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CATEGORY: Questioning the Foundations Essay Contest (2012) [back]
TOPIC: Physical Reality - On Dirac, Quaternions and the Wave Structure of Matter in Space by Geoffrey Haselhurst [refresh]
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Author Geoffrey Haselhurst wrote on Sep. 6, 2012 @ 11:19 GMT
Essay Abstract

In 1928 Paul Dirac factorised Schrodingers relativistic wave equation into complex plane waves that had a structure similar to Clifford algebra (complex quaternions). The importance of the Dirac equation cannot be disputed as it led to the prediction of spin and antimatter, both later confirmed by experiment, and provided the foundation for modern quantum physics. However, for the past 80+ years no one has fully appreciated the significance of this solution. We can now show that these complex plane waves in three dimensional space are real waves, and from this foundation we can deduce the main equation of quantum physics and Einstein's relativity. Once we understand this then we are in a position to state precisely which of our physical assumptions are correct and incorrect.

Author Bio

Geoffrey Haselhurst is a natural philosopher - one who studies Nature and the universe. He lives quite isolated from society on the South West coast of Australia with his partner and two beautiful young daughters. For the past 20 years he has read on physics, philosophy, metaphysics, evolution, education, politics, etc., believing that we must know the truth about things if we are to think and act wisely (philosophy). He enjoys the freedom to pursue knowledge, free from customary beliefs and academic pressures to conform to existing beliefs that tend to blind us to obvious truths.

Download Essay PDF File

Gary Simpson wrote on Sep. 6, 2012 @ 23:25 GMT
Nicely done Geoff ... glad you could join the party ... but you did not mention Milo ... or did I miss it?

If you have the time, take a look at my essay. I extended Milo's thoughts to time. The scalar solutions are ... interesting:-)


Gary Simpson

Houston, Tx

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Author Geoffrey Haselhurst replied on Sep. 7, 2012 @ 01:05 GMT
Hi Gary,

Nice to see you here - have been meaning to write you to discuss quaternions, Dirac and the wave structure of matter (life is very busy with two young girls and I have just finished building house extensions - my new living room is also a projection room / movie theater as i plan on devoting a lot of my life to film making).

I did reference Milo Wolff, his work deducing the...

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Gary Simpson replied on Sep. 7, 2012 @ 03:42 GMT
Agree regarding spin ... quaternions give the answer. Spin is a vector and Milo's work simply does not produce a vector. I've posted this paper and another (both with the Appendices) to There are some derivations that might be of inteest to you. You've gathered together a good collection of references ... a curious student will do the rest:-)

Regarding spherical structures ... I am thinking that allowing each structure to have spherical time is equivalent to stating that each structure is a preferred frame of reference. Then when they are summed up into macroscopic objects, the time frame of the larger mass becomes controlling ... still fuzzy as to whether it has any meaning or is simply a mathematical game.

Good Luck,

Gary Simpson

Houston, Tx

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Author Geoffrey Haselhurst replied on Sep. 7, 2012 @ 07:25 GMT

I was thinking about your essay this morning (to read about such fundamental things then go for a walk in the sunshine and nature (reality) and think about it. I greatly enjoyed it!

One thing I was thinking was the same as you;

"...still fuzzy as to whether it has any meaning or is simply a mathematical game."

Good to have that awareness of the limitations of maths, but also their usefulness and logical exploratory power.

So I really respect what you are doing, my maths is not good enough to quite grasp what it is saying.

I wonder, does a spherical wave have a different time in different directions, and we could assume here that the spherical wave may have different velocities in different directions that are the cause of this. Thus maybe it is a better conception of time as a tool for measuring the change of 3D spherical waves, now that we better understand this internal structure of matter 'particles'.

This is further confused by my understanding of Dirac, and these spherical waves are formed from plane waves flowing through space in all directions, their transverse (vector / complex) wave components cancelling to form these scalar / longitudinal spherical standing waves.

Your work in this area sounds interesting - I will study it and try to understand it.

Cheers and thanks,


Anonymous wrote on Sep. 7, 2012 @ 00:43 GMT
That was a nice history, and some great reading about quaternions in general. Nice work.

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Author Geoffrey Haselhurst replied on Sep. 7, 2012 @ 01:07 GMT
Thank you - quaternions are very cool and powerful maths - glad you appreciated it.

