Infinite in All Directions

Hi,

I`m taking the course on consciousness offered on the net by Arizona University and I have speculated that perhaps even elementary particles have some kind of rudimentary consciousness, because, if nature were totally unconscious, then how could a particle, or wavelet, or whatever, `know` that it was interacting with another particle or wavelet? The problem with the current theories of physics is that they are trying to produce interaction without any `knowing` and in my gut, my instinct tell me that this is never going to be really satisfactory. It`s sort of the `dead hand` theory that says that the dead hand of God moves everything around without God knowing what is happening. Nonsense!

It seems mysterious how force is transmitted between particles. Why couldn`t it be that there is an elementary form of consciousness involved that these particles have. Then perhaps human consciousness could be explained by the massing together, or focusing, or whatever, together of these more elementary consciusnesses.

If you take the time to reply I will post on on the course comment board. I`d like to see how the other students and teachers react if you offer an opinion on this.

Your article was very nice. Very clear. Thank-You,

Wayne

You mentioned that most of the latest theories are ignoring gravity. Would you be interested in seeing a different theory? I know a lot of ideas abound but this one is straight forward and explains gravity, electromagnetism and nuclear strong forces. I can`t find any holes in it. I would like to submit it to someone who could evaluate it. It is based upon concentrated space. It fits into Einstein`s General Theory of Relativity, Durac`s Quantum Mechanics, the Fine Structure Constant, and a few other pieces. I have an article written with pictures and math. If you are interested e-mail me. --Dave

Re: Wasiq

So, infinities have not entirely been swept under the rug :)
Thanks for the preview. I will wait for part 2 before making any further comments.

Fozia

Re: Fozia

Thanks for your comments.

Remarkably, your observation about renormalization is at the heart of the reason why people have been exploring options beyond Quantum Field Theories (QFT) as models of the natural world. (A mathematician`s eye quickly spots the trouble spots ... ) I was hoping to get more into the idea and method of renormalization in the second part of the article, before I described what comes next.

But here`s a preview ...

A sensible QFT should not only be solvable, but also interpretable. Consider a generic p.d.e that I wish to solve, first in the absence of a source term, DX=0 (D is the operator). The general solution is obtained by characterizing the Green`s function, DG=delta(X). In the presence of a source term, the calculation of a general solution may not be possible, even with the knowledge of the Green`s function, so one is forced to approximate methods like a perturbation expansion, with the lowest order term being the source-less system. The validity of the perturbation expansion depends on the identification of a small expansion parameter, and on the fact that successive terms in the series should be (progressively) small, in order to avoid divergence. That is usually how one goes about solving a QFT.

In QFT, however, one often finds that successive terms, are not only large compared to the leading term, but infinite. Therefore, we look at how we interpret those results, and try to find a reinterpretation that leads to finite answers for OBSERVABLE parameters. This process, renormalization, involves first making the solutions finite by imposing a cutoff parameter (i.e M), which in the limit to infinity gives the original divergent answer. Next, within the equations themselves, we have parameters that we identify with an observable, like the charge (e) or the mass (m) of a particle. In the presence of a source term, the meaning of those parameters needs to be redefined. Without a redefinition, these parameters diverge, causing the infinities.

Let me be somewhat concrete: Consider a physical theory whose Lagrangian depends on two parameters, say e0 and m0. We would interpret these as the charge and the mass respectively. Now if I calculate two physical processes from which I would measure the true charge and mass, e and m, I will find that the results would diverge. So one first makes the theory finite, by introducing the cut-off parameter M, and then considering e and m to be arbitrary parameters (c.f my earlier statement about the reinterpretation in the presence of a source) re-write them in terms of so called ``bare`` parameters e0 and m0:

m = m(m0,e0,M)

e = e(m0,e0,M)

We want to make m and e independent of M, therefore, we can choose e0 and m0 to be functions of M in such a way that dm/dM = de/dM = 0. These lead to coupled equations that describe a trajectory in parameter space. Of course, it may happen that e0 and m0 may not have enough freedom to make the answers finite in the limit M to infinity. In that case, one will need to add additional terms and parameters to the original Lagrangian to make it finite. As long as those new terms are local and finite in number, the theory is renormalizable.

What has happened is that the infinities have been swept away into the ``bare`` parameters, e0 and m0, but that is ok, since, they are not observable.

