The limits of mathematics

Dear Ian,

Thank you for your message. I am thinking about bringing up specifics with regard to the problems I see in theoretical physics.

"...there is a serious discord between theoretical physics and empirical physics. I'm not entirely sure I agree it goes all the way back to Newton, ..."

Maybe I am right and maybe I am wrong. However, what I see in f=ma is a refutation of relativity theory. Changing mass changes almost everything. Getting it right, I think, will correct almost everything. I am certain it is not yet correctly defined. I say only those things which I am prepared to explain. I may be wrong; however, I have reasons for saying the things that I say. Maybe I will get to share them.

It is not easy to participate in a physics forum setting and challenge theoretical physics as strongly as I do. It certainly would be advantageous to actually be a theoretical physicist. Still, I would like to see this through. I cannot believe the patience of FQXi. Probably no one was more surprised than me to have Brendan approve my input, at least for a while. I think what I have to say may be a valuable leasson, maybe for me or maybe for others. I have a lengthy website available for anyone to view. I do not have problem, I think, with being corrected. However, correctness appears to exist oftentimes in our viewpoints. Who knows? I would like to know. Anything you have to say would be welcome.

James

Dear Ian,

Thank you for your message. I am reposting part of a message I wrote today to Jason, because, I think it is relevant to your topic. That is, unless I am wrong in the example I give below:

....I think its too early to judge who has the truth. I think relativity theory is clearly wrong. I think many other ideas carried along by theoretical physics are also wrong. Why should anyone care what I think? My conclusions will certainly not win any respect by themselves. There is only one place for me to participate and that is at the fundamental level. That is where the changes, as I see them, must begin to be made. I think it is the only place where I have any chance of scoring points. So, I mentioned elsewhere, in another message, the idea that defining mass in f=ma as being a unique fundamental property requiring its own unique indefinable units of measurement was a guess, and, I add now that it was a wrong guess.

Why should anyone care? The equation f=ma is long established newtonian physics. It is very successful up to the point where Einstein's theory corrects it. The success of the two of them together make the original theoretical interpretation of f=ma appear to be truth. That is a very big hill for any challenger to climb.

You (Jason) said: "In an earlier entry, I asked: what causes gravity? I still think the question deserves an answer."

I missed seeing this. I have looked back and could not find a previous message where you asked about the cause of gravity. But, now to my point for bringing this up now. The answer, as I see it, to the cause of gravity lies in reinterpreting mass in f=ma. Mass should not have indefinable units of measurement. It should have units of some combination of distance and time. When this change is made, then a possible answer for what causes gravity appears immediately. Again, why should anyone care about this viewpoint? If we mess around with mass then almost everything will change. Why change that which has worked so wonderfully well in practice?

I will offer a possible reason. The universal gravitational constant is equal in magnitude to a physical event. Consider two ideal, simple protons at a distance of separation equal to the radius of the hydrogen atom. I am using protons instead of neutrons because I want to avoid getting into a discussion about the nature of neutrons. Completely disregard electric effects. I am speaking only about gravitational effects.

An observer on one of the protons believes himself to be stationary. He sees the other proton approaching his proton due to the force of gravity. I will refer to this as the local acceleration of gravity. Now the point: The magnitude of the fundamental gravitational constant is equal in magnitude to the square of the local acceleration due to gravity of one proton toward the observer's proton multiplied by the square of the distance between them at the instant that that distance is equal to the radius of the hydrogen atom.

I have to refer only to the magnitudes because, the units do not match. Now I refer anyone interested back to my point regarding f=ma. If the units of mass are corrected back at the beginning of theory, then the units in the above conclusion match and I do not have to refer only to their magnitudes.

James

Stop the Weirdness!

It all started with Planck's 'energy quanta' and Einstein's 'photons'. The first explained 'blackbody radiation' while the second explained the 'photoelectric effect'. From these beginnings we have a view of the world evolve that has become increasingly mathematically abstract and counter-intuitive. But what if we could turn back the clock some 100 years and consider a more intuitive and 'continuous' explanation of these experimental results? What if we can prove that "Planck's Law is an Exact Mathematical Identity" (a tautology) that describes the interaction of energy? Or that we can explain "The Photoelectric Effect without Photons"? Or give "A Plausible Explanation to the Double-slit Experiment in Quantum Physics"? Or provide an intuitive interpretation to "The Meaning of psi: An Interpretation of the Schrodinger's Equation"? Or can "Let there be h! A Plausable Argument for the Existence of Planck's Constant"? Or mathematically demonstrate that we cannot know a physical quantity through the "The Interaction of Measurement"? Or that established results in Quantum Physics imply a "Time-dependent Local Representation of Energy"? Or can define a "Primary 'physis' and the Mathematical Derivation of Primary Law" in Physics? Or be able to define "The Temperature of Radiation" in a non-Thermodynamic way, yet be equivalent to it?