Eckard Blumschein wrote on Sep. 7, 2012 @ 04:55 GMT
Dear Geoffrey Haselhurst,

You wrote your essay in just one day. I will need more time as to carefully check how some striking discrepancies to my essays 1364 and 1548 can be resolved.



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Patrick Alan Hutchinson wrote on Sep. 7, 2012 @ 12:03 GMT
Hello Geoffrey

Thanks for your essay. Please excuse me for putting a spanner in the works, but it does not seem to depict the original theory with the most appropriate maths. This has a substantial bearing on interpretation and future progress.

The point at issue is the algebra underlying Dirac's equation. At each point, this is the Clifford algebra of the metric on space-time. You write that it is "similar to Clifford algebra (complex quaternions)". This statement is unfortunately true - unfortunately, because it will lead future researchers astray.

Point 1: it isn't just "similar to Clifford algebra". It really IS Clifford algebra.

Point 2: by a chance quirk of algebra, it may well be that this particular Clifford algebra happens to be isomorphic to the complex quaternions, but this really is just a coincidence. Any such isomorphism will preserve the algebraic structure, but will lose the underlying geometry and motivation.

Point 3: this matters. Dirac's original theory can be extended very easily to

- curved space and Einstein's General Relativity

- asymmetric metrics, via Hannabuss's extension of Clifford algebras, and it may thus provide a model of other real physical features such as perhaps the weak interaction.

However, these extensions are ONLY apparent when the original GEOMETRIC origin of the algebra is kept obvious. If the algebra is treated as complex quaternions, or some other algebraic isomorph such as an exterior algebra, then they are lost.

Please see my essay, (1366), for more details.

Best wishes

Alan H.

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Author Geoffrey Haselhurst replied on Oct. 4, 2012 @ 21:32 GMT
Hi Alan,

Thanks for your comment.

In your essay you write;

"• The underlying mathematical language used to describe GR is the language of smooth

curved surfaces, using the “real” numbers, IR. There is nothing in Einstein’s original

account of GR which lets a physicist “add” two states of space-time.

By contrast

• The language of SM is that of algebra over the “complex” numbers, C, using functions

on a flat space."

The reason for this is that complex numbers in quantum theory relate to the transverse wave components of the plane waves in 3D space. The scalar / real numbers relate to how matter is formed, where there are four solutions where these transverse waves cancel producing scalar spherical standing waves (the two spin states of the electron and its opposite phase positron). This is the spherical (ellipsoidal) geometry of matter found in GR.

I did not understand your comments about complex quaternions and Geometry. Apparently Clifford called his complex quaternions 'Geometric Algebra', and David Hestenes uses this term, there is no loss of geometry in using them.

Hope this helps (and sorry for very late reply!)



PS - You will also find Declan Traill's essay interesting, it shows a deduction of Einstein's GR based on Euclidean space assuming the velocity of light varies with the energy density of space (waves in space are non-linear).

Joel Rice wrote on Sep. 7, 2012 @ 13:13 GMT
Uh ... complex quaternion algebra is Pauli algebra - not Dirac algebra.

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Author Geoffrey Haselhurst replied on Oct. 4, 2012 @ 21:41 GMT

All three algebras are isomorphic.

The complex quaternions are the correct mathematics to use, as they are the correct mathematics for describing transverse plane waves in 3D space (this space we all experience existing in!).

Gurcharn Singh Sandhu wrote on Sep. 7, 2012 @ 14:34 GMT
Dear Geoffrey ,

I have read your essay and found it interesting. You have presented an entirely different perspective and that is important.

You say, "what we call empty space is in fact full of waves". In your opinion, what are the physical properties of this empty space that facilitate the creation or propagation of waves in it? Which parameter is supposed to oscillate in these waves?

As you know, with arbitrary assumptions we can build wonderful fantasies. But to come close to building a model of reality, we must use barest minimum of assumptions and such assumptions that are used must be plausible and compatible with physical reality. For this reason I think FQXi has chosen a most appropriate topic for this contest.

Kindly read my essay titled,"Wrong Assumptions of Relativity Hindering Fundamental Research in Physical Space". Do let me know if you don't get convinced about the invalidity of the founding assumptions of Relativity or regarding the efficacy of the proposed simple experiments for detection of absolute motion.

