Arcanorium CollegeCollege News and Views

Pete Carroll

Wednesday, 12 January 2022 13:42

Quantum Principle of Relativity

Quantum Principle of Relativity

This recent paper by Andrzej Dragan and Artur Ekert : -

appears to derive some of the basic strangeness of quantum mechanics from a consideration of the conventionally discarded superluminal (faster than light) solutions of Special Relativity. In particular, the Lorentz transformations suggest that in a superluminal reference frame, the dimensional signatures undergo sign reversal changing space into time and time into space.

The Dragan & Ekert paper also suggests that incorporating both the subluminal and superluminal reference frames explains the apparent indeterminacy, the multiple paths, and the Huygens wavefront phenomena of quantum mechanics, whilst positing additional time-like dimensions. 

Now the Transactional Interpretation of Quantum Mechanics similarly does not discard the Advanced Wave solutions to Maxwell’s equations of electromagnetism, and it explains quantum mechanics in terms of advanced waves traveling ‘superluminally’ backwards in time and retarded waves traveling forwards in time.

Some interpretations of quantum mechanics describe antiparticles as time-reversed particles, and bosons as particle-antiparticle pairs.

A full inclusion of frames of reference on both sides of the lightspeed barrier seems to lead to a Six-Dimensional Quantum Spacetime.

Spacetime Metric, where  + = space,  - = time.

                                                              Dimensions (Minkowski)                      

Subluminal Retarded Wave (R)             +R  +R  +R  -R   (3 space, 1 time)

Superluminal Advanced Wave (A)        +A   -A   -A  -A  (1 space, 3 time)


Overall result (Subluminal reference frame)

Space,  1, +R +A,   Direction of travel, forwards or backwards. X axis.

Space,  2,   +R. Orthogonal to direction of travel. Y axis.

Space,  3,   +R, Orthogonal to direction of travel. Z axis.

Time,    1,  -R -A, Direction of travel, forwards or backwards.

Time,    2,   -A, Orthogonal to ordinary time, imaginary time or ‘pseudo-space’.

Time,    3,   -A,  Orthogonal to ordinary time, imaginary time or ‘pseudo-space’.

Further, it is interesting to note that within the subluminal reference frame only quanta carrying imaginary time pseudo spatial spins 2 and 3, responsible for electric and nuclear charges, have mass and sub-lightspeed velocities, whilst photons and neutrinos which lack these spins always travel at lightspeed.

Work continues........

Sunday, 19 December 2021 14:58

Winter Solstice 2021

Winter Solstice 2021 Blog.

Seasonal Greetings.

Herewith from the halls of Chateaux Chaos the goddess Apophenia atop the festive tree.

Cosmology News

The James Webb Space Telescope should soon set off to take station 1.5 million kilometres from the Earth at a Lagrange point between Earth and Sun. It has cost about twice as much as the large Hadron Collider. I profoundly hope that it launches successfully and deploys its delicate structures as planned, as we do not currently have the ability to fly out and fix it.

I entertain high hopes that observations made by this telescope will lead to the demise of the Big-Bang expanding universe LCDM theory, and the triumph of Hypersphere Cosmology.

The JWST will take long hard looks at galaxies near to the limits of observation because the older Hubble telescope unexpectedly found a vast number of galaxies with many that looked far too well developed to fit into the official Big Bang story.

Hypersphere Cosmology asserts that the universe always remains roughly isotropic and homogenous at all points of space and time. We should find galaxies at all stages of their circular evolution and recycling in every observable region of spacetime.

The universe is closed according to Hypersphere Cosmology, its own gravity curves it back in on itself. That same curvature creates redshift and the illusion of expansion through lensing.

Several other ‘Crises in Cosmology’ already threaten the official Big Bang model; attempts to pin down the apparent expansion rate, the so called Hubble Constant, give inexplicably different results. A recent study of the cosmic lensing of the microwave background radiation strongly indicates a closed (hyperspherical) universe.

Quantum News.

With the Hypersphere Cosmology thesis now seemingly complete and awaiting confirmation or falsification, attention returns to Quantum Ontology, what the heck really goes on in the quantum realm that appears to underlie reality?