These results are all logically grounded on a purely mathematical derivation: "A 'Planck-like' Characterization of Exponential Functions". Start by first reading "Planck's Formula is a Mathematical Identity" and follow the links to more topics and further discussions presented in a series of short papers that together present a different view of the universe, one that is confluent with Classical Physics and with our experience of our world.

Dear Constantinos Ragazas,

While I need time for digesting your arguments, I already would like asking you to comment on my possibly related ones to be found at fqxi topics 369 and 527 and my IEEE paper 'Adaptation of Spectral Analysis to Reality' and a manuscript 'A Still Valid Argument by Ritz'.

I just wonder why you wrote 'energy quanta' instead of 'quanta of action' and you did not reveal your scientific background and affiliation. At least, you should indicate what part of currently accepted theory you are considering ill-founded or possibly flawed, why, and with which testable consequences. We should be careful before declaring the many many experts wrong.

Eckard Blumschein

Dear Eckard Blumschein.

Since you asked, I am a retired math teacher having taught at The Lawrenceville School in NJ for some thirty years. But this is not about me. It's about a result that I stumbled upon by accident some ten years ago and more recently developed into a series of short notes. Foremost of these is the mathematical derivation of Planck's Law (or variation of it) showing that it is an exact mathematical identity (a tautology) that describes the interaction of energy.

I cannot comment on your many referenced works since I don't have the background to do so. But I have no doubt you will be able to follow my simple mathematical derivations and arguments. Since ultimately we are all seeking the same thing, an understanding of our world that 'makes sense', I trust that you will consider these independent of me. I humbly submit these results for your consideration and welcome a sustained dialog on them.

Best regards,

Constantinos

Hi Constantinos,

"Foremost of these is the mathematical derivation of Planck's Law (or variation of it) showing that it is an exact mathematical identity (a tautology) that describes the interaction of energy."

I thought your first message was quite general. I think this one is more specific. In my opinion, you have enterred a forum that is especially thoughtful and patient. However, there is more action to be found in the blogs section. I think that posting in both locations will help you receive more varied results. You will find, because of the convenient listing of recent messages, that the blogs section attracts more attention and also the risk of strongly opposite, even possibly offensively posed, views.

Most of which gets posted in the blogs section does not pertain to the subject of any particular blog. FQXi is very patient with new postings. Choose one that is not currently very active and hopefully fits at least minimally with your ideas. Your post will stay visual longer. I do not know what Ian might say about your ideas; but, judging from what you have said thus far, I think that you may have something worthwhile to add to these discussions. I suggest that you post simultaneously in both locations. As, I mentioned above, you have a chance of receiving a better variety of responses. You need to be prepared to explain, in relatively short form, that which you want to communicate.

James

Greetings James,

Thank you for your comments and suggestions. They come as a cool evening breeze in a scorching desert. Personally I can handle all manner of attacks, but it disheartens me when the ideas themselves fall in the fray. I am looking for an intellectually honest and open discussion motivated by a common passion for Truth and Reason. I am encouraged by your mission statement that I may have found such with your community of members.

Best,

Constantinos

Dear Constantinos,

You might be surprised: I do not just consider your argument correct that points at a detector are randomly distributed point-like responses to stimulating waves. I see it even the first convincing explanation to obviously wrong measurements by Gompf et al. published in PRL and mentioned in 527.

Thank you.

Best regards,

Eckard

Constantinos,

Good. I think that FQXi may benefit from your input. I will not speak for you. I know that you know that you have to make your case. Supporters may follow.

If you happen to be online near this time, here is an example from the blogs section, it was directed at me by Tom (T H Ray), of the kind of response you may have to contend with:

"...Your claim is instructive, however. When Einstein became known, the Nazis denounced his work as "Jewish mathematics." It is only when we allow science to be interpreted in tribal terms, that one can even entertain ridiculously false statements as these. And when taken to its furthest extreme, when truth resides only in the mind of an individual (your view) there is only anti-science. Your opinion is harmless as it is here; one can take it or leave it. Suppose, however, you were a king with limitless power--you issue a decree that henceforth relativity is false because you have seen the truth, and anyone who breathes a word to the contrary shall be beheaded. Don't laugh, it has happened in analogous ways; correction: is happening. ..."

