Category Archives: Debates

I engaged in long discussions on physics and philosophy through email and in Internet forums. Some of them are a bit nasty, but most were conducted in good taste. Here they are, both for your reading pleasure and my archival purposes.

Risk – Wiley FinCAD Webinar

This post is an edited version of my responses in a Webinar panel-discussion organized by Wiley-Finance and FinCAD. The freely available Webcast is linked in the post, and contains responses from the other participants — Paul Wilmott and Espen Huag. An expanded version of this post may later appear as an article in the Wilmott Magazine.

What is Risk?

When we use the word Risk in normal conversation, it has a negative connotation — risk of getting hit by a car, for instance; but not the risk of winning a lottery. In finance, risk is both positive and negative. At times, you want the exposure to a certain kind of risk to counterbalance some other exposure; at times, you are looking for the returns associated with a certain risk. Risk, in this context, is almost identical to the mathematical concept of probability.

But even in finance, you have one kind of risk that is always negative — it is Operational Risk. My professional interest right now is in minimizing the operational risk associated with trading and computational platforms.

How do you measure Risk?

Measuring risk ultimately boils down to estimating the probability of a loss as a function of something — typically the intensity of the loss and time. So it’s like asking — What’s the probability of losing a million dollars or two million dollars tomorrow or the day after?

The question whether we can measure risk is another way of asking whether we can figure out this probability function. In certain cases, we believe we can — in Market Risk, for instance, we have very good models for this function. Credit Risk is different story — although we thought we could measure it, we learned the hard way that we probably could not.

The question how effective the measure is, is, in my view, like asking ourselves, “What do we do with a probability number?” If I do a fancy calculation and tell you that you have 27.3% probability of losing one million tomorrow, what do you do with that piece of information? Probability has a reasonable meaning only a statistical sense, in high-frequency events or large ensembles. Risk events, almost by definition, are low-frequency events and a probability number may have only limited practical use. But as a pricing tool, accurate probability is great, especially when you price instruments with deep market liquidity.

Innovation in Risk Management.

Innovation in Risk comes in two flavors — one is on the risk taking side, which is in pricing, warehousing risk and so on. On this front, we do it well, or at least we think we are doing it well, and innovation in pricing and modeling is active. The flip side of it is, of course, risk management. Here, I think innovation lags actually behind catastrophic events. Once we have a financial crisis, for instance, we do a post-mortem, figure out what went wrong and try to implement safety guards. But the next failure, of course, is going to come from some other, totally, unexpected angle.

What is the role of Risk Management in a bank?

Risk taking and risk management are two aspects of a bank’s day-to-day business. These two aspects seem in conflict with each other, but the conflict is no accident. It is through fine-tuning this conflict that a bank implements its risk appetite. It is like a dynamic equilibrium that can be tweaked as desired.

What is the role of vendors?

In my experience, vendors seem to influence the processes rather than the methodologies of risk management, and indeed of modeling. A vended system, however customizable it may be, comes with its own assumptions about the workflow, lifecycle management etc. The processes built around the system will have to adapt to these assumptions. This is not a bad thing. At the very least, popular vended systems serve to standardize risk management practices.

The Big Bang Theory – Part II

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.

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.

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.]

Tsunami

The Asian Tsunami two and a half years ago unleashed tremendous amount energy on the coastal regions around the Indian ocean. What do you think would’ve have happened to this energy if there had been no water to carry it away from the earthquake? I mean, if the earthquake (of the same kind and magnitude) had taken place on land instead of the sea-bed as it did, presumably this energy would’ve been present. How would it have manifested? As a more violent earthquake? Or a longer one?

I picture the earthquake (in cross-section) as a cantilever spring being held down and then released. The spring then transfers the energy to the tsunami in the form of potential energy, as an increase in the water level. As the tsunami radiates out, it is only the potential energy that is transferred; the water doesn’t move laterally, only vertically. As it hits the coast, the potential energy is transferred into the kinetic energy of the waves hitting the coast (water moving laterally then).

Given the magnitude of the energy transferred from the epicenter, I am speculating what would’ve happened if there was no mechanism for the transfer. Any thoughts?

Universe – Size and Age

I posted this question that was bothering me when I read that they found a galaxy at about 13 billion light years away. My understanding of that statement is: At distance of 13 billion light years, there was a galaxy 13 billion years ago, so that we can see the light from it now. Wouldn’t that mean that the universe is at least 26 billion years old? It must have taken the galaxy about 13 billion years to reach where it appears to be, and the light from it must take another 13 billion years to reach us.

