scalar fields

13.05.17 // Updated my physics window for the first time in ages! Had some thoughts over the past few weeks surrounding a free scalar field universe model so I drew them up as well as some old game theory because I watched a Beautiful Mind and felt nostalgic. I hope you are all having wonderful days / evening / whatever plane of existentialism you currently observe 😉

What IS the canonical momentum?

This post is going to try and explain the concepts of Lagrangian mechanics, with minimal derivations and mathematical notation. By the end of it, hopefully you will know what my URL is all about.

Some mechanicses which happened in the past

In 1687, Isaac Newton became the famousest scientist jerk in Europe by writing a book called Philosophiæ Naturalis Principia Mathematica. The book gave a framework of describing motion of objects that worked just as well for stuff in space as objects on the ground. Physicists spent the next couple of hundred years figuring out all the different things it could be applied to.

(Newton’s mechanics eventually got downgraded to ‘merely a very good approximation’ when quantum mechanics and relativity came along to complicate things in the 1900s.)

In 1788, Joseph-Louise Lagrange found a different way to put Newton’s mechanics together, using some mathematical machinery called Calculus of Variations. This turned out to be a very useful way to look at mechanics, almost always much easier to operate, and also, like, the basis for all theoretical physics today.

We call this Lagrangian mechanics.

What’s the point of a mechanics?

The way we think of it these days is, whatever we’re trying to describe is a physical system. For example, this cool double pendulum.

The physical system has a state - “the pieces of the system are arranged this way”. We can describe the state with a list of numbers. The double pendulum might use the angles of the two pendulums. The name for these numbers, in Lagrangian mechanics, is generalised coordinates.

(Why are they “generalised”? When Newton did his mechanics to begin with, everything was thought of as ‘particles’ with a position in 3D space. The coordinates are each particle’s \(x\), \(y\) and \(z\) position. Lagrangian mechanics, on the other hand is cool with any list of numbers can be used to distinguish the different states of the system, so its coordinates are “generalised”.)

Now, we want to know what the system does as time advances. This amounts to knowing the state of the system for every single point in time.

There are lots of possibilities for what a system might do. The double pendulum might swing up and hold itself horizontal forever, for example, or spin wildly. We call each one a path.

Because the generalised coordinates tell apart all the different states of the system, a path amounts to a value of each generalised coordinate at every point in time.

OK. The point of mechanics is to find out which of the many imaginable paths the system/each coordinate actually takes.

The  Action

To achieve this, Lagrangian mechanics says the system has a mathematical object associated with it called the action. It’s almost always written as \(S\).

OK, so here’s what you do with the action: you take one of the paths that the system might take, and feed it in; the action then spits out a number. (It’s an object called a functional, to mathematicans: a function from functions to numbers).

So every path the system takes gets a number associated with it by the action.

The actual numbers associated with each path are not actually that useful. Rather, we want to compare ‘nearby’ paths.

We’re looking for a path with a special property: if you add any tiny little extra wiggle to the path, and feed the new path through the action, you get the same number out. We say that the path with this special property is the one the system actually takes.

This is called the principle of stationary action. (It’s sometimes called the “principle of least action”, but since the path we’re interested in is not necessarily the path for which the action is lowest, you shouldn’t call it that.)

But why does it do that

The answer is sort of, because we pick out an action which produces a stationary path corresponding to our system. Which might sound rather circular and pointless.

If you study quantum field theory, you find out the principle of stationary action falls out rather neatly from a calculation called the Path Integral. So you could say that’s “why”, but then you have the question of “why quantum field theory”.

A clearer question is why is it useful to invent an object called the action that does this thing. A couple of reasons:

  • the general properties actions frequently make it possible to work out the action of a system just by looking at it, and it’s easier to calculate things this way than the Newtonian way.
  • the action gives us a mathematical object that can be thought of as a ‘complete description of the behaviour of the system’, and conclusions you draw about this object - to do with things like symmetries and conserved quantities, say - are applicable to the system as well.

The Lagrangian

So, OK, let’s crack the action open and look at how it’s made up.

So “inside the action” there’s another object called the Lagrangian, usually written \(L\). (As far as I know it got called that by Hamilton, who was a big fan of Lagrange.) The Lagrangian takes a state of the system and a measure of how quickly its changing, and gives you back a number.

The action crawls along the path of the system, applying the Lagrangian at every point in time, and adding up all the numbers.

Mathematically, the action is the integral of the Lagrangian with respect to time. We write that like $$S[q]=\int_{q(t)} L(q,\dot{q},t)\dif t$$

What can you do with a Lagrangian?

Lots and lots of things.

The main thing is that you use the Lagrangian to figure out what the stationary path is.

