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CATEGORY: The Nature of Time Essay Contest (2008) [back]
TOPIC: daerengD Time Paradigm by Brian Beverly [refresh]
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Brian Beverly wrote on Nov. 6, 2008 @ 11:14 GMT
Essay Abstract

This essay is the result of six years of reflection on time. I believe the fundamental nature of time is one change which distinguishes a before and after. In general I believe time is fully derived from combinatorics. The arrow of time is the result of entropy that is derived from microstates, macrostates and multiplicities. For time in quantum mechanics, I believe fundamental objects with no internal structure must experience change through interactions. The best mathematics for this approach is the derangement. I have focused only on wavefunctions and the measurement problem. I show that derangements produce the linear time evolution of wavefunctions and provide a mechanism for collapse. Sections I-IV will be a review for experts but I consider the ideas essential for a complete understanding of time.

Author Bio

Brian Beverly recently graduated in the spring of 2008 with a physics and math degree from the University of Colorado. He is 23 and has been passionate about physics since he was 13. In high school he held a one year internship with Lockheed Martin, and once convinced Nobel laureate Eric Cornell to excuse him from a chemistry test. In college he became obsessed with time in quantum mechanics. For the past year he has worked for a large corporation remotely monitoring and maintaining fiber optic circuits. In the near future he plans on attending graduate school.

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Brian Beverly wrote on Nov. 7, 2008 @ 08:42 GMT
When I think of dimensions I think of a linear combination of basis vectors that represent every vector in some vector space. The bases states I refer to in my paper are the imaginary Hilbert ones. I do not want anyone to confuse my conclusion as having rid my idea of dimensions. In fact I believe derangements may explain dimensions. For one object (x) there is no possible derangement. Add y, a second object, and the two could interact creating a change (xy). However, the (xy) derangement is (yx), and there is no new relative change. The minimum number of objects required to produce continuous change is three: (xyz), (yzx), (zxy)...repeat. I suppose that would make the fourth dimension the derangement, suach as (xyz) to (yzx). I could be wrong, but at least it is simple.

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Dr. E (The Real McCoy) wrote on Nov. 8, 2008 @ 16:38 GMT
Hello Brian,

Thanks for the interesting essay!

You never mention the radiative arrow of time in your paper. This is puzzling, as the emission and propagation of photons powers so many clocks, including the clocks in your cell phone and computer, as well as on your wrist. And too, the emission and propagation of photons is ultimately responsible for your very own aging, as your body...

view entire post

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Dr. E (The Real McCoy) wrote on Nov. 9, 2008 @ 16:38 GMT
Hello Brian,

Your theory seems like it was written to please the antitheory elders and John Baez, instead of to adavance physics. I don't know how much longer the antitheory/quantum gravity regimes are going to last, so you may wish to focus more on physics and *physical* reality, than pleasing elders who spend their time devising crackpot indexes, instead of following their curiosities...

view entire post

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Alex Nelson wrote on Nov. 10, 2008 @ 01:51 GMT
"Dr" E wrote:

"Then, later on in teh blog, Cool Hand Luke rides in, like a Cowboy, to set Baez straight:"

Perhaps you should take responsibility for your own actions and admit that was you posting that message (as Dr Woit remarked later in the replies in that particular post)?

"I hope that Baez someday has an opportunity to read the original papers of Faraday, Boltzman, Maxwell, Einstein, Bohr, Newton, Wheeler, DeBroglie, and Einstein.

"You will notice that the simple logic, reason, and motivation are all contained in beautiful words which far eclipse the presence of math."

Yeah! Like the in the Principia! Oh, wait...that was entirely math.

No, perhaps like Einstein's "Relativity: The Special and General Theory"...oh wait, he devoted half of the book to math.

Or perhaps Heaviside? No, perhaps not, although he did a lot of the important work that Maxwell got credit for, he also invented a number of new mathematical tools that are used in signal processing.

Now, Lagrange, he was a real...wait, no, not Lagrange he just did math.

Or perhaps "Dr" E can stop blowing smoke out of his...?

Dr. E (The Real McCoy) wrote on Nov. 10, 2008 @ 02:34 GMT
Hello Alex,

Now I love math and harbor a vast respect for it, as without math the attached figure for the artificial retina for the blind, from my dissertation, would not work.

Also in that dissertation in an appendix was the first treatment of Moving Dimenisons Theory. In many ways Moving Dimensions Theory respects math far more than quantum gravity and string theory, as while...

view entire post

attachments: artificial_retina.jpg

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Alex Nelson wrote on Nov. 10, 2008 @ 04:45 GMT
"Of course math is vastly important to physics--it's just that snarky, postmodern math shouldn't be allowed to trump physics, as when that happens, you get thirty+ years of frozen progress in physics and burgeoning hundred-million-dollar groupthink regimes that excel in snark and intimidation, while rendering actual progress in theoretical physics uncool and unfashionable."

You do realize the glaringly obvious flaw with this argument is that everything that Newton used in his physics, as well as everything Einstein used in his theory of General Relativity, was thought of at the time as nothing more than a mathematical toy that would have no application to reality.

Hell, this is true with Heisenberg's work as well. Matrices were thought of as useless in physics and applied math until Einstein and Heisenberg used them in the two pioneering theories of the twentieth century.

Newton invented the math necessary to deal with Classical Mechanics effectively and in doing so united the motion of heavenly bodies and normal bodies.

Archimedes effectively used infinitesimals in his static analysis, which he ironically did not believe in.

I can go on and on with counter-examples in history where these "postmodern maths" were used to come up with new approaches to problems.

Your Luddite fear of mathematics approach to physics is no more going forward than an ostrich digging its head in the sand avoids a Lion.

Of course, your approach is unconvincing due to its lack of rigor. You *assert* but yield no proof of success in unification, which is most unsatisfying. Worse, you constantly use appeals to authority while ignoring the contradictions in doing so; the beauty of science and math is *it doesn't matter what anyone says, what matters is the proof!*

But sadly none is provided in your approach...

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Dr. E (The Real McCoy) wrote on Nov. 10, 2008 @ 06:08 GMT
Hello Alex,

do not take my word for it--hear Einstein, "But before mankind could be ripe for a science which takes in the whole of reality, a second fundamental truth was needed, which only became common property among philosophers with the advent of Kepler and Galileo. Pure logical thinking cannot yield us any knowledge of the empirical world; all knowledge of reality starts form...

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Brian Beverly wrote on Nov. 11, 2008 @ 07:15 GMT
Alex thank you for your comments. Mr. E. please avoid extremely long non sequitur posts. Useful feedback is worth more to me than any contest prize. Let me define what I consider useful feedback:

1) A mathematical error.

Showing where there is a division by zero or something axiomatically unacceptable.

2) An error in scientific reasoning

Violation of the thermodynamic laws, an argument showing a violation of energy conservation or the uncertainty principle... etc.

3) A physical paradox

E.g. Grandfather, twin etc.

4) Experimental evidence

evidence that supports my ideas or destroys them are the most useful posts.

