Quantum mechanics is a complex world of infinite possibilities and probabilities, one that cannot be easily defined. Quantum physics describes the nature of the universe as being far different from that which we see. This is exciting to me because every field recording I make, I listen to in this way: I do not hear it as it sounds, rather, I hear what I can take from it to create a new sound.
I developed a strong interest in science, specifically quantum mechanics around 2008-2009 as a renewed interest in string theory led the scientific community to believe that we may be close to a unifying theory of everything. I found it fascinating that we could explore the idea of living within 11 dimensions as opposed to the four we were aware of.
Possessing no quantum mechanics background made my quest more arduous, but I remained aware of new theories, albeit on a peripheral level, lacking the time to explore further. The onset of the pandemic enabled me to dive deep into the world of quantum mechanics, specifically quantum entanglement which I find fascinating. It is the weirdest phenomenon in modern physics, one that defies explanations, along with gravity.
The learning curve for such studies is quite steep and I found myself in a complete haze for the first six months of studies, which led me to the following observation: probabilities are intrinsic to quantum mechanics, and feeling lost and confused is therefore not so much a hinderance but rather an advantage, one that prepared me for the many possibilities and uncertainties of this fascinating quirky world. I continued to acquire knowledge with the help of Richard H-Brown, PhD student, who kindly agreed to mentor me during my studies.
Quantum entanglement
Quantum entanglement is one of the bizarre phenomena found when considering the quantum realm. When two or more non-interacting particles link up in a certain way, no matter how far apart they are in space, their states remain linked, sharing a common, unified quantum state. Observations of one of the particles can automatically provide information about the other entangled particles, regardless of the distance between them, and any action to one of these particles will invariably impact the others in the entangled system.
In the quantum world, nothing is ever known for certain; for example, you never know exactly where an electron in an atom is located, only where it might be. A quantum state summarizes the probability of measuring a certain property of a particle, like its position or angular momentum. So, for example, the quantum state of an electron describes all the places you might find it, together with the probabilities of finding the electron at those places.
Another feature of quantum states is that they can be correlated with other quantum states, meaning that measurements of one state can affect the other. In 1935, Albert Einstein, Boris Podolsky and Nathan Rosen examined how strongly correlated quantum states would interact with each other and published a paper about their findings. They found that when two particles are strongly correlated, they lose their individual quantum states and instead share a single, unified state. This unified state would become known as entangled quantum states.
The first physicist to use the word “entanglement” was Erwin Schrödinger, one of the founders of quantum mechanics. He described entanglement as the most essential aspect of quantum mechanics, saying its existence is a complete departure from classical lines of thought.
As Einstein, Podolsky and Rosen discovered, entanglement appears to be instantaneous: The moment you have knowledge of one quantum state, you automatically know the quantum state of any entangled particles. In principle, you could place two entangled particles on opposite ends of the galaxy and still have this instantaneous knowledge, which appears to violate the lightspeed limit of information travel prescribed by Einstein’s general theory of relativity.
This result is known as the EPR paradox (short for Einstein, Podolsky and Rosen), an effect Einstein dubbed “spooky action at a distance.” He used the paradox as evidence that quantum theory was incomplete. Experiments have repeatedly confirmed that entangled particles do influence each other regardless of distance, and quantum mechanics remains verified to this day.
There are many ways to entangle particles. One method is to cool the particles and place them close enough together so that their quantum states (representing the uncertainty in the position) overlap, making it impossible to distinguish one particle from the other.
Another way is to rely on some subatomic process, like nuclear decay, that automatically produces entangled particles. It’s also possible to create entangled pairs of photons, or particles of light, by either splitting a single photon and generating a pair of photons in the process, or by mixing pairs of photons in a fibre-optic cable.
Perhaps the most widely used application of quantum entanglement is in cryptography. In this scenario, a sender and a receiver build a secure communication link that includes pairs of entangled particles. The sender and receiver use the entangled particles to generate private keys, known only to them, that they can use to encode their messages. If someone intercepts the signal and attempts to read the private keys, the entanglement breaks, because measuring an entangled particle changes its state. That means the sender and receiver will know that their communications have been compromised.
This means you could send information to someone and it would be literally impossible for someone else to listen in on the way, as you would instantly know. Another application of entanglement is quantum computing, in which large numbers of particles are entangled, thereby allowing them to work in concert to solve some large, complex problems. For example, a quantum computer with just 10 qubits (quantum bits) can represent the same amount of memory as 2^10 traditional bits.