Using a field of maths called calculus of variations, you can show that the path that stationaryises the action can be found from the Lagrangian by solving a set of differential equations called the Euler-Langrange equations. If you’re curious, they look like $$\frac{\dif}{\dif t}\left(\frac{\partial L}{\partial \dot{q}_i}\right) = \frac{\partial L}{\partial q_i}$$but we won’t go into the details of how they’re derived in this post.

The Euler-Lagrange equations give you the equations of motion of the system. (Newtonian mechanics would also give you the same equations of motion, eventually. From that point on - solving the equations of motion - everything is the same in all your mechanicses).

The Lagrangian has some useful properties. Constraints can be handled easily using the method of Lagrange multipliers, and you can add Lagrangians for components together to get the Lagrangian of a system with multiple parts.

These properties (and probably some others that I’m forgetting) tell us what a Lagrangian made of multiple Newtonian particles looks like, if we know the Lagrangian for a single particle.

Particles and Potentials (the new RPG!)

In the old, Newtonian mechanics, the world is made up of particles, which have a position in space, a number called a mass, and not much else. To determine the particles’ motion, we apply things called forces, which we add up and divide by the mass to give the acceleration of the particle.

Forces have a direction (they’re objects called vectors), and can depend on any number of things, but very commonly they depend on the particle’s position in space. You can have a field which associates a force (number and direction) with every single point in space.

Sometimes, forces have a special property of being conservative. A conservative force has the special property that

  • depends on where the particle is, but not how fast its going
  • if you move the particle in a loop, and add up the force times the distance moved at every point around the loop, you get zero

This is great, because now your force can be found from a potential. Instead of associating a vector with every point, the potential is a scalar field which just has a number (no direction) at each point.

This is great for lots of reasons (you can’t get very far in orbital mechanics or electromagnetism without potentials) but for our purposes, it’s handy because we might be able to use it in the Lagrangian.

How Lagrangians are made

So, suppose our particle can travel along a line. The state of the system can be described with only one generalised coordinate - let’s call it \(q(t)\). It’s being acted on by a conservative force, with a potential defined along the line which gives the force on the particle.

With this super simple system, the Lagrangian splits into two parts. One of them is $$T=\frac{1}{2}m\dot{q}^2$$which is a quantity which Newtonian mechanics calls the kinetic energy (but we’ll get to energy in a bit!), and the other is just the potential \(V(q)\). With these, the Lagrangian looks like $$L=T-V$$and the equations of motion you get are $$m\ddot{q}=-\frac{\dif V}{\dif q}$$exactly the same as Newtonian mechanics.

As it turns out, you can use that idea really generally. When things get relativistic (such as in electromagnetism), it gets squirlier, but if you’re just dealing with rigid bodies acting under gravity and similar situations? \(L=T-V\) is all you need.

This is useful because it’s usually a lot easier to work out the kinetic and potential energy of the objects in a situation, then do some differentiation, than to work out the forces on each one. Plus, constraints.

The Canonical Momentum

The canonical momentum in of itself isn’t all that interesting, actually! Though you use it to make Hamiltonian mechanics, and it hints towards Noether’s theorem, so let’s talk about it.

So the Lagrangian depends on the state of the system, and how quickly its changing. To be more specific, for each generalised coordinate \(q_i\), you have a ‘generalised velocity’ \(\dot{q}_i\) measuring how quickly it is changing in time at this instant. So for example at one particular instant in the double pendulum, one of the angles might be 30 degrees, and the corresponding velocity might be 10 radians per second.

The canonical momenta \(p_i\) can be thought of as a measure of how responsive the Lagrangian is to changes in the generalised velocity. Mathematically, it’s the partial differential (keeping time and all the other generalised coordinates and momenta stationary): $$p_i=\frac{\partial L}{\partial \dot{q}_i}$$They’re called momenta by analogy with the quantities linear momentum and angular momentum in Newtonian mechanics. For the example of the particle travelling in a conservative force, the canonical momentum is exactly the same as the linear momentum: \(p=m\dot{q}\). And for a rotating body, the canonical momentum is the same as the angular momentum. For a system of particles, the canonical momentum is the sum of the linear momenta.

But be careful! In situations like motion in a magnetic field, the canonical momentum and the linear momentum are different. Which has apparently led to no end of confusion for Actual Physicists with a problem involving a lattice and an electron and somethingorother I can no long remember…

OK a little maths; let’s grab the Euler-Lagrange equations again: $$\frac{\dif}{\dif t} \left(\frac{\partial L}{\partial \dot{q}}\right) = \frac{\partial L}{\partial q_i}$$Hold on. That’s the canonical momentum on the left. So we can write this as $$\frac{\dif p_i}{\dif t} = \frac{\partial L}{\partial q_i}$$Which has an interesting implication: suppose \(L\) does not depend on a coordinate directly, but only its velocity. In that case, the equation becomes $$\frac{\dif p_i}{\dif t}=0$$so the canonical momentum corresponding to this coordinate does not change ever, no matter what.

