Animals have different sensory capabilities compared to us humans. Cats, for instance, can hear up to 60kHz, while the highest note we have ever heard was about 20kHz. Apparently, we could hear that high a note only in our childhood. So, if we are trying to pull a fast one on a cat with the best hifi multi-channel, Dolby-whatever recording of a mouse, we will fail pathetically. It won’t be fooled because it lives in a different sensory world, while sharing the same physical world as ours. There is a humongous difference between the sensory and physical worlds.
Tag Archives: perception
Richard Feynman — How Much Can We Know?
We open our eyes, we see the world, we discern patterns. We theorize, formalize; we use and rationality and mathematics to understand and describe everything. How much can we really know, though?
To illustrate what I mean, let me use an analogy. I wish I had the imagination to come up with it, but it was Richard Feynman who did. He was, by the way, quirky enough to compare physics with sex.
Why did Federer Lose?
I am a Federer fan. His inevitable decline has been a source of grief for me. When it comes to shot selection, imagination and pure magical talent, there isn’t another tennis player who could ever hold a candle to him. Why did he have to go and lose in the second round of Wimbledon? It damn near broke my heart.
Ok, we all know the answer. He is getting too old. But he is only 31, and has to be in terrific shape. I am pushing fifty and can still put in a couple of hours of vigorous badminton. Sure, weekend badminton is no world class tennis, and the effects of aging are very different. Still…, I wish he would stick around a bit longer.
A few months ago, I listened to a series of interesting lectures on the effects of aging on our perception and sensory processes. One thing new that I learned there was that we all have a sixth sense, in addition to sight, hearing, touch, taste and smell. It is the kinesthetic, muscle feedback, which is the sense that allows you to apply just the right amount of pressure, for instance, when braking your car, or holding a baby. You may lose this sense when you get angry and break the glass you are holding, if we are to believe Hollywood movies. In certain games, this sense can make an enormous difference. I had a friend who was a pool shark. He once told me that at the top of his game, he could feel the tiny nicks and scratches on the cue ball through the cue stick in his hand. When I knew him, he was well past his prime, but he could still call shots like bank off the point of the side pocket, and double kiss into the corner pocket. And make them. So I believe him and Eddie Felson (The Hustler) when he says the cue stick, when he holds it, has nerves. I bet Federer could feel the seams of the tennis ball and the amount of spin he was putting on them through the strings and the grip of his racket.
Age blunts the sharpness of all of your senses. The most obvious is your sight. In your forties, you have to hold your smart phone farther and farther away from your face to read the tiny screen. At some point, your hand is not long enough and you end up using reading glasses — reluctantly at first, but more readily as the years roll by and the images get blurrier. Apparently you lose your sensitivity to high pitched sound as well. So teenagers can download ringtones that their parents and teachers are deaf to. But the first sense to go is the muscle feedback, which begins to decline in your teens. This, apparently, is the reason why the Olympic gymnasts are all teenagers. By the time they are in their twenties, this sense of theirs is already too weak to keep them competitive at that level. I guess it is this sense that has deserted Roger Federer as well.
Frederer’s brand of tennis with its finesse and artistry demanded more of this sense. His opponents tend to hit flatter and harder. I read somewhere that they use stiffer rackets for this purpose, and can hold Federer behind the baseline. The champion stubbornly refuses to switch to this style and this kind of rackets. May be he is getting a bit too old. Reminds me of Bjorn Borg, when he attempted a mini come-back with his wooden racket.
Free Will — An Illusion?
If we can let ourselves be amazed at the fact that our non-material ethereal mind can really actuate things in the physical world, we will find ourselves wondering — do we really have free will? If free will is merely a pattern in the electrical activities in our brain, how can such a pattern cause changes and rearrangements in the physical world? Could it be that this pattern is really causing an illusion of free will?
Logic in the form of Occam’s Razor should direct us to the latter possibility. But logic doesn’t apply to many or most of the fundamental hypotheses of life, which answer to a different set of rules. They answer to the mythos, the sum total of the intangible knowledge and wisdom passed down from the past, from the ancient, forgotten masters talking to us through our teachers and folklore, through the structure of our languages and the backdrop of our thoughts, and through the very foundation of our sense of being and consciousness. The mythos tell us that we do have free will, and the logic that came later is powerless to break this notion. So it may be that these words that flow out of my pen into this notepad and later to your computer screen were all predetermined and I had no choice but to write then down. But it certainly is not the way I feel. I do feel as though I can delete any word here. Heck, I can delete the whole post if I want to.
