entangled photon pair

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This from Wikipedia

Entropy { Information Theory}

In information theory, the entropy of a random variable quantifies the average level of uncertainty or information associated with the variable’s potential states or possible outcomes. This measures the expected amount of information needed to describe the state of the variable, considering the distribution of probabilities across all potential states.

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Entropy in information theory is directly analogous to the entropy in statistical thermodynamics. The analogy results when the values of the random variable designate energies of microstates, so Gibbs’s formula for the entropy is formally identical to Shannon’s formula. Entropy has relevance to other areas of mathematics such as combinatorics and machine learning. The definition can be derived from a set of axioms establishing that entropy should be a measure of how informative the average outcome of a variable is. For a continuous random variable, differential entropy is analogous to entropy.

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Introduction

The core idea of information theory is that the “informational value” of a communicated message depends on the degree to which the content of the message is surprising. If a highly likely event occurs, the message carries very little information. On the other hand, if a highly unlikely event occurs, the message is much more informative. For instance, the knowledge that some particular number will not be the winning number of a lottery provides very little information, because any particular chosen number will almost certainly not win. However, knowledge that a particular number will win a lottery has high informational value because it communicates the occurrence of a very low probability event.

The information content, also called the surprisal or self-information, of an event E is a function that increases as the probability of an event p(E) decreases. When p(E) is close to one the surprisal of an event is low, if p(E) is close to zero then the surprisal of an event if it occurs is high.

There is zero surprise when the probability is one.

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Are dreams high entropy?

What happens when p(E) is close to zero?

And do dreams contain information of high informational value?

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On and off over the years I have had “intuitional discomfort” about the notion of quantum superposition states. Is it physics or our description of physics? Are we making an ersatz by making a quantum supposition, a sticking plaster for some deeper physics we do not yet understand. It does look a bit of a hotch-potch.

Quantum physics has a God-like quality which dare not be questioned…

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From Microsoft Quantum

Superposition is a fundamental concept in quantum mechanics, describing the condition in which a quantum system can exist in multiple states or configurations simultaneously. Classical bits can exist in two possible states, typically labeled as “0” and “1”. In contrast, because a qubit is a quantum mechanical system, it can exist in the “0” state, the “1” state, or any state that is a linear combination of 0 and 1.

Mathematically, superposition is a linear combination of “0” and “1” and can be written as:

|ψ⟩ = α|0⟩ + β|1⟩

where |ψ⟩ is the state of the qubit, |0⟩ and |1⟩ are the basis states (or the computational basis states), and α and β are complex numbers called probability amplitudes. The probability amplitudes determine the probability of measuring the qubit in either state when a measurement is made.

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Is the prepared qubit then “natural” or have we imbued it with information which we have decided for it in our labelling. This labelling presupposes no extra physics. A photon might have vertical polarisation, horizontal polarisation or if paired a superposition of both; horizontal and vertical as opposed to horizontal or vertical.

Unless the superposition is somehow aware of our labelling how does it know how we expect it to behave?

If one of a photon pair is measured as horizontal it must communicate that information instantaneously to its erstwhile twin.

Is it physics or information?

A good question.

How much entropy is associated with that information?

If the superposition collapses on measurement then in an idealised physics the probability of the other pair member “knowing” its state is one. It has little informational value as it comes as no surprise.

If eigenfunctions are used to prepare a description of a quantum supposition then they must have a difference in the set of quantum number qualities to be eigenfunctions. They may be energy eigenvalue degenerate in isolation but because of the difference in quantum number that degeneracy must be split, if only slightly under some condition or other, which means that they do not share entirely equal probability on being prepared into a superposition.

The qubit will have a tiny inherent bias.

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I keep getting this sense of discomfort that there is something we are not getting and that we are happy sitting with an intuitionally uncomfortable quantum superposition description…it just seems cobbled together.

It is a bit of a mind fuck…

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Do dreams bring real world information?

If so is it surprising and of high informational value?

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I have just re-read a dream of mine from 2008 in which I see a Breton landscape and am chatting with an extroverted French man who is the spitting image physically and in behaviour of my recent physiotherapist.

Was this information, coincidence or my confirmation bias retro-fitting a dream to a current observable?

If dreams do indeed carry information then the implications of this are high.

I personally will trust what my dreams say about a situation over and above what a human being may or may not assert. If there is good physical evidence I will trust that over dream…

This notion of surprise as being a component of information {new} is interesting. The concept of information entropy in a world of fake news and a verbose Trumpian professor, is appealing.

Information and opinion are not the same. It is possible to speak for a long time without giving any reliable information which comes as no surprise. Were there to be anything new {and reliable} that would be very surprising and information rich.

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Any description or model must occlude at least partially an occult reality of some kind. Because we do not know the true and extensive nature of that reality we can at best describe it. Such a description must be informative and allow a measure of prediction as to the measurable evolution of events in space-time. We should be honest that our description is not ultimate truth. Behind all known physics there is always something occult, unseen and as yet unknown. History teaches us this

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Jut kicking a few ideas around ….

