The Spin Mechanism In QFT - Quantum Field Theory - & Quantum Computing

The concept sits right at the crossroads of foundations and emerging tech. I’ll break it down in layers, moving from spin in QFT, to spin as information, and finally to spin in quantum computing and memory, tying the concepts together as one coherent story.

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1. What “spin” really is in Quantum Field Theory (QFT)

Spin is not rotation

Despite the name, spin is not a particle literally spinning. In QFT, spin is:

an intrinsic quantum number that labels how a quantum field transforms under spacetime symmetries.

More precisely:

• Spin arises from representations of the Lorentz group

• It tells us how a field behaves under rotations and boosts

Examples:

• Spin-0 → scalar fields (Higgs)

• Spin-½ → fermion fields (electrons, quarks)

• Spin-1 → vector fields (photons, gluons)

• Spin-2 → graviton (hypothetical, but important conceptually)

So in QFT, particles are excitations of fields, and spin is a property of the field itself, not a classical motion.

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2. Spin quantum number: the formal backbone

The spin quantum number $s$ determines:

• The dimensionality of the spin space

• The allowed spin projections $m_s$

For a particle with spin $s$:

$$m_s = -s, -s+1, \ldots, s$$

Examples:

• Electron: $s = \frac{1}{2} \Rightarrow m_s = \pm \frac{1}{2}$

• Photon: $s = 1 \Rightarrow m_s = \pm 1$ (no zero state due to gauge symmetry)

In QFT:

• Spin is encoded in spinor, vector, or tensor fields

• The spin-statistics theorem links spin to behavior:

  • Half-integer spin → fermions → Pauli exclusion

  • Integer spin → bosons → collective occupation

This connection is deeply structural, not optional.

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3. Spin as information 

Here’s where things get really interesting.

Spin = a minimal quantum information carrier

Spin systems are:

• Discrete

• Robust

• Naturally quantum

A spin-½ particle is literally a qubit:

$$|\psi\rangle = \alpha |↑\rangle + \beta |↓\rangle$$

This means:

• Spin orientation encodes information

• Superposition encodes parallel information

• Entanglement encodes correlations beyond classical limits

In QFT terms:

• Spin information is stored in the internal degrees of freedom of a field excitation

• Measurements extract classical bits from quantum spin states

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4. Spin memory: how spin stores information

Physical meaning of spin memory

“Spin memory” refers to the ability of a spin system to preserve its quantum state over time.

Key mechanisms:

• Long coherence times

• Weak coupling to environment

• Controlled interactions

Examples:

• Electron spins in quantum dots

• Nuclear spins in NV centers (diamond)

• Phosphorus donor spins in silicon

Spin memory is powerful because:

• Spin couples weakly to charge noise

• Spin states can persist for milliseconds to hours (nuclear spins!)

In QFT language:

• Decoherence = unwanted coupling between the spin field and environmental fields

• Spin memory survives when those couplings are suppressed or engineered

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5. Spin dynamics: how information moves

Spin doesn’t just store information — it processes it.

Mechanisms:

• Spin precession (via magnetic fields)

• Spin–spin interactions (exchange coupling)

• Spin–orbit coupling (bridges motion and internal state)

Mathematically:

$$\frac{d\vec{S}}{dt} = \vec{S} \times \vec{B}$$

In quantum computing:

• Gates = controlled rotations in spin space

• Entanglement = correlated spin states across particles or sites

In QFT:

• These interactions arise from field couplings

• Gauge fields mediate spin-dependent forces

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6. Spin in quantum computing

Why spin is ideal for qubits

Spin qubits are attractive because they are:

• Compact

• Scalable

• Naturally two-level systems

Implementations:

• Electron spin qubits (fast, sensitive)

• Nuclear spin qubits (slow, extremely stable)

• Hybrid systems (electron for control, nuclear for memory)

Logical operations:

• Single-qubit gates → spin rotations

• Two-qubit gates → spin–spin interaction or mediation via photons

From a field-theoretic view:

• A quantum computer is a controlled, low-energy quantum field system

• Computation = engineered evolution in Hilbert space

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7. Big-picture synthesis (QFT → QC)

Here’s the unifying idea:

Spin is the smallest unit where spacetime symmetry, quantum mechanics, and information meet.