Superposition of states
The superposition of states is an interesting consequence of quantum mechanics. The superposition principle encompasses within itself the idea of entanglement. It is what Schrödinger tried to explain with his thought experiment “Schrödinger’s cat”, which illustrates an apparent paradox of quantum superposition. In the thought experiment, a hypothetical cat may be considered simultaneously both alive and dead as a result of its fate being linked to a random subatomic event that may or may not occur.
From the viewpoint of quantum mechanics, the whole universe is basically one big wavefunction. It starts out in a wavelike manner, propagating outwards, and before it collapses, it is in an infinite number of different states, and the evolution of these states is governed by two different mathematical rules. After collapse, a wavefunction describes a particle in one specific state.
The principle of quantum superposition states that if a physical system may be in one of many configurations – arrangements of particles or fields – then the most general state is a combination of all of these possibilities, where the amount in each configuration is specified by a complex number.
“Entanglement is an application of the superposition principle to a composite system consisting of two (or more) subsystems.
A subsystem here is a particle.
Suppose that particle 1 can be in one of two states, A, or C, and that these states represent two contradictory properties, such as being at two different places. Particle 2, in the other hand, can be in one of two states, B, or D. Again these states could represent contradictory properties such as being in two different places
The state AB is called a product state. When the entire system is in state AB, we know that particle 1 is in state A and particle 2 is in state B.
Similarly, the state CD for the entire system means that particle 1 is in state C and particle 2 is in state D. Now consider the state AB + CD. We obtain this state by applying the superposition principle to the entire two particle system. The superposition principle allows the system to be in such a combination of states, and the state AB+CD for the entire system is called an entangled state. While the product state AB (and similarly CD) ascribes definite properties to particles 1 and 2 (meaning, for example, that particle 1 is in location A and particle 2 in is location B), the entangled state – since it constitutes a superposition – does not. It only says that there are possibilities concerning particles 1 and 2 that are correlated, in the sense that if measurements are made, then if particle 1 is found in state A, particle 2 must be in state B; and similarly for states C and D.
Roughly speaking, when particle 1 and 2 are entangled, there is no way to characterize either one of them by itself without referring to the other as well.
This is so even though we can refer to each particle alone when the two are in the product state AB or CD, but not when they’re in they superposition AB+CD. It is the superposition of the two product states that produces entanglement. “*1
If you have one quantum interaction, one wave can interact with another and a two-particle wavefunction is produced for the two different particles. It is not one wave and another, it’s one big wavefunction, both of the particles are described by one object, a wavefunction.
The superposition of waves explains the phenomenon of interference. Consider the famous double-slit experiment: light goes through both slits and their wavefunctions contain a superposition of all the states of the incoming photons. The slits change the shape of the wavefunction, and, using the “Born rule” to calculate the probabilities, if the shape changes, the probabilities change and the possible outcomes as well.
When the quantum system contains more than one particle, the superposition principle gives rise to the phenomenon of entanglement – it is a system interfering with itself.
There are two main interpretations of quantum mechanics: the “many worlds” and “Copenhagen” interpretations. Both interpretations are mathematically the same: the Schrödinger equation, the fundamental equation describing quantum systems, is used both in the Copenhagen interpretation and many worlds interpretation. The difference occurs in the interpretation of the process which causes one particular state rather than many (as described by the Schrödinger equation) to represent e.g. a particle. In the Copenhagen interpretation, this is wavefunction collapse. In the many worlds interpretation, this is decoherence. With the many worlds interpretation, different states describe different things happening in different copies of the universe.
Bell’s theorem:
John Steward Bell (1928 – 1990) deduced that if measurements are performed independently on the two separate halves of an entangled pair, then the assumption that the outcomes depend upon “hidden variables” within each half implies a constraint on how the outcomes on the two halves are correlated. This constraint would later be named the Bell inequality. Bell then showed that quantum physics predicts correlations that violate this inequality. Consequently, the only way that hidden variables could explain the predictions of quantum physics is if they are “nonlocal”, somehow associated with both halves of the pair and able to carry influences instantly between them no matter how widely the two halves are separated. As Bell wrote later, “If [a hidden-variable theory] is local it will not agree with quantum mechanics, and if it agrees with quantum mechanics it will not be local. This “nonlocality” appears to violate Einstein’s general theory of relativity.