Which is known in Newtonian mechanics as conservation of momentum. So Lagrangian mechanics shows that momentum being conserved is equivalent to the Lagrangian not depending on the absolute positions of the particles…

That’s a special case of a very very important theorem invented by Emmy Noether.

The canonical momenta (or in general, the canonical coordinates) are central to a closely related form of mechanics called Hamiltonian mechanics. Hamiltonian mechanics is interesting because it treats the ‘position’ coordinates and ‘momentum’ coordinates almost exactly the same, and because it has features like the ‘Poisson bracket’ which work almost exactly like quantum mechanics. But that can wait for another post.

Coming up next: Noether’s theorem

Lagrangian mechanics may be a useful calculation tool, but the reason it’s important is mainly down to something that Emmy Noether figured out in 1915. This is what I’m talking about when I refer to Lagrangian mechanics forming the basis for all the modern theoretical physics.

[OK, I am a total Noether fangirl. I think I have that it common with most vaguely theoretical physicists (the fan part, not the girl one, sadly). To mathematicians, she’s known for her work in abstract algebra on things like “rings”, but to physicists, it’s all about Noether’s Theorem.]

Noether’s theorem shows that there is a very fundamental relationship between conserved quantities and symmetries of a physical system. I’ll explain what that means in lots more detail in the next post I do, but for the time being, you can read this summary by quasi-normalcy.


Higgs Boson

On the 4th of July 2012, ATLAS and CMS experiments both reported a particle with a mass of around 126GeV at CERN’s Large Hadron Collider. The particle is consistent with the Higgs boson predicted by the standard model.

The Higgs boson creates a Higgs field which theoretically exists everywhere in the universe and interacts with subatomic fundamental particles like quarks and leptons to give them mass. How much mass a particle has depends on how much interaction is has with the field, all particles are equal before they enter the Higgs field, it is the Higgs field that gives the particles mass depending on their interactions with it.

In the Standard Model, the higgs field is a scalar tachyonic field ( “scalar” meaning that it doesn’t transform under Lorentz transformations and “tachyonic” referring to the field as a whole having imaginary, or complex, mass). While tachyons are purely theoretical particles that move faster than the speed of light, fields with imaginary mass have an important role in modern physics.


Why cosmic inflation’s last great prediction may fail

“[I]f the measured value for n_s stays what it’s thought to be right now, and after a decade we’ve constrained r < 10-3, then the simplest models for inflation are all wrong. It doesn’t mean inflation is wrong, but it means inflation is something more complicated than we first thought, and perhaps not even a scalar field at all.

If nature is unkind to us, the last great prediction of cosmic inflation — the existence of primordial gravitational waves — will be elusive to us for many decades to come, and will continue to go unconfirmed.”

Cosmic inflation, our earliest theory of the Universe and the phenomenon that sets up the Big Bang, didn’t just explain a number of puzzles, but made a slew of new predictions for the Universe. In the subsequent 35 years, five of the six have been confirmed, with only primordial gravitational waves left to go. Inflation predicts that they could be large or small, but based on the simplest classes of models and the measured value of the density fluctuations, the gravitational waves must, according to cosmologist Mark Kamionkowski, be within the range of telescopes during the next decade. If we find them, either one of the two simplest models could be correct, but if we don’t, then the two simplest classes of inflationary models are all wrong, and gravitational waves from inflation may be invisible to us for the foreseeable future.

 the 3 basic forms/movements/processes:

  • Sphere: galactic centers, (super)nova, heliospheres, stars, planets
  • Hourglass: Star births
  • Spiral disc (equatorial energizing/expansion/rotation): galaxy formations,solar systems, Kuiper belt, cyclones

Scalar fields: these are parallel EM fields (of a certain flux typology) nested within each other without entanglement.

    Thoughts Through Space: a Pioneering Long-Distance Telepathy Experiment

    “Those who reject even telepathy have reached the point where they are impugning either the honesty or the sanity of several thousand scientific researchers on all major continents over a period of decades. Such expedient ways of disposing of data are shared only by the most ardent anti-Evolutionists among the Fundamentalist sects.” ~ R.A. Wilson, from the book Cosmic Trigger.

    Thoughts Through Space

    The term “telepathy” was coined in 1882 by Frederick W.H. Myers, a founding member of the London Society for Psychical Research (SPR). The word means “feeling at a distance”, though this may be slightly misleading in that this is not usually how the term is deployed. Telepathy is essentially mind-to-mind contact, or the exchange of information between two different consciousnesses separated by an arbitrarily large distance (it doesn’t matter how large). Though many of the more narrow-visioned would claim any discussion involving telepathy is “unscientific” by default, we can see that many years ago there were eminent scientists who not only recognized its existence but sought to understand the phenomenon.