I consider useless feedback to be:

1) Tangents.

e.g. You have not explained this and that....I have not submitted a theory of everything. I am working on entanglement but it is still in its infancy.

2) Long Posts.

Do not torture me with prose but finish me quickly with sweet, short and elegant mathematics.

3) Self Promotion

e.g. Ignore this paper because my ideas are better follow this URL link....

4) Impatient Posts

I will not quickly respond because I will spend the time to understand the counter arguments. I will not respond if I believe the person submitting the post does not have an elementary understanding of math or physics.

Thank you,


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Dr. E (The Real McCoy) wrote on Nov. 11, 2008 @ 16:48 GMT
Hello Brian,

You write, "Do not torture me with prose but finish me quickly with sweet, short and elegant mathematics."

Have you ever read the foundational papers of quantum mechanics in: "
Physics/dp/0691083169/ "

You will find that they are by and large written in prose.

I understand that postmodern...

view entire post

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Brian Beverly wrote on Nov. 12, 2008 @ 03:02 GMT
Mr. E, I have written a paper using combinatorics (it comes from the Latin word to count) if combinatorics is "snarky" then I apologize. The physics I discuss requires an understanding of entropy and wavefunctions. I use combinatorics a.k.a. microstates, macrostates, multiplicity (entropy) and derangements to resolve the measurement problem. Now, please stop being a forum troll and stop spamming me with nonsensical psychobabble (this includes the youtube surfing videos). Leave me alone.

Forum moderator please help me....

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Dr. E (The Real McCoy) wrote on Nov. 12, 2008 @ 17:59 GMT
Hello Brian,

In a hit-and-run, you posted a list of snarky, off-topic, red-herring questions and commentary in my forum, while completely ignoring MDT's novel *physical* concepts: "Brian Beverly wrote on Nov. 8, 2008 @ 11:12 GMT."

Even though your questions reminded me of the anti-theory elders and their snarky grad studnets, I took the time...

view entire post

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Brian Beverly wrote on Nov. 12, 2008 @ 23:45 GMT
E, if I am going to discuss your idea I will discuss it in your forum so lets take our discussion there. I would like to save my forum for my essay, is that selfish of me?

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Brian Beverly wrote on Nov. 13, 2008 @ 00:08 GMT
If you are going to post make sure you have read my essay many of your comments show you have not bothered to.

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Anonymous wrote on Nov. 19, 2008 @ 14:24 GMT
Please note that insulting and/or excessively long postings will be removed as per the forum guidlines.


K Rajanna


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FQXi Administrator Kavita Rajanna wrote on Nov. 19, 2008 @ 14:25 GMT
Please note that insulting and/or excessively long postings will be removed as per the forum guidlines.


K Rajanna

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Doug wrote on Nov. 22, 2008 @ 16:03 GMT
Hi Brian,

Great essay, as promised! Congratulations. I want to comment on several aspects, but have to make time for it. I really look forward to discussing it with you.



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Brian Beverly wrote on Nov. 23, 2008 @ 02:00 GMT
Hey Doug,

I look forward to your comments. I know you have put a lot of work into your idea and I know how difficult it can be to find people who are willing to listen. If you give me your email address I will give you some feedback on your ideas even after the contest has ended.

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Doug wrote on Nov. 24, 2008 @ 17:11 GMT
Thanks Brian. I’ll do that. In the meantime, I’m trying to correlate the ideas in your essay with those in two new essays, one by Sean Carroll and the other by Chen Tze. Have you had a chance to read either of them yet?

I would really, really, be interested in your comments on them, in view of your own essay.

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Narendra Nath wrote on Nov. 26, 2008 @ 06:19 GMT
Dear Brain,

somehow the first word of the title made me feel avoid studying your essay. After reading it i have sensed the originality in your 'young' ideas that i admire.I enjoyed your describing time as a step between the two and its significance tied to entropy. it is also nice to say that a macrostate as destination while the microstate as one path to destination. Philosophically, i see closeness between your essay and that of Kyle Miller's Here and Now!

With this summary may i put some queries to you so late in the contest:-

The order contains disorder but not the other way round. Silence contains noise but not the other way round. In sciences, we work out probability for a process by averaging over a large number of individual events. Can all physical processes happening in the Universe follow no order? Where the order hides as probabilities describe the process?

Entropy tends to increase with passage of time if a system is confined without external interference.What happens if events within start to feel some interaction with one another? Why such internal interactions are ruled out?

Time and space are just concepts generated by the human mind. Can we not have alternate concepts and still understand the nature of physical processes?

We hold Physical Constants as holy? Also, we talk of more or less fixed relative strengths for the four force-fields.

In my own essay in the contest, i have discussed such possibilities. May i have your comments on such aspects?

The last query i have concerns the State of the Universe prior to the Big Bang. Do you visualize that before the Physical world came into being, there was/is/will remain the presence of a non-physical entity called 'consciousness'?

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Brian Beverly wrote on Nov. 28, 2008 @ 01:47 GMT

Thank you for taking the time to read my essay. Perhaps the first word in the title may explain the lack of comments. My paper was a careful study of the derangement and the original title was, "Deranged Time Paradigm". However, before I submitted it, about 5 A.M., I thought the reader might interpret deranged as meaning crazy. Since a derangement is an arrangement in which no element remains in its original position I thought I would derange the word Deranged, hence daerengD.

My analogy of microstates as several different paths that lead to the same macrostate destination was intended to help keep the ideas clear in the reader's mind. I used this analogy because when I first studied the subject the similar sounding words easily confused me. If you have gained anything philosophical from my essay I consider that to be an unexpected bonus.

I do not like to think of entropy in terms of order and disorder. The popular analogy is a child's room and that it is most likely to be disordered with toys scattered everywhere. An ordered room would have the toys on neat shelves with the child doing their homework. Thinking of entropy as disorder makes the idea appear ugly. The child's room analogy does not show the depth and beauty of entropy nor does it even hint at quantifying it. The entropy of the universe always increases even if the system we are examining is closed or open. Also I considered internal interactions and I agree science should. I don't believe physical constants are holy but just very important ideas. If these constants are contradicted and experimentally falsified I wouldn't hesitate to abandon them.

You should know that I am an atheist and I typically do not care to comment on subjectivism or the many worlds interpretation. I consider those ideas to be a matter of faith. I think the stereotype of an atheist is someone who is closed minded, however, they are general curious about everything including religions. The benefit of being an atheist is you can study any religion without prior bias. The philosophy I like the most is Taoism but I draw a clear line between liking it and a spiritual belief.

I can tell you are Indian, most likely Hindu, and your references to consciousness makes me think of Krishna consciousness. Even though I am an atheist I have been to one of their temples (I'm not sure temple is the accurate word), but it was many years ago. Can you tell the significance of the Ganges water? I have forgotten the purpose, I thought it was for spiritual cleansing. I also remember symbolically touching the fire of a lantern and then my head. The most important thing I learned and the most vivid memory from the experience came from the adjacent gift shop. A sign above the gift shop door read, "Stealing is Bad Karma". So for the sake of "Karma" I will read your essay and try to provide a good comment or two.