On the side of logic, I will describe an experiment that casts doubt on our notion of free will. From neuroscience, we know that there is a time lag of about half a second between the moment “we” take a decision and the moment we become aware of it. This time lag raises the question of who is taking the decision because, in the absence of our conscious awareness, it is not clear that the decision is really ours. In the experimental setup testing this phenomenon, the subject is hooked up to a computer that records his brain activities (EEG). The subject is then asked make a conscious decision to move either the right hand or the left hand at a time of his choosing. The choice of right or left is also up to the subject. The computer always detects which hand the subject is going to move about half a second before the subject is aware of his own intention. The computer can then order the subject to move that hand — an order that the subject will be unable to disobey. Does the subject have free will in this case?
In fact, I wrote about it in my book, and posted it here some time ago. In that post, I added that free will might be a fabrication of our brain after the real action. In other words, the real action takes place by instinct, and the sense of decision is introduced to our consciousness as an afterthought. Some of my readers pointed out that being unaware of a decision was not the same as having no free will over it. For instance, when you drive, you take a series of decisions without really being aware of them. It doesn’t mean that these decisions are not yours. Good point, but does it really make sense to call a decision yours when you don’t have any control over it, even if you would take the same decision if you did? If something flies into your eyes, you will flinch and close your eyes. Good survival instinct and reflex. But given that you cannot control it, is it a part of your free will?
A more elaborate example comes from hypnotic suggestion. I heard this story from one of the lectures by John Searle — a man was hypnotically instructed to respond to the word “Germany” by crawling on the floor. After the hypnosis session, when the man was lucid and presumably exercising his free will, the trigger word was used in a conversation. The man suddenly says something like, “I just remembered, I need to remodel my house, and these tiles look great. Mind if I take a closer look?” and crawls on the floor. Did he do it of his own volition? To him, yes, but to the rest, now.
So, how do we know for sure that our sense of free will is not an elaborate scam that our brain is perpetrating on “us” (whatever that means!)
Now I am actually pushing the argument a bit further. But think about it, how can the spaceless, massless, material-less entities that are our intentions make real changes in the physical world around us? In writing this post, how can I break the laws of physics in moving things around quite independent of their current state just because I want to?
Is free will an epiphenomenon — something that emerges after-the-fact? A good analogy is that of froth riding on the waves on a beach. The froth may be thinking, “Oh my god, what a tough life! I have to haul all these big waves back and forth. Every day of my life, no break, no vacation!” But that is not what is going on. The waves are just sloshing around, and the froth just happens to emerge. Are our lives just moving along on their own preordained paths, while we, like the epiphenomenal froth, think that we have control and free will?
What is Space?
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.
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| 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.]
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 
is moving with respect to another system 
along the positive X axis of , then an object at rest in at a positive 
is receding while another object at a negative is approaching an observer at the origin of .
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 
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.
Are Radio Sources and Gamma Ray Bursts Luminal Booms?
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.
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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).
Gamma Ray Bursts are very brief, but intense flashes of 
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 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 emission, and the spectrum softens as the fireball cools down. The model calculates the energy released in the region as 
—
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 
—
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).
to 
through 
and 
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 ) reaches the observer at 
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 also reaches . So, the sound emitted at 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 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.
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 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 
The Unreal Universe — Seeing Light in Science and Spirituality
We know that our universe is a bit unreal. The stars we see in the night sky, for instance, are not really there. They may have moved or even died by the time we get to see them. This delay is due to the time it takes for light from the distant stars and galaxies to reach us. We know of this delay.
The same delay in seeing has a lesser known manifestation in the way we perceive moving objects. It distorts our perception such that something coming towards us would look as though it is coming in faster. Strange as it may sound, this effect has been observed in astrophysical studies. Some of the heavenly bodies do look as though they are moving several times the speed of light, while their “real” speed is probably a lot lower.
Now, this effect raises an interesting question–what is the “real” speed? If seeing is believing, the speed we see should be the real speed. Then again, we know of the light travel time effect. So we should correct the speed we see before believing it. What then does “seeing” mean? When we say we see something, what do we really mean?
Light in Physics
Seeing involves light, obviously. The finite speed of light influences and distorts the way we see things. This fact should hardly come as a surprise because we do know that things are not as we see them. The sun that we see is already eight minutes old by the time we see it. This delay is not a big deal; if we want to know what is going on at the sun now, all we have to do is to wait for eight minutes. We, nonetheless, have to “correct” for the distortions in our perception due to the finite speed of light before we can trust what we see.