    The first studies of telepathy were based on collections of spontaneous experiences, with 1886 seeing the publication of the seminal classic Phantasms of the Living, by the British scholars Edmund Gurney, Frederick Myers, and Frank Podmore — who actually took the time and effort to analyse all reports to identify the best and most reliable cases for publication and eliminate the fraudulent.

    Over a decade later, the eminent chemist and physicist Sir William Crookes — also an avid and meticulous researcher into “paranormal” phenomena — spoke on telepathy before the Royal Society at Bristol, England, in 1898. This address was, in the words of occultist Swami Panchadasi (a.k.a. William Walker Atkinson), “made before an assemblage of distinguished scientists, many of them rank materialists and quite skeptical of all occult phenomena.” Crookes, facing this gathering as its president, expressed the view that it is a “fundamental law… that thoughts and images may be transferred from one mind to another without the agency of the recognized organs of sense — that knowledge may enter the human mind without being communicated in any hitherto known or recognized ways.”

    If telepathy occurs, he continued, “we have two physical facts — the physical change in the brain of A, the suggestor, and the analogous physical change in the brain of B, the recipient of the suggestion.” While Crookes would eventually be vindicated in these comments by the development of the EEG and other modern technology and experimental designs, he assumed that “between these two physical events there must exist a train of physical causes”, which we can accept if we modify our definition of “physical” to include subtle energies (such as torsion/scalar fields), as well as the plasma-like particulate matter of the various aetheric densities (etheric, astral, mental, etc.).

    In the modern world, the commonest kind of human telepathy occurs in connection with telephone calls, according to biologist and paranormal researcher Rupert Sheldrake. Over 80% of people claim to have thought of someone for no apparent reason, who then phoned them; or that they have known, in a telepathic sort of way, who was on the phone before answering it. Sheldrake reports that controlled experiments have provided highly statistically significant repeatable positive results. Many people (probably about 80%!) however, will need no convincing of the fact, as repeated personal experience has a way of making experimental proofs a little bit redundant sometimes.

    A World-First Experiment in Telepathy

    In 1942 the remarkable though little-known book Thoughts Through Space, by Australian-born aviator-explorer Sir Hubert Wilkins (1888–1958) and American author, playwright, and “sensitive” Harold Sherman (1898–1987), was published. It detailed the first experiment (conducted from late 1937 through to early 1938) of its kind: a long-distance and long-term telepathy experiment where Wilkins, who was aiding in the aerial search for a missing Russian craft and its crew in the Arctic, would attempt to telepathically send information regarding his activities to Sherman, who would attempt to receive the messages and record them. This would take place over a period of some five months.

    However, as it turned out, Wilkins never got the opportunity to take time to deliberately send any impressions to Sherman, who faithfully conducted his “psychic vigil” each night at the same time, ever unaware of Wilkins’ situation or activities. What Wilkins did instead was to record events and details in his log, this being the usual habit with an explorer. When Wilkins returned from the Arctic, his dated log was compared with the dated impressions of Sherman so the latter’s psychic accuracy and reliability could be assessed.

    Early in the book, Wilkins made a point of noting that, a) Sherman had already demonstrated his ability to receive impressions without the necessity of Wilkins’ consciously willing thoughts to him at the time of their scheduled “sittings,” and, b) Sherman could respond directly to Wilkins’ thoughts on the occasions he was able to keep their “psi appointments.”

    The role of emotion was significant in these experiments (as it is in many psi experiments), as the two participants ultimately acknowledged. Wilkins noted that despite his inability to regularly keep to the appointed “sending” time for the experiments, he did continue his habit of thinking the unusual incidents strongly to Sherman. When Wilkins was anxious, Sherman seemed to be particularly effective at detecting his thoughts.

    Wilkins also agreed with the occultist’s axiom that the intensity of a sender’s emotional reaction to what is happening to him, or has happened, determines the degree of intensity of the “thought-waves” discharged. (In my book The Grand Illusion: A Synthesis of Science and Spirituality (Vol.1), I have portrayed these thought waves as torsion/scalar waves in the vacuum/aether/zero point field/time-space/implicate order.)

    Also worth noting is that in some ways, this epic experiment — lasting as it did over five months — was something of a precursor to what would later become known as remote viewing. It also featured elements of prevision, evincing a predictable unpredictability so common to psi functioning, thus blurring the lines[*] between telepathy in real time and other forms of clairvoyance — much as this tended to occasion Sherman’s uncertainty as to precisely what he was seeing at the precise moment of seeing. Sometimes visions would turn into previsions, precipitating out of the aether days later without apparent warning. This was a complicating factor at times, as was the initial lack of feedback for Sherman, which caused him a degree of anxiety (was he “hitting” more than missing?). Nevertheless, the experiment overall can only be described as a stunning success, with some indisputably spectacular hits by Sherman to be found scattered throughout.