• In QFT, spin encodes how matter exists in spacetime

• In quantum information, spin encodes how information exists in Hilbert space

• In quantum computing, spin encodes how computation exists physically

Spin quantum number → defines what is possible
Spin information → defines what is known
Spin memory → defines what can persist

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8. Conceptual takeaway

Spin is not just:

• a quantum number

• a magnetic property

• a computational resource

It is:

a symmetry-labeled container for quantum information

That’s why spin shows up everywhere — from particle physics to quantum chips.

Creative Digital Marketing Vs STEAM Education

Writer: Menelaos Gkikas

Happy New Year creatives, marketers and science people! Today’s scientists as well as creative digital marketers are quested not to invent the wheel and furthermore, learn the lessons of digital transformation in the 21st century, align with hybrid visual development solutions in AI and focus on better productive models. Let me just state my inspiration of how the entire today’s discussion started!

AI cannibalizes its own foundations as well. From the very moment we came up with Gemini and ChatGPT, the era of developers stochastically theorizing for weeks to produce one simple piece of code started to erode. Why should we need over 1 week to stochastically theorize for commands over one piece of code, when we can put the task into ChatGPT, produce the program, fix the code on our own and come up with a solution in less than 1 hour? This disruptive change in traditional programming and industry shifts is boosted by software platforms that function as hybrid visual development asking for tinier code samples together with object-oriented tasks, as well as the need of outsourcing digital marketing to independent martech as long as we conceptualize effectively our bottom need which is data, meaning, data production displayed with a data production line.

No matter the industry, for a computer to produce effective data, means that all its components function harmonically and effectively together that is the same logic with a production line inside a food industry. You can’t override the daily tasks of the factory and if they’re not daily, weekly or bi-weekly…

For digital marketers, we need content production. This means scripts, photos, music, videos. This production line has to be followed and applied regularly inside our mediums and from the very moment of regular flow, digital tools like Google Analytics are immediately activated and authorized to display qualitative and quantitative data.

The above truly mean you have activated machine learning, data analytics and AI qualitative and quantitative data further deployed with extra martech and SEO and digital PR tools.

Data flow on the other hand, a time-dependent dynamical system, reminds us something from differential equations possibly redirecting our thoughts to the Schrodinger equation in quantum physics. Here we have elements of the connections of advanced math to how data scientists think with data and numbers evolved… Different notions in data shift to different notions in equations. If you wake up one day and you’re in the mood of thinking whether you shall make articles about Cirque du Soleil or K-Means Clustering AI, means that your perception on what to talk about shapes outcomes…! If you could model that, perception shaping outcomes means pure quantum physics.

But what about the real logic and the rationale of bridging creative digital marketing with STEAM education initiatives? Pay attention to the following bullets:

1.) Martech

Complex digital marketing happens with tailor made complex technologies. To scale-up digital marketing projects means to carefully outsource expertise to low cost or free outside products in terms of SEO and outreach campaigns, digital PR, analytics as well as manual programming.

2.) Hybrid Visual Development

Coding is no longer king. The era of conceptualizing for weeks and thinking you’re Schrodinger only to write essential code is now gone. This does not mean we don’t need programming. It means programming should be combined with complex visual development products.

3.) Traditional Programming Starts Becoming Obsolete

The evolutions in AI in the last 10 years start threatening traditional programmers. Tools like ChatGPT, Gemini and automated production of code start to emerge, that make the demand for programming less and shifted to more valuable options. Which brings us to the next bullet argument.

4.) AI cannibalizes its own roots

The previous do not mean we don’t need math and programming. If we live in the 4th industrial revolution of AI, then coding and math are part of that AI as well. It just means that not ‘you’, but ‘other’ coding and science examples will survive.

5.) Data Vs Mathematics

It’s important to think like a data scientist. Different notions in data are equivalent with different parts in mathematic equations. For example, we know even before we enter the university that f is defined as the derivative of F and we learn statistics in university that say that this f is the probability density function of the cumulative distribution function F, the major definition of all statistics and since we know differential and integral calculus, F can be expressed as the integral of f. Here, we have founded math for data analysis. Using the same logic we should seek equivalences of data flow with a differential equation and possibly seek the differential equation of Schrodinger in Quantum Physics. Less exercises and problem solving as a university student and more like applying elemental basic principles.

6.) STEAM Education As Content

Science and especially STEM are being defined quantitatively. Nevertheless, equations in books and courses are classified as general statistics that may not comply with the unique example of us, furthermore, they do not comply when we make our own single measurements. Unique measurements may be something else completely. So, it’s important to embrace science as content and see what we can learn as digital marketers by other products that incorporate metrics, not inventing the wheel on our own.