Best Wishes

G S Sandhu

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Rick Lockyer wrote on Sep. 9, 2012 @ 00:23 GMT

You came out of one roundabout on the correct road for the Quaternions, but down the road you missed the sign with the arrow saying This Way to Division Algebras. Maybe it was not your fault, for the boys with the gambling house try to get more traffic on their road by cutting the sign down. Check it out if you like.

In all good fun,


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Anthony DiCarlo wrote on Sep. 13, 2012 @ 15:35 GMT

Your "complex quaternion" reduction actually follows the Space Time of David Hestene's, EXCEPT, David never envokes any complex numbers. David's "i" has the geometric meaning of plane (an outer product). A plane is a simple entity and not too complex. This would hardly obey Wheeler's description of simple when you start at the premise with the word "complex!"

Best regards,


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Author Geoffrey Haselhurst replied on Oct. 4, 2012 @ 21:57 GMT
Hi Tony,

Simple = One substance, space, exists, infinite and eternal, and has transverse plane waves propagating through it in all directions.

Complex = There are four solutions where the transverse wave oscillations cancel forming scalar spherical (ellipsoidal) standing waves, the two spin states of the electron and opposite phase positron. And with a frequency of 10^20 Hz and around 10^40 of these potentially forming in a cubic meter of space, well its gets very complicated!!

I have read a bit of Hestene's work over the past month (thanks). His geometric algebra / spacetime algebra is equivalent to complex quaternions, and yes, as I explained in the essay the complex numbers i, j, k, are used to represent three orthogonal planes.

It is interesting that he makes the comment that it is surprising that the great physicists of early 20th century never realised the geometry inherent in the Dirac equation.

What is more surprising is that no one seems to realise why. My essay explains this, because intersecting complex plane waves in 3D space can form scalar spherical standing waves, the spherical (ellipsoidal) geometry of matter, and central to Einstein's relativity.



Sreenath B N. wrote on Sep. 13, 2012 @ 16:29 GMT
Dear Geoffrey,

Your endeavour to explain whole of physics on a single assumption evokes interest on your article.You have dared to question eight of our fundamental assumptions of physics, where as I have dared to question only one assumption of physics as applied to micro world.To know this ,please,go through my article ( B N),and express your comments on it in my forum.

Regards and good luck in the essay contest.


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Anonymous wrote on Sep. 23, 2012 @ 20:00 GMT
This essay does not offer anything new. Please read Leibniz, Whitehead 1906, Epperson 2004 and about a million other current quantum theorists like Zurek (2002. The rating for this essay is 'no shit sherlock.'

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the door bitch replied on Jan. 10, 2013 @ 15:25 GMT
I think part of Geoffreys point is that it has been an obvious solution for some time.

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Jim Wright wrote on Sep. 27, 2012 @ 13:12 GMT

I have started reading your essay and think I'll like it. I had, earlier this year, sent in a response to a "Your Cosmology Hypothesis Invited" and it turned up on Google under "Cosmology Hypothesis". My ideas generally run afoul those of the Establishment.

I'd be interested in any real arguments, but not in 'put downs' as these are a 'dime a dozen'.


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Author Geoffrey Haselhurst replied on Oct. 4, 2012 @ 19:58 GMT
Do you have a link to essay?



Jim Wright wrote on Sep. 27, 2012 @ 13:35 GMT

In the above Post I should have mentioned that I am currently planning to correct errors and revise portions of the Google article.


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Hoang cao Hai wrote on Sep. 28, 2012 @ 03:51 GMT
Dear Geoffrey Haselhurst

Very satisfied when to see you essay.

I am also select the natural philosopher and seem to have success with the ABSOLUTE theory (a draft for the proposal of the TOE)

Kind Regards !


August 23, 2012 - 11:51 GMT on this essay contest.

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Declan Traill wrote on Oct. 3, 2012 @ 09:31 GMT
Hi Geoff,

Thanks for your comments on my Essay, I will try to find time to respond to them soon. I have read your essay briefly & given you a high Community rating. Again I will try to find time to give it more attention...