The Copenhagen and Many Worlds Interpretations
These two interpretations are competing frameworks for understanding the mathematics of quantum mechanics. This is not a question of science, it is one of philosophy and interpretation. At the moment, there are no experiments we can really do to discriminate between the many worlds and the Copenhagen interpretations – it basically comes down to opinion and reasoning.
Quantum entanglement is happening – the explanation does depend on whether you choose the Copenhagen interpretation or the many worlds interpretation. Whichever you choose, it is not compatible with classical physics. It is still important and philosophically interesting because of how we think of physics and reality. Quantum entanglement is one of the main ways we can demonstrate that our common sense view of reality is definitely incorrect. The way in which it is incorrect depends on your interpretation, but everyone agrees that quantum entanglement is legitimate and that our naïve view of reality is incorrect.
Copenhagen interpretation:
When we deal with quantum systems, each with an associated wavefunction, we no longer deal with precisely known elements. A quantum particle can only be described by its probabilities – never by exact terms. These probabilities are completely determined by the wavefunction. The probabilistic interpretation of quantum mechanics was first discovered by Max Born, although it was inspired by prior probabilistic theories by Einstein. The probability that a particle is to be found in a given place is equal to the square of the amplitude of the wavefunction of that location.
You make a measurement and the wavefunction collapses, you observe one specific thing, you can’t see a wave, you can only see a particle.
The second essential element of the quantum theory brought to light by Schrödinger’s equation is the superposition principle. Waves can always be superimposed on one another. The reason for this is that the sine curve and the cosine curve for various parameters can be added to one another, and be completely demodulated. This is the principal of Fourier analysis, discovered by the great French mathematician Joseph Fourier.
While the wavefunction could collapse at any one of these points, Born said that the probability of it going to any point is the square of the wavefunction. The square of the amplitude of the wavefunction therefore sums up to one.
When, in certain processes, we have two particle produced, both particle are described by a single wavefunction, describing all the states of the particles: velocity, momentum, etc.
The wavefunction object contains all the information. When you make a measurement of the wavefunction, it collapses both particles at once and you automatically make a measurement on one particle when you make a measurement of the other particle: this is fundamentally what entanglement is. The really bizarre aspect is that if a measurement is made on one side of the universe, the entangled particle could be on the other side of the universe, yet the other particle changes instantly.
In other words, when a quantum system contains more than one one particle ie: one wavefunction describing more than one particle, the superposition principle give rise to entanglement, one wavefunction which collapses both particles.
Many worlds interpretation:
In the many worlds interpretation, you do not have this wavefunction collapse. Every time you take a measurement, you have a quantum interaction and you decohere, you separate out into your own copy of the world, where one particular quantum state is the true quantum state and all other quantum states are there but they are just in another reality, inaccessible to us, kind of snapshots as David Deutsch describes.
It seemingly raises simple questions that yields complicated answers. Two common problems highlighted with this interpretation are as follows:
1- What is the process of splitting between two separate worlds – a split between two realities?
2- It postulates too many things, and is not simple enough.
Let’s say we have two particles – momentum is always conserved, one particle here and one particle there. They start together and some quantum interaction happens and they separate because nothing outside influenced their state. The combined momentum of the two particles after they separate must be the exact same as the momentum of the state before they separate. The two parts must add up to the same momentum.
There are loads of different ways they could share momentum, you cannot add to momentum, and you can’t take away – it could be 90-10, 55-45, you dont know before you measure because of the probabilistic nature of the many worlds interpretation, you dont know which world they are in. In the Copenhagen interpretation, nothing happens until you make a measurement and the wavefunction collapses. In either interpretation, you don’t know until you make a measurement, what the split is made of.
A larger group of physicists say we should not be speculating about the interpretation at all, all that really matters is the maths behind it; and until we can do an experiment which can differentiate one from the other, it doesn’t matter.
Uncertainty principle – Heisenberg
The Heisenberg uncertainty principle states that uncertainty cannot be removed from quantum systems.
Quantum entanglement says that when you take a measurement of one particle, and find it has one third of the total quantity of an observable, then we know the other has two thirds; this is the same in classical physics. Quantum mechanics however has the uncertainty principle, meaning that with different quantum observables such as position and momentum, the more accurately you know a particle’s position, the less accurately you know its momentum and the smaller your uncertainty is on position – the higher your uncertainty on the momentum.