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Brian Beverly wrote on Nov. 28, 2008 @ 01:49 GMT
Doug, thanks for pointing out the two essays I enjoyed them. Do you have any other ones you liked?

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Narendra wrote on Nov. 28, 2008 @ 06:17 GMT
Dear Brian,

It is so pleasant to see the response of young person who is working hard to earn his living in order to pursue Graduate studies. i wish you all luck in Physics as i feel sure you will make a mark to raise present day stagnant Physics through freshness of ideas. Besides my essay kindly see one by another young man, Kyle Miller on Here and Now. The future of Physics in young men like you is bright.

Though you satisfied me partly but you refrained from providing your opinion on Entropy, in contrast to the common belief that it represents the state of order/disorder!

Although you wrote some queries that are not concerned with theme here, if i find time,i shall communicate with you on Internet ( my ID is ).However, i like that you giving respect to"KARMA" means ' Actions'. It may surprise you that this very word has been emphasized by Krishna in the scripture ' GITA/Bhagwatgita' where he extols that the Dharma or religion of a person is what he practices in his Actions and not what he professes or belongs to on virtue of Birth! Pure consciousness for you as an 'atheist' is all powerful, timeless non-physical entity that can be considered to have generated the physical universe and all its contents and still permeate the entire Creation! i have attempted to bring such holistic considerations to science, based on my own experiences as a scientist second, human being first.

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Doug wrote on Nov. 29, 2008 @ 18:20 GMT
Hi Brian,

There are so many good ones, I hate to try to choose, but three I’ve mentioned before are Rovelli’s, Gibbs’, and, my favorite so far, Lynds’, but I really like Gambini’s too. Then there is Carl Brannen’s, Kiefer’s, Pitkanen’s, Prati’s, and many others, like Sherbon’s. I’m afraid I’m going to leave out someone. There are so many good reads.

It almost goes without saying that I have also enjoyed the essays of those most vociferous in the forums, like McGluken, Merryman, Le Rouge, Nath. Of course, there’s this one by Stanbridge – what do you think of that?

Clearly, I’m not done. I’ve got many more to go and many I want to re-read. How about your recommendations, Brian?

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Doug wrote on Nov. 30, 2008 @ 02:03 GMT

I neglected to mention Tom Ray's essay. I'm sure I've left out others too. It's hard to keep track. I probably should gen up a spread sheet with some sort of matrix evaluation to help me keep track of all the goodies!

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Narendra Nath wrote on Nov. 30, 2008 @ 11:07 GMT
Dear Brian,

Please use your own judgement instead of others recommendations. In fact, i was not expecting such suggestions in the postings. Unfortunetely, our bias plays a role that 'good science needs to avoid'. Best of luck for you and appreciation for your post on my essay!

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Doug wrote on Dec. 1, 2008 @ 17:15 GMT
Oh man! Twenty new essays in today, just under the deadline! I checked the names for someone familiar, and to my great surprise and delight, one of them is by Hestenes!

It’s a doozy!!!!!!!

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Brian Beverly wrote on Dec. 2, 2008 @ 02:55 GMT
Doug, there are so many new essays! I have been obsessed with time for a long time. The good news is reading so many essays on the nature of time has cured my time addiction. Although the essays have driven me to drinking and rants about eigenvalues.

A good comic about the grandfather paradox:

Here is an awesome idea about changing the way humanity thinks about time. I just finished his book I highly recomend it:

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Armin Nikkhah Shirazi wrote on Dec. 3, 2008 @ 02:15 GMT
Hi Brian,

I enjoyed reading your essay and find it highly original. Also, I only learned about the concept of derangement through your essay.

I do have a question: Wouldn't according to your idea an unstable charged particle decay faster in a strong field than in a weak field because there are more source charges contributing to the field, hence a greater number of possible derangements?

I have written an essay as well, which you can take a look at if you like. I appreciate tough questions.


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Brian Beverly wrote on Dec. 6, 2008 @ 07:42 GMT

Thank you for the comment; I'm glad you found it original and learned about derangements. The big idea is time = change. I assumed the universe has some fundamental objects with no internal structure. Without any internal structure there can be no internal change. Therefore such objects would only experience change by interactions outside of themselves. I took a combinatorics course a year ago and I think combinatorics is an important but often neglected theoretical tool. Combinatorics seems to naturally fit with entropy and my idea for time.

I also like tough questions because it makes good ideas stronger and eliminates the dead ends. If my approach is wrong I don't want to waste my life pursuing it.

I'm not sure I fully understand your question or the consequences of it. Are you implying the quantum Zeno experiment? In it a collapse of the wavefunction prevents the decay of a radioactive isotope until the "measurement" ceases.

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Anonymous wrote on Dec. 7, 2008 @ 21:47 GMT

Thank you for your comments on my essay. I will respond to them there.

I see space (or at least distance) as an equal partner when considering time and change because without it, I cannot visualize how it is possible for change to occur. In other words, the consideration of a "before" and "after" requires in my view a locational background through which these notions become meaningful, but I think I am becoming a bit philosophical.

I am taking thermodynamics/statistical mechanics this term and I think I tend to agree that combinatorics can be a useful tool in physics (although I have not taken a course on this).

When it comes to receiving constructive criticism you are fortunate to possess the wisdom that eludes many people who are much older than you.

wrt to my question, I was not referring to anything as sophisticated as the quantum zeno effect. Let me give a simple example to illustrate what I mean:

Consider the muon. As far as we know, it is a fundamental particle and therefore, by your idea, it can experience time only by means of its interactions outside of itself. Here I will consider interactions with an electric field, since the muon carries a non-zero electric charge. It is also unstable, and therefore the decay time (when considering a large sample of muons) can act as a clock.

Scenario 1:

Consider a muon that travels through a field set up by two identical electric charges q1 and q2. For simplicity assume the charges are equidistant from the Muon. There are two arrangements associated with the electric field sources(q1,q2) and (q2,q1) which are derangements of each other.

Scenario 2:

Consider a muon that travels through a field set up by three identical electric charges q1, q2 and q3. For simplicity, again assume the charges are equidistant from the muon (they would have to be in a plane perpendicular to the muon's direction of motion). There are six arrangements associated with the electric field sources (q1,q2, q3) (q1,q3,q2) (q2,q1,q3) (q2,q3,q1) (q3,q1,q2) (q3,q2,q1) which can be divided into three deranged pairs.

There are more derangements associated with the second scenario. Here each individual combination has only one derangement but with n(q)>3 it can have more than one.Would it therefore not be expected that the average decay time of a large sample of muons passing through a field created by more source charges i.e. a stronger field be shorter than that of one passing through a weaker one?


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Narendra Nath wrote on Dec. 9, 2008 @ 14:25 GMT
Dear Brian,

i enjoyed our exchange of posts on your original essay that i enjoyed very much. Wish you all the success in your upcoming Graduate School studies. i will be happy to interact you through e-mailing if you too care. My ID is .