I handle my own challengers, some of which are qualified, skilled, theoretical physicists who have earned their Doctorate and are to be respected for their academic accomplishment. I think you may be able to accomplish something at FQXi.

You said: "Personally I can handle all manner of attacks, but it disheartens me when the ideas themselves fall in the fray."

The ideas will not fall in the fray if you stay with it.

James

Hello Eckard,

Thank you for your comments. It is gratifying to know that my explanation helps answer some questions for you. Forgive me if I do not address the specific references you mention. I am just not familiar with these.

Perhaps you can give me your thoughts on my equally short note "Planck's Law is an Exact Mathematical Identity". This does not use 'quanta' and is based on simple continuous processes.

Best,

Constantinos

James,

. . . as bad as the comment directed to you is, believe me when I say I've had worst! Really vicious! But I wont dwell on that. By nature I am a very positive and optimistic person. My love of ideas would not let me be anything else. Nothing can dissuade me from reasoning other than reasoning itself. Hard to abandon what you know to be True. So feel assured that I will persist, since really this is not about me!

Dear Constantinos,

I was trained as an electrical engineer almost fifty years ago, and I meanwhile I found out that the relationship between momentum and position corresponds to the relationship between frequency and timespan if we use h as a constant factor. Both pairs are conjugate ones, related to each other via an integral transform. As a mathematician you learned to apply the complex Fourier transform in this case. I found out that avoidance of any arbitrary reference requires restriction to only positive time-spans and therefore the real cosine transform is tailor-made to reality.

Admittedly, I did not yet deal thoroughly with the papers of concern with respect to Planck although I have some of them at hand in the book 100 years of Planck's Quantum by Duck and Sudarshan, World Scientific 2000. Could you please explain to me why you you are using Einstein's expression "energy quantum"

E = h f instead of the quantum (or coefficient) of action h?

Look at my results of running cosine transforms in MATLAB. You will find an example at http://www.fqxi.org/community/forum/topic/527 and further results at

http://home.arcor.de/eckard.blumschein/M284.html

It looks to me as if a photon corresponds to the first ripple but it is not the smallest product analog to the hyperbola f times t = constant.

I fear you are a too well educated mathematician as to understand that my point of view is very uncommon while nonetheless reasonable.

Best regards,

Eckard

Why should physical quantities follow mathematical formalisms? Without getting into long and protracted philosophical discussions, I just want to say that the essence of Physics is 'measurement' while the essence of Math is 'logical consistency'. So why should mathematical derivations be reflected in physical experiments? I like to propose that the way this would be possible is if all Basic Universal Law are mathematical identities (tautologies) that describe the interactions of measurement.

In the short paper "Plancks' Law is an Exact Mathematical Identity" we show this to be true for measurements of energy. In the equally short paper "The Interaction of Measurement" we show that a physical quantity cannot be 'known' by measurements of it. Thus, there is an underlying 'hidden reality' that we can never know but can only 'measure' and all our derivations of this 'hidden reality' are mathematical certainties that only relate to our measurements.

If we seek to describe such underlying 'hidden nature' directly through our mathematical formalisms and physical theories, if we try to theoretically model it as something separate and beyond our measurements of it, we risk falling into the same 'rabbit's hole' that medieval intellectuals had fallen seeking to count the number of angles that can sit at the head of a pin!

We can only know what we can 'observe' and 'measure'. Thus it all comes back to us, our human Understanding of what Is to Us, but not what Is in Itself! Our very Understanding is a form of 'measurement'. And just as you cannot truly know someone by taking 'measures' of their behavior, equally we cannot know a physical quantity by taking 'measurements' of it.

There is nothing 'absolutely real' about our theories! There are just theories that 'make sense' and theories that 'make none-sense'. When a theory has become so abstract and so removed from the 'sensible experience' of our lives, when it creates 'mathematical certainties' that are counter-intuitive and 'weird', it's time to 'stop the weirdness' and to re-think our Universe and re-Create it anew.

Constantinos

Constantinos,

Didn't you look into http://en.wikipedia.org/wiki/Planck's_law ?

It offers clever mathematics and a lot of expert discussion on Planck's law.

Planck made Einstein accepted. However it was Einstein, not Planck, who wrote: ... in einer endlichen Zahl von in Raumpunkten lokalisierten Energiequanten, welche sich bewegen ohne sich zu teilen und nur als Ganze absorbiert und erzeugt werden koennen" (Ann. Phys. 17, 132, 1905). Compton wrote in 1923 "Light Elements".

Admittedly, I did not yet understand your point.