We have no shortage of Quantum Epistemology; we have the mathematically baroque description of Quantum Field Theory which gives precise predictions in some areas but only probabilistic ones in other areas. It gives very little that we can readily re-express in images or words. Thus, we have a growing suite of Interpretations about what the current mathematical epistemology could mean for the ontological structure of reality – what really exists or how does it do what it does.

We seem in a situation similar to that of the medieval alchemists struggling to understand what happens when we start experimenting with metallurgy and heating and mixing and separating substances, we have developed a very complicated set of rules of thumb but not yet any understanding of the underlying reality (in this case of atoms) which can explain the chemistry involved more clearly than ideas about green and red dragons, peacocks of antimony and phlogiston.

The current suite of Interpretations includes a rich menagerie of weirdness from the many-worlds interpretation, through pilot-wave theory, to reversible-time transactional interpretations, to interpretations with any number of extra spatial and temporal dimensions, to the alternately zen-like inscrutability, agnosticism, or cosmic nihilism of the Copenhagen Interpretation which eschews any interpretation, either because we currently cannot do so definitively, or because either no underlying reality exists, or because it cannot exist in any form that we could possibly understand.

I had wondered if my speculations on quanta as fast rotating multidimensional spinorial toroids seemed an intuitive leap too far but published it here on 2nd June anyway.

Now I notice that the illustrious Gerard 't Hooft published something which seems to explore a similar line of speculation on 29th July.

See Gerhard’s discussion of 'fast variables' and multidimensional toroids.

If god does not play Dice, perhaps she plays Roulette instead, but so fast that we cannot see it.

Azathoth seems subtle, yet more indifferent than malicious.

Magical News.

With the revisions to Liber Null and Psychonaut complete, and with the Occultaris provisionally tucked in as a 20-odd page appendix to Interview with a Wizard, work has begun on a revision of Liber Kaos for a classic edition. This will entail a few upgrades to the opening science sections where science has caught up with magic in the interim. The closing chapters which deal with the contentious matters of grades, hierarchies, temples, and orders, will receive the benefits of a lifetimes experience and some wry observations about what achievements and disasters can result from them.

And in summary of 2021…….

On the downsides, most of the powerful players copped out of their responsibilities at COP26 and kicked the can down the road. The anthropogenic climate crisis visibly worsened as did the conflicts which it creates. The globalisation of just about everything has brought with it not only creative chaos but also a seemingly uncontrollable surge in entropy. In terms of biological cultures or thermodynamics, the prospects for our current forms of overpopulated overconsuming civilisation do not look promising.

On the upsides, the pandemic has put the Scottish Independence fantasy on hold, where more careful reflection upon its multiple fallacies quietly erodes it. The same goes for anti-Brexit sentiment, the EU has responded poorly to covid, Belgium, the rotten heart of the EU, has some of the worst pandemic figures on the planet.

The pandemic has brought home to many just who and what matters to them. Introverts with a rich inner life have generally fared better than the extroverts that our culture and media favours. For many of them lockdown has proved an annus mirabilis in terms of the appreciation and production of ideas, literature, art, and science. Lockdown economics has demonstrated that we could in principle, and with a bit of redistribution, easily thrive on a lot less work and consumption.

All the best for 2022, Choyofaque, Stokastikos, Pete.

Thursday, 02 December 2021 21:57

Decblog 2021

DecBlog 2021

Rebel Physics.

Hypersphere Cosmology has finally defeated LCDM Big-Bang Cosmology!

The universe has always existed, and it always will. Merry Christmas.

The final battle recently occurred on a cosmology forum where HC took the last remaining bastion of LCDM by accounting for the Cosmic Microwave Background Radiation in terms of its own model.

Herewith the plan of attack used: -

Herewith the tactics in full:

The fighting was brief and bitter this time, the losers ended up cancelling and no-platforming the victor.

It all had the flavour of an atheist demonstrating the non-existence of god to a theological college.

Japanese Chaoism.