In answering my question, Martin and Swansont (who I assume are academic phycisists) point out my misconceptions and essentially ask me to learn more. All shall be answered when I’m assimilated, it would appear! :-)

This debate is published as a prelude to my post on the Big Bang theory, coming up in a day or two.

Mowgli 03-26-2007 10:14 PM

Universe – Size and Age
I was reading a post in http://www.space.com/ stating that they found a galaxy at about 13 billion light years away. I am trying to figure out what that statement means. To me, it means that 13 billion years ago, this galaxy was where we see it now. Isn’t that what 13b LY away means? If so, wouldn’t that mean that the universe has to be at least 26 billion years old? I mean, the whole universe started from one singular point; how could this galaxy be where it was 13 billion years ago unless it had at least 13 billion years to get there? (Ignoring the inflationary phase for the moment…) I have heard people explain that the space itself is expanding. What the heck does that mean? Isn’t it just a fancier way of saying that the speed of light was smaller some time ago?
swansont 03-27-2007 09:10 AM

Quote:

Originally Posted by Mowgli
(Post 329204)
I mean, the whole universe started from one singular point; how could this galaxy be where it was 13 billion years ago unless it had at least 13 billion years to get there? (Ignoring the inflationary phase for the moment…)

Ignoring all the rest, how would this mean the universe is 26 billion years old?

Quote:

Originally Posted by Mowgli
(Post 329204)
I have heard people explain that the space itself is expanding. What the heck does that mean? Isn’t it just a fancier way of saying that the speed of light was smaller some time ago?

The speed of light is an inherent part of atomic structure, in the fine structure constant (alpha). If c was changing, then the patterns of atomic spectra would have to change. There hasn’t been any confirmed data that shows that alpha has changed (there has been the occasional paper claiming it, but you need someone to repeat the measurements), and the rest is all consistent with no change.

Martin 03-27-2007 11:25 AM

To confirm or reinforce what swansont said, there are speculation and some fringe or nonstandard cosmologies that involve c changing over time (or alpha changing over time), but the changing constants thing just gets more and more ruled out.I’ve been watching for over 5 years and the more people look and study evidence the LESS likely it seems that there is any change. They rule it out more and more accurately with their data.So it is probably best to ignore the “varying speed of light” cosmologies until one is thoroughly familiar with standard mainstream cosmology.You have misconceptions Mowgli

  • General Relativity (the 1915 theory) trumps Special Rel (1905)
  • They don’t actually contradict if you understand them correctly, because SR has only a very limited local applicability, like to the spaceship passing by:-)
  • Wherever GR and SR SEEM to contradict, believe GR. It is the more comprehensive theory.
  • GR does not have a speed limit on the rate that very great distances can increase. the only speed limit is on LOCAL stuff (you can’t catch up with and pass a photon)
  • So we can and DO observe stuff that is receding from us faster than c. (It’s far away, SR does not apply.)
  • This was explained in a Sci Am article I think last year
  • Google the author’s name Charles Lineweaver and Tamara Davis.
  • We know about plenty of stuff that is presently more than 14 billion LY away.
  • You need to learn some cosmology so you wont be confused by these things.
  • Also a “singularity” does not mean a single point. that is a popular mistake because the words SOUND the same.
  • A singularity can occur over an entire region, even an infinite region.

Also the “big bang” model doesn’t look like an explosion of matter whizzing away from some point. It shouldn’t be imagined like that. The best article explaining common mistakes people have is this Lineweaver and Davis thing in Sci Am. I think it was Jan or Feb 2005 but I could be a year off. Google it. Get it from your local library or find it online. Best advice I can give.

Mowgli 03-28-2007 01:30 AM

To swansont on why I thought 13 b LY implied an age of 26 b years:When you say that there is a galaxy at 13 b LY away, I understand it to mean that 13 billion years ago my time, the galaxy was at the point where I see it now (which is 13 b LY away from me). Knowing that everything started from the same point, it must have taken the galaxy at least 13 b years to get where it was 13 b years ago. So 13+13. I’m sure I must be wrong.To Martin: You are right, I need to learn quite a bit more about cosmology. But a couple of things you mentioned surprise me — how do we observe stuff that is receding from as FTL? I mean, wouldn’t the relativistic Doppler shift formula give imaginary 1+z? And the stuff beyond 14 b LY away – are they “outside” the universe?I will certainly look up and read the authors you mentioned. Thanks.
swansont 03-28-2007 03:13 AM

Quote:

Originally Posted by Mowgli
(Post 329393)
To swansont on why I thought 13 b LY implied an age of 26 b years:When you say that there is a galaxy at 13 b LY away, I understand it to mean that 13 billion years ago my time, the galaxy was at the point where I see it now (which is 13 b LY away from me). Knowing that everything started from the same point, it must have taken the galaxy at least 13 b years to get where it was 13 b years ago. So 13+13. I’m sure I must be wrong.