It is always nice to interact with youngsters like you who like to follow an innovative approach instead of just following the beaten pathways in science. i am convinced the future of Physics that is a bit stagnant currently , is bright in the hands of youngsters like you. You have my vote! Best wishes, Narendra Nath

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Brian Beverly wrote on Dec. 10, 2008 @ 02:00 GMT

Thanks for all your encouraging comments. For some reason your email address did not make it into the above post. I worry that people will stop bouncing ideas off each other when the contest is over. I am also interested in nuclear physics, especially fusion. I'm sure our friendship will continue to flourish. You or anyone else from the contest can contact me at:

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Brian Beverly wrote on Dec. 10, 2008 @ 14:17 GMT

I agree space and time are linked and therefore "change" in space must always occur. I relate to the fact that absolute zero can never be reached. Temperature is related to motion in space and it is impossible to stop all motion.

Ah, thank you for clarifying your question. I was very liberal in my use of the word fundamental. Muons do decay into electrons and neutrinos but I usually think of space itself as quantized and fundamental.

In both scenarios you touch on the key idea you mention identical particles, however, my core idea was fundamental but different interactions. I like to think of walking in a solid black room then imagine passing through a permeable wall into a white room. Both rooms are empty there are no clocks on the walls and both rooms are different and distinct from each other. If I kept walking from room to room my concept of time and distance would be the number of times I measured change.

I think in the scenarios the force carrying particles must also be included. I have been thinking of trying to divide the derangements according to their particle spins. I know that by the exclusion principle two electrons with the same quantum numbers can not occupy the same orbit. Perhaps the exclusion principle is woven into the fabric of space-time?

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Brian Beverly wrote on Dec. 10, 2008 @ 14:23 GMT
I forgot to mention the regard q1 and q2 as identical therefore the derangement q1q2 and q2q1 are identical and are both mircrostates of the qq macrostate. In the second case all the derangements would be microstates of the qqq macrostate.

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Armin Nikkhah Shirazi wrote on Dec. 11, 2008 @ 04:51 GMT
Hi Brian,

Thank you for clarifying the point I raised. I am a little unclear on the following points, though:

-do you consider particles like electrons protons etc. as fundamentally indistinguishable or distinguishable?

-is you room example a metaphor for the quantization of space? what are the room colors metaphors for?

As you likly know, the Pauli Exclusion principle is a direct consequence of the antisymmetrization requirement, so that would seem to be a suitable point of attack. Also, if you want to incorporate spin into your theory, you will probably have to address the spin-statistics theorem. There is a book edited by Julian Schwinger that has Pauli's original paper in which he derives his principle (as well as Feynman's original papers on path integrals) and which you can buy from amazon for under 5 bucks (excl. S&H). It is called 'Selected papers on Quantum electrodynamics'. It may be good resource for your efforts (I am certainly glad I bought it)


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Brian Beverly wrote on Dec. 11, 2008 @ 14:13 GMT
I never tried to picture a proton or electron, for years it was only a philosophical idea. Then I found the derangement which fit and also looked similar to the time evolution of the wavefunction. As I played with it I saw it worked with entropy and the collapse of the wavefunction. The goal was to create a mathematically simpler wavefunction with a conceptual idea of time. I started with a philosophy followed some mathematics and there is the smallest chance it is important to physics. So I'm not sure what I would consider fundamental obviously protons have quarks and this quickly leads to discussions on nuclear forces. A string theorist would tell us the strings are fundamental and all the particles that we observe are vibrational modes of the fundamental strings. I was thinking of Fermi-Dirac/Bose-Einstein statistics which may give me some insight. After all both statistics are related to entropy, quantum mechanics and the exp(-n) function.

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Armin Nikkhah Shirazi wrote on Dec. 16, 2008 @ 06:45 GMT

I don't think that it is absolutely necessary to have a picture of atoms in order to be able construct a useful scientific theory about them. Look at how 'easy' it is to picture the wavicles of quantum mechanics! (There is actually a QM text book called the "picture book of quantum mechanics"; while I have not read it, I think the concept is intriguing.)

But even without a picture, one can still assign certain properties to them, and it seems that for your idea the property of distinguishability (or lack thereof) is going to be an indispensible part.

I agree that intuitively it seems that there may well be a place for the concept of derangement in boson/fermion statistics, but as I found out this semester, this subject is too abstract for my taste to cause me to become as passionate as I am about the foundations of qm and relativity, which is what it would take to compel me to look for such a place.


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Brian Beverly wrote on Dec. 19, 2008 @ 02:32 GMT
Agreed, the next aspect to focus on is the distinguishably. Seeing as how you took thermo this semester I'm not surprised you dislike the FD/BE statistics. They are usually covered at the end, are poorly explained and the student is exhausted. The only thing I pictured and tried to explain was the properties of the probabilistic wave aspect.


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John Merryman wrote on Dec. 19, 2008 @ 12:26 GMT

I thought I'd post this in response to a comment of yours on George Ellis' discussion;


"I think that "infinity" (i.e. a quantity that can never be attained or measured) is a mathematical concept that cannot occur in the real physical universe."

If I may paraphrase this, it would seem to say that because infinity doesn't have measurable boundaries, i.e, is not finite, it doesn't exist?

If I may extend this logic a little further, it could be argued that nothing has finite boundaries, as everything, you, me, the moon, are nodes in some larger network. Even defining the entire universe runs up against dark energy and matter, the possibility of other universes, worlds, dimensions, etc. What came before the Big Bang, where the energy of the universe goes next etc. It would seem quite difficult to argue the entire universe, if it is defined as singular, isn't also some node in a larger network.

So it would seem that no thing has absolutely finite boundaries. Does that mean that nothing is "real"?"

Infinity does consist of any number of measurable quantities, but without an overall description of them. There is no "God" perspective because an objective perspective is an oxymoron.

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Brian Beverly wrote on Dec. 20, 2008 @ 08:51 GMT
Astronomers can not see infinitely into the past, and physicists can not measure an infinitesimal distance of length or time. There could be an infinite number of extra dimensions or universes and there may eventually be evidence for them. For instance, if energy conservation is violated (don't count on it) or if I were to meet my twin from a parallel universe.

In physics the infinite denotes a large enough number to make an approximate prediction. I did this in my essay, I took the limit of the derangement as it approached infinity to ensure it "converges" and is well behaved for large numbers. I take comfort in infinity if I stare into the existential abyss long enough, I understand the appeal. Asking why not infinity? Focuses us on the wrong question.

Why not extra or even infinite dimensions? Why not the multiverse? Why not the many worlds interpretation? If pressed by someone fanatical about such ideas I would say I'm sitting on the fence because I don't want to hurt their feelings. Ultimately I believe if we can not directly do experiments to test an idea, then we must cut the fat from them judiciously using Occam's razor.

I praised George's paper because he understands the fundamental nature of quantum mechanics while others still imply it is an incomplete theory. By real and existing I mean from real analysis by fake, imaginary, etc I mean complex analysis. Quantum calculations involve complex analysis. The measured experimental results are real numbers. If I can get the results using finite real numbers instead of infinite real or imaginary numbers then I should try to, but ultimately we may never know.