What is surprising (and seldom highlighted) is that when it comes to sensing motion, we cannot back-calculate the same way we take out the delay in seeing the sun. If we see a celestial body moving at an improbably high speed, we cannot figure out how fast and in what direction it is “really” moving without making further assumptions. One way of handling this difficulty is to ascribe the distortions in our perception to the fundamental properties of the arena of physics — space and time. Another course of action is to accept the disconnection between our perception and the underlying “reality” and deal with it in some way.
Einstein chose the first route. In his groundbreaking paper over a hundred years ago, he introduced the special theory of relativity, in which he attributed the manifestations of the finite speed of light to the fundamental properties of space and time. One core idea in special relativity (SR) is that the notion of simultaneity needs to be redefined because it takes some time for light from an event at a distant place to reach us, and we become aware of the event. The concept of “Now” doesn’t make much sense, as we saw, when we speak of an event happening in the sun, for instance. Simultaneity is relative.
Einstein defined simultaneity using the instants in time we detect the event. Detection, as he defined it, involves a round-trip travel of light similar to Radar detection. We send out light, and look at the reflection. If the reflected light from two events reaches us at the same instant, they are simultaneous.
Another way of defining simultaneity is using sensing — we can call two events simultaneous if the light from them reaches us at the same instant. In other words, we can use the light generated by the objects under observation rather than sending light to them and looking at the reflection.
This difference may sound like a hair-splitting technicality, but it does make an enormous difference in the predictions we can make. Einstein’s choice results in a mathematical picture that has many desirable properties, thereby making further development elegant.
The other possibility has an advantage when it comes to describing objects in motion because it corresponds better with how we measure them. We don’t use Radar to see the stars in motion; we merely sense the light (or other radiation) coming from them. But this choice of using a sensory paradigm, rather than Radar-like detection, to describe the universe results in a slightly uglier mathematical picture.
The mathematical difference spawns different philosophical stances, which in turn percolate to the understanding of our physical picture of reality. As an illustration, let us look at an example from astrophysics. Suppose we observe (through a radio telescope, for instance) two objects in the sky, roughly of the same shape and properties. The only thing we know for sure is that the radio waves from two different points in the sky reach the radio telescope at the same instant in time. We can guess that the waves started their journey quite a while ago.
For symmetric objects, if we assume (as we routinely do) that the waves started the journey roughly at the same instant in time, we end up with a picture of two “real” symmetric lobes more or less the way see them.
But there is different possibility that the waves originated from the same object (which is in motion) at two different instants in time, reaching the telescope at the same instant. This possibility explains some spectral and temporal properties of such symmetric radio sources, which is what I mathematically described in a recent physics article. Now, which of these two pictures should we take as real? Two symmetric objects as we see them or one object moving in such a way as to give us that impression? Does it really matter which one is “real”? Does “real” mean anything in this context?
The philosophical stance in implied in special relativity answers this question unequivocally. There is an unambiguous physical reality from which we get the two symmetric radio sources, although it takes a bit of mathematical work to get to it. The mathematics rules out the possibility of a single object moving in such a fashion as to mimic two objects. Essentially, what we see is what is out there.
On the other hand, if we define simultaneity using concurrent arrival of light, we will be forced to admit the exact opposite. What we see is pretty far from what is out there. We will confess that we cannot unambiguously decouple the distortions due to the constraints in perception (the finite speed of light being the constraint of interest here) from what we see. There are multiple physical realities that can result in the same perceptual picture. The only philosophical stance that makes sense is the one that disconnects the sensed reality and the causes behind what is being sensed.
This disconnect is not uncommon in philosophical schools of thought. Phenomenalism, for instance, holds the view that space and time are not objective realities. They are merely the medium of our perception. All the phenomena that happen in space and time are merely bundles of our perception. In other words, space and time are cognitive constructs arising from perception. Thus, all the physical properties that we ascribe to space and time can only apply to the phenomenal reality (the reality as we sense it). The noumenal reality (which holds the physical causes of our perception), by contrast, remains beyond our cognitive reach.
The ramifications of the two different philosophical stances described above are tremendous. Since modern physics seems to embrace a non-phenomenalistic view of space and time, it finds itself at odds with that branch of philosophy. This chasm between philosophy and physics has grown to such a degree that the Nobel prize winning physicist, Steven Weinberg, wondered (in his book “Dreams of a Final Theory”) why the contribution from philosophy to physics have been so surprisingly small. It also prompts philosophers to make statements like, “Whether ‘noumenal reality causes phenomenal reality’ or whether ‘noumenal reality is independent of our sensing it’ or whether ‘we sense noumenal reality,’ the problem remains that the concept of noumenal reality is a totally redundant concept for the analysis of science.”