That would depend on how you do your calibration. Looking only at a Doppler shift and ignoring all the other factors, if you know that speed correlates with distance, you get a certain redshift and you would probably calibrate that to mean 13b LY if that was the actual distance. That light would be 13b years old.

But as Martin has pointed out, space is expanding; the cosmological redshift is different from the Doppler shift. Because the intervening space has expanded, AFAIK the light that gets to us from a galaxy 13b LY away is not as old, because it was closer when the light was emitted. I would think that all of this is taken into account in the measurements, so that when a distance is given to the galaxy, it’s the actual distance.

Martin 03-28-2007 08:54 AM

Quote:

Originally Posted by Mowgli
(Post 329393)
I will certainly look up and read the authors you mentioned.

This post has 5 or 6 links to that Sci Am article by Lineweaver and Davis

http://scienceforums.net/forum/showt…965#post142965

It is post #65 on the Astronomy links sticky thread

It turns out the article was in the March 2005 issue.

I think it’s comparatively easy to read—well written. So it should help.

When you’ve read the Sci Am article, ask more questions—your questions might be fun to try and answer:-)

Twin Paradox – Take 2

The Twin Paradox is usually explained away by arguing that the traveling twin feels the motion because of his acceleration/deceleration, and therefore ages slower.

But what will happen if the twins both accelerate symmetrically? That is, they start from rest from one space point with synchronized clocks, and get back to the same space point at rest by accelerating away from each other for some time and decelerating on the way back. By the symmetry of the problem, it seems that when the two clocks are together at the end of the journey, at the same point, and at rest with respect to each other, they have to agree.

Then again, during the whole journey, each clock is in motion (accelerated or not) with respect to the other one. In SR, every clock that is in motion with respect to an observer’s clock is supposed run slower. Or, the observer’s clock is always the fastest. So, for each twin, the other clock must be running slower. However, when they come back together at the end of the journey, they have to agree. This can happen only if each twin sees the other’s clock running faster at some point during the journey. What does SR say will happen in this imaginary journey?

(Note that the acceleration of each twin can be made constant. Have the twins cross each other at a high speed at a constant linear deceleration. They will cross again each other at the same speed after sometime. During the crossings, their clocks can be compared.)

Unreal Time

Farsight wrote:Time is a velocity-dependent subjective measure of event succession rather than something fundamental – the events mark the time, the time doesn’t mark the events. This means the stuff out there is space rather than space-time, and is an “aether” veiled by subjective time.

I like your definition of time. It is close to my own view that time is “unreal.” It is possible to treat space as real and space-time as something different, as you do. This calls for some careful thought. I will outline my thinking in this post and illustrate it with an example, if my friends don’t pull me out for lunch before I can finish. :)

The first question we need to ask ourselves is why space and time seem coupled? The answer is actually too simple to spot, and it is in your definition of time. Space and time mix through our concept of velocity and our brain’s ability to sense motion. There is an even deeper connection, which is that space is a cognitive representation of the photons inputs to our eyes, but we will get to it later.

Let’s assume for a second that we had a sixth sense that operated at an infinite speed. That is, if star explodes at a million light years from us, we can sense it immediately. We will see it only after a million years, but we sense it instantly. I know, it is a violation of SR, cannot happen and all that, but stay with me for a second. Now, a little bit of thinking will convince you that the space that we sense using this hypothetical sixth sense is Newtonian. Here, space and time can be completely decoupled, absolute time can be defined etc. Starting from this space, we can actually work out how we will see it using light and our eyes, knowing that the speed of light is what it is. It will turn out, clearly, that we seen events with a delay. That is a first order (or static) effect. The second order effect is the way we perceive objects in motion. It turns out that we will see a time dilation and a length contraction (for objects receding from us.)

Let me illustrate it a little further using echolocation. Assume that you are a blind bat. You sense your space using sonar pings. Can you sense a supersonic object? If it is coming towards you, by the time the reflected ping reaches you, it has gone past you. If it is going away from you, your pings can never catch up. In other words, faster than sound travel is “forbidden.” If you make one more assumption – the speed of the pings is the same for all bats regardless of their state of motion – you derive a special relativity for bats where the speed of sound is the fundamental property of space and time!