Re: MAK

Thanks for your kind comments. I decided to follow a simple formula in my article, which (sadly) is that the number of readers falls off exponentially with the number of equations in an article. That is perhaps one reason why I did not delve into the details of any particle statistics. The other reason was that in doing so, I would have to justify my statement about the spin of a particle and its statistics ... and things would get out of hand there. However, hopefully, I will have the opportunity to write a book sometime.

I think you have pointed out a very important thing, which is the role played by one`s mentors in encouraging/discouraging the path followed subsequently. I share your interest in fundamental physics also, and hope that despite your primary occupations in applied areas, you continue to keep in touch with the developments at a more fundamental level. Hopefully, in the second part of the article, I will get into more of that.

regards

Re: Amar Dev

Interestingly, this quote of Blake has been used by many physicists also when initially confronted by the infinities hidden in theoretical constructs. Whether they are `physical` infinities or not is a different issue ...

SR, You`re right, orders of magnitude quickly spiral out of the empirical capacity of our senses and mind. Maybe that is not so surprising, since the world around us does not afford us ways to condition our minds to the immensely large or small, or to things that we do not experience.

Mathematics, in this regard, is the equivalent of a tool, which just like a microscope or a telescope, brings what is beyond the experience of the senses, to within the reach of our cognitive abilities. It is not necessary that every concept be translatable into something that we experience every day.

On the contrary, I think it is wonderful that our minds are capable of imagining more than what the world around us apparently offers to us. For example, though we live in a strictly three-dimensional world, mathematically, dealing with infinite dimensional worlds is a matter of routine for many. And there exist some ``demons`` who can even visualize complicated objects in higher dimensional spaces. I personally have a prescription in my mind on how to think about four dimensional objects ... :-)

Re: Amber

Thank you for your kind comments. You`re right, almost all concepts can be conveyed to almost all people. Some may take more work because they assume the existence of a certain level of expertise.

I glanced at this article last week and realized that to do justice to it I had to read it over the weekend! I did, and I must say this is an extremely well written article. Wasiq, you have managed to impart the fundamentals in a remarkably lucid way.

Would it be possible for you to shed some more light on the process of Renormalization? The concept sounds interesting. My area of expertise is mathematics and as such Infinity is very much part of my `reality`....but how does a physicist go about conducting this separation of the infinite and the finite?

Looking forward to the next part.

Fozia

I just noticed this article and very surprised to see such an scholastic and intellectual article on Chowk. When I saw other articles and the number of replies on them I came to know why we are far behind in science. The fundamental difficult concepts in theoretical concepts have been eleborated in a very exquisite fashion that a layman could grasp with a little or no effort. Theoretical Physics has always been considered an abstract and conceptual subject difficult to be understood and expounded. My interest in theoretical physics vanished when my professor of Advanced Quantum Mechanics `explained` some concepts in more dubious manner and irked to the subject. Now with my current applied work of the dynamic in upper atmosphere I feel very comfortable but sometimes I try to read and understand some striking topics in Quantum Field Theory (QFT) and Quantum Electro Dynamics (QED).

What you think if you would have introduced the basic Fermi Dirac, Bose Einstein and Maxwell BoltzMan statistics in the article? I understand this could be explain considering a system of 3 levels and two particles and in terms of occupation numbers (ni) those statistics can be explained. Since you have excellent way of describing difficult concepts in a very easy manner I would suggest you spare some time to write book on such topics of physics for students in Pakistan so they can understand real physics and grasp the basic concepts. I know university students of physics from pakistan who even can`t explain Heisenberg`s principle. Please think of writing book(s) and that would be a beneficence on Pakistan.

Waiting the second part.

MAK

when the doors of perception are truely cleansed

things will appear as they truely are - infinite

blake

Re: Wasiq Bokhari

Thanks for your detailed response and for expressing your good wishes. By no means did I wish to imply that your elucidation was unclear. In fact, you have never stated anything on Chowk that can be called `unclear`, no matter how cumbersome your subject. What I was trying to express was my own inadequacy in being able to `feel` the concepts in my bones. Let me explain what I mean.

