daerengD Time Paradigm by Brian Beverly

Brian,

Thanks for the reply. I don't believe time is fixed in a background. And in response to your mention of the twin paradox and acceleration, I recommend that you read my essay since it uses relativity as a starting point to analyze the nature of time. I'm not going to use your thread as advertizement for my essay so if you are interested, you can make further comments on this topic on my thread.

Happy New Year!

CJ

Chris,

I think your essay compliments my essay. Your essay is very well written and highlights why the nature of time must ultimately be due to a quantum mechanical mechanism. I'll post it in my forum so others will not have to search for it.

I'm glad we agree that background space and time are inadequate. I believe my deranged idea is a possible type of mechanism you are looking for.Attachment #1: Kennedy_kennedy_chris_natur.pdf

Brian,

Thanks for reading the essay and the kind words. And thanks for the advertizing space!! (or spacetime??) It is very possible that your essay's analysis of probability on the quantum behavior level could play an important role in describing time's cause and effect on the most fundamental level. I think this contest has already allowed some progress to be made in defining the nature of time. I made am additional comment on my thread too.

Good luck and happy new year.

CJ

Brian,

Thanks for what is a very generous offer. As your time is undoubtfully valuable, a few links would suffice. While my little bit of free time and extra mental capacity for abstract thinking is currently entertained by this contest, the subject of the nature of light is of interest to me.

John, here are some links that I've found useful for understanding physics

1) http://vega.org.uk/video/subseries/8

This is a 3 lecture series by Richard Feynman on QED it you are interested in light this is a great place to start.

2) http://www.learner.org/resources/series42.html

This website requires that you register with a valid email and then every episode of the "Mechanical Universe" is free to watch.

3) http://ocw.mit.edu/OcwWeb/Physics/index.htm

If you have the time and dedication then MIT's open courseware will teach you everything you need to know about physics.

Have fun,

Brian

Hello Brian,

You might smile about my suggestion to restrict to elapsed time and blame lacking understanding of either complex time domain or complex frequency domain for apparent symmetries.

I consider you able answering an old question of mine. I learned from those who followed Boltzmann that it is just a question of probability after two containers of gas, one of which was empty the other one was full, were connected with each other until the system was by chance again in the original state. I understood that for assumed equally distributed probability no combination was impossible.

However, are the probabilities really independent of each other? Was Einstein correct in his dispute with Ritz who argued that the future cannot influence the past? Is T-symmetry justified?

Regards, Eckard

Hey Eckard,

I definitely smiled while reading most of your paper. Your understanding of Fourier and complex analysis is broad. My favorite blurb from your essay was a fact I was unaware of about Neumann.

[Immediately after the famous article by Einstein, Podolsky and Rosen in 1935, John v. Neumann confessed: "I do not absolutely believe in Hilbert‐space any more." He revealed a

possible incorrectness: Replacement of a finite linear basis by the assumptions completeness and separability might be questionable.]

In regards to your question the answer is yes it is a matter of probability, however, this probability is very, very, very (one more for extra emphasis), very small. I'm glad you mentioned probability because everyone seems to ignore it. I hope to answer your questions and show you why I believe quantum got stuck with imaginary numbers but I can't do it with words (words alone make poor mathematical arguments). I'm going to write it out mathematically and just post it as a PDF. It will take me some time to get it organized.

Thanks,

Brian

Dear Brian,

Quite a while after my scientific carrier and possibly close to the end of my life, I appreciate young people who understand what I consider possibly important. When Prof. em. Zeh in his most recent blog on superluminality called acceptance of questionable papers by editors of PRL, nature, and IIRC PNAS a skandal, he might have initiated the end of a scientific bubble. At least I hope so.

You seem to firmly trust in mathematics. Be cautious! I like the clear insight by Galilei that the relations larger, equal to, and smaller are inappropriate for infinite quantities. Weierstrass, Heine, Dedekind, G. Cantor, and Hilbert created and defended, respectively, the "paradise" of real numbers.