7.) Redefining Science & Coding

In the 21st century of the 4th industrial revolution we’ll be needing less coders and more scientists. It’s important to bridge the gaps and apply inclusion successfully but it’s also important to focus on the science and codes that matter, not on our personal story…

8.) Paradigm Shifts

All the previous mean that as we live in the age of computers, there will be other paradigms that will lead the reigns of evolution and these paradigms will not be the same with the previous generations or the scientists and coders that have been left behind.

9.) Why Digital Marketing

Projects need ROI and Lead Generation. The same counts for the entire company as well. A big company that cannot sell anymore, faces the risk of closing down operations. My personal evaluations on the other hand say that heads of marketing and heads of companies will not allow complete and hostile take overs by AI… Electronic commerce will not beat physical commerce and physical presences completely in all industries. It’s just that there are paradigm shifts, new equilibrium points defined and we have to comply with disruptive change modelling and digital transformations. All the previous bring at the frontiers of the revolution marketing and digital marketing.

10.) Acceptance Vs Reinvention

It’s not what you say it’s how you say it and more specifically the delicate way you will serve it to others. Discovering the how and the mediums to apply STEM are more important than saying your lesson as a university parrot. Meaning, to discover what’s truly important in science and how it’s applied rather than merely applying your classroom contents by-heart.

11.) Nature’s Smarter Than People Think…

We cannot defeat science and science will defeat us more if we override it. Whatever you abandon, it abandons you. Future generations will be heavily science oriented, so it’s important to realize not only the mediums we use but the fact that today’s scientists are a ship that finds no harbor for we are making wrong usage of our tools. We have to thoroughly investigate our previous and current tools before we venture with new ones and more importantly, science is not for the faint at heart. Science is for the brave ones, so make brave choices and let the future evolve at its own…!

God Plays Loaded Dice With The World!

All Quantum Field Theories (QFT) are described by a Lagrangian density accompanied by equations of the physical system on study.

Quantum Field Theories are the vehicle to understand complex phenomena related to symmetries – invariance under spatial, time and rotational transformations of equations’ variables – including the nature of ‘God particle’, meaning, the Higgs boson.

The Higgs field – scalar - permeates the entire universe and interacts with other vector fields. Fields are dynamical systems, meaning, subject to change over time and these changes are portrayed with variable equations. 

Before symmetry breaking there are certain states – 2 and 2 – for the vector field and the Higgs field. These states are related with the fluctuation of the fields, for example, up and down, left and right…

After symmetry breaking and through the interaction, the Higgs field gets a non-zero expectation value that actually breaks the symmetry.

Consequently, the vector field becomes massive.

The fluctuations of the potential of the scalar Higgs field are described by an equation called ‘Mexican Hat Potential’ or in other words, ‘Sobrero Potential’.

The previous introduction guys, was an induction to the nature of God’s particle quantum physics, essential to understand the experimental narrative of today’s subject, whether we can unify quantum randomness and pseudo randomness and prove that not only God plays dice, but in the face of a spectrum of alternate probabilities in the multiverse – under no conditions this is the full spectrum of all possible events, not everything is possible – these dice are loaded as well – introducing partiality in other words -. 

Einstein was wrong. God plays dice with the world.

Nevertheless, there have been numerous papers, including these at the hyperlinks at top of this blog – that each one scientist, under a fully different spectrum than the previous ones, tries to prove with their own experiments, narratives or philosophical inquiries that God plays dice. Everyone seems to possess different tools of theorization to prove the argument.

The burning issue of this article will be understood sooner or later. Before this happens, we need bridges to understand the nature of the systems we study.

Everything in the universe corresponds to a bubbling cloud of energy – not easily definable, we’re not much interested to the energy beyond the fact it has been proved with equations and exists beyond unreasonable doubt – that works with different and non-compatible laws if compared with the human physiology. 

Understanding this energy via the use of quantum fields, we insert the concepts we discussed above, meaning, the values of the ‘Mexican Hat Potential’ into a neural network to understand how the physics of the mind interacts and becomes a receptor of the environment - that more or less rules our fates -…

Before engaging into deep philosophical and teleological questions of whether God plays loaded dice with us, I’m setting up the frame to understand quantum consciousness.

Quantum and classical experiments – including quantum consciousness – can be understood on different layers – these are the code layer, the math layer, the visual layer, the engineering layer and the experimental narration layer.

Since we’re too little and too insignificant to know even the tiniest bits of how our complete brain works, the mechanical analogies of this article – narratively portrayed – are just a simplified introduction for the few of us that would really like further exploration of these topics, digging deeper and deeper afterwards in other words.