Thanks for the comments,


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John Merryman wrote on Dec. 20, 2008 @ 18:15 GMT

For me, it is something of a fractal issue, in that a finite reality requires a boundary that is far more complex to explain than accepting endless repetition of the measurable. In other words, it fits Occam's razor.

The measurable, quanta or universe, are nodes in a network which is implied, but not measurable.

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Brian Beverly wrote on Dec. 21, 2008 @ 02:33 GMT

I'm glad you asked about infinity because it shows why combinatorics can give a conceptual understanding of quantum. The typical infinity thread leads to a mention of fractals. Fractals require the same type of structures on all scales. If the universe is anything close to being a fractal I would expect the problem of gravity in quantum mechanics to be much easier. Unfortunately, the fundamental quantum mechanical nature of the universe is very dissimilar to its large scale structures.

I'd like to summarize my above argument on infinity because I think it is a very important topic:

Quantum mechanics and experiments give finite real numbers:


How should physicists and mathematicians calculate the finite real numbers to give valid predictions?


1) Infinite real numbers?


2) What about finite complex (imaginary) numbers?


3) Infinite complex numbers?


The best, with minimum assumptions, is to calculate the finite real numbers using other finite real sets. It is impossible to prove infinity via experiment. The proof in mathematics usually comes from induction:

1) Basis: Does it work for n = 0?

2) Inductive step: If it works for n does it work for n+1?

A proof by induction works for the infinite or the finite, but it does not tell us if our universe is infinite.

The quanta in quantum mechanics means discrete and that these numbers are not arbitrarily small. Here is a simplified argument with mathematical hyperbole:

E = nh ---> [E1 = h, E2 = 2h, E3 = 3h ----> [1,2,3,...?

It is incorrect to have an energy that can be E= 1.34645h Energy is a quanta, whole numbers, integers.

I think we should focus on the real numbers; pure mathematics can not tell us if our universe is finite or infinite. An experiment would only tell us a finite n value. If a later experiment finds n+1 then we still do not know if there is an n+2. George and I are playing it safe. We think an argument that says, "infinity explains everything" is not experimentally nor mathematically rigorous. An idea using finite real sets can be confirmed and falsified via experiment.

How many angels can fit on a pin head?

Prove it.

Sorry for the ranting,


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John Merryman wrote on Dec. 22, 2008 @ 00:49 GMT

It's a basic dichotomy between object and process.

You think of quanta as discrete entities, but are they particles?

Yes, they are set quantities, but if they were distinct, how could they become entangled, such that when separated and measured in isolation, they possess identical properties? Could it be the quantity is a function of context and process, somewhat like drops of water tend to be similar in size, due to surface tension and gravity?

What about strings, with their external vibrations and internal dimensions? Are they an object, or a process?

What is the relationship between object and process? Which do you think is primary? Does form follow function, or is function a consequence of form? Is it a dichotomy?

Think of a factory; The products, the objects, go from initiation to completion, while the production line, the process, faces the other direction, consuming raw material and expelling finished product. Now put that in the context of time; The units of time, seconds, minutes, days, etc. are first in the future and after the hands pass over them, recede into the past, as the hand starts at their beginning and goes to their end. Meanwhile the process, the hands of the clock, just like the production line, is constantly going onto the next unit, as it finishes the old. It's a dichotomy.

So is reality discrete objects/numbers, or is it the process of counting them? Yes, the objects are finite, but where does the process end?

The coin has two sides, but it's difficult to see both at the same time. Do you think what you believe is the only way to see it, or is there a way to see it from the opposite perspective?

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Brian Beverly wrote on Dec. 22, 2008 @ 17:14 GMT
I think a few of your misconceptions of quantum mechanics are common and shared by the majority of others. The confusion is lifted with a better understanding of probability theory. Classical physicists believe that physics should be able to yield exact and certain outcomes of experiments. Quantum mechanics does not predict the exact outcomes of the experiment only the exact probabilities. In...

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John Merryman wrote on Dec. 22, 2008 @ 19:49 GMT

"I'm an optimist so I'm going with the big bangs happen idea."

Wouldn't that imply infinity?

Not that I have any proof either, but while objects are by definition, finite, proposing processes are finite requires both initiation and completion mechanisms that seem far more complex and arbitrary than assuming they have no beginning or ending.

Which gets back to my point about time; That the very concept of beginning and end only applies to units of time, while the process of time is always going on to the next unit. Even the life span of the earth and the Big Bang universe constitute units of time which are first in the future and eventually will be in the past. Entropy, or not.

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Brian Beverly wrote on Dec. 23, 2008 @ 12:36 GMT
Entropy and time are linked. The future and the past are consequences of increasing multiplicity. The time I use for quantum comes from derangements which I show have microstates and macrostates. When the wavefunction collapses it is due to an increase in multiplicity creating an overwhelming probable macrostate. From combinatorics I am able to derive a wavefunction and explain collapse. This is the thread I would like to be discussing because I have put a lot of time into it.

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John Merryman wrote on Dec. 23, 2008 @ 17:34 GMT

Sorry for going off topic in your thread. I only did that as a reply to a comment of yours in George Ellis' discussion.

As I read it, your Derangement model is a version of Many Worlds, with each derangement as a world line. ?

If I may, though, I would like to raise a point;

"A discrete fundamental object cannot be subdivided. Therefore, such an object is not capable of internal change. To experience change it would need to interact with other objects in the surrounding environment."

There are two parts to this construct. The "object" and the "interaction." My observation has been that while objects go from past interactions to future interactions, these specific interactions go from being in the future, to being in the past.

The issue is whether time is a fundamental dimension along which reality travels, in which case it is the objects traveling along their "world tubes" through "block time." On the other hand, if it is simply the motion of these objects bouncing into one another and creating the interactions, then time is the series of interactions going from future to past.

" One is from the irreversible collapse of the wavefunction, and the other from the reversible time evolution of the wavefunction:"

The collapse is future probability becoming past circumstance. The evolution is past to future cause and effect of the objects interacting.

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Brian Beverly wrote on Dec. 24, 2008 @ 08:28 GMT
John, I appreciate your interest and your good questions.

I believe there must be at least two fundamental objects in order for there to be an interaction. When the two objects interact there is a moment which separates the before and after. There is some initial condition say, (x)(y), then an “interaction” resulting in a final condition, (xy). I do not call this the past or the future because the objects have no internal entropy so time for them is reversible. The larger scale effect of entropy from the wavefunction collapse is what distinguishes the past from the future. The collapse from measurement changes the reversible time into the linear arrow of time we experience. The wavefunction may start to spread out after a measurement, but the total entropy of the universe increased from the initial measurement and can not decrease.

I do not use the many worlds interpretation and I’m proud of that. Each macrostate is initially a possible world line; some macrostate then becomes the world line when the wavefunction collapses as seen in George’s essay. I use derangements to mathematically quantify the microstates interactions, provide macrostates and give probability coefficients. I also use the derangement’s nearest integer property, [n!exp(-n)], which allowed me to remove the imaginary numbers in the wavefunction’s time dependence. In the traditional wavefunction the exp(-it) function drops out during a measurement through a complex conjugate. In a deranged wavefunction the exp(-t) function “drops out” because it is actually the nearest integer function [exp(-t)] and it represents quantized values of time. Both wavefunctions have mathematically identical properties. The important difference between the two wavefunctions is the deranged one is real. A real wavefunction allows us to understand measurement and explain time on a fundamental level. The imaginary wavefunction can only be treated as a mathematical placeholder and it is unable to explain what time really is.