We have to dig a little deeper and appreciate that space is no more real than time. Space is a cognitive construct created out of our sensory inputs. If the sense modality (light for us, sound for bats) has a finite speed, that speed will become a fundamental property of the resultant space. And space and time will be coupled through the speed of the sense modality.

This, of course, is only my own humble interpretation of SR. I wanted to post this on a new thread, but I get the feeling that people are a little too attached to their own views in this forum to be able to listen.

Leo wrote:Minkowski spacetime is one interpretation of the Lorentz transforms, but other interpretations, the original Lorentz-Poincaré Relativity or modernized versions of it with a wave model of matter (LaFreniere or Close or many others), work in a perfectly euclidean 3D space.

So we end up with process slowdown and matter contraction, but NO time dilation or space contraction. The transforms are the same though. So why does one interpretation lead to tensor metric while the others don’t? Or do they all? I lack the theoretical background to answer the question.

Hi Leo,

If you define LT as a velocity dependent deformation of an object in motion, then you can make the transformation a function of time. There won’t be any warping and complications of metric tensors and stuff. Actually what I did in my book is something along those lines (though not quite), as you know.

The trouble arises when the transformation matrix is a function of the vector is transforming. So, if you define LT as a matrix operation in a 4-D space-time, you can no longer make it a function of time through acceleration any more than you can make it a function of position (as in a velocity field, for instance.) The space-time warping is a mathematical necessity. Because of it, you lose coordinates, and the tools that we learn in our undergraduate years are no longer powerful enough to handle the problem.

Of Rotation, LT and Acceleration

In the “Philosophical Implications” forum, there was an attempt to incorporate acceleration into Lorentz transformation using some clever calculus or numerical techniques. Such an attempt will not work because of a rather interesting geometric reason. I thought I would post the geometric interpretation of Lorentz transformation (or how to go from SR to GR) here.

Let me start with a couple of disclaimers. First of, what follows is my understanding of LT/SR/GR. I post it here with the honest belief that it is right. Although I have enough academic credentials to convince myself of my infallibility, who knows? People much smarter than me get proven wrong every day. And, if we had our way, we would prove even Einstein himself wrong right here in this forum, wouldn’t we? :D Secondly, what I write may be too elementary for some of the readers, perhaps even insultingly so. I request them to bear with it, considering that some other readers may find it illuminating. Thirdly, this post is not a commentary on the rightness or wrongness of the theories; it is merely a description of what the theories say. Or rather, my version of what they say. With those disclaimers out of the way, let’s get started…

LT is a rotation in the 4-D space-time. Since it not easy to visualize 4-D space-time rotation, let’s start with a 2-D, pure space rotation. One fundamental property of a geometry (such as 2-D Euclidean space) is its metric tensor. The metric tensor defines the inner product between two vectors in the space. In normal (Euclidean or flat) spaces, it also defines the distance between two points (or the length of a vector).

Though the metric tensor has the dreaded “tensor” word in its name, once you define a coordinate system, it is only a matrix. For Euclidean 2-D space with x and y coordinates, it is the identity matrix (two 1’s along the diagonal). Let’s call it G. The inner product between vectors A and B is A.B = Trans(A) G B, which works out to be a_1b_1+a_2b_2. Distance (or length of A) can be defined as sqrt{A.A}.

So far in the post, the metric tensor looks fairly useless, only because it is the identity matrix for Euclidean space. SR (or LT), on the other hand, uses Minkowski space, which has a metric that can be written with [-1, 1, 1, 1] along the diagonal with all other elements zero – assuming time t is the first component of the coordinate system. Let’s consider a 2-D Minkowski space for simplicity, with time (t) and distance (x) axes. (This is a bit of over-simplification because this space cannot handle circular motion, which is popular in some threads.) In units that make c = 1, you can easily see that the invariant distance using this metric tensor is sqrt{x^2 - t^2}.

Lorentz transformation is a rotation in the Minkowski space. In order to see it, let’s first look at rotation in Euclidean space, which can be written as X’ = R X. In the 2-D case, the matrix of rotation R is,
left[ {begin{array}{*{20}c}{cos theta } & { - sin theta }  \{sin theta } & {cos theta }  \end{array}} right]
So, the matrix equation expands to

where theta is the angle of rotation. This is how a point X=(x,y) in the original frame transforms to in the rotated frame.