I have almost no idea what sort of Chaos Magic goes on in Japan, apparently my works have appeared in translation there, but language difficulties prove a barrier to communication. Nevertheless, a group over there sent me this delightful artefact: -

It’s a magic scrying mirror that resumes both late medieval grimoire symbolism and the alphabet of desire as given in Liber Null & Psychonaut.

21st Century Catastrophe.

I’ve had a fair bit of feedback about King Crimson’s 21st Century Schizoid Man lyrics from the previous blog: -

"Poets' starving children bleed"

There's a 2-minute clip here that predicts one nasty future consequence I haven't seen described before:

"Blood rack barbed wire"

This report finds that the world’s biggest emitters of greenhouse gases are spending, on average, 2.3 times as much on arming their borders as they are on climate finance. This figure is as high as 15 times as much for the worst offenders.

I suspect that most national leaderships in powerful nations must have already calculated that in the absence of sufficient international action, national preservation takes precedence and that their populations will back them on this.

Finally, a Poem. In celebration of HC CMBR victory.

             The Starlit Sky

Away from the glare of our burning cities

The sky at night looks black as pitch betwixt the stars

Olbers said that cannot be

In a universe of infinity

Yet look again with a microwave eye

And it’s all aglow betwixt the stars

Is this the relic of a mighty blast

From distant aeons in the past

Or does the light from here

Go round a cosmic hypersphere

Coming back a little tired and cold

After all, it’s very old.

Sunday, 21 November 2021 16:44



The Cosmic Microwave Background Radiation has become interpreted as evidence for the Big-Bang expanding universe LCDM standard cosmological model.

The CMBR consists of electromagnetic microwave radiation that peaks at a frequency corresponding to blackbody radiation with a temperature of 2.70  Kelvin above absolute zero. It comes to observers here from all directions in space.

Standard cosmology interprets the CMBR as relic radiation leftover from a primeval fireball about a third of a million years into the supposed expansion of the universe from a spacetime singularity or near singularity. At this time the universe had supposedly expanded to a radius of a third of a million light years and cooled to a temperature of about 3,000K, at which point it deionised from a proton-electron plasma and allowed photons to pass freely through it. Such photons which allegedly had very high energies and short wavelengths, subsequently became much lower energy longer wavelength photons due to the expansion of space and they now appear to us as the microwave background radiation.

We cannot see the CMBR with the naked eye, but if we could the night sky would not appear dark between the stars because about 400 CMBR photons per square centimetre per second impinge from all directions, they represent a significant cosmic phenomena that demands an explanation.

In Hypersphere Cosmology, all the electromagnetic radiation that does not become absorbed on its journey will eventually return towards its point of origin after about 13 billion years but in a much redshifted form due to gravitational redshifting and lensing by the small positive spacetime curvature of the entire universe.

Cosmologists estimate that our galaxy, the Milky Way, has an age alarmingly close to the supposed age of the universe itself, somewhere around the thirteen billion year mark. They remain adamant that it cannot possibly have an age greater than their estimate of the age of the universe. Yet the Milky Way contains the so-called Methuselah star (HD 140283), whose apparent longevity does seem to severely challenge the cosmic age limit.

The average surface temperatures of all the billions of stars in a galaxy or a galactic cluster adds up to something resembling a blackbody radiation source at about 3,000K when seen from a cosmic distance.

Thus, the CMBR we observe in this region of the hyperspherical cosmos may well have originated from this region and reconverged back here in highly redshifted form thirteen billion years later. Observers in a deep intergalactic void may not observe any CMBR at all.

The following two diagrams show the combined effects of Hyperspherical Lensing and Hyperspherical Vorticitation. Hyperspherical Lensing brings electromagnetic radiation to a focus at the antipode point to its emission. Hyperspherical Vorticitation moves the source of emission to its antipode point in the same period. The first diagram shows this effect in the reduced dimension surface of a sphere representation of a hypersphere, and the second shows it in the reduced dimension ‘two-ball’ representation of a hypersphere. Thick arrows represent the movement of the source due to vorticitation; thin arrows represent the paths of emitted radiation.