In classical physics, due to some hidden variable, the uncertainties just represent knowledge of the system and not anything fundamental about the system itself. It does not make sense for a particle to have real physical uncertainty on its position and momentum, it must have a real position and one real momentum. This is not due to limitations on our knowledge, it is fundamental property of reality itself.
If we measure the position, we don’t know what the momentum is, as the momentum measurement is spread between many universes or across a wavefunction, depending on the interpretation.
“When the big debate started between Einstein and Bohr, Heisenberg typically took Bohr’s point of view while Schrodinger took Einstein’s.
Measuring the position of a particle is associated in quantum mechanics with applying the position operator to the wavefunction. Measuring a particle is understood in QM as applying the partial derivative-with-respect-to-position operator to the wave function (momentum, p, is classically the mass of the particle times its velocity, and velocity is defined as the derivative of position with respect to time). The two operators, position and momentum, do not commute with each other. We cannot measure them both together.
If we know one of them to good precision (the one we measure first), then the other one will be known with poor precision. This fact, that the position and the momentum of the same particle cannot both be localized with high precision is called the uncertainty principle. Heisenberg’s uncertainty principle is his second important contribution to quantum theory after his formulation of matrix mechanics.’*2
Quantum decoherence
It is maybe worth describing further what makes the MWI different to the Copenhagen Interpretation – MWI doesn’t have a wavefunction collapse, but rather quantum decoherence creates the illusion of such an effect.
In quantum decoherence, the wavefunction goes from being defined over many states to one state through something a little different to wavefunction collapse. In this view, the wavefunction gradually tends towards a certain state after many repeated interactions with the environment (which is also made up of wavefunctions, everything in the universe is!). The wavefunction gets entangled with all of these wavefunctions, producing a very complex, entangled system.
Schrödinger’s cat, for example, is not a complete thought experiment. The radioactive sample would only be in a 50-50 chance of decay if you have not made a measurement yet: in principle that is true, practically, it is not. Even though you have not personally made a measurement of the system, a cat is a very big system consisting of many particles, and all individual particles effectively take lots a measurements to collapse the wavefunction. It’s not a very controlled situation, and this is the essence of decoherence: introduction of macro to micro, the issue with the big macro world making the quantum effect extremely hard to isolate. In terms of entanglement – it is very difficult to recreate in large systems.
Time in Modern Physics
All the mysteries of time stem from its basic, common sense attribute, namely that the present moment, which we would call now, is not fixed but moves continuously in future direction. This motion is called a flow of time.
It is often said that the present seems to be moving forward in time: the present is defined only relative to our consciousness, and our consciousness is sweeping forwards through the moments. But our consciousness cannot, and could not do that. When we say that our consciousness seems to pass from one moment to the next, we are merely paraphrasing the common sense theory of the flow of time. But it makes no more sense to think of a single “moment of which we are conscious” moving from one moment to another, than it does to think of a single present moment, or anything else, doing so. Nothing can move from one moment to another. To exist at all at a particular moment means to exist there for ever. Our consciousness exists at all our (waking) moments.
What we experience is the differences between our present perceptions and our present memories of past perceptions. We interpret those differences, correctly, as evidence that the universe changes with time. We also interpret them incorrectly, as evidence that our consciousness, or the present, or something moves through time.
If the moving present capriciously stopped moving for a day or two, and then started again up 10 times its previous speed, what would we be conscious of? Nothing special – or rather, that question makes no sense. There is nothing there that couldn’t move, stop or flow, nor could anything be meaningfully called the speed of time. Everything that exists in time is supposed to take the form of unchanging snapshots arrayed a longer timeline. That includes the conscious experiences of all observers, including their mistaken conception that time is “flowing”. They may imagine a moving present traveling along the line, stopping and starting, or even going backwards or ceasing to exist altogether. But imagining it does not make it happen. Nothing can move along the line. Time cannot flow.
The reason why we cling to these two incompatible concepts – the moving present and the sequence of changing moments – is that we need them both, or rather, we think we do. We continually invoke both of them in everyday life, albeit never quite in the same breath; when we are describing events, we think in terms of a sequence of unchanging moments, and when we are explaining events as causes and effects of each other, we think in terms of the moving present.