It always happens to me that when I read the description of a new travel destination I form a subconscious image of the place in my mind`s eye. The image may be foggy, but there is an image of some kind. Then after I visit that destination and experience its actual reality my old mental image is replaced by the new image, which is formed of the actual sensory inputs from the place. At that point the mind completely forgets the old vision that was imagined. In fact, it`s not even possible to recall those imaginary images because now the actual reality exists in the memory. The point, however, is that even before I go to the destination I am able to form an image because the `concepts` are not alien to me. That is so because any destination on earth would have common elements and those elements are within our power of perception. Now, let`s take this example further.

When I look at a map and see how far a place is from where I am, it gives me some kind of an idea. However, if I get in the car and drive that distance, then I have a different appreciation of what the distance in question really means. Now if I have to walk that same distance, my understanding and realization of the distance will be very different. Similarly, when I try to imagine how far the moon is from us, all I can relate to is a number. I cannot really `feel` the reality of that distance. If we go a bit further and talk of Alpha Century, then even the numbers become very ethereal and abstract. After all, how can I really imagine what that distance really means. I can comprehend ten raised to the power three, even four or five maybe, but beyond that it gets too abstract.

Let me tell you about ten raised to the power five. I fully KNOW what that means. In 1981 I was working on a project that involved data punch cards. We had to run those punch cards on an IBM mainframe that operated on JCL. I had to move the entire data set from one building to another. There were one hundred and thirteen thousand or so records. Each record was on a card. You would think that is no big number, but I had to physically move the cartons containing those data cards and it took me the whole hot summer afternoon to move them five two blocks away. It is daunting to imagine that a million cards would have been ten times that many. A billion would be ten thousand times. I`m sorry, but I cannot really pretend that I actually comprehend these numbers. Yes, I can intellectualize and describe the words and have some foggy feel for what they are, and yes, I can calculate their practical implications, but I can`t really feel the reality in my bones.

I once tried to comprehend how much time is a nanosecond. I simply couldn`t relate to a billionth of a second. To me it was a figurative concept with no hope ever of me understanding what it really means. (I was reading something about neutron starts and their very brief life cycle possibilities etc.) Ultimately, I calculated the distance that light would travel in that time and came up with the number. Then I took a piece of wire and cut that length out. That was the distance light travels in a nanosecond. I have forgotten what the exact number of centimeters was (and am too lazy to recalculate it right now), but in my mind`s eye I can still see that piece of wire which I had cut. It was barely over one foot long. I kept it with me for quite sometime and that is how I relate to a nanosecond.

It is the outlandishness of the scales involved in these concepts that I have an emotional hang-up about. I mean, seriously, how much are a hundred billion stars? STARS. Each, as big (or bigger) as our Sun. But that`s just the Milky Way. What about Inter-galactic distance? Those are mind boggling thoughts. Those are just unreal numbers. Almost fictional concepts. I try to imagine the proton decay process and its implications and the elaborate water-tank experiments devised to study the phenomenon. I think about the Cyclops project and its almost absurd ramifications and my head starts hurting.

So you see the problem is very much with me, not with your explanation. I could probably convey your article`s concepts to a friend and pretend that I fully know what they mean and I may sound convincing, yet I cannot get rid of the awful feeling of amazment and disbelief. We have indeed come a long way from the cave.

I can relate to how Allis must have felt when she went on the other side of the looking glass.

Sincerely…SR

Doctor sahib,

I`ve read and reread your elucidating article. i must confess that with my brief knowledge it was a very fascinating experience! It is an applaudable effort and the beginning of a new era in chowk where we can share a clear insight into each other`s worlds and specialities. I can understand that a layman in your field will not grasp the concepts quickly but it is a relief that he CAN GRASP THE CONCEPT with a little patience and concentration. I know no book that could help him more without confusing him further. I am eagerly looking forward to the next part of this piece. In the meantime i`d like to share this one with a group of people who would be keen to comment on it. I`ll get back to you later. Good JOb.....keep writing.

best wishes,

Amber

Rabbani Sahib,

I hope all is well with you. Thank you for your kind comments on the article. Some of the concepts that I have tried to present are not that difficult to grasp, once they are discovered (i.e. the famous Eureka! reaction and the post-Eureka this-was-so-simple-why-didnt-I-think-of-this-before). So I feel that I need to work more on my elaboration of these concepts. If you`re interested, I could revisit some of the things that you thought were not clearly presented, hopefully in a more understandable way this time.