I would rather prefer to not unnecessarily enforce an allegedly rigorous union between discrete numbers and continuum. Why not admitting the 4th logical variant || instead and use infinity as pragmatically as did Lagrange, Leibniz, Euler, Fourier, Gauss and Cauchy and as still do less educated engineers like me?

I imagine discrete points that do not have parts and a continuum every part of which has parts two mutually excluding and simultaneously complementing ideal models.

Spectral analysis converts sets of points into continua and vice versa. That's why I suggested to distinguish between rational numbers and their equivalents embedded into a homogeneous genuine continuum of not completely adressable irreal "numbers" with actually infinitely much of decimals. Mathematicians are trained as to not accept this subtle distinction but eat the cake and still have it.

I appreciate you promise. Do you know on what issue Einstein and Ritz agreed to not agree?

Looking forward getting your mathematical arguments.

Eckard Blumschein

Dear Eckard,

Sorry it took me so long to respond but I thought I would spend a few hours writing this out but it easily turned into several days. I think someone with a firm understanding of EE and complex analysis as well as number theory can see that the complex aspects of quantum mechanics are questionable. Earlier I posted a reply to John Merryman about imaginary numbers where I ordered them. Ordering imaginary numbers is not possible I only did it because it made the argument easier. In fact, I think this is the same type of thinking that has lead to the measurement problem. The attached file contains some quasi derivations of what quantum mechanics is all about. In regards to Einstein and Ritz I had never heard of their disagreement before and I'm glad you mentioned it. Ultimately I agree with Einstein that the arrow of time is a result of probabilities. You seem to have a better understanding of number theory than I do and I would appreciate your input regarding the measurement problem.

Thanks,

Brian Beverly

Ah, 1MB limit sorry the resolution won't be as good.Attachment #1: FQXI_Quantum.pdf

The measurement problem in physics is where it is implied that imaginary time is ordered:

(...[-itn,...,-it2,-it1,0,it1,it2,...,itn]...)

The mathematical axioms tell us that complex numbers can not be ordered.

Order Axioms:

1) A number can not be less than itself

2) x > y, x < y, or x = y

3) if x > 0 and y > 0, then xy > 0

4) if x < y, then for all z, x + z < z + y

5) if x < y, then for all z, xz < yz

set x = i and y = 2i and z= 2 + i

1) makes sense

2) i < 2i makes sense

3) a bit tricky:

0 = 0 + 0i and i = 0 +1i therefore i>0 and 2i>0

(i)(2i) > 0 ---> -2 > 0 FALSE!

4) 2 + 2i < 2 + 3i (complex # is of the form a + bi)

5) This is the key axiom!

xz = what exactly? xz or x*z (* is complex conjugate i*=-i)

If we distribute xz as we do for real numbers then axiom 5 is false. If we take the complex conjugate x*z then axiom 5 is true.

Quantum mechanics relies on C* algebra which is ordered. What is the big idea of C* algebra? C*C, multiply a complex number by a complex conjugate and you end up with a real order/countable number.

By the axioms of math the measurement problem does not exist in physics.

I almost forgot I found an interesting paragraph on Wolfram's mathworld:

http://mathworld.wolfram.com/ComplexNumber.html

"Historically, the geometric representation of a complex number as simply a point in the plane was important because it made the whole idea of a complex number more acceptable. In particular, "imaginary" numbers became accepted partly through their visualization. Unlike real numbers, complex numbers do not have a natural ordering, so there is no analog of complex-valued inequalities. This property is not so surprising however when they are viewed as being elements in the complex plane, since points in a plane also lack a natural ordering."

Thank you Brian,

With complex numbers I did not have any problem except for the lacking readiness of many experts to believe that the complex representation of a natural function of time is just blown up with arbitrarily added redundancy. Nonetheless, I appreciate your effort. Maybe, I will support my trials to get generally accepted in this question.

I hoped you could explain to me why Einstein rejected the argument by Ritz that the future cannot influence the past.

I merely guess, Einstein immediately followed Boltzmann. However, I did not find anything that could convince me. Why should the arrow of time be the result of probabilities?