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John Merryman wrote on Dec. 24, 2008 @ 17:42 GMT

While I'm more conceptual than mathematical, that is an interesting method of quantizing time. I think we have the same understanding of time as emergent effect, rather than fundamental dimension.

This does assume a finite universe, since entropy requires a closed set. Which does get back to the point of our discussion. If the universe is infinite, energy loss in one context would be energy gain in other contexts, with a total conservation of energy. The result would be cyclical time, as opposed to the linear time of entropy.

The past is viewed as immutable as one can't go back and change it, so this leads to the idea of block time, but this projected dimensionality is misleading, since all that is past is constantly being recycled and consumed, both energy and information, to manifest and define the present and as the present will be to cause the future. So time is both collapsing into the past and evolving into the future.

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Brian Beverly wrote on Dec. 25, 2008 @ 03:13 GMT
John, reading your essay reminds me of how I started thinking about time. Since you are more conceptual than math oriented I’ll write out your major ideas using some math on your forum. That way other physicists will understand your conceptual approach instead of them thinking, “a simple farmer” (simple farmer?! Too modest!) used some physics nomenclature out of context, etc. Physicists...

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John Merryman wrote on Dec. 25, 2008 @ 16:09 GMT

I'm of the opinion math is a useful tool, but it can be abused. Essentially math is complex pattern recognition. The problem is that patterns are ubiquitous, frequently limited in application, often contradictory with other patterns, generally over interpreted and applied, easily manipulated, promote obsessive compulsive behavior, etc. Pattern recognition is also the basis and purpose of the thought process. It is foundational to politics, religion, economics, history and just about any other academic discipline you care to consider. I originally started studying physics as a way to understand the foundational patterns to nature and human nature. What I found is that physicists are human and subject to the same tendencies of over interpretation as other people. Witness various of the conversations going on in this contest, of people focused on the patterns they have latched on to and try to project on to others, as the others are equally committed to their own conceptual insights, equally over applied. Not that I excuse myself from this habit either, but I do try to keep thinks in perspective, to the best of my ability. I'm not an expert at math or physics and am not setting out to be. Given the state of the world economy and environment, my interests are only in those patterns which can be very broadly applied and useful to understand what is happening on this little blue ball in space.

To a certain extent, your idea is also a pattern you have recognized in probabilities and find useful for explaining time. Having grown up in the horse racing world, I have a great deal of respect for probability theories and you may well be on to something, but be careful. Something that seems to fit may only be a form of mathematical analogy that is useful up to a level of application, but might lead to serious navigational errors, if over applied.

You are still quite young and very smart, so my old fogy advice is always to keep things in perspective. Like riding a bike, you need to keep your balance in order to keep moving forward.

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Brian Beverly wrote on Dec. 26, 2008 @ 03:05 GMT

The only time math is misleading is when the "human" element is involved. That human element is the obedience to the expert authority on a subject. Once you learn the math yourself you can derive ideas you can challenge that paradigm with a proof or counter proof. I believe the measurement problem was created from using the shortcut of imaginary numbers. The classical physics wave equation for the evolution of a plane wave does not match the Schrodinger equation. The difference is in the time derivative; the Schrodinger equation is first order and the classical equation is second order. I wanted to understand time which meant I had to remove imaginary numbers but maintain the wavefunctions predictive properties.

I believe mathematics represents the apex of human reasoning and logic. With only qualitative descriptions of Newton's laws and quantum mechanics we would be in the dark ages. Quantitative mathematics in any field such as: medicine, economics, politics and especially physics is the only way they can make progress. The power of math helps us make sense of the double slit experiment or a research questionnaire on political views. Ignoring mathematics results in stagnant fields mired with group think.

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John Merryman wrote on Dec. 26, 2008 @ 04:46 GMT

I wasn't trying to be cynical about math. Yes, it is the most rigorous pattern analysis. The fact is that the amount of potential information far exceeds our ability to comprehend more than thin slices of it. Relativity and QM are good examples of patterns which make sense in the context for which they apply, but don't easily relate to one another. As I said, it is the basis and purpose of thought.

The fact that it is the apex of logic also means it is the most distilled and reductionistic. The problem with that is that linear logic necessarily doesn't operate in a completely linear reality. Time is a linear causal chain, while temperature is a non-linear scalar average. It's been my contention that the intervals between temporal quanta are non-linear activity, such as that described by temperature or pressure. Consider time in terms of worldtubes as the causal chains. There is no objective perspective to view all these subjective realities and they interact and counteract, like molecules of water moving about. So all this linear motion exists in a larger non-linear reality and is at its most elemental level, composed of non-linear energies and polarities. Time is the transitions which have some degree of credible connection. That these series define the processes of our lives makes them fundamental to the life experience. Math is the apex of that reasoning awareness.

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Brian Beverly wrote on Dec. 27, 2008 @ 03:19 GMT

I know you were not being cynical. You’re very smart and the advice is not “old and foggy”. You should study math because you would quickly be able to recognize the patterns and it helps prevent dementia too! I hope you take my young and arrogant advice : ). Studying math is very boring, but the trick is to find a problem you like which motivates you to understand more. Look up the four color theorem it is a conceptual math problem I think you would like.

Pressure and temperature are well understood such as the ideal gas law:

PV = nRT

P = pressure

V = volume

n = number of moles

R = a constant

T = temperature (k)

When thinking about pressure and temperature it is impractical to calculate the dynamics (position, momentum, etc) of each atom. That is the strength of entropy in physics we can understand the system by generalizing the macrostate without knowing the systems microstate. Knowing the microstate would mean knowing the dynamics of every atom.

I know the point you were trying to make, it was not lost on me. I agree that pure math alone will not help us understand the universe. I think what you are trying to argue is something similar to the incompleteness theorem. In physics we do experiments to prove the equations and show that our understanding of the “pattern” is correct. Quantum physics has been experimentally tested to a high degree of precision equivalent to measuring the distance from the west coast to east coast and being off by a hair’s width. Many mathematicians do not consider physicists’ math proofs as rigorous or axiomatic because physics proves equations through experiment. The physicists do not like pure mathematics because they can not experimentally test it. A compromise has to be used like applied math.

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John Merryman wrote on Dec. 27, 2008 @ 12:14 GMT

Thanks for your respect of my seat of the pant theorizing.

It's not that I question the precision of math, or physics. The problem, as I see it, is that the process of deducing laws of nature has some feedback issues which create errors in the process. "Law" is necessarily a static concept, yet reality is fundamentally dynamic. Unless this fact is constantly kept in mind,...