I agree with you, that to an outsider, some of the concepts and jargon of a science becomes as abstract as the concept of angels dancing on a needle-point. But as you pointed out, there exists the element of experimentation, which constitutes the supporting evidence. About the efficacy of the scientific method itself, there has been a lot of work during this century, prominently by Popper and later Kuhn. Whereas Popper would allow the realization of only the falsification of a theory and nothing more, post-modernist Kuhn takes away even that consolation. But surely that is a separate discussion. But in real terms, the efficacy of science lies not in its abstraction, but in being able to communicate its key concepts to everyone and attracting interested people to continue the thought process. A detached and incommunicable knowledge quickly becomes useless, to put it another way, the vitality of science lies in its constant change. The parallels to other things in this context are rather obvious.

The question about the recent announcement of the expansion rate of the universe is a very interesting one. I have not heard much about the issue since its first publication some time ago, and it is unclear what is the exact status now. Roughly speaking, one could understand the issue as follows: When one assumes a given amount of density of matter in the universe, one can calculate how the gravitational pull of that matter would slow down the expansion rate of the universe. Now what these guys did was to look at galaxies that are extremely far away, more than approx. 6 billion light years, and by looking at their spectra, inferred the velocity at which they were receding from us. That velocity in very distant galxies, they found, was larger than what one would expect if one had assumed the retarding effect of matter on the expansion of the universe. One of the explanations given for this was to hypothesize the presence of a long-range repulsive force which would be pushing stuff away.

Like all things in science, the best attitude is that of a reserved caution. There are many things that could change that conclusion. Suppose they discover that there was a problem in their measurement (caused by something as mundane as a slight problem with their instruments), then the result would no longer hold. Similarly, even if the instruments were correct, but they were off in determining the distance of the galaxies, or the assumption that they had made about their structure. The details of the mathematical calculation performed to determine the expected deceleration of the universe are extremely important etc. etc. All of that will take time to precisely pin down and therefore, I would not start writing a science fiction novel based upon the presence of such a force yet :)

Talking about science fiction, I think sometimes certain preliminary observations get blown out of proportion once they get into the hands of eager journalists. All of that does not hurt the credibility of the newspaper, but only of the people who have spent years looking at something. Usually then researchers try to be very cautious in releasing their finds, and try to elucidate the preliminary nature of their findings. We have often seen cases where even a cautious attitude leads to a publishing of a result that is later discovered to be flawed or even wrong.

Bokhari sahib:

This is perhaps the most esoteric piece to have appeared on Chowk. I applaud your patience and passion for the microcosmic enigmas that are wrapped in sub-atomic mysteries. You have tackled a complex set of concepts with your customary clarity and thoroughness. Fascinating.

Its is brilliantly presented, yet owing to the nebulous nature of the concepts themselves at least this reader could barely manage a tenuous grasp of them. Admittedly, having only read soft stuff like: The Tao of Physics, and The Dancing Wu Lee Masters doesn`t nearly allow one to develop a comfortable concept of this dimension of microreality.

Unlike most of my enlightened friends I am one of those dim-wits who, even after three readings, could only partially understand (Steve Hawkins) A Brief History of Time. Likewise, I confess that though I `think` that I have followed all the concepts you present, at some point they became only words which I couldn`t really relate to in the sense of gaining a deeper, clearer understanding.

In the end, it all sounds very outlandish. Not too different from a discussion of the number of angels on the tip of a sword. But I realize there is a fundamantal difference. In this era we have experimentation, and thus something approaching `evidence`.

By the way, slightly off the subject, but within the scope of physics I have a question? What is this I hear about astrophysists and particle physists putting their head together in order to solve the problem of the discrepency in the value of the universal gravitational constant? I think the problem was noticed when someone discovered (using red-shift analysis) that the expansion of the universe was ACCLERATING, thus giving rise to concepts like anti-gravity and the like.

The universe was so much easier to comprehend when all we had to worry about was ghosts, gennies, angels and gods. These leptons, quarks and neutrinos are far more unfathomable. Yet we must take them on faith I suppose. No wonder physists have no trouble grasping the concept of the divine.

...SR

Very well written Boki. I am still in the middle of the History of the Standard Model (this article takes longer to get through than a piece on the demerits of politicians).

Will send in more comments later.