Declan Traill

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Author Geoffrey Haselhurst replied on Oct. 3, 2012 @ 10:14 GMT
Hi Declan,

Seems our young daughters take a lot of our 'free time' (which is important!). I have had good intentions to reply to posts above - hopefully over the next few days.

I would really appreciate your careful thought and comments on my comments to you and on my essay - I think we are closing in on a complete simple sensible description of physical reality - exciting times!!


John Merryman wrote on Oct. 3, 2012 @ 16:32 GMT

That is a very interesting and concise view of major issues. I can't say I can verify every aspect, but it certainly matches alot of what I see as the direction needed to resolve these problems. There is one additional misconception I would add though. Action creates the effect of time, but we experience it as sequence and physics emphasizes sequence by treating it as a measurement issue between events, rather than a change of configuration. For example, the earth doesn't travel that narrative dimension from yesterday to tomorrow, but tomorrow becomes yesterday because the earth rotates. This makes time an emergent effect of action, similar to temperature. In terms of waves, time is frequency and temperature is amplitude.

I go into much of this is in my own entry. Much of what I write about is the psychology of how something this basic gets overlooked, but sequence is foundational to experience and rationality, so it can be a significant filter to look through. In fact, it seems the more educated the person I point this out to, the more resistant they are to considering it. It really does require stepping back from one's own train of thought for it to really be appreciated.

One would think that if time were a vector from past to future, a faster clock would travel into the future more rapidly, but the opposite is true. Since it ages/burns faster, it travels into the past more quickly. Remember that in the twins thought experiment, the one in the faster frame has died, by the time her twin in the slowed frame has returned, so with every passing day, her life recedes further into the past.

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Craig Smith wrote on Oct. 3, 2012 @ 20:43 GMT
I enjoyed the article. I think it is progressively compelling and logical in its presentation and conclusions.

As a lay person without the advantage of the Math background I found it simplified enough to follow and appreciate!

Good job

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Author Geoffrey Haselhurst replied on Oct. 4, 2012 @ 00:51 GMT
Thanks Craig - nice comment - very much appreciated!



Sergey G Fedosin wrote on Oct. 4, 2012 @ 04:07 GMT
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is
was the quantity of people which gave you ratings. Then you have
of points. After it anyone give you
of points so you have
of points and
is the common quantity of the people which gave you ratings. At the same time you will have
of points. From here, if you want to be R2 > R1 there must be:
In other words if you want to increase rating of anyone you must give him more points
then the participant`s rating
was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process.

Sergey Fedosin

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M. V. Vasilyeva wrote on Oct. 5, 2012 @ 00:54 GMT
Mr. Haselhurst,

a fine essay. Very upbeat and optimistic too. I especially appreciate this quote:

"What we call empty space is in fact full of waves, but the transverse wave components do not cancel so space vibrates in an infinite variety of patterns, what we now call the quantum field."

You also write, " Basically the terms on the left represent the phase of the complex /...

view entire post

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Concerned Public wrote on Oct. 6, 2012 @ 09:21 GMT
Sergey G Fedosin is bombing entrants' boards with the same "why your rating has dropped" message. They are all dated Oct. 4... same message.

WTH? I've seen one fine essay drop 89 (eighty-nine) positions, in "Community Rating" in the past 24 hours, and “Sergey’s note” came BEFORE it plummeted. Hmm.

The vote/scaling of this contest is quite nebulous.

"Hackers Rule!", I suppose!

Well??? What else is one to think? The General Public is... Watching…

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Karoly Kehrer wrote on Oct. 6, 2012 @ 22:47 GMT
Dear Geoff

"What we call empty space is in fact full of waves..."

If one want to understand nature one has to understand the fabric of space.

You have helped to get closer to understanding this mystery. Thanks.

Sincerely Karoly

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The Chaos Faerie wrote on Oct. 7, 2012 @ 11:49 GMT
Can you market this as proof potentially all religions are correct because of the fact the stories are a human construct and therefore there could be vibrational space existent formulated by the patterns of belief placed? It would be great to say physics says that, so people can act like little quaternions, and be conscious of the waves they are spreading.