The structure of reality already contains the future and the past, the present is just an artefact of the way consciousness works. In reality, we make no choices. Even as we think we are considering a choice, its outcome is already there, on the appropriate slice of space-time, unchangeable like everything else in space-time, and impervious to our deliberation. It seems that those deliberations themselves are changeable and already in existence of their allotted moments before we ever know of them.
“if…then…” statements are not solvable in spacetime physics – there is no avoiding the fact that in spacetime exactly one thing happens in reality, and everything else is fantasy. We are forced to conclude that, in spacetime physics, conditional statements whose premise is false (if Faraday had died in 1830…) have no meaning. Logicians call such statements counterfactual conditionals, their status is a traditional paradox.
My four inspirations that I will interpret in future works.
Source 1 – The fluidity of time
Einstein, whose death of his friend Michel Besso affected him greatly, wrote a now famous letter to Besso’s family. “Now he has departed this strange world a little ahead of me. For us believing physicists, the distinction between past, present and future is only a stubbornly persistent illusion. ”
This perception of time, researched during the grief of my mother and sister, has helped me so positively that it is now one of the four sources that inspire me.
How can I translate this theory that the fluidity of time does not exist when music is created within a span of time?
Source 2 – The principle of entanglement
Quantum entanglement or just “entanglement” is a phenomenon in which two particles form a linked system, and exhibit quantum states dependent on each other regardless of the distance between them. Such a state is said to be “entangled” because there are correlations between the observed physical properties of these distinct particles. Bell’s theorem shows that entanglement gives rise to non-local actions between the particles. Thus, two entangled objects O1 and O2 are not independent even if separated by a great distance, and we must consider {O1 + O2} as a single system.
I’m going to create four albums, perceiving them as systems, within which these albums (particles) depend on each other no matter how far apart. From the perspective of my project, distance is time. States and physical correlations will be represented by the fact that a first album produced will be dependent on the second so that the two albums must be listened to simultaneously, therefore the two albums will be considered as a single system and referencing the principle of nonlocality.
At the moment, the two most prominent explanations of quantum entanglement are: The Schrödinger equation as interpreted by the Copenhagen interpretation, and the multiple universes of Hugh Everett.
Source 3 – The Copenhagen interpretation
Schrödinger’s equation is generally related to the Copenhagen interpretation of quantum mechanics. This interpretation, essentially shaped by Niels Bohr, consists of calling into question the existence of an absolute time and an existence independent of space and time. According to Bohr, we must not lose sight of the fact that physics describes above all that which is observable.
The universe of the Schrödinger equation is composed of a large quantum field within which many wavefunctions undulate. These represent the quantum state of a system in a base of infinite dimension. Wavefunction collapse is a fundamental concept of this approach to quantum mechanics, according to which, after a measurement, a physical system (for example a particle) sees its state entirely reduced to that which has been measured. Thus the particle cannot be assigned a precise position in space and time before measurement.
The mere fact of observing a wavefunction causes it to collapse, thus giving us a panoply of probabilities of the position of a particle. Only at the moment of the collapse of the wavefunction does the particle appear.
The Copenhagen interpretation explains quantum entanglement as the instantaneous collapse of a wavefunction describing two separated particles into a single measured state for both particles.
How can I emulate wavefunction collapse by translating the concept into musical waves and frequencies?
Source 4 – Many Worlds Interpretation
Hugh Everett introduced a new conception of reality into physics: it was he who invented a quantum theory of multiple universes, often called the “Many worlds interpretation” or MWI. Although the idea of multiple universes is far from being unanimous even today, the methods by which he arrived at this idea heralded the notion of quantum decoherence – which today explains why the probabilistic strangeness of quantum mechanics disappears into the world of our daily experience.
A key difference between the MWI and the Copenhagen interpretation is that the MWI does not have a wavefunction collapse, but rather uses only the concept of quantum decoherence. Quantum decoherence describes the loss of information of a specific quantum state as it repeatedly interacts with its environment. This is analogous to a classical particle randomising its state when it enters into equilibrium with a heat bath. The apparent phenomenon of wavefunction collapse is instead a result of quantum decoherence: interaction between the quantum system and a macroscopic system leads to many separate instances of the observing apparatus, and the final measurement the observer sees is found in just one of these instances (worlds).
Without wavefunction collapse, the MWI can explain entanglement more simply: no collapse occurs, and the particles retain their initial state after interacting. The apparent randomness in the measured state comes from the many worlds generated from decoherence with measuring apparatus.
