Category Archives: Philosophy

Philosophy is never too far from physics. It is in their overlap that I expect breakthroughs.

Philosophy

What is the Word?

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I know very little about religion. Although my smart-ass comments may appear, once in a while, as profound, I’m really ignorant in matters of theology and religion. After all, I have no formal background in these fields that scholars spend their whole life exploring. So, forgive me if this post comes across as pontificating on something I’d better leave to the scholars; but I cannot help wondering what the Word is. I mean, when they say, “In the beginning, there was the Word,” what exactly is the word?

The verse, John 1:1 “In the beginning was the Word, and the Word was with God, and the Word was God”, is again something people have spent much time researching and pondering over. My cursory search unearthed a couple of lines of thought. These lines were mostly concerned with the accuracy of the translation of the verse from Greek, which was complicated by the lack of “the” or “a” articles in the original language. So the verse could be translated as, for instance, “The Word was the God,” consistent with the monotheist notion of Christianity. Or it could be “The Word was a god,” giving quite a different, perhaps pagan, coloration to the issue.

For obvious (atheistic) reasons, I am not interested in this aspect of the verse, nor in these lines of thought. I found another translation, allegedly more literal, that went like, “When the beginning began, the Word was already there.” This suited my purpose better. Still, what exactly was this Word?

My understanding of this statement is as follows. In the philosophy of language, it can be argued that life, universe and everything exists in language, in thoughts, in your brain. The term “language” as defined here doesn’t just mean the communication tool, it also encompasses your thoughts and ideas. It is the vehicle of your thought process. In the absence of language, you have no thoughts, only animal instincts. You have no conscious awareness, only unthinking reactions to your surroundings. You don’t know that you exist, you don’t know that the world exists. The nothingness that engulfs you in the absence of a language is most poignantly depicted in the inspiring story of Helen Keller, coming up in a few days.

In my view, the “Word” that was there in the beginning is language, the ensemble of your thoughts and ideas, and the thought-processing mechanism. It creates our reality. Before we had language, we had no reality; we had nothing. And John 1:1 is a statement of intention to attribute this world of reality, or the opposite of nothingness, created by language to God. And, to me, this statement is the clearest proof that the saint knew how god was born. Obviously, I am rushing in where angels fear to tread. This view of mine will not be embraced (or even tolerated) by anybody who believes in the theological meaning attached to this text of scripture. And to them, I humbly point out that it is just a view, a mere mortal’s view at that! It probably only goes to show that “The devil can cite Scripture for his purpose!”

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.

Life and Death, Philosophy, Topical, Work and Life

Of Dreams and Memories

I recently watched The Diving Bell and the Butterfly (Le scaphandre et le papillon), which describes the tragic plight of the French journalist Jean-Dominique Bauby, who suffered a severe stroke and became “locked-in.” During my research days, I had worked a bit on rehabilitation systems for such locked-in patients, who have normal or near-normal cognitive activities but no motor control. In other words, their fully functional minds are locked in a useless body that affords them no means of communication with the external world. It is the solitary confinement of the highest order.

Locked-in condition is one of my secret fears; not so much for myself, but that someone close to me might have to go through it. My father suffered a stroke and was comatose for a month before he passed away, and I will always wonder whether he was locked-in. Did he feel pain and fear? So I Googled a bit to find out if stroke patients were conscious inside. I couldn’t find anything definitive. Then it occurred to me that perhaps these stroke patients were conscious, but didn’t remember it later on.

That thought brought me to one of my philosophical musings. What does it mean to say that something happened if you cannot remember it? Let’s say you had to go through a lot of pain for whatever reason. But you don’t remember it later. Did you really suffer? It is like a dream that you cannot remember. Did you really dream it?

Memory is an essential ingredient of reality, and of existence — which is probably why they can sell so many digital cameras and camcorders. When memories of good times fade in our busy minds, perhaps we feel bits of our existence melting away. So we take thousands of pictures and videos that we are too busy to look at later on.

