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Creative, Philosophy, Physics, Quotes, Science

Change the Facts

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There is beauty in truth, and truth in beauty. Where does this link between truth and beauty come from? Of course, beauty is subjective, and truth is objective — or so we are told. It may be that we have evolved in accordance with the beautiful Darwinian principles to see perfection in absolute truth.

The beauty and perfection I’m thinking about are of a different kind — those of ideas and concepts. At times, you may get an idea so perfect and beautiful that you know it has to be true. This conviction of truth arising from beauty may be what made Einstein declare:

But this conviction about the veracity of a theory based on its perfection is hardly enough. Einstein’s genius really is in his philosophical tenacity, his willingness to push the idea beyond what is considered logical.

Let’s take an example. Let’s say you are in a cruising airplane. If you close the windows and somehow block out the engine noise, it will be impossible for you to tell whether you are moving or not. This inability, when translated to physics jargon, becomes a principle stating, “Physical laws are independent of the state of motion of the experimental system.”

The physical laws Einstein chose to look at were Maxwell’s equations of electromagnetism, which had the speed of light appearing in them. For them to be independent of (or covariant with, to be more precise) motion, Einstein postulated that the speed of light had to be a constant regardless of whether you were going toward it or away from it.

Now, I don’t know if you find that postulate particularly beautiful. But Einstein did, and decided to push it through all its illogical consequences. For it to be true, space has to contract and time had to dilate, and nothing could go faster than light. Einstein said, well, so be it. That is the philosophical conviction and tenacity that I wanted to talk about — the kind that gave us Special Relativity about a one hundred years ago.

Want to get to General Relativity from here? Simple, just find another beautiful truth. Here is one… If you have gone to Magic Mountain, you would know that you are weightless during a free fall (best tried on an empty stomach). Free fall is acceleration at 9.8 m/s/s (or 32 ft/s/s), and it nullifies gravity. So gravity is the same as acceleration — voila, another beautiful principle.

World line of airplanesIn order to make use of this principle, Einstein perhaps thought of it in pictures. What does acceleration mean? It is how fast the speed of something is changing. And what is speed? Think of something moving in a straight line — our cruising airplane, for instance, and call the line of flight the X-axis. We can visualize its speed by thinking of a time T-axis at right angles with the X-axis so that at time = 0, the airplane is at x = 0. At time t, it is at a point x = v.t, if it is moving with a speed v. So a line in the X-T plane (called the world line) represents the motion of the airplane. A faster airplane would have a shallower world line. An accelerating airplane, therefore, will have a curved world line, running from the slow world line to the fast one.

So acceleration is curvature in space-time. And so is gravity, being nothing but acceleration. (I can see my physicist friends cringe a bit, but it is essentially true — just that you straighten the world-line calling it a geodesic and attribute the curvature to space-time instead.)

The exact nature of the curvature and how to compute it, though beautiful in their own right, are mere details, as Einstein himself would have put it. After all, he wanted to know God’s thoughts, not the details.

Philosophy, Physics, Science

Why the Speed of Light?

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

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

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

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

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

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

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

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

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

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

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

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

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

Articles and Essays, Philosophy, Physics, Science, Unpublished

Light Travel Time Effects and Cosmological Features

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

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Abstract

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

Introduction

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

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

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

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

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

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

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

Similarities between Light Travel Time Effects and SR

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

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

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

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

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

Conclusions

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

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

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

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

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

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

Articles and Essays, Physics, Science

Are Radio Sources and Gamma Ray Bursts Luminal Booms?

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

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

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

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

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Abstract

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

Introduction

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

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

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

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

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

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

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

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

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

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

Conclusions

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

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

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

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

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


Photo by NASA Goddard Photo and Video

Philosophy, Science

Genetics of Good and Evil

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.

Science

End of Evolution

To a physicist, life is a neat example of electromagnetic interaction. To a biologist, however, life is a DNA replication algorithm. Let’s mull over the biology view for a few moments.

The genes in our body have only one motive–to get replicated. Our body is created in accordance with a blue print encoded in the genes to “run” this algorithm. How this algorithm gets mapped to our higher level goals and emotions is what life is all about to most people who are not physicists or biologists.

A simple mapping of this algorithm leads to the maxim in evolution “the survival of the fittest.” Any mutation that has the tiniest advantage in terms of survivability gets amplified over time. Similarly, all disadvantaged genes get wiped out.

But evolution in humans (and through our influence, the whole echo-system) has taken a new turn. Survival of the fittest used to mean the survival of the strongest or the smartest. For instance, if I had a genetic condition that made me prone to some life-threatening disease (in other words, if I was not very strong), my chances of passing on my genes would be a little smaller.

However, because of the advances in medicine, the survival chances for such disadvantaged genes are normalized to roughly the same level as those of the rest of the species. Then again, because of the dependence of the quality of health care on money, the survival chances get distorted in favor of the rich. So, is the mapping of the DNA algorithm now “the survival of the richest?”

Wealth is considered a product of intelligence. But intelligence (as defined by money-making ability) is not necessarily genetic. It may be, but we do not know that yet. So over several generations, it is not even the richest that survive, because time averages out the survival chances.

So what exactly is going to survive?

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