However, the name “multiple universes” sometimes associated with this theory is misleading: in Everett’s interpretation, there is never only one universe, which is divided into several portions which can hardly interact with each other. The macroscopic consequences of the existence of these different portions are still today impossible to measure directly.
How can I emulate this discovery, the loss of coherence when the macro world destroys the quantum purity? The loss of information of a system into the environment can provide further inspiration.
Through my research I have now found the sources of inspiration that I will be working with for the four albums that I will produce. The methods used will be defined according to the principle of entanglement by creating 2 pairs of “entangled” albums, the Schrödinger equation by emulating wavefunction collapse with my own frequencies and musical waves, and quantum decoherence by introducing vinyls and digital albums which will represent the introduction of a macro world into a digital world. In order to listen to both albums together, line up the track 01 Unified quantum state from ROOM40 and track 01 Instantaneous knowledge from Erototox Decodings in your DAW, and adjust volume accordingly. You can do the same with tracks 02 from each album. If you do not have a DAW, download audacity, it’s free.
My interpretation of shadow photons
Between 2017 and 2019, I maintained an association with an unusual bedfellow, death. The loss of Mika Vainio, as well as three members of my own family, has had a profound effect on me and spurred a lengthy reflection on life, death, and everything in between. In parallel, while studying the philosophy of science, I came across shadow photons:
Tangible photons are the ones we can see or detect with instruments whereas shadow photons are intangible (invisible) detectable only indirectly through the interference effects on the tangible photons.
There is no intrinsic difference between tangible and shadow photons: each photon is tangible in one universe and intangible in all the other parallel universes.
They travel at the speed of light, bounce off mirrors, are refracted by lenses, and are stopped by opaque barriers or filters of the wrong colour. Yet, they do not trigger even the most sensitive detectors. The only thing in the universe that a shadow photon can be observed to affect is the tangible photon that it accompanies. This is the phenomenon of interference.
Shadow photons would go entirely unnoticed, were it not for this phenomenon and the strange pattern of shadows by which we observe it.
Thus the existence of a seething, prodigiously complicated hidden world of shadow photons has been inferred.”*
I have drawn a parallel between shadow photons and death. The interference phenomenon, parallel universes, and how shadow photons affect tangible photons they accompany, offer, in my opinion, similarities, to an unknown universe which is death and how we, remaining tangible human beings, are affected. This quest has led me to be more willing to accept chaos in my life and to conclude that Death is perfection, everything else is relative.
*The fabric of reality, David Deutsch, Penguin Press 1997.
Finally, I leave you with this quote with the hope that it sheds a light on our concept of reality:
“Bohm believed the reason subatomic particles are able to remain in contact with one another regardless of the distance separating them is not because they are sending some sort of mysterious signal back and forth, but because their separateness is an illusion.”
“An enormous thank you to Richard Hodgskin Brown for his mentorship, patience and skills which enabled me to gain a profound understanding of quantum entanglement. His ability to keep me focused and structured kept my thoughts organized and his ability to explain difficult concepts was astounding. I am grateful because my apprenticeship is still ongoing. A good mentor is the fondamental difference between quitting altogether and being inspired to continue.
France Jobin ©2023
Sources:
Articles and books
https://www.livescience.com/what-is-quantum-entanglement.html
The Fabric of Reality – David Deutsch, Penguin Press 1997
Seven brief lessons in physics – Carlo Rovelli, Riverhead Books, 2014
Reality is not what it seems – Carlo Rovelli, iverhead Books, 2017
Entanglement – Amir Aczel, John Wiley & sons Ltd, 2003
Quantum entanglement, Jeff Brody, MIT Press, 2020
The God effect, Brian Clegg, St-Martin’s Press. 2006
A brief history of time, Stephen Hawking, Bantam Book, 1988
Hyperspace, Michio Kaku, Oxford University Press 1994
Lectures:
The Illusion of time – Carlo Rovelli
Le photon onde ou particule ? L’étrangeté quantique mise en lumière – Alain Aspect –
The Biggest Ideas in the Universe | 5. Time – Sean Carroll
The Biggest Ideas in the Universe | 8. Entanglement – Sean Carroll
MIT Open Course Ware:
*1Entanglement, Amic C Aczel , Entanglement – Amir Aczel, John Wiley & sons Ltd, 2003
*2 Entanglement, Amic C Aczel , Entanglement – Amir Aczel, John Wiley & sons Ltd, 2003