    Official Results

    Sherman sat three times a week to act as receiver, depositing copies of his nightly impressions to third party witnesses to ensure there could be no question of his having failed to record his impressions before receiving Wilkins’ log. Let’s look at some of the data. Sherman’s report of Wilkins’ activities for February 14 reads:

    “Impression you talked three times before different interested groups since arrival at Edmonton — first time before some luncheon club — like Rotary Club — you have found a motor — you plan to take off with it tomorrow or Wednesday, if weather permits. You have dinner with three men and their wives…One of Edmonton’s wealthiest and most prominent men has entertained you and given you some assistance relative to the expedition — word McKenzie flashes to my mind — is there a company of that name supplying you with plane? Seem to see you as guest of Church Brotherhood… Sunday occasion — you called on to speak—you have appointment with two men who will take you to some plant or place where you will see the packing of the equipment.”

    Keep in mind that Sherman had been receiving little feedback on previous recordings prior to this session, and had not been forewarned of any of these activities, making it all the more remarkable that Wilkins was able to subsequently confirm every detail, including the fact that McKenzie Airways were furnishing the plane that would fly the new engine back to Aklavik. All of these things took place between February 10 and 14.

    As noted, sometimes the information being received by Sherman was a blur of present (or recent past) information and information pertaining to some point in the future. Wilkins stated that in his March 1 record Sherman had recorded almost all of his most prominent thoughts as well as describing the conditions Wilkins experienced. The latter part of the entry from Sherman mentions liquor in connection with a commercial interest (possibly a company seeking his endorsement). Sherman states that Wilkins is wondering whether they will offer him enough money for it, and then moves on to things flight-related. He suggests checking the oil and gas lines leading to the engine as a possible source of trouble—“something appears to get clogged or choked” as a result of the low ambient temperature.

    Wilkins’ analysis of Sherman’s psi report confirms that Hiram Walker had indeed sought Wilkins’ endorsement for a certain whiskey, but did not offer sufficient remuneration to garner Wilkins’ advocacy. It was the one time that year that Wilkins had received such an offer. As for Sherman’s concern over gas and oil lines, sure enough, the next day during flight, the feed on the automatic control did clog. Towards evening, the oil temperature indicated some clogging of the line, according to one of Wilkins’ collaborators (Cheeseman) on the plane with him.

    Evidently, darkness proved to be an aid in Sherman’s sittings, eliminating visual stimuli so he could become more receptive to the nonlocal stimuli filtering through from his subconscious mind. Sitting in darkness to receive psi information is a good and standard way to increase the psi signal to noise ratio (not dissimilarly to Ganzfeld tests).

    An interesting fact to note is that after some time of sitting three times a week for his sessions, Sherman had trained his subconscious to feed him psi information more consistently. He commented that his mind had become so highly sensitized and habituated to the psi task that it continually brought him un-asked-for impressions and “unusual mental flashes.” These flashes appeared sometimes to come from the mind of anyone he focused his attention on, regardless of the fact that there were unbidden insights he did not seek. There are many pieces of evidence that demonstrate that the psi faculty, like our muscular system, is responsive to training. This has been known to mystics and occultists for many centuries.

    As well as this, Sherman suffered serious ill health effects because of his other commitments, which left him virtually no rest and recovery time. We need not go into Sherman’s exact method in eliciting his results, but it is worth noting that during the sessions he could feel his mind “contact” Wilkins’ mind, he sensed a force, line, or stream of energy which seemed to connect the two subconscious minds of the men. During the sittings when he felt this sensation the strongest, he got his best results.

    A conclusion reached by both men (and one in full accordance with occult thought) was that the degree of intensity of emotional reaction to external experience determines the intensity of the thought force projected. In their view, human emotions were the power source behind the electrical currents of the brain. A recurring motif in “paranormal” and parapsychological research is the important role of emotion, creative force that it is.

    Sherman also noted that he sensed thought impressions at two places in his body: the brain (center of crown and third eye chakras) and solar plexus (where the manipura chakra is).He would get a nerve reaction in the pit of his stomach (not unlike that felt when one receives a sudden shock or becomes anxious), which he came to realize always accompanied a genuine telepathic communication. Elsewhere, in his psi research, Dr. Hiroshi Motoyama has connected the lower three chakras (one of which is the solar plexus chakra/manipura) with passive or receptive psi abilities, such as Sherman employed in this telepathy experiment.