Similarly, LT in Minkowski space is X’ = L X. Lorentz Transformation matrix (in our 2-D case) is,
left[ {begin{array}{*{20}c}gamma  & { - beta gamma }  \{ - beta gamma } & gamma   \end{array}} right]
where beta  = v/c and gamma  = 1/sqrt {1 - beta ^2 }

This expands to

Note that rotation (and so LT) is a linear transformation, which means that the matrix R (or L) has to be independent of the vector it transforms. What happens when the matrix is a function of x, y or t? The geometry becomes non-flat and the metric tensor we defined doesn’t define the invariant distance any longer. The geometry requires a different metric tensor. Therefore, rotation or LT as we defined it and the associated single component equations is not valid any more. I will illustrate it further using 2-D rotation in the next post and show what they mean when they say that space-time is curved.

The Unreal Universe — Discussion with Gibran

Hi again,You raise a lot of interesting questions. Let me try to answer them one by one.

You’re saying that our observations of an object moving away from us would look identical in either an SR or Galilean context, and therefore this is not a good test for SR.

What I’m saying is slightly different. The coordinate transformation in SR is derived considering only receding objects and sensing it using radar-like round trip light travel time. It is then assumed that the transformation laws thus derived apply to all objects. Because the round trip light travel is used, the transformation works for approaching objects as well, but not for things moving in other directions. But SR assumes that the transformation is a property of space and time and asserts that it applies to all moving (inertial) frames of reference regardless of direction.

We have to go a little deeper and ask ourselves what that statement means, what it means to talk about the properties of space. We cannot think of a space independent of our perception. Physicists are typically not happy with this starting point of mine. They think of space as something that exists independent of our sensing it. And they insist that SR applies to this independently existing space. I beg to differ. I consider space as a cognitive construct based on our perceptual inputs. There is an underlying reality that is the cause of our perception of space. It may be nothing like space, but let’s assume, for the sake of argument, that the underlying reality is like Galilean space-time. How would be perceive it, given that we perceive it using light (one-way travel of light, not two-way as SR assumes)? It turns out that our perceptual space would have time dilation and length contraction and all other effect predicted by SR. So my thesis is that the underlying reality obeys Galilean space-time and our perceptual space obeys something like SR. (It is possible that if I assume that our perception uses two-way light travel, I may get SR-like transformation. I haven’t done it because it seems obvious to me that we perceive a star, for instance, by sensing the light from it rather than flashing a light at it.)

This thesis doesn’t sit well with physicists, and indeed with most people. They mistake “perceptual effects” to be something like optical illusions. My point is more like space itself is an illusion. If you look at the night sky, you know that the stars you see are not “real” in the sense that they are not there when you are looking at them. This is simply because the information carrier, namely light, has a finite speed. If the star under observation is in motion, our perception of its motion is distorted for the same reason. SR is an attempt to formalize our perception of motion. Since motion and speed are concepts that mix space and time, SR has to operate on “space-time continuum.” Since SR is based on perceptual effects, it requires an observer and describes motion as he perceives it.

But are you actually saying that not a single experiment has been done with objects moving in any other direction than farther away? And what about experiments on time dilation where astronauts go into space and return with clocks showing less elapsed time than ones that stayed on the ground? Doesn’t this support the ideas inherent in SR?

Experiments are always interpreted in the light of a theory. It is always a model based interpretation. I know that this is not a convincing argument for you, so let me give you an example. Scientists have observed superluminal motion in certain celestial objects. They measure the angular speed of the celestial object, and they have some estimate of its distance from us, so they can estimate the speed. If we didn’t have SR, there would be nothing remarkable about this observation of superluminality. Since we do have SR, one has to find an “explanation” for this. The explanation is this: when an object approaches us at a shallow angle, it can appear to come in quite a bit faster than its real speed. Thus the “real” speed is subluminal while the “apparent” speed may be superluminal. This interpretation of the observation, in my view, breaks the philosophical grounding of SR that it is a description of the motion as it appears to the observer.

Now, there are other observations of where almost symmetric ejecta are seen on opposing jets in symmetric celestial objects. The angular speeds may indicate superluminality in both the jets if the distance of the object is sufficiently large. Since the jets are assumed to be back-to-back, if one jet is approaching us (thereby giving us the illusion of superluminality), the other jet has bet receding and can never appear superluminal, unless, of course, the underlying motion is superluminal. The interpretation of this observation is that the distance of the object is limited by the “fact” that real motion cannot be superluminal. This is what I mean by experiments being open to theory or model based interpretations.