Hyperspherical vorticitation will send this galaxy to its antipode point in the universe in a period of 13 billion years. Light emitted from this galaxy will also travel to the same antipode point in the same period and appear as incoming light. The galaxy travels in just one direction, the light travels in every direction. The incoming light will appear highly redshifted from stellar surface temperatures to 2.70 K.

Hyperspherical lensing will make the incoming light appear to have come from a surrounding sphere with a diameter very much larger than the antipode distance but compressed into a smaller field of view and thus multiply imaged. This will effectively smear out temperature variations and absorption and emission lines to yield a CMBR with blackbody radiation characteristics as shown below.

Redshift-Distance-Apparent Distance Graph. Vertical scale = distance, antipode distance at 1. Horizontal scale = Redshift.

Red line = Redshift - Distance relationship. Green line = Redshift - Apparent Distance relationship.

Note that the Apparent Distance of a Redshift = 0.625 source gives an almost exact figure for the Antipode Distance of the universe.

Sunday, 14 November 2021 19:36

Novblog 2021

Novblog 2021

Remembrance Day. In the UK, on this eleventh day of the eleventh month we traditionally stand for two minutes silence at the eleventh hour, to remember those fallen in war. This began after WW1, ‘The war to end all wars’, which somehow ushered in a century of wars instead. It seems also a time to reflect on future conflicts that now seem inevitable.

COP26 has predictably ended with universal agreement that Something Must Be Done, but that nobody needs to oblige themselves to do anything they really don’t want to.

I'm getting the feeling that, historically, COP26 will mark the beginning of serious universal appreciation of the problems but that insufficient action will follow until the problems worsen and the costs of inaction by the big players start to hideously outweigh the costs of radical action even in the short term. That seems normal for Homo Sapiens. 

Our species suffers from the morality paradox. Telling others what to do and then not doing it yourself usually proves the best course of action.

I think we can now confidently make three predictions about the coming decades; global temperatures will rise well past 20C, human-made catastrophes and wars will multiply hugely in frequency, and by mid to late century, world human population will have decreased markedly from current levels. Mind the cull.

As I listened to the results of COP26, a friend put on an old prophetic 1969 King Crimson track.

Cat's foot iron claw

Neuro-surgeons scream for more

At paranoia's poison door.

Twenty first century schizoid man.

Blood rack barbed wire

Politicians' funeral pyre

Innocents raped with napalm fire

Twenty first century schizoid man.

Death seed blind man's greed

Poets' starving children bleed

Nothing he's got he really needs

Twenty first century schizoid man.


Delayed Choice Quantum Eraser Ansible?

Perhaps worth a try, the Elder Gods may well maintain Cosmic Indifferentism, but some lesser aliens might reply.

See here


Distraction Hobbies.

Lithonian Space Navy.

The shipyards of Lithonia have closed for the winter along with our holiday lodge but working in them has provided  a stimulating distraction from reading and writing during the social isolations and lockdowns of covid.

An arms race with surrounding planetary civilisations has led to the development and deployment of new classes of Lithonian warship.

Herewith the LSN Flagship Draconia and two escorting SMVs, stealth missile vessels.

The Draconia has a standard silicate hull hewn from the rocks of the metal poor beach world of Lithonia and it carries an array of long and short range weaponry forged from scavenged coat hooks, dismantled electric razors, metal scraps, and vape accessories.

The SMVs have tougher hulls selected from huge unworked slabs of seaworn vesicated basalt and they rely on speed, stealth, and rock armour to close with opposing vessels.

I can foresee a sprawling boardgame evolving out of all this in the fullness of time, it will probably require a fair area of the beach to lay it all out on.

I used to make ships from plastic kits over half a century ago but always found it more interesting to discard the instructions and create something new. Now I eschew plastic altogether and take inspiration from whatever more durable junk comes to hand and eye. Having enjoyed the first one, I figured that I may as well start on my second childhood early.

Herewith the fleet so far.


Monday, 08 November 2021 19:37

Delayed Choice Quantum Eraser Ansible

Delayed Choice Quantum Eraser Ansible.