    On top of Sherman’s amazingly accurate reports of Wilkins’ far removed activities either as they happened or soon after, he also sensed events yet to happen to Wilkins, as previously noted. Wilkins only had two accidents occur involving his plane during his five months away, and Sherman sensed both ahead of time, witnessing previsions of these events days before they happened.

    To give further insight into the remarkably successful nature of this experiment, several friends and/or collaborators of Sherman and Wilkins signed affidavits testifying to the validity of the experimental procedure as well as Sherman’s undeniable accuracy. Dr. Henry S.W. Hardwicke, a research officer for the Psychic Research Society of New York, stated in his affidavit that the authenticity of the telepathic phenomena was unquestionable. Dr. A.E. Strath-Gordon was effusive in his own affidavit, stating that Sherman’s amazing telepathic consistency, clarity, and accuracy was something he had not seen in all his years of research around the world. Such was Sherman’s telepathic acuity that, to Strath-Gordon, it seemed almost as if he was taking dictation from some unseen intelligence.

    This is not to construe that Sherman only ever “hit” and never “missed.” He did, as any intuitive will, miss occasionally, but more often than not he was accurate, far too often and with such exquisite detail that it cannot logically be asserted that he obtained his results by lucky guesses over this extended period, and no evidence at all exists to implicate anyone in any fraudulent activities. But for the most part, even Sherman’s misses were intriguingly close to the mark, seemingly mixing fact with fiction.

    Little more need be said to convince the sane of the success of this epic psi experiment. However, Sherman’s talents provide much food for thought. For instance, it is notorious among psychics that sensing specific numbers, dates, names, and such particulars represents one of the most difficult tasks. Sherman was exceptional at sensing names of people, companies, and more, as well as having some spectacular hits with numerical data (remembering that he was operating totally “blind” to Wilkins’ Arctic activities).

    On November 30, one of his data points was simply this: Latitude 68, Longitude 133. Wilkins recorded: Latitude 68, Longitude 135. These numbers bear no further comment. In his next sitting (December 2), Sherman recorded several spectacular hits, including a note of the intended first flight of Wilkins which was to be a distance of 600 miles. In his own notes, Wilkins had recorded that this flight was indeed slated to be 600 miles. Note again that Wilkins did not offer foreknowledge of his intended plans or movements in these letters.

    To add yet another complicating factor to all of this, Sherman found that it was difficult to distinguish between a thought in the mind of an individual and the actual materialization of that thought in action. He said he was certain that there had been occasions where he had unwittingly confused these two thought-forms.

    In his many experiments several decades later, former CIA polygraph expert Cleve Backster found, interestingly, that his plants — leaves wired to a polygraph machine — initially encountered something of a similar situation when it came to detecting silent human intent to harm them, though they rapidly learned to distinguish between real and imagined threats.

    The process for a human attempting telepathy seems to present more challenges — perhaps because plants do not have much in the way of an individuated conscious mind to block subconscious perceptions: they belong to a group consciousness or “morphic field,” and lack a personal subconscious. The human, whether particularly intelligent or not, has this discriminatory disadvantage built in. So, while it may not be much of a compliment to be told you have the intelligence of a house plant, it could, in a sense, be something of an accolade to be told you have the intuition of one!

    In January 1938, Sherman made some interesting notes regarding some technicalities of the telepathic downloading process. At 11.30 on the designated nights of the appointments, wherever he was he would begin to receive strong feelings from Wilkins. He stated that unless he was somewhere he could clear his mind, he did not try to interpret those feelings, since this invited interference from his imagination before he was ready to complete the entire operation. So long as he kept the impressions in his mental “dark room” until he was ready to bring them out and process them, he was able to retain them.

    Final Thoughts

    With two peoples’ brain-minds acting as a nonlocally correlated system, the connection is maintained by nonlocal consciousness (in aether/time-space/implicate order) — facilitated, Amit Goswami believes, by the brains’ “quantum nature.” Such “paranormal” phenomena could be attributable to torsion waves passing between the participants’ minds. The two parties have synchronized their operations in time; now spatial distance is irrelevant — they act as one system in time. It is interesting to note that torsion fields cannot be shielded by conventional means (including Faraday cages), and evidence no attenuation when propagated arbitrary distances. “As pointed out by A. Akimov, empirical exhibits of torsion fields have possibly been found previously in conventional scientific research, but not yet recognized as such.” One such example may be the phenomenon of quantum nonlocality, “which can be attributed to superluminal transmission of torsion potential.”

