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}.

Continued…

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.

Discussion on the Daily Mail (UK)

On the Daily Mail forum, one participant (called “whats-in-a-name”) started talking about The Unreal Universe on July 15, 2006. It was attacked fairly viciously on the forum. I happened to see it during a Web search and decided to step in and defend it.

15 July, 2006

Posted by: whats-in-a-name on 15/07/06 at 09:28 AM

Ah, Kek, you’ve given me a further reason to be distracted from what I should be doing- and I can tell you that this is more interesting at the moment.I’ve been trying to formulate some ideas and there’s one coming- but I’ll have to give it to you in bits.I don’t want to delve into pseudoscience or take the woo-ish road that says that you can explain everything with quantum theory, but try starting here: http://theunrealuniverse.com/phys.shtml

The “Journal Article” link at the bottom touches on some of the points that we discussed elsewhere. It goes slightly off-topic, but you might also find the “Philosophy” link at the top left interesting.

Posted by: patopreto on 15/07/06 at 06:17 PM

Regarding that web site wian.One does not need to ead past this sentence –

The theories of physics are a description of reality. Reality is created out of the readings from our senses. Knowing that our senses all work using light as an intermediary, is it a surprise that the speed of light is of fundamental importance in our reality?

to realise that tis web site is complete ignorant hokum. I stopped at that point.

16 July, 2006

Posted by: whats-in-a-name on 16/07/06 at 09:04 AM

I’ve just been back to read that bit more carefully. I don’t know why the writer phrased it like that but surely what he meant was:(i) “Our perception of what is real is created out of the readings from our senses.” I think that most physicists wouldn’t argue with that would they? At the quantum level reality as we understand it doesn’t exist; you can only say that particles have more of a tendency to exist in one place or state than another.(ii) The information that we pick up from optical or radio telescopes, gamma-ray detectors and the like, shows the state of distant objects as they were in the past, owing to the transit time of the radiation. Delving deeper into space therefore enables us to look further back into the history of the universe.It’s an unusual way to express the point, I agree, but it doesn’t devalue the other information on there. In particular there are links to other papers that go into rather more detail, but I wanted to start with something that offered a more general view.

I get the impression that your study of physics is rather more advanced than mine- as I’ve said previously I’m only an amateur, though I’ve probably taken my interest a bit further than most. I’m happy to be corrected if any of my reasoning is flawed, though what I’ve said so far s quite basic stuff.

The ideas that I’m trying to express in response to Keka’s challenge are my own and again, I’m quite prepared to have you or anyone else knock them down. I’m still formulating my thoughts and I wanted to start by considering the model that physicists use of the nature of matter, going down to the grainy structure of spacetime at the Plank distance and quantum uncertainty.

I’ll have to come back to this in a day or two, but meanwhile if you or anyone else wants to offer an opposing view, please do.

Posted by: patopreto on 16/07/06 at 10:52 AM

I don’t know why the writer phrased it like that but surely what he meant was:

I think the write is quit clear! WIAN – you have re-written what he says to mean something different.

The writer is quite clear – “Once we accept that space and time are a part of the cognitive model created by the brain, and that special relativity applies to the cognitive model, we can ponder over the physical causes behind the model, the absolute reality itself.”

Blah Blah Blah!

The writer, Manoj Thulasidas, is an employee of OCBC bank in Singapore and self-described “amateur philosopher”. What is he writes appears to be nothing more than a religiously influenced solipsistic philosophy. Solipsism is interesting as a philosophical standpoint but quickly falls apart. If Manoj can start his arguments from such shaky grounds without explanation, then I really have no other course to take than to accept his descriptions of himself as “amateur”.

Maybe back to MEQUACK!

What is Real? Discussions with Ranga.

This post is a long email discussion I had with my friend Ranga. The topic was the unreality of reality of things and how this notion can be applied in physics.

Going through the debate again, I feel that Ranga considers himself better-versed in the matters of philosophy than I am. I do too, I consider him better read than me. But I feel that his assumption (that I didn’t know so much that I should be talking about such things) may have biased his opinion and blinded him to some of the genuinely new things (in my opinion, of course) I had to say. Nonetheless, I think there are quite a few interesting points that came out during the debate that may be of general interest. I have edited and formatted the debate for readability.

It is true that many bright people have pondered over the things I talk about in this blog and in my book. And they have articulated their thoughts in their works, probably better than I have in mine. Although it is always a good idea to go through the existing writings to “clear my head” (as one of my reviewers suggested while recommending David Humes), such wide reading creates an inherent risk. It is not so much the time it will take to read and understand the writings and the associated opportunity cost in thinking; it is also the fact that everything you read gets assimilated in you and your opinions become influenced by these brilliant thinkers. While that may be a good thing, I look at it as though it may actually be detrimental to original thought. Taken to the extreme, such blind assimilation may result in your opinions becoming mere regurgitation of these classical schools of thought.

Besides, as Hermann Hesse implies in Siddhartha, wisdom cannot be taught. It has to be generated from within.

Ranga’s words are colored Green (or Blue when quoted for the second time).

Mine are in White (or Purple when quoted for the second time).

Mon, May 21, 2007 at 8:07 PM.

I’m, to different extents, familiar with the distinction philosophers and scientists make in terms of phenomenal and physical realities – from the works of Upanishads, to the Advaitas/Dvaitas, to the Noumenon/Phenomenon of Schopenhauer, and the block Universe of Special Relativity, and even the recent theories in physics (Kaluza and Klein). The insight that what we perceive is not necessarily what “is”, existed in a variety of ways from a long time. However, such insights were not readily embraced and incorporated in all sciences. There is a enormous literature on this in neuroscience and social sciences. So, it is indeed very good that you have attempted to bring this in to physics – by recollecting our previous discussion on this, by reading through your introduction to the book in the website and understanding the tilt of your paper (could not find it in the journal – has it been accepted?). To suggest that there could be superluminal motion and to explain known phenomena such as GRBs through a quirk (?) in our perception (even in the physical instruments) is bold and needs careful attention by others in the field. One should always ask questions to cross “perceived” boundaries – in this case of course the speed of light.

However, it is quite inaccurate and superficial (in my opinion) to think that there is some “absolute” reality beyond the “reality” we encounter. While it is important to know that there are multiple realities for different individuals in us, and even different organisms, depending on senses and intellect, it is equally important to ask what reality is after all when there is no perception. If it cannot be accessed by any means, what is it anyway? Is there such a thing at all? Is Absolute Reality in the movement of planets, stars and galaxies without organisms in them? Who perceives them as such when there is nobody to perceive? What form do they take? Is there form? In applying philosophy (which I read just as deeper and bolder questions) to science (which I read as a serious attempt to answer those questions), you cannot be half-way in your methods, drawing imaginary boundaries that some questions are too philosophical or too theological for now.

While your book (the summary at least) seems to bring home an important point (at least to those who have not thought in this direction) that the reality we perceive is dependent on the medium/mode (light in some cases) and the instrument (sense organ and brain) we use for perceiving, it seems to leave behind a superficial idea that there is Absolute Reality when you remove these perceptual errors. Are they perceptual errors – aren’t perceptual instruments and perceptions themselves part of reality itself? To suggest that there is some other reality beyond the sum of all our perceptions is philosophically equally erroneous as suggesting that what we perceive is the only reality.

All the same, the question about reality or the lack of it has not been well incorporated into the physical sciences and I wish you the best in this regard.

Cheers
Ranga