The following thought experiment shows that in principle instantaneous communication remains possible over any distance, including interstellar and intergalactic distance; and further that this need not lead to paradoxes or causality violations in a universe with finite a lightspeed; and further that something akin to a cosmic internet probably already exists.

Consider what a delayed choice quantum eraser can do: -

Light from the Source passes through a Double Slit. The Spontaneous Parametric Down Converter Crystal splits each quantum of light into two Entangled quanta, each of half the energy of the original, and these quanta follow divergent paths.

The quanta which diverge upwards meet at a nearby Interference Detector which could in principle consist of a simple screen. The quanta which diverge downwards go through a suitably sophisticated ‘lens’ arrangement which can focus them at any distance including theoretical infinity.

Because of the entanglement between the quanta  which go to each of the separate detectors, any action at either detector site which destroys the interference pattern will instantaneously destroy the interference pattern at the other site no matter how far apart they lie.

Simply turning one of the Interference Detectors on and then off will cause the other detector to show an on and then an off signal and thus the whole arrangement can transmit binary code instantaneously over any distance.

This need not lead to paradoxes or causality violations in a universe with finite a lightspeed.

Imagine two groups of aliens, A and B, living on planets a hundred light years distant from each other. When A receives light from B it knows that the light left B a hundred years ago, and when B receives light from A it knows that light left A a hundred years ago. If either A or B tries to send an ordinary lightspeed message to the other, it will take a hundred years to get there, and a spaceship journey will take at least a hundred years at minimum.

However, if either A or B detects Ansible light from the other and decides to modulate its reception by alternately directing it into an interference detector and not doing so, then the other will notice a signal at the time at which they sent the Ansible light.

Thus, it can appear as if each party sends a signal back into the past, but the ‘past’ to which they send it lies a hundred light years away in space, so the space and time cancel each other out.                        

d = sqrt(s2 + (ict)2(Minkowski, after Pythagoras.)

Absolute spacetime distance = sqrt(space2 – (lightspeed x time)2 )This can equal zero.

In practise if two alien civilisations, separated by a hundred light years, simultaneously came up with the idea of Ansibles and both guessed the same most likely frequencies to use, then they could both start exchanging binary code immediately. They would not have to wait for a hundred years for the Ansible light to pass between them.

According to  the current standard cosmology, life has had over ten billion years to develop in the universe. According to Hypersphere Cosmology it has had unlimited time. In the first case a universe wide Ansible network probably already exists, in the second case it almost certainly does.

We just need to hack into it and decode it. That, rather than the discovery of Faster Than Light drive, may constitute the real entry requirement to interstellar society.

Monday, 25 October 2021 15:20

Octblog 2021

Octblog 2021


The make or break Climate Conference in Glasgow looms, and there seem few grounds for optimism because it looks set to avoid the underlying issues.

I just sat through an edition of the BBCs Question Time and in response to the question ‘The Environment or The Economy?’ all the assembled politicos predictably said ‘Both’ and then proceeded to fantasise about how we could all both eat our cake and have it. This probably reflects the attitude of most humans currently.

Unfortunately, the science and the maths say something completely different. Business as usual cannot continue for much longer. None of the technical fixes we currently tinker with or theorise about will make much difference, the economy and the environment will both decline for many generations to come now. They will do so because since WW2 everything has gone exponential in population, consumption, production, pollution, and environmental damage, and we have already overshot the limits of the resources that this planet can provide and the damage it can absorb whilst sustaining us.

Progress has failed. Analysts of ‘progress’ in terms of wellbeing and life satisfaction generally conclude that developed countries achieved a maximum of wellbeing and life satisfaction sometime in the 1970s. Since then, economic growth has begun to erode general wellbeing and life satisfaction.

Global economic activity cannot grow or even continue without provoking the environmental changes that will undermine it and cause a gradual or catastrophic decline.

Humanity has a choice. It can either choose an acceptable level of degrowth, or it can choose to see what level of degrowth becomes forced upon it by inaction.