In the case of moving clocks being slower, it is never a pure SR experiment because you cannot find space without gravity. Besides, one clock has to be accelerated or decelerated and GR applies. Otherwise, the age-old twin paradox would apply.

I know there have been some experiments done to support Einstein’s theories, like the bending of light due to gravity, but are you saying that all of them can be consistently re-interpreted according to your theory? If this is so, it’s dam surprising! I mean, no offense to you – you’re obviously a very bright individual, and you know much more about this stuff than I do, but I’d have to question how something like this slipped right through physicists’ fingers for 100 years.

These are gravity related questions and fall under GR. My “theory” doesn’t try to reinterpret GR or gravity at all. I put theory in inverted quotes because, to me, it is a rather obvious observation that there is a distinction between what we see and the underlying causes of our perception. The algebra involved is fairly simple by physics standards.

Supposing you’re right in that space and time are actually Galilean, and that the effects of SR are artifacts of our perception. How then are the results of the Michelson-Morley experiments explained? I’m sorry if you did explain it in your book, but it must have flown right over my head. Or are we leaving this as a mystery, an anomaly for future theorists to figure out?

I haven’t completely explained MMX, more or less leaving it as a mystery. I think the explanation hinges on how light is reflected off a moving mirror, which I pointed out in the book. Suppose the mirror is moving away from the light source at a speed of v in our frame of reference. Light strikes it at a speed of c-v. What is the speed of the reflected light? If the laws of reflection should hold (it’s not immediately obvious that they should), then the reflected light has to have a speed of c-v as well. This may explain why MMX gives null result. I haven’t worked out the whole thing though. I will, once I quit my day job and dedicate my life to full-time thinking. :-)

My idea is not a replacement theory for all of Einstein’s theories. It’s merely a reinterpretation of one part of SR. Since the rest of Einstein’s edifice is built on this coordinate transformation part, I’m sure there will be some reinterpretation of the rest of SR and GR also based on my idea. Again, this is a project for later. My reinterpretation is not an attempt to prove Einstein’s theories wrong; I merely want to point out that they apply to reality as we perceive it.

Overall, it was worth the $5 I payed. Thanks for the good read. Don’t take my questions as an assault on your proposal – I’m honestly in the dark about these things and I absolutely crave light (he he). If you could kindly answer them in your spare time, I’d love to share more ideas with you. It’s good to find a fellow thinker to bounce cool ideas like this off of. I’ll PM you again once I’m fully done the book. Again, it was a very satisfying read.

Thanks! I’m glad that you like my ideas and my writing. I don’t mind criticism at all. Hope I have answered most of your questions. If not, or if you want to disagree with my answers, feel free to write back. Always a pleasure to chat about these things even if we don’t agree with each other.

- Best regards,
– Manoj

Anti-relativity and Superluminality

Leo wrote:I have some problems with the introductory part though, when you confront light travel effects and relativistic transforms. You correctly state that all perceptual illusions have been cleared away in the conception of Special Relativity, but you also say that these perceptual illusions remained as a subconscious basis for the cognitive model of Special Relativity. Do I understand what you mean or do I get it wrong?

The perceptual effects are known in physics; they are called Light Travel Time effects (LTT, to cook up an acronym). These effects are considered an optical illusion on the motion of the object under observation. Once you take out the LTT effects, you get the “real” motion of the object . This real motion is supposed to obey SR. This is the current interpretation of SR.

My argument is that the LTT effects are so similar to SR that we should think of SR as just a formalization of LTT. (In fact, a slightly erroneous formalization.) Many reasons for this argument:
1. We cannot disentagle the “optical illusion” because many underlying configurations give rise to the same perception. In other words, going from what we see to what is causing our perception is a one to many problem.
2. SR coordinate transformation is partially based on LTT effects.
3. LTT effects are stronger than relativistic effects.

Probably for these reasons, what SR does is to say that what we see is what it is really like. It then tries to mathematically describe what we see. (This is what I meant by a formaliztion. ) Later on, when we figured out that LTT effects didn’t quite match with SR (as in the observation of “apparent” superluminal motion), we thought we had to “take out” the LTT effects and then say that the underlying motion (or space and time) obeyed SR. What I’m suggesting in my book and articles is that we should just guess what the underlying space and time are like and work out what our perception of it will be (because going the other way is an ill-posed one-to-many problem). My first guess, naturally, was Galilean space-time. This guess results in a rather neat and simple explantions of GRBs and DRAGNs as luminal booms and their aftermath.