But I wonder. When I die, my memories will die with me. Sure, those who are close to me will remember me for a while, but the memories that I hold on to right now, the things I have seen and experienced, will all disappear — like an uncertain dream that someone (perhaps a butterfly) dreamt and forgot. So what does it mean to say that I exist? Isn’t it all a dream?

Books, Creative, Life and Death, Philosophy

The Razor’s Edge by W Somerset Maugham

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May be it is only my tendency to see philosophy everywhere, but I honestly believe Maugham’s works are the classics they are because of their deep philosophical underpinnings. Their strong plots and Maugham’s masterful storytelling help, but what makes them timeless is the fact that Maugham gives voice to the restlessness of our hearts, and puts in words the stirring uncertainties of our souls. Our questions have always been the same. Where do we come from? What are we doing here? And where are we headed? Quo vadis?

Of all the books of this kind that I have read, and I have read many, The Razor’s Edge takes on the last question most directly. When Larry says, out of the blue, “The dead look so awfully dead.” we get an idea of what his quest, and indeed the inquiry of the book, is going to be.

Larry Darrell is as close to human flawlessness as Maugham ever gets. His cynical disposition always produced vivid characters that were flawed human beings. We are used to snobbishness in Elliott Templeton, fear and hypocrisy in the vicar of Blackstable, self-loathing even in the self-image of Philip Carey, frivolity in Kitty Garstin, undue sternness in Walter Fane, the ludicrous buffoonery of Dirk Stroeve, abysmal cruelty in Charles Strickland, ultimate betrayal in Blanche Stroeve, fatal alcoholism in Sophie, incurable promiscuity in Mildred — an endless parade of gripping characters, everyone of them as far from human perfection as you and me.

But human perfection is what is sought and found in Larry Darrell. He is gentle, compassionate, single-mindedly hardworking, spiritually enlightened, simple and true, and even handsome (although Maugham couldn’t help but bring in some reservations about it). In one word, perfect. So it is only with an infinite amount of vanity that anybody can identify himself with Larry (as I secretly do). And it is a testament to Maugham’s mastery and skill that he could still make such an idealistic character human enough for some people to see themselves in him.

As I plod on with these review posts, I’m beginning to find them a bit useless. I feel that whatever needed to be said was already well said in the books to begin with. And, the books being classics, others have also said much about them. So why bother?

Let me wind up this post, and possibly this review series, with a couple of personal observations. I found it gratifying that Larry finally found enlightenment in my native land of Kerala. Written decades before the hippie exodus for spiritual fulfillment in India, this book is remarkably prescient. And, as a book on what life is all about, and how to live it to its spiritual fullness in our hectic age, The Razor’s Edge is a must read for everybody.

Debates, Philosophy, Physics, SFN - Science Forums

The Big Bang Theory – Part II

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

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

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

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

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

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

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

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

My views revolve around the following questions.

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

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

Philosophy, Physics, Science

Why the Speed of Light?

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

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

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

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

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

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

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

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

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

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

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

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

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

Debates, Philosophy, Physics

What is Space?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Articles and Essays, Philosophy, Physics, Science, Unpublished

Light Travel Time Effects and Cosmological Features

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

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Abstract

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

Introduction

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

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

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

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

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

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

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

Similarities between Light Travel Time Effects and SR

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

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

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

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

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

Conclusions

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

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

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

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

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

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

Books, Philosophy

Siddhartha by Hermann Hesse

3 Comments

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

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

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

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

For one who seeks symbolism, Siddhartha provides it aplenty.

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

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

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

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

Articles and Essays, Creative, Philosophy, Physics

Constraints of Perception and Cognition in Relativistic Physics

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

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

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

1. Introduction

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

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

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

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

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

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

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

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

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

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

2. Similarities between LTT Effects & SRT

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

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

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

2.1 First Order Perceptual Effects

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

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

2.2 Perception of Speed

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


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

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

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

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

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


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

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

2.4 Length Contraction

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


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

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

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

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

5 Conclusions

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

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

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

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