I use "actually it's a physics thing, kinda" in my stories, when I explain my whole idea of waves and frequencies and patterns and paths to other people, and they then believe me. 95% more success in people accepting what I have to say, because they believe in physics. I bet you'd get a crazy large percent more people believing you, if you gave faith a nod, plus it would moot a lot of flames of hate. I'd really like physics to pump this whole idea so we could remove religion out of politics and socio-everything, and place it strictly in culture, and get along like little quaternions do, and figure stuff out like that. That, would be a real great way to solve some current global problems.

I don't know how to write that in math. I wish a physics person would do it. Nobody knows whats inside a black hole after the hole, or where the photon dissappears to? I don't know. I imagine I understand, but I may not.

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The Chaos Faerie wrote on Oct. 7, 2012 @ 11:57 GMT
I mean place, when I say quaternion. Each moment, capable of complete change in pathway, infinite. Like a potential. I see potential in this.

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Demi Levendis wrote on Oct. 22, 2012 @ 14:45 GMT
Dear Geoff,

I find your essay refreshing and very interesting. I have passed it on to a retired colleague of mine, Jan Boeyens, who I'm sure will also take great delight in the fact that there are other truth seekers out there. He has written several books, too expensive to buy, but you can find them on some Russian and Chinese sites for free ( :-) I did not tell you). One you might enjoy is Chemical Cosmology. He is also just completing an invited chapter entitled Debunking the Big Bang.




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Author Geoffrey Haselhurst replied on Oct. 30, 2012 @ 23:12 GMT
Thanks Demi,

Yep, truth seekers are rare creatures!

I look forward to reading his work on debunking the big bang. According to the wave structure of matter (WSM) space is necessarily infinite and eternal (as only one substance space exists, it cannot be bounded by or created by a second substance).

Thanks for posting.



Kimberley wrote on Dec. 16, 2012 @ 01:47 GMT
What kind of films?

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steven macleod wrote on Apr. 8, 2013 @ 22:02 GMT
bla bla can one of you brainy guys please come up with a way of extracting energy/heat from the sea,solving two problems at once please

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Rick Delmoico wrote on May. 23, 2013 @ 15:00 GMT
I have been looking for clues in sacred geometry and prime numbers. The series of prime numbers hints at 8 dimensions. Time is not 1/2 a dimension. 1/2 a dimension of time is what we perceive. Time is moving in a wave like pattern through the other dimensions at very specific frequencies and at various amplitudes. The frequencies change depending on the fields or energy at that location. The amplitude becomes very important in the case of a singularity at the center of a black hole. In the singularity of the big bang the amplitude for time would become infinite. There may be clues in something called cymatic cellular automata. Jim Gates has found clues that error correcting codes are written into the fabric of space/time. Symbols of power, Adinkras

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Rick Delmonico replied on May. 23, 2013 @ 16:08 GMT
It appears that humans can perceive the future at very short intervals. This is why I am thinking that time behaves like a wave.

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Rick Delmoico wrote on May. 23, 2013 @ 15:48 GMT

I do not own my heart

But I have no-one to blame when it wanders

I did not chose my name

And I'll have nothing to claim when it's gone

Even if the whole world flinches

Straining to relieve the pressure

Some approximation bares a striking resemblance to dawn

I cannot find my way

But I have nothing to lose at this moment

I do not think it's strange

That I'm not required to know or respond

Even if the whole thing hinges

On our vision of the future

Most would fail to find the flaws neatly nested in the chaos beyond

We have forgotten how light pierces the darkness and is consumed

Nor have we considered that life is a hollow vessel, filled and then poured out again

If gravity should win

And everything is pulled apart as it tumbles

All the information lost

And nothing remains when it's done

Even if we can't preserve life

Or find a way to save our memories

Some illusionary moment shared the only treasure we have won

Perhaps at the event horizon

Time dilated, we appear to freeze

We're smeared upon its rippling surface

Swirling vortex of a summer breeze

Are we neither alive nor dead but echos from another life

Our path enfolded so we only see

Fields and fluctuations, vibrations, discord, harmony

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William H. F. Christie wrote on Jul. 29, 2015 @ 21:13 GMT
Hi Geoffrey,

I read your article in order to 1) compare it to the Rotating Wave (soliton) which I think is the basic form of fermion (eg electron) matter and 2) to see if I could find any enlightenment on quaternions, spin and Dirac Equation relating to the Rotating Wave.

To me wave particle duality does not necessarily mean that there is a particle there guided by a piloting wave....

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