Involuntary degrowth could easily mean returning to Dark Age or Neolithic level economies and civilisations after resource conflicts, mass migrations, and social order collapses have devastated industrial societies, and the four horsemen of apocalyptic War, Famine, Pestilence, and Megadeath have done their work.

Voluntary degrowth to a sustainable level might just prove achievable if humanity collectively aimed for something like the 1970s and preserved some but not all the technical innovations made since then. This would of course involve levelling the developing world up to that. We should for example, keep the internet as a valuable communication and information resource, but scrap social media entirely.

Imagine a world in which everyone has the basics but where long distance travel and trade have become a rarity, the burning of fossil fuels has become illegal along with private transport, a local rather than a globalised world, where very little except information moves between continents, a world in which people lead simpler material lives but work less and have richer social and cultural lives.

Interview with a Wizard.

The first series of thirteen Blumberg-Carroll email interviews came to over eighty thousand words, enough for a book.

We seem to have pioneered the literary equivalent of a late night chat show series, except that here the interviewer and the interviewee have each had at least whole day to think about each of the 365 questions, so expect some penetrating questions and provocative answers. Lionel Snell has graciously offered to write a preface.


I wonder what casualty allowance the UK government has given itself for its current policy of relaxing Covid restrictions and precautions and relying entirely on vaccination. Scientific opinion and the political opposition have turned against it.

As the new wave of infections and deaths rises here, it does seem surprising that the government and the media do not give greater publicity to the percentage of the unvaccinated amongst the newly hospitalised and dead.

Lastly, leaf fall from the deciduous trees around here seems oddly delayed this year, and look who seems to enjoy the unseasonable climate:-

I may have done them a favour; Greece may well become too hot for their kind in years to come.

Tuesday, 05 October 2021 09:24

Quantum Chess

Quantum Chess, or WPD Chess, (Wave-Particle Duality Chess).

Herewith a simple way to represent quantum effects in a game of chess by the addition of a small number of additional rules.

All the normal rules of chess apply and in addition: -

1) Any piece that can move to two or more empty squares can move to two of them at once by splitting the piece down the middle. (Either saw all pieces in half beforehand or use two pieces in place of each one at the start, on a board which can accommodate two pieces per square comfortably.)

2) Whenever a half piece interacts with an opposing piece, either by taking it or being taken by it, the other half of it instantly re-joins it, and both halves then occupy the position of the taken piece or both halves become eliminated if one of them gets taken.

3) A Player moving a half piece must also move its corresponding other half.

4) Halved pieces occupy squares and block movement and support and threaten other pieces in the same way as whole pieces.

These four rules lead to a challenging but playable game that has many intriguing properties.

A whole piece represents the piece in ‘particle’ mode, it has a definite position. Halved pieces represent the piece in ‘wave’ mode, it could occupy either position, but it will come to occupy a definite position only when it interacts.

At the end of a game, a record of the game that does not include the moves of all the half-pieces that ‘disappeared’ because their corresponding half interacted, will still look like a standard game of chess although some of the moves may appear as legal but as very strange choices.

The following picture shows a representation of Quantum Chess in the early stages of a game, using doubled pieces rather than pieces sawn in half. (The numbers on some of the pieces make it easier to remember which pieces go together.)

White has taken the Black Kings Pawn with Kings Knight.

Black has replied by moving its Kings Bishop to two possible places simultaneously, one possibility puts White’s King in check, the other possibility threatens White’s Knight.

White now has a quantum problem. White must take its King out of check by either moving it or by moving its Queen or Queen’s Bishop to block, or its Queen’s Bishop Pawn to both block and threaten the ‘possible presence’ of the Black Bishop.

Black can then take the White Knight and the entire Black Bishop will then occupy the White Knight’s square, thus removing any threat to its ‘possible presence’ by  the White Pawn.

Black has effectively used a quantum trick to threaten two pieces at once with two possible presences of its Bishop and then taken the White Knight. The result of this manoeuvre looks like a legal move in ordinary (particle) chess, but White’s failure to  protect its Knight remains inexplicable if the match record does not include the possible wavelike moves that later disappeared.