The quantum consciousness mind is what we, humans have, so that we can perceive, think or feel and try to interact or influence decision making or other phenomena. For example, use mind’s quantum consciousness and try to make the above concepts be assimilated by classical data and classical experiments in the realm of classical probabilities, as it’s stated it happens in the papers portrayed at top.

There can be numerous occasions falling under the umbrella of classical probabilities, luck, the economy, informatics cases, game theory, decision sciences, other classical experiments of Bayesian and behavioral statistics, etc, etc.

The frame is complete. But can we argue much, still, with regard to God? Not exactly. In the book “Discussions with Einstein”, Einstein himself expressed strong oppositions with the facts that God is not merely anthropomorphic and doesn’t possess exclusively human attributes. He created Man in the image and likeness of Him, but he is much more not familiar to us… God is not familiar to anyone…

Einstein again, expressed strong contradictions to the facts of a God merely mingling with fate, a God that approves the good and punishes the bad to decide whether we should be worthy of Heaven or Hell, a case merely related with the primitive perceptions of the Church, that direct humans merely out of their fear of hunger, illness, or death.

Einstein, with his rights and wrongs connected to the previous arguments as I’ll state later, had walked away from the God of Bible, and was worrying for the Universal God, how God is manifested in nature.

Fate? All of us are less or more favored in almost all aspects of our lives. Literature, Philosophy, Fairytales, Arts, Psychology, etc, can all mingle with notions such as destiny, free will, welfare, intelligent design, fate, luck, death and resurrection, partiality, creative expression and many more didactive concepts.

If the scientists of 20th century as we understand them today, had exhibited in their works the concept of “synthesis”, our world would be better. For example, DNA biology connected to information is a terrific idea to understand the previous.

In reality, the previous concepts of luck, partiality, etc, etc, should not be distinct from the world of science… We don’t seek to cancel but to synthesize…

You can now get the full picture, that in a universe of fully quantum physical and fluid probabilities, God plays pseudo-random dice and he becomes partial with certain outputs in e.g. the multiverse, for it is true that not ‘everything everything’ is possible, just a spectrum of possibilities.

The final comprehension concepts will be set up with the following pseudo-code:

1.) Construct the Mexican Hat Potential. Get a sense of its domain and pictures.

2.) Input the potential into a neural network and try to construct quantum consciousness structurally, not only computationally.

3.) Use the previous concept to assimilate it with classical data and classical probabilities in terms of all possible phenomena interpreted this way. Meaning, pick up an experiment and apply interpretation, influence or decision making from step 2.

Now you have a complete picture not only of quantum randomness and pseudo-randomness, equivalent to loaded dice, neither of a mechanism that would be infinitely more complicated if compared to the previous concepts – impossible for now? – but a logic on the importance of synthesis.

Have a great time!

The Coin Toss Experiment As a Single-Qubit Metaphor

Hello folks and science creatives! Today, I’m gonna discuss the first case study of actual problem solving in the Luminous Quanta project. The problem entitled above is the inception of integrated key concerns regarding physics, math and programming combined… Here, I will start with discussions related with “The Double-Slit Experiment”, another experiment we will find useful to discuss, the background world behind every experiment in physics, the logic behind it as well as paradoxes related with the nature of being a scientist. All that for the purpose of an integrated presentation of “The Coin Toss Experiment As A Single-Qubit Metaphor” related with Python and pseudo-code.

Every Physicist who initiates an experiment has to decide on his experimental setup and conduct it by decomposing every tiny bit and interaction inside the experiment with a vast network of knowledge, experience and interpretational ability. That’s not easy, as Physicists who possess one skill don’t necessarily possess the other. It’s common fact that simple argumentations in an experiment many times require evidence even from Nobel Laureates and that demands empathy in terms of asking ourselves “who are we” and “why we are here”. Learning to play a game is more important than learning to impose your ego… But let’s start from the inception of today’s discussion!

When we try to determine the position of an electron we have 4 different values, these are principal number, orbital angular momentum, magnetic measurement and electron spin. Spin is an intrinsic notion of angular momentum. When we observe an electron into a superposition the whole system collapses into spin up or spin down. In fact, electrons do not spin as this is a property that takes place only after measurement. When we measure, we lose the information of before. There’s an analogy to this with the thought experiment of Schrodinger’s cat and we can find an analogy in quantum computing where the spin up is equivalent with the bit value of 1 and spin down with the bit value of 0. Superposition in other words collapses into classical bits. When 2 electrons interact with each other there is entanglement, meaning that their spins have some kind of correlation between them. If you measure one electron as spin up the other one immediately is spin down, it doesn’t even matter where they’re located, in a quantum computing technology or outer space…!