Nonetheless, I appreciate your hint to "Einstein, Millikan and the Photoelectric Effect by Richard Keesing".

May I ask you for objections in any discussions you already had concerning your argument that the single photon at the detector is not the original one? I suggest striving for a clarification because of serious consequences. The manufacturer and user of single photon technology will not like such plausible and compelling, at least to, me criticism. Not just my hint to Gompf et al. was stubbornly ignored. I was already made aware of the ignored oddity in a laudatio for Eisenmenger by Kutruff many years ago.

I do not appreciate your rhetoric "stop the weirdness" in combination with your claim of a mathematical proof.

Regards,

Eckard

Dear Eckard,

Please don't take offense when I don't directly respond to specific points or references you make. Most often I may not know what the reference portends or how it fits in the topic of discussion for me. If you describe the idea rather than the reference I may have a better crack at it and better respond. I have not and do not closely follow all the relevant literature and latest esoteric controversies and discussions. Rather, I am compelled to follow my own ideas and my own reasoning, trusting that there is relevance to these even in the very complex and intellectually bewildering landscape of Theoretical Physics - for no other reason than because these ideas are grounded on sensible experience. I am prepared to argue these results in themselves, supported by simple sound mathematics that anyone can follow.

Physics does not lack intellectual intricacy and abstract mathematical edifice. Rather, it lacks 'physical explanations' that make sense. So in spite of the mathematical formalism of QM that yields impressive results, no one has a physical interpretation of QM that makes sense - even great physicists admit to this. To quote Feynman, "no one understands Quantum Mechanics". But if the Physics we do is devoid of 'physical explanation', than we risk the possibility of engaging in an endless mental game of producing mathematical results that are just plain 'weird' (sorry that you are offended by this term! It's not mine! It refers to 'quantum weirdness' that collectively references all such counter-intuitive formal consequences).

You write,

"Didn't you look into http://en.wikipedia.org/wiki/Planck's_law ? "

Yes! But not very relevant since this derivation was based on Planck's 'quantization hypothesis' using statistics. I do something that entirely avoids the 'quantization hypothesis' and uses continuous, not discrete, processes.

You also write,

"May I ask you for objections in any discussions you already had concerning your argument that the single photon at the detector is not the original one?"

I am afraid the objections were in the form of profanities that I cannot repeat here! In all honesty, there just wasn't a reasoned refutation to any of my claims. Just that these explanations do not follow the accepted orthodoxy, coupled with a strong admonition that I should go and "read the scriptures" more carefully. My fear is that Physics has now replaced the Catholic Church of Galileo's times! At least now heretical views are just ignored rather than imprisoned. Yet, intellectual isolation is just as harsh.

Eckard, I be happy to engage you in more specific questions that you have concerning any of the claims in my papers. But let's find a way of conducting such a discussion. Using the language in my short papers would be the most appropriate such way for me. If you even want to quote passages directly from these, I'd be happy to elaborate further what I have in mind. Certainly there is much room for misinterpretation to anything that is written down. But a sustained dialog should in time clear these up.

Best regards,

Constantinos

Dear James Putnam,

What this evolutionary approach implies is that mathematics does not work in nature because it is magic, it works for the simple reason that it was a tool that was specifically designed and honed to work in nature, and whose current effectiveness is due to a long evolutionary history of trial and error. I'm not sure if that is exactly what you meant by saying that this view accepts "intelligent results without intelligent causes".

About your second point on macroscopic approaches, I do analyze the evolution of the human brain and of mathematics from a macroscopic view, but I am only aware of the macroscopic nature of this view after I have accepted that the human brain has evolutionarily developed in a macroscopic world, as opposed to other scales (microscopic/quantum/cosmologic/etc.), and thus, that the human brain is an evolutionary product of the macroscopic scale and that its mathematical reasoning is also the result of evolution in the macroscopic scale. Considering I am using this mathematical system to analyze the evolution of the human brain, then yes, I am indeed using a type of reasoning that comes from (and is adapted to) the macroscopic world. In other words, I am talking about the evolution of the human brain and of mathematical reasoning in the language of a macroscopic creature.

Does this answer your questions?

Genevieve

Dear Constantinos,

Please find my reply at

topic 630, a perhaps more appropriate place .

Best,

Eckard

Dear Genevieve Mathis,

Thank you for your answer. I think you give an interesting take on the limits of mathematics. I asked my questions because conclusions are based upon beginning premises. As the reader, whether I do or do not accept the beginning premises determines my position on the conclusions. I think that I am not the best person to discuss your original post. I am somewhat surprised that it didn't receive more interest from others here. Best wishes.

James