Shannon who also dealt with probabilities and also arrived at the log law stated that the past is known to us in principle while we cannot influence it but the future is unknown to us while we can influence it.

I consider this a key question.

Sorry for bothering you again,

Eckard

You're Welcome Eckard,

Thank you for focusing me on the imaginary number. In regards to your Einstein, Ritz and Boltzmann question I'll have to use a mathematical argument. Again it will take me some time to organize it. It is not a bother but a pleasure because Entropy is my favorite idea of all time (pun intended).

Eckard,

Here is a breakdown of entropy expect several more PDFs on it :)Attachment #1: FQXI_Entropy_1.pdfAttachment #2: FQXI_Entropy_2.pdf

Please find my thanks at 369

Eckard

Eckard,

I would like to persuade you against adopting a continuous model. Following where my last post left off I derive the Boltzmann distribution, also known as the canonical distribution. From the Boltzmann distribution we are able to understand the birth of quantum physics from Planck's method for solving the blackbody ultraviolet catastrophe. I believe that Planck created the discrete theory to solve the blackbody but still kept the continuous idea of frequency which is another "problem with time". I do not believe the reasoning for continuous time is justified and attempts to make time continuous add only additional and unnecessary complications.

I have also re-posted three pages on the Schrodinger equation because where Planck and Einstein took the theory is where Schrodinger picked it up. In the end only a discrete model solved the problems from the early 1900's including the ultraviolet catastrophe and the photoelectric effect. I believe we should entirely let go of the classical notion of the continuum.

I will probably submit only one more derivation to make my argument much more rigorous. I appreciate your feedback because it seems that you are the only person who still cares. I will also be sure to follow up on your forum too.

Thank you,

Brian BeverlyAttachment #1: FQXI_Nublackbody.pdfAttachment #2: FQXI_Schrodinger.pdf

Brian,

Thank you for your effort. Even if your style reminds me of rather confusing lectures, I may have got an important point from Nublackbody.pdf. You conclude that time must be discrete because frequency is discrete. I will let many other objections of mine out of consideration and state nearly the opposite.

I am no expert in quantum physics and it took me a while until I understood what Dirac caused to be immediately inspired from Heisenbergs funny speech on July 28, 1925 "Termzoologie und Zeemanbotanik" at the Kapitza club in Cambridge UK in front of an audience that included Fowler but not Dirac: the change into the Hamiltonian point of view.

In terms of an integral transform, time and frequency are a so called "canonically" conjugate pair. In better words, a continuous function of time in the original time domain would necessarily correspond to a function of discrete frequencies that was complex and did exhibit Hermitian symmetry. Because H., D, and all the others were convinced that frequencies are not negative, in the end Schroedinger's wave function was introduced as a somewhat strange complex function of positive and negative time.

Anyway, you should be aware that a discrete function of frequency or energy or momentum does not imply that the belonging function of time or distance, respectively, is also discrete but on the contrary, it must be continuous and vice versa. The switch from discrete to continuous and back is even more obvious with cosine instead of complex Fourier transform because cosine transform is its own inverse: CT of CT already returns the original. In so far, the question whether the reality is discrete or continuous seems to be open. It depends on your point of view whether the cat is dead or alive.

I did not yet clarify all details. Nonetheless, it seems already to be obvious that both descriptions are likewise complete, and complex representation does not provide an additional degree of freedom as usually believed but it is just redundant.

Did you read part 1 and part 2 of mine? If you have questions, I will try and answer them in a part 3.

Eckard

Eckard,

Thank you for the reply, for me the argument for discretness is in the derivation of quantum. I did take fourier analysis as a college sophomore, however, I attended about 5 lectures and earned a C. What I remember from the first lecture was that fourier developed his method in order to understand heat. We are fortunate that thermodynamics does a better job. I agree that imaginary numbers do not belong in a physical theory.

I am posting the derivation for the derangment and I'm sorry I have not been reciprocating feedback as much as I should. The problem is once you start deriving an idea it becomes impossible to stop. Actually it is not a problem I was just having so much fun :)

BrianAttachment #1: FQXI_InExclusion.pdf