    I should note: any form of meaningful contact between people can establish a nonlocal correlation, as any clairvoyant or occultist worth their salt can tell you — this is how legitimate psychics (let us ignore the plethora of phonies) can carry out “readings” over the phone or internet without ever having so much as been in the same country as the sitter or client. That telepathy exists is doubtless — countless experiments and spontaneous real-world events confirm its reality. However, a larger scientific paradigm within which to view this and other “paranormal” phenomena has been missing for too long now. Parapsychology has failed to provide one, and mainstream Western physics has been too handicapped by its own prejudices and conceptual roadblocks to really do this subject matter justice.

    In my book The Grand Illusion: A Synthesis of Science and Spirituality (Vol.1) I provide the kind of far-reaching paradigm needed within which to place such phenomena — something that the world seems to be increasingly ready for.

    By: Brendan D. Murphy

    Time to work.

    Before we start: I know a lot of people think that this moment wasn’t real but imagined by Sherlock. It can maybe be true, though I don’t think it is, but in any case, let’s put that fact aside and consider this as something real. We’ll see later for the Inception-like stuff.

    • Redbeard being the title for the page is important, obviously. And we know that Redbeard isn’t a dog for sure but can be a code name for the third brother, which would be making much more sense.

    •  Vernet - some people thought about the Vernet syndrome, because of the fact Mycroft is maybe ill - the fact they say he will die soon - but I don’t think this is it.
    Vernet is actually - by Sherlock Holmes own words, in The Greek Interpretor (the story where we met Mycroft) - one of his ancestors. He says that his grand-mother is Vernet’s sister.
    The thing is, there is three French painter (all related) that are called Vernet and Doyle never precise which one he is talking about.

    →  Émile Jean-Horace Vernet (30 June 1789 – 17 January 1863). Vernet was a French painter of battles and soldiers, in non academic way.

    Vernet quickly developed a disdain for the high-minded seriousness of academic French art influenced by Classicism, and decided to paint subjects taken mostly from contemporary culture. Therefore, he began depicting the French soldier in a more familiar, vernacular manner rather than in an idealized, Davidian fashion. Some of his paintings that represent French soldiers in a more direct, less idealizing style, include Dog of the Regiment, Trumpeter’s Horse, and Death of Poniatowski.

    In a way, that was what Doyle was doing with John.

    One interesting anecdote is this one:

    One well known and possibly apocryphal anecdote maintains that when Vernet was asked to remove a certain obnoxious general from one of his paintings, he replied, “I am a painter of history, sire, and I will not violate the truth,” hence demonstrating his fidelity to representing war truthfully.

    There is no need to seek too deep to understand why Conan Doyle may have referenced this particular painter, making him Sherlock Holmes’ relative.

    Antoine Charles Horace Vernet aka. Carle Vernet (14 August 1758 – 17 November 1836) (father of the previous)

    In his Triumph of Aemilius Paulus, he broke with tradition and drew the horse with the forms he had learnt from nature in stables and riding-schools. His hunting-pieces, races, landscapes, and work as a lithographer were also very popular.

    Carle’s sister was executed by the guillotine during the Revolution.

    After this, he gave up art.When he again began to produce under the French Directory (1795–1799), his style had changed radically. He started drawing in minute detail battles and campaigns to glorify Napoleon. His drawings of Napoleon’s Italian campaign won acclaim as did the Battle of Marengo, and for his Morning of Austerlitz Napoleon awarded him the Legion of Honour. Louis XVIII of France awarded him the Order of Saint Michael. Afterwards he excelled in hunting scenes and depictions of horses.In addition to being a painter and lithographer, Carle Vernet was an avid horseman. Just days before his death at the age of seventy-eight, he was seen racing as if he were a sprightly young man.

    Here we have the idea of a sibling being executed, which I think is important. Because what Holmes says is that his grand mother is Vernet’s sister, so it could be Carle’s sister.

    Claude-Joseph Vernet (14 August 1714 – 3 December 1789) (father of the previous)

    In 1734, Vernet left for Rome to study landscape designers and maritime painters, like Claude Gellee, where we find the styles and subjects of Vernets paintings.

    Slowly Vernet attracted notice in the artistic milieu of Rome. With a certain conventionality in design, proper to his day, he allied the results of constant and honest observation of natural effects of atmosphere, which he rendered with unusual pictorial art. Perhaps no painter of landscapes or sea-pieces has ever made the human figure so completely a part of the scene depicted or so important a factor in his design. In this respect he was heavily influenced by Giovanni Paolo Panini, whom he probably met and worked with in Rome. Vernet’s work draws on natural themes, but in a way that is neither sentimental or emotive. The overall effect of his style is wholly decorative.“Others may know better”, he said, with just pride, “how to paint the sky, the earth, the ocean; no one knows better than I how to paint a picture”. His style remained relatively static throughout his life. His works’ attentiveness to atmospheric effects is combined with a sense of harmony that is reminiscent of Claude Lorrain.

    I bolded the part that I think is interesting. Sound like a theme we know.