One, almost accidental, difficulty in redefining the effects of the finite speed of light as the properties of space and time is that any effect that we do understand gets instantly relegated to the realm of optical illusions. For instance, the eight-minute delay in seeing the sun, because we readily understand it and disassociate from our perception using simple arithmetic, is considered a mere optical illusion. However, the distortions in our perception of fast moving objects, although originating from the same source are considered a property of space and time because they are more complex.
We have to come to terms with the fact that when it comes to seeing the universe, there is no such thing as an optical illusion, which is probably what Goethe pointed out when he said, “Optical illusion is optical truth.”
The distinction (or lack thereof) between optical illusion and truth is one of the oldest debates in philosophy. After all, it is about the distinction between knowledge and reality. Knowledge is considered our view about something that, in reality, is “actually the case.” In other words, knowledge is a reflection, or a mental image of something external, as shown in the figure below.
In this picture, the black arrow represents the process of creating knowledge, which includes perception, cognitive activities, and the exercise of pure reason. This is the picture that physics has come to accept.
While acknowledging that our perception may be imperfect, physics assumes that we can get closer and closer to the external reality through increasingly finer experimentation, and, more importantly, through better theorization. The Special and General Theories of Relativity are examples of brilliant applications of this view of reality where simple physical principles are relentlessly pursued using formidable machine of pure reason to their logically inevitable conclusions.
But there is another, alternative view of knowledge and reality that has been around for a long time. This is the view that regards perceived reality as an internal cognitive representation of our sensory inputs, as illustrated below.
In this view, knowledge and perceived reality are both internal cognitive constructs, although we have come to think of them as separate. What is external is not the reality as we perceive it, but an unknowable entity giving rise to the physical causes behind sensory inputs. In the illustration, the first arrow represents the process of sensing, and the second arrow represents the cognitive and logical reasoning steps. In order to apply this view of reality and knowledge, we have to guess the nature of the absolute reality, unknowable as it is. One possible candidate for the absolute reality is Newtonian mechanics, which gives a reasonable prediction for our perceived reality.
To summarize, when we try to handle the distortions due to perception, we have two options, or two possible philosophical stances. One is to accept the distortions as part of our space and time, as SR does. The other option is to assume that there is a “higher” reality distinct from our sensed reality, whose properties we can only conjecture. In other words, one option is to live with the distortion, while the other is to propose educated guesses for the higher reality. Neither of these options is particularly attractive. But the guessing path is similar to the view accepted in phenomenalism. It also leads naturally to how reality is viewed in cognitive neuroscience, which studies the biological mechanisms behind cognition.
In my view, the two options are not inherently distinct. The philosophical stance of SR can be thought of as coming from a deep understanding that space is merely a phenomenal construct. If the sense modality introduces distortions in the phenomenal picture, we may argue that one sensible way of handling it is to redefine the properties of the phenomenal reality.
Role of Light in Our Reality
From the perspective of cognitive neuroscience, everything we see, sense, feel and think is the result of the neuronal interconnections in our brain and the tiny electrical signals in them. This view must be right. What else is there? All our thoughts and worries, knowledge and beliefs, ego and reality, life and death — everything is merely neuronal firings in the one and half kilograms of gooey, grey material that we call our brain. There is nothing else. Nothing!
In fact, this view of reality in neuroscience is an exact echo of phenomenalism, which considers everything a bundle of perception or mental constructs. Space and time are also cognitive constructs in our brain, like everything else. They are mental pictures our brains concoct out of the sensory inputs that our senses receive. Generated from our sensory perception and fabricated by our cognitive process, the space-time continuum is the arena of physics. Of all our senses, sight is by far the dominant one. The sensory input to sight is light. In a space created by the brain out of the light falling on our retinas (or on the photo sensors of the Hubble telescope), is it a surprise that nothing can travel faster than light?
This philosophical stance is the basis of my book, The Unreal Universe, which explores the common threads binding physics and philosophy. Such philosophical musings usually get a bad rap from us physicists. To physicists, philosophy is an entirely different field, another silo of knowledge. We need to change this belief and appreciate the overlap among different knowledge silos. It is in this overlap that we can expect to find breakthroughs in human thought.