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Chris Kennedy wrote on Dec. 27, 2008 @ 20:18 GMT
Hi Brian,

I enjoyed your essay. I have also read some of your thread comments (but not all). I am very glad fqxi has set up these threads instead of just posting only the essays to view. It has allowed us to clarify and expand our ideas while putting them through a test for consistency, accuracy and possibility. I have found some of your thread comments to be just as valuable as you essay text. I see that you have been chatting with John Merryman. I not only enjoyed his essay but have found his questions and dialogue among various threads to be incredibly useful. John’s insightful questioning has repeatedly drawn additional information out of authors that has been extremely helpful. Some contestants have written great essays but have barely said a word after submitting. I understand that shouldn’t necessarily influence the judging process - but can you imagine how much less we would have gotten out of this if it were nothing but a bunch of essays? If there was a separate award for thread discussion (or contest MVP), I would give it to John.

Okay, my question for you is: Does a discrete fundamental object create time while interacting with other objects, or is it expressing what time it is in? Also -Do you have any thoughts on what the root cause(s) could be for the slowing of discrete fundamental interactions during increased velocity or entering a gravitational field? I apologize if this was covered on a previous post.

Thanks – CJ

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John Merryman wrote on Dec. 28, 2008 @ 15:27 GMT
I'm away for a few days.

Chris, Thanks for the compliments. I suspect not everyone has been as appreciative of my input.

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Brian Beverly wrote on Dec. 29, 2008 @ 18:18 GMT

Chris is right your questions are important as all questions are. Most of the answers I think you would be able to satisfy yourself with some research. The laws of physics are not static the field is constantly growing and unifying ideas makes the subject simpler. I believe the static, dynamic questions you have as well as the process are satisfied with the function, f(x).

Your questions about photons touches nearly every branch such as: optics, E&M, quantum, relativity and thermodynamics. To understand entanglement you should start by researching the stern gerlach experiment. Also learn about mixed states, pure states, decoherence and the measurement problem. These subjects are advanced and if you like I could write them out and attach a PDF. I'll do my best to break down the advanced math but it will take some time.

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Brian Beverly wrote on Dec. 29, 2008 @ 18:54 GMT

I like the comments section too because discussion of the problem with time is necessary for there to be a solution. When most people think about time they think it is fixed and in the background. This idea has always bothered me because I like to think of it from the smallest possible perspective.

I left the "object" loosely defined I would like to think that space itself it what becomes deranged for time. The number of dimensions fits nicely and there is no longer a fixed background. I think that the "objects" time is defined by the changing surroundings when it notices a change then it experiences a moment in time. Time for us would be the net effect of the random microstate changes that create an overall macroscopic effect we call time.

I think overall the word time should be replaced with change. Microscopically time is changing surroundings which may repeat, cycle and reverse. Macroscopically time is a change to higher amount of entropy.

I used the partial derangement to prevent simultaneity and it creates the macrostates. The twin paradox in special relativity is resolved because one twin undergoes an acceleration. Similarly the equivalence principle states that an accelerating body has the same relativistic effects as a body in a gravitational field. Relativity is about the forces being applied to a body and becomes useful in extreme situations like black holes. If I think of space being deranged then the change in space, the derangement, would be equivalent to a velocity. You would also be able to say this area experiences on overage x derangements relative to the y derangements somewhere else. The change in the relative amounts of x compared with y would be relativity and something similar to acceleration.

It is not the best of arguments and the ideas is still gestating. Also I have not studied the Dirac equation in depth for over a year. So relativistic quantum is a stretch for me right now. At the moment I'm focusing on entanglement.

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Brian Beverly wrote on Dec. 29, 2008 @ 19:11 GMT
I just thought of one possibility. I think acceleration in one direction would have to suppress time by changing the derangement. (X,Y,Z) allows for different derangements (Y,Z,X) etc. If the Z direction is where the acceleration is occurring then it could be something like (X,Y) which has the derangement (Y,X) there would be no relative change with only two dimensions. Similarly for (Z,Y) and (Z,X). Maybe that is a way to throttle the derangement.

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Chris Kennedy wrote on Dec. 30, 2008 @ 15:57 GMT

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!


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Brian Beverly wrote on Dec. 31, 2008 @ 05:01 GMT

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.

attachments: Kennedy_kennedy_chris_natur.pdf

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Chris Kennedy wrote on Jan. 1, 2009 @ 05:44 GMT

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.


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John Merryman wrote on Jan. 1, 2009 @ 17:01 GMT

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.

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Brian Beverly wrote on Jan. 5, 2009 @ 17:29 GMT
John, here are some links that I've found useful for understanding physics


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


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


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

Have fun,


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Eckard Blumschein wrote on Jan. 12, 2009 @ 17:05 GMT
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

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Brian Beverly wrote on Jan. 14, 2009 @ 05:44 GMT
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.



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Eckard Blumschein wrote on Jan. 14, 2009 @ 15:45 GMT
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

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Brian Beverly wrote on Jan. 17, 2009 @ 09:47 GMT
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.


Brian Beverly

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Brian Beverly wrote on Jan. 17, 2009 @ 10:35 GMT
Ah, 1MB limit sorry the resolution won't be as good.

attachments: FQXI_Quantum.pdf

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Brian Beverly wrote on Jan. 18, 2009 @ 03:32 GMT
The measurement problem in physics is where it is implied that imaginary time is ordered:


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.

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Brian Beverly wrote on Jan. 18, 2009 @ 03:37 GMT
I almost forgot I found an interesting paragraph on Wolfram's mathworld:

storically, 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."

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Eckard Blumschein wrote on Jan. 18, 2009 @ 08:28 GMT
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,


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Brian Beverly wrote on Jan. 18, 2009 @ 09:44 GMT
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).

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Brian Beverly wrote on Jan. 24, 2009 @ 12:11 GMT

Here is a breakdown of entropy expect several more PDFs on it :)

attachments: FQXI_Entropy_1.pdf, FQXI_Entropy_2.pdf

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Eckard Blumschein wrote on Jan. 25, 2009 @ 09:08 GMT
Please find my thanks at 369


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Brian Beverly wrote on Jan. 26, 2009 @ 16:14 GMT

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 Beverly

attachments: FQXI_Nublackbody.pdf, FQXI_Schrodinger.pdf

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Eckard Blumschein wrote on Jan. 27, 2009 @ 20:33 GMT

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.


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Brian Beverly wrote on Jan. 27, 2009 @ 21:38 GMT

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 :)


attachments: FQXI_InExclusion.pdf

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Eckard Blumschein wrote on Jan. 28, 2009 @ 22:33 GMT

I have no idea whether a C is good or bad. Perhaps it does not matter. However, I strongly disagree: Imaginary numbers and complex calculus are very important. Modern technology was impossible without reduction of differential equations to algebraic ones. My point is: One has to use them not blindly but correctly. Heisenberg and Schroedinger frankly uttered that they did not always understood what they did. The original papers are written in German but meanwhile translated into English to a large extent.

What about derangement, it is a word the meaning of which I was trying to guess from my knowledge of Latin roots. Now I looked into my Cobuild Dictionary and found: Someone who is deranged behaves in a wild or strange way, often as a result of mental illness.