Nothing may come out of it…

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The single biggest problem in communication is the illusion that it has taken place.

George Bernard Shaw

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The above succinct quotation is a lot more apt than many are willing to acknowledge. It is widely applicable. It takes a lot of effort, willingness and practice to enhance communication so that one can be “en rapport” with another. One has to be on similar wavelengths and not too divergent in intellect. There must be some shared commonality of allegory and metaphor, usually some overlap of life experiences. There needs to be some kind of tie, perhaps emotional or deeper. The sharing of space and time with another helps, sharing trauma or profound experience can enhance a shared experiential which enables communication. One can communicate well with someone who one “hates” because that intensity adds focus to communication. This intensity can aid or degrade communication. There are a lot of assumptions and biases present in most attempts to communicate.

Above all one needs to listen attentively and try to communicate, to convey. My experience suggests that many are unskilled in listening. To tune in to another requires one to be passive like a radio receiver. One needs to find the wavelength of transmission on the dial.

If there is poor rapport using conventional methods such as talking it is not surprising that unconventional methods such as telepathy are not well experimentally proven. I like the analogy of an electronic instrument. If the noise in the instrument is high its ability to detect true signal is reduced. The “minds” of most are a cacophony of internal dialogue unable to pick up signal. If the mind is distracted and unfocussed the spoken word fails to register with any longevity in the consciousness. {Oh look a butterfly, my ‘phone has just pinged with a text, what is for tea?}

I’ll speculate that profound inter-human rapport is on the wane.

In the media when a psychic is consulted to solve a complicated murder case, perhaps find a body, they are given a piece of clothing, a photograph. This enables the psychic-seer to tune into to the missing person or object. Logically the rapport gained from a scarf or a photograph cannot be as strong as that gained from a genuine relationship with that individual. Perhaps by taking time to immerse into the life, the bedroom, the friends of the missing person a non-proximal rapport can be gained. But it would not be the same as if they worked together for a decade and shared life’s highs and lows. There may be some more predisposed to such a skill. We have the notion of empath on one hand and trained skilled psychological profiler on the other hand. One uses a subjective rapport and the other builds from a quasi-objective evidence base.

The notion of rapport is of course subjective and perhaps elusive. Rapport must vary in a temporal sense. For example I am markedly different in outlook now than I was two decades ago. Any rapport people had with me from back then has probably passed its expiry date. I can still put on my Worzel-Gummidge science head if needed. It is at the back of the barn behind the haystack.

Because we may lack a genuine rapport we can easily assume that we understand people and their motivation much better than we actually do…

Rapport has cultural elements too. This has been clear here in France. I have had conversations where I know we are not on the same page, in the same book or even the same library. I have noted the case. The other person has not. There is no way that you can convince the adamant that they have gotten the wrong end of the stick, even when you know they have.

Communication is way trickier that we imagine.

In Buddhism the notion of mind to mind transfer is active in the hagiography and key in the Zen lineages. Things are passed on non-verbally. This strays into the parapsychological notion of telepathy. In such instances the follower and teacher have shared considerable time, they have had grumbling bellies when the alms bowls were sparsely filled. They have meditated together. Their way of life has been shared, their philosophies have converged, their wavelengths have become similar and synchronised. Under such circumstances the likelihood of mind-to-mind transfer must be enhanced. They did not go home to their wives nor watch Strictly of a Saturday night. They are not worried about losing their jobs nor distracted by the next vagaries issuing out of Trump’s jumbled mind.

Rapport then is an unquantifiable but when shared is a common subjective experience. Communication is less difficult and mutual understanding more easily reached. A convergence of being enables rapport.

I liken this mental rapport to the phenomenon of quantum entanglement. Two photons created as an entangled photon pair have their wavefunctions coupled, they are en rapport with each other. When one photon is “asked” about its state of polarisation and answers. The other photon telepathically knows what its state is too, despite any geometric distance between them.

Rapport can be thought of as a form of entanglement, a loss of harsh individuality, where a shared outlook is held, however briefly. During full rapport communication is “instantaneous”. The separate I, me, is melded into an us. In full rapport we might think as one.

The wavefunction contains everything we might want to know about a photon {or pair}. The mind contains everything we might want to know about the non-biological part of a being. Two minds fully en rapport share. Of course mental rapport is unlikely to be total though it could be significantly partial. A shared mental rapport might enable a telepathic transfer, being to being. Physical plane distance need not hinder.

If one studies an individual for an extended period one might get to know them and have a measure of predictivity concerning their thoughts and behaviour. This could be an ersatz rapport when you think you know but don’t really. The grey area between advised intuition and genuine telepathic rapport is probably experimentally inseparable. A stalker thinks they know the victim, a spook understands the target. To generate an accurate rapport with someone personally unfamiliar is not facile. We may imagine we know. We may be overly optimistic as to extent.

What we wish for and what is actual, can differ.

Hmnn…

Tag: entangled photon pair

Entropy in Information Theory and Dreaming

Rapport and Communication