This philosophical grand-standing may sound presumptuous and the veiled self-admonition of physicists understandably unwelcome; but I am holding a trump card. Based on this philosophical stance, I have come up with a radically new model for two astrophysical phenomena, and published it in an article titled, “Are Radio Sources and Gamma Ray Bursts Luminal Booms?” in the well-known International Journal of Modern Physics D in June 2007. This article, which soon became one of the top accessed articles of the journal by Jan 2008, is a direct application of the view that the finite speed of light distorts the way we perceive motion. Because of these distortions, the way we see things is a far cry from the way they are.
We may be tempted to think that we can escape such perceptual constraints by using technological extensions to our senses such as radio telescopes, electron microscopes or spectroscopic speed measurements. After all, these instruments do not have “perception” per se and should be immune to the human weaknesses we suffer from. But these soulless instruments also measure our universe using information carriers limited to the speed of light. We, therefore, cannot escape the basic constraints of our perception even when we use modern instruments. In other words, the Hubble telescope may see a billion light years farther than our naked eyes, but what it sees is still a billion years older than what our eyes see.
Our reality, whether technologically enhanced or built upon direct sensory inputs, is the end result of our perceptual process. To the extent that our long range perception is based on light (and is therefore limited to its speed), we get only a distorted picture of the universe.
Light in Philosophy and Spirituality
The twist to this story of light and reality is that we seem to have known all this for a long time. Classical philosophical schools seem to have thought along lines very similar to Einstein’s thought experiment.
Once we appreciate the special place accorded to light in modern science, we have to ask ourselves how different our universe would have been in the absence of light. Of course, light is only a label we attach to a sensory experience. Therefore, to be more accurate, we have to ask a different question: if we did not have any senses that responded to what we call light, would that affect the form of the universe?
The immediate answer from any normal (that is, non-philosophical) person is that it is obvious. If everybody is blind, everybody is blind. But the existence of the universe is independent of whether we can see it or not. Is it though? What does it mean to say the universe exists if we cannot sense it? Ah… the age-old conundrum of the falling tree in a deserted forest. Remember, the universe is a cognitive construct or a mental representation of the light input to our eyes. It is not “out there,” but in the neurons of our brain, as everything else is. In the absence of light in our eyes, there is no input to be represented, ergo no universe.
If we had sensed the universe using modalities that operated at other speeds (echolocation, for instance), it is those speeds that would have figured in the fundamental properties of space and time. This is the inescapable conclusion from phenomenalism.
The role of light in creating our reality or universe is at the heart of Western religious thinking. A universe devoid of light is not simply a world where you have switched off the lights. It is indeed a universe devoid of itself, a universe that doesn’t exist. It is in this context that we have to understand the wisdom behind the statement that “the earth was without form, and void” until God caused light to be, by saying “Let there be light.”
The Quran also says, “Allah is the light of the heavens and the earth,” which is mirrored in one of the ancient Hindu writings: “Lead me from darkness to light, lead me from the unreal to the real.” The role of light in taking us from the unreal void (the nothingness) to a reality was indeed understood for a long, long time. Is it possible that the ancient saints and prophets knew things that we are only now beginning to uncover with all our supposed advances in knowledge?
I know I may be rushing in where angels fear to tread, for reinterpreting the scriptures is a dangerous game. Such foreign interpretations are seldom welcome in the theological circles. But I seek refuge in the fact that I am looking for concurrence in the metaphysical views of spiritual philosophies, without diminishing their mystical or theological value.
The parallels between the noumenal-phenomenal distinction in phenomenalism and the Brahman-Maya distinction in Advaita are hard to ignore. This time-tested wisdom on the nature of reality from the repertoire of spirituality is now reinvented in modern neuroscience, which treats reality as a cognitive representation created by the brain. The brain uses the sensory inputs, memory, consciousness, and even language as ingredients in concocting our sense of reality. This view of reality, however, is something physics is yet to come to terms with. But to the extent that its arena (space and time) is a part of reality, physics is not immune to philosophy.
As we push the boundaries of our knowledge further and further, we are beginning to discover hitherto unsuspected and often surprising interconnections between different branches of human efforts. In the final analysis, how can the diverse domains of our knowledge be independent of each other when all our knowledge resides in our brain? Knowledge is a cognitive representation of our experiences. But then, so is reality; it is a cognitive representation of our sensory inputs. It is a fallacy to think that knowledge is our internal representation of an external reality, and therefore distinct from it. Knowledge and reality are both internal cognitive constructs, although we have come to think of them as separate.
Recognizing and making use of the interconnections among the different domains of human endeavour may be the catalyst for the next breakthrough in our collective wisdom that we have been waiting for.