Having looked over InExclusion.pdf, I would like to advise you: Be careful with the meaning of "all" in case of infinite quantities.


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Brian Beverly wrote on Jan. 29, 2009 @ 08:18 GMT

Either way I am correct because if the universe is deranged then I would be deranged too. If the universe does not involve derangements then that makes me a crackpot which means I am still deranged. Both could be true! You bring up a good point about “all” and infinities which requires one final proof by induction. I think I will leave the inductive proofs for the readers.

I agree with your point because physicists are in love with differential equations yet none of them seem to care about real or complex analysis and they completely ignore combinatorics.

Newton knew a lot of geometry and from this geometric approach he deduced calculus. Calculus allowed Newton to understand physics using the infinitesimal time, dt. Einstein used a geometric approach for time he created space-time and the gamma factor. Quantum physics at its heart is probability theory. I am willing to bet the final theory will be about combinatorics.

I believe the universe is discrete and you believe the universe is continuous. I think we should agree to disagree :)

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Eckard Blumschein wrote on Jan. 29, 2009 @ 16:32 GMT

You got me wrong several times.

I do not believe anything. I found out that discrete models of reality and continuous ones can be shown to be mathematically equivalent via cosine transform. It is a matter of chosen point of view which one you prefer.

While I do not consider differential equations the primary relations, I nonetheless love differential equations too.

My point includes that physical quantities do not need a sign, and consequently transformation into a complex domain might be indispensable for the sake of feasible calculation but not for general reasons.

Huge electric circuits with lumped resistors, capacitors and inductances can only be calculated with complex calculus instead of differential equations.

Newton's (1642-1727) geometry has perhaps its roots mainly via Descartes (1596-1650) in ancient geometry. Descartes hesitated to introduce coordinates between -oo and +oo.

Incidentally, matrices with Hermitian symmetry are equivalent to complex representation.

Infinite quantities means: Abstract models without limits of size. There is no infinite value of a quantity. Infinity is a property, not a quantum.


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Brian Beverly wrote on Jan. 30, 2009 @ 05:08 GMT

Sorry for the miscommunication. I thought by infinity you were asking if my reasoning held for n = 0,1,2,....infinity which it does. How much of an approximation is the continuous cosine transform relative to the discrete model?

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Eckard Blumschein wrote on Jan. 31, 2009 @ 04:46 GMT

Someone who may or may not approve our post was perhaps unhappy when I wrote:

My point is: One has to use [complex calculus] not blindly but correctly. Heisenberg and Schroedinger frankly uttered that they did not always understood what they did.

I pointed to some cases elsewhere, and I could give further examples.

Continuous cosine transform does not specify a restricted n.

Therefore, discrete cosine transform is an approximation to the continuous one, not the other way round.


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Brian Beverly wrote on Jan. 31, 2009 @ 06:25 GMT

Thank you for the clarification. I see some strengths in your idea for the cosine transform. What ways are you considering to explain the wavefunction collapse and probabilistic coefficients? I know the uncertainty principle comes directly from Fourier analysis. This makes sense because if the momentum is related to wavelength and measuring its position collapses the wavefunction, then it is impossible to know the values of both observables with certainty at the same time.

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Eckard Blumschein wrote on Jan. 31, 2009 @ 17:01 GMT

When I was a child, I read that there are quanta of action.

Meanwhile I understand h_bar as a natural constant, a coefficient of proportionality between distance and momentum. Accordingly I do not see any difference in principle between uncertainties for the orthogonal pair distance/momentum and for the likewise orthogonal pair time/frequency. An exact value of frequency precludes exactness of the belonging value of timespan, no matter whether or not one tries to measure the two values.

Heisenberg speculated: "I believe that the existence of the classical path can be formulated as follows: The path comes into existence only if we observe it."

While it would be unfair suspecting Heisenberg stupid just because he failed his exam and he later on failed to correctly calculate the critical mass, we should consider this seemingly logical conclusion a challenge to clearly distinguish between reality and theory. Uncertainty is something mathematical and relates to the tacit switch from continuous to discrete or vice versa. After Cantor managed to create a General-Gouvernement of discrete numbers, after Hilbert, Zermelo, Fraenkel and others tried to save this paradise, nobody in Berlin and Goettingen was ready to abandon this putative treasure just for the sake of a reasonable while godless physics.

Let me anticipate a frequent error: Cosine transform cannot provide a spectrum for sine transform. Doesn't this matter?

No. It is true that one cannot decide how large the angle phi is for a cos(phi) that does not noticeable differs from one. Bicyclist know the dead point, however it does not prevent healthy people from using a bicycle. At first, sinusoidal functions are always approximations to reality in the sense that no oscillation in reality reaches to infinity. Secondly, if we decide to refer to the natural zero of elapsed time between past and future, the sine function would only apply for an infinitely small and therefore irrelevant timespan.


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Eckard Blumschein wrote on Jan. 31, 2009 @ 17:06 GMT
Sorry, when I wrote sine transform, I meant sine function.

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Cristi wrote on Mar. 9, 2009 @ 17:51 GMT
Happy birthday, Brian!


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Brian Beverly wrote on Apr. 27, 2009 @ 05:05 GMT

I have been thinking about the cosine function and its only attractive fixed point. I find it interesting that this fixed point is where the cosine function intersects the y = x line. The y = x line is also defined as the speed of light and creates the future and past light cones in a minkowski space.

This makes me wonder if the speed of light looks like a constant because we are observing the attractive cosine fixed point after a large number of iterations.

The cosine function is also identical to f(x) = (A)exp(-x^2) on the interval [-1, 1]. Maybe the speed of light is a direct consequence of the quantum mechanical wavefunction's attractive fixed point.

If this were true then quantum teleportation would not be spooky, because it would be a consequence of the same mathematics which make the speed of light a constant.

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Eckard Blumschein wrote on May. 6, 2009 @ 14:22 GMT

I am claiming that effectively any one-sided function f(x) can be expanded into an infinite sum of cosine functions rather than sine and cosine functions or sine functions alone.

Since the point f(0) is always of interest and sin(0)=0, one would need a sum of actually infinitely many zeros in order to get f(0)=|=0. This would not work.

I do not understand why you refer to the point cos(x)= x approximately at 0.739.

What about cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! ... it looks indeed similar to exp(-x^2) = 1 - x^4/1! + x^4/2! - x^6/3! ... Let's check: cos(0.5)=0.87758

while exp(-0.25)=0.7788

The speed of light was perhaps first calculated by Maxwell with reference to Weber and Kohlrausch as the ratio of electrostatic by electromagnetic units. Notice, in the cgs system by Gauss my_zero was equal to one. In the SI, my_zero equals to 4 pi 10^-7 Vs/Am, and c = 1/sqrt(my_zero eps_sero). Impedance of vacuum Z = sqrt(my_zero/eps_sero).

Admittedly, I did not yet understand your ideas. I am just an old electrical engineer.



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Jamina Jamina Jamina wrote on Sep. 29, 2017 @ 09:11 GMT
Both quantum mechanics and chaos theory suggest a world constantly in flux.

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