The Coin Toss Experiment As A Single-Qubit Metaphor is an attempt to show with coding samples, numerical graphs in Jupyter Notebooks and less interaction with the actual code, the logic behind the pseudocode and what do these things mean in terms of the nature of the experiment. The coin-toss experiment in statistics follows the pattern of the binomial or in other words, the Bernoulli distribution. The single-qubit metaphor in quantum computing works with quantum states of ket 0 and ket 1. To understand the parallelization, we draw concepts from what Python knows as tuples of probability amplitudes. I’m gonna write a pseudocode and I’m gonna write a Python code, so this sample can work as a vector space algebra, whereas the first time the variables denote we live in the universe of the luck experiment to be known as coin-toss and the second time the laws of the luck experiment assigned to Bernoulli are being transformed into the laws of a single qubit. The fantastic question is, what if we could use hundreds or hundreds of thousands of coin tosses to simulate a universe or a quantum computer with different laws than what we know today? But that’s a different story…

- Pseudocode
Repeat the following experiment 100 times:
1.) Toss a coin 10 times
2.) For each toss multiply the result of the toss with the corresponding part of the tuple of probability amplitudes (f)
3.) Create a list of tosses for the 10 tosses so to know each time the result of the tosses cumulatively up until the end – of 10 tosses (tails)
4.) Create a list with the results of the tuple of probability amplitudes after the tosses (Toss)
5.) For every ten of tosses create a list with the final sum of heads or tails. (final_tails)
6.) Print final_tails and Toss

(Click at the picture to enlarge)

Bear in mind folks viewing the above code that here, for a coin-toss we use a random number generator the way it is constructed by the inventors and creators of the programming language Python, meaning the result of a simple toss obeys the rules of the random number generator machine. Nevertheless, we multiply the result of the coin toss with 0.48 the first time and 0.52 the second time, as we know from the academic real world, the coin is not absolutely clean and the Bernoulli distribution gives the results of 0.48 and 0.52 for each side of the coin, that here have been configured with a tuple of probability amplitudes as a constant outside the second and third loops. The nature of this tuple multiplied with the coin results can simulate with a different analogy – that is the random number generator – the quantum state of a single qubit!

Below is a graph of the above:

(Click at the picture to enlarge)

To move from a quantum universe into a universe of a game of luck, we could possibly use a transformation not on the 2 engines but on the final output data. Meaning, not the complex numbers of the quantum computer nor the random number generator but in terms of what they communicate at the level of metadata…! This concern is also relevant with a concept from cryptography where we actually substitute physical locks and use ciphers instead, but we mean nothing related to physics when we say physical locks, but actually the encryption and decryption metadata that could indeed, simulate physics!

Below we can see the cumulative results after the end of the total experiment:

 

 

(Click at the picture to enlarge)

We observe a slightly negative skew at the above distribution. As we progress with processing the data of this experiment, I’d like to discuss about further real-world impacts related with the quantum probabilities of the physical system of the coin toss connected with the classical Bernoulli probabilities in statistics. The priming to recreate and correlate the problems will rise if we could somehow design the real-world simulation. Meaning, the force we exercise to the coin with our hand, the speed of the coin, the height it acquires, its spin, the height at which we catch the coin, etc, integrated into a coin toss of a quantum physical system defined by a superposition of spins, up until we can measure it and the system collapses, hence verifying by repetitions aligned with the laws of big numbers, the distribution of Bernoulli…!

Can you now understand how this leading example actually entangles a physical system of spins and quantum probabilities, with the classical probability in statistics? This is a powerful example of uniting two different worlds, the way we wanted to unite our quantum universe with a universe obeying on the laws of a game of luck, that is the coin toss. But we’ll always need to be extremely cautious with the analogies and the meters with which we unite one world with another, a case omnipresent in business, factories, and different experimental setups than the coin toss or the double slit experiment.

Below we can view the total outcomes of the experiment as a dictionary in Python:

 

(Click at the picture to enlarge)

Note here that the verification of Bernoulli coincides not with the results, 521, 479, these are defined by the random number generator engine, but with the assigned probabilities as before.

I truly hope this experiment and the process of analyzing it actually sheds powerful light on conclusions and the actual joy of science! Have a great time folks!