    Note that the three of them are painting landscapes, or battle paintings. (They are extremely beautiful by the way, they were amazing painters).

    611174 or 6///74 or 6/1/74 or 6 1 1174 (etc)-  this combination of numbers is leading to Vernet. So I thought it was maybe a date. Maybe a birth date (1st of June 1974?), maybe Redbeard’s birth date? (which would make him just 2 years older than Sherlock if his birth date in the show is Benedict Cumberbatch birth date - 19 of July 1976).

    But also, it could be the 6th of January, which is actually the hypothetical Sherlock’s birth date:

    An estimate of Holmes’s age in “His Last Bow” places his year of birth at 1854; the story, set in August 1914, describes him as 60 years of age. Leslie S. Klinger, author of The New Annotated Sherlock Holmes, posits the detective’s birthdate as 6 January.


    So what if Sherlock’s birth date in the show is the 6th of January 1974 (is birth date not being the same as BC’s).
    What if it’s Redbeard’s birth date?

    So, remind the “not twins” conversation and what I said about it earlier here. What if. Yah.. twisted, a bit, I know, but what if Redbeard is not Mycroft’s twin brother but Sherlock’s?

    NOTE: I’m doubting about all the signs being 1 because look at the equation next to it. In the first line, Mycroft wrote a 1 as a I and the others looks like this: 1. It’s not unusual to switch graphy when we write, I do this all the time, for instance. But maybe it’s intentional, we can’t know for sure.

    • The “1000/0100/0010/0001″ code - I am no mathematician but I’ve read this meta saying it was Minkowski metric / The Minkowski distance / space. For what I understood it’s a way to calculate coordinates by including the notion of time in it. It’s the calculation of a distance not only in space but in time.
    This equation is related to something called the matrix, which says how to find out how far apart two events in the space-time are. (If I’m saying something wrong feel free to correct).
    Though I don’t agree at all with the conclusion of this meta, the mathematical explanation is actually interesting and important.
    It may just be a Doctor Who reference, you know, but I think that associated with Vernet and Redbeard the code isn’t just here to make a reference. It also references the fact mathematics is a field of knowledge we heard about before. Don’t forget Maman Holmes.
    But also: don’t forget Professor Moriarty.
    Both knew about mathematics on a high level.

    It still appeals to family but also to something that Mycroft is working on. The question is, why would he want / need to calculate a distance in space-time? And I don’t think at all this is something about science-fiction, this isn’t really a thing in Sherlock Holmes’ universe. :o)

    Scarlet roll m[…] o (?)-  the only stuff I found is that it’s a specific kind of dress, but I don’t think it’s really helpful.

    But we can start by saying that scarlet is echoing to A Study in Scarlet, or that scarlet is actually a kind of red, so “Redbeard”. But I don’t see how it has to do with “roll” or which word is beginning with an m. Maybe it’s linked to the math equations below. The thing is this part is highlighted - underlined twice -  which is something you do for important parts usually.

    - Nabla - E = 0 ; Nabla x E = 2B/2E - mathematics again, yay! :o) (not that I don’t like it but I’m dyscalculic, see my problem :o) )
    Nabla is a reversed Delta, as you see. It’s also called “Del”.

    Del, or nabla, is an operator used in mathematics, in particular, in vector calculus, as a vector differential operator, usually represented by the nabla symbol . When applied to a function defined on a one-dimensional domain, it denotes its standard derivative as defined in calculus. When applied to a field (a function defined on a multi-dimensional domain), del may denote the gradient (locally steepest slope) of a scalar field (or sometimes of a vector field, as in the Navier–Stokes equations), the divergence of a vector field, or the curl (rotation) of a vector field, depending on the way it is applied.

    Strictly speaking, del is not a specific operator, but rather a convenient mathematical notation for those three operators, that makes many equations easier to write and remember. The del symbol can be interpreted as a vector of partial derivative operators, and its three possible meanings—gradient, divergence, and curl—can be formally viewed as the product with a scalar, dot product, and cross product, respectively, of the del “operator” with the field. These formal products do not necessarily commute with other operators or products.


    I don’t understand what it means and I couldn’t find this equation on internet, so I don’t know what it means.

    Some help from someone studying mathematics would be very very very appreciated.
    All I can say about it is that mathematics reminds us about the Holmeses mother and about Professor Moriarty.


    My theory is: Mycroft is currently trying to track and find Redbeard - which is family, the third brother -, he is looking for him. He is trying to solve the whole Redbeard problem and it will be maybe what will kill him two years later.

    My string theorist friend posted on facebook that he has “a new favorite metric”

    when I clicked the link to the paper:

    We calculate the ground state energy of a massive scalar field in the background of a cosmic string of finite thickness (Gott-Hiscock metric).