Quanta take off and land like particles, but they seem to fly as waves. We can only observe their particle behaviours but from their particle behaviours we can infer their wavelike behaviours.   

Imaginary phenomena can have real effects.

Herewith the world’s first fully operational Quantum Chess Piece!

Note the cunning base design which gives extra stability to each of the two halves and helps to secure them together.

Handmade from an ornamental curtain rail endpiece, a length of 2x2 inch softwood, and a disc cut from a length of batten, it took hours with chisels and files, followed by a delicate sawing in half. I don’t have a lathe. I doubt that I’ll try making the other 31 pieces this way.

If anyone wants to manufacture these in say plastic, please let me know, the pawns, rooks, queens, and kings would only require one mould each to this design as they have rotational symmetry about their long axes, the bishops and knights would probably require two moulds for each complete piece.

There follows some general musing on the physics/metaphysics of Quantum Chess: -

Probability – the two halves of each piece represent, in some sense, the probability of its presence on a particular square.

‘Quantum Entanglement’ – the two halves of each piece remain instantly linked over any distance by rule 2 which states that whenever one of them interacts with another piece by taking it or becoming taken by it, then the other half of it undergoes a ‘Wave Function Collapse’ and instantly re-joins the interacting half.

‘Quantum Superposition’ – we can regard the two halves of a piece as representing a quantum superposition when they occupy the same square.

‘Quantum Ontology’ – this model offers as many questions as answers about the reality underlying quantum phenomena: -

Does a piece in wave mode ‘really’ exist in the same way as a piece in particle mode? The wave modes can undoubtedly influence the progress of play, but we can still create a record of the game that does not include them or break the rules of ordinary ‘particle chess’.

Does the wave function collapse of an interacting piece look remarkably like retroactive causation?

If each particle piece can do two different things at once by splitting into two wave modes, does this imply Multidimensional Time?

Technical notes on play -  the rigorous application of the standard rules of chess plus the additional quantum chess rules, only allows pawn particles to split into waves on their first move when they can move one and two squares forward simultaneously. There seems no reason to forbid a player moving the two wave components of a particle piece to the same square to recreate a single particle piece, but this will rarely prove advantageous.

Checkmate and ending the game – Placing the opposing whole King in checkmate wins the game and so does placing either half of an opposing King. Note that a player with half a King in apparent checkmate may have the option of taking an opposing piece with its other half thus evading checkmate. At the end of a game players can elect to collapse any remaining wave positions by moving either one of two halves of the same piece to a square occupied by one of them, but the two halves of a halved checkmated King must move to the square in which checkmate occurred. This restores the semblance of an ordinary game of standard chess.  

Quantum Chess, Q-Chess, WPD-Chess, Copyright Peter J Carroll 09/10/2021 

Thursday, 23 September 2021 10:06

Septblog 2021

Septblog 2021

Esoteric Horticulture.

At Chateaux Chaos the Autumnal Mandrakes have sprouted surprisingly early, before autumn equinox, with Circe already a foot into the sky and Boris and Igor just getting started. This year they will have an experimental outdoor season, note the slug repellent copper wire around their new home. Let us hope that the increasingly unpredictable climate does not bring any early frosts.

Magical Book.

The world’s most illustrious academic historian of the esoteric arts has prepared a splendid preface for the forthcoming Classic Edition of ‘Liber Null and Psychonaut’, the book that initiated an epic paradigm change in magical thought. Since its first publication this book has attracted both aggressive dismissal and laudatory recommendation. A new paradigm will always make some people very angry and other people ecstatic. Weiser’s Classic Edition which includes some new material, will appear sometime next year.


Retirement from most of the more time demanding business activities has led to a life of concentric holidays and research sabbaticals with frequent sojourns in remote Wales where  a lot of wildlife still thrives. Herewith an adder sunning itself on some concrete. Some bright spark decided that this area would provide adders with an excellent habitat and released a few hundred captive bred specimens some decades ago, now we have thousands of them here. Shoes now seem essential in the dunes, but on the upside, they do bite dogs that people don’t keep on leads.

Herewith also a friendly cricket. Until recently I could always hear their high pitched chirping at night. This year my youngest daughter, a professional ecologist, told me that they were making their customary racket, but I could barely hear them. Oddly, I found this a greater portent of mortality than my need for reading glasses, something may soon disappear from my universe forever as my faculties fade. I seem to have just eaten a pot of dog ice cream having mistaken the picture on the carton for a polar bear. I may have only few decades more to discover the remaining secrets of the universe and the quantum realm presents bizarre difficulties akin to juggling spaghetti whilst blindfolded in a hailstorm.

Quantum Chess?

During discussions of the concept of dimensions with my interviewer/biographer, the following analogy or thought experiment emerged to illustrate the possibilities of multiple time dimensions.  

The record of a game of chess provides its temporal dimension, it shows what happened over time. It does not show the moves not taken. However, we could have multiple timelines in which alternatives moves occur. A player unable to decide between two moves can elect to make both of them by replacing a single piece by two smaller shadow pieces in different positions with the provisos that whenever one of the shadow pieces interacts with an opposing piece, the other shadow piece becomes removed, and a player moving one of the shadow pieces must also move the other corresponding one as well. Otherwise, all the usual rules of chess apply.

Now here comes the really strange bit: -

Afterwards, we could write a single timeline move sequence to describe the whole game that does not include the shadow pieces that became removed! However, an expert would probably notice something very odd about some of the moves chosen when looking at the record afterwards. Such a Quantum-Chess analogy can in principle explain many of the mysteries of quantum mechanics and magic. What may have happened, and what could happen, can affect what does seem, to us, to have actually happened. ‘Imaginary’ phenomena can have very real effects.

Afterthought – simply sawing each piece of a chess set down the middle and numbering the two halves the same provides an easy way of preparing a quantum chess set. The two halves of each piece begin the game on the same square.

Tuesday, 17 August 2021 08:14

Frontier Space War 3

Alternative Tactical Spacecraft Combat System.

When opposing vessels meet at a system, transfer all conflicting vessels from the main interstellar board to the combat space tactical board above. Only one vessel of any type per square. Position the defending vessels on any of the nine central squares, or on immediately surrounding squares if defending with more than nine vessels. Then place attacking vessels on any of the squares that lie five squares from the middle square.

Defender moves first, defender second, and then turns proceed alternately.

All vessels may move during a turn and all vessels may either move then fire or fire then move. Any vessel may fire at any designated target within range regardless of anything in the intervening spaces.

Any hit destroys any vessel. The combat power of any vessel depends entirely on the range at which it can score hits.

To score a hit, a vessel must throw a number equal to, or greater than, twice the number of squares away that the designated target lies.

Thus, a target one square away requires a throw of two or more, a target two squares away requires a score of four or more, a target three squares away requires a score of six or more, and so on.

Vessels use dice of different sizes to represent their combat power.

Battleships – D12 dodecahedron. Battlecruisers – D10 di-pentagon. Cruisers – D8 octahedron

Destroyers – D6 cubes. Frigates  – D4 tetrahedron.

Fortresses – D20 Icosahedron.

D12, D10, and D8 vessels may move one square per turn, D6 and D4 vessels may move two. D20 Fortresses remain immobile.

Thus, vessels have the following chances of scoring a hit at each of these squares: -

Squares            First      Second      Third     Fourth     Fifth     Sixth.

Score for hit      2             4                6           8             10         12.

Battleship      11/12         9/12         7/12       5/12        3/12      1/12.

Battlecruiser    9/10        7/10         5/10       3/10        1/10.

Cruiser               7/8          5/8          3/8         1/8.

Destroyer           5/6          3/6          1/6.

Frigate               3/4          1/4.

Combat continues until only vessels from one side occupy the combat space. Vessels which manage to move off the combat space have escaped and must move to a new position on the  main interstellar board in their next main board turn.

This system allows smaller faster vessels to rush heavier more powerful vessels, it also allows smaller vessels to assist heavier vessels in attack or defence or escape.

Vessels may attempt to pass through enemy held systems by escaping the combat space.

Defending vessels may attempt to abandon a system by escaping the combat space.

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