We already know that classical (Newtonian, deterministic) physics canot be a theory of anything because it leads to the utraviolet catastrophy, that is to infinity. To avoid infnity we must introduce quanta. But this is not where story ends. In order to preserve limits like Lambert's law, an unaviodable consequence of quantization is randomness. So we have the following chain:
Infinity -> quantization -> randomness. The equations we form on this deduction path have wavy solutions, hence superposition, which by the way is already there in classical physics.
But why is entanglement there? Is this really necessary? Why the heck is God torturing us with that? Is it just a bonus? A little annoying, unwanted sample bottle that comes in a promotion pack? How would Universe look like, what would be missing, without the entanglement?
Mario Stipčević
In all experiment of entanglement are used "standard equipment" which include linear polarizers. But, since the photon is a rotating entity, what happens to a photon when passing through the polarizer?
Also, the photon pair have an interaction at the moment of creation, producing two photons with opposite polarisation.
These two points make the result from such experiments rather dubious, IMO.
JES
Stellan Gustafsson No, no quantum entanglement exists, I am measuring it every day in my lab. The question is: can a closed theory be formulated without entanglement?
Sorry, Mario Stipčević ,
I'm quite sure that entanglement doesn't exist, as explained above, there is a serious problem in the experimental setup.
I can even go further, in my opinion, the QM-theory is just a superficial theory due to the non-understanding of the associated wave.
There is no probabilistic function for the whereabouts of the electron. The electron is a small spherical object, with a distinct position and velocity.
JES
There is a fundamental difference between the superpositions in classical and quantum arenas.
Entanglement in multiparticle systems results from local superposition of the constituent particles and superposition principle is the key assumption of quantum theory. If a theory without entanglement be formulated, it won't utilize superposition. Such a theory will have nothing to share with the present quantum theory.
Salman Khan Are you sure about that? Can you write a bunch of formulae to support this? For example superposition exists in classical mechanics. String on a guitar vibrates in superposition of many modes - totally in acordance with superposition in quantum mechanics. However, there is no entanglement (super-correlation). So, superposition is NOT where entanglement comes in mathematics of QM. It must be from somewhere else.
Mario Stipčević Classical superposition occurs only at the dynamical levels whereas, in addition to dynamical levels, quantum superposition also occurs in the structure (between the internal dimensions) of a quantum system. It is this structural superposition of quantum particles that results in entanglement, only in quantum system.
For example, a bipartite qubit system lives in a four dimensional Hilbert space with computational basis |00>, |01>, |10>, |11>. A superposition of the first and last bases results in an entangled state (an example of structural superposition) of the form |psi>= a|00> + b |11>, and for equal probability amplitudes it becomes a Bell's state.
Salman Khan OK, you got me cornered, but I see a way out. Superposition is not a cause of entanglement: it i just a "+" sign, which is quite a classical stuff. In the above example, also in a|01> + (or -) b|10>, which presents the other doublet of 4 basic Bell states, the crucial thing for entanglement is very existence of wavefunction |alpha,beta> which says us that the system can have the same treatment (set of quantum numbers alhpa, beta) as any of its constituents. This effectively limits quantity of information that system can hold and that enables the entanglement (but it is still not mandatory). If I can limit a system of 2 particles to hold max only 1 bit of information, which is a weird stuff and does not stem from suerposition, while each particle can aslo hold max 1 bit of information, then they must be correlated and we call that "entanglement". Two things seem crucial: universal quantization of information carried by a(ny) system of 1, 2 or any number of particles. Do we agree on that?
Mario Stipčević
I am not an expert by any means, But, I would say that the randomness aspect of quantum physics is the source of its weirdness.
Randomness is our inability to account for all factors.
I also believe that Bell Inequality is where things start to go wrong. and there are few efforts on this particular point.
Ali Houadef Ali, even more, puzzling thing is that while QM is the only theory that requires randomness in it, randomness is not a part of the theory: the theory itself is mathematical therefore deterministic! When you calculate the wavefunction, even if time dependent, there is only one solution and this solution is mathematically exact - just a normal function. But, when you want to masure the system then physicists are in despair, they shout: "wavefunction collapse". But nothing has collapsed: this only means, in plain English: "Whatever you calculated STOPS TO BE VALID from the point you measure, because you did not include measurement in the previous calculation." And why did you not? Because what happens then is - randomness. And noone knows how to include randomness in the theory. And if we did, it would break uniqueness of the solution. And then "theory" means nothing, because the whole purpose of a theory is to predict. So we got ourselves a probabilistic theory. But not quite as classical ones. Because we can tweak a QM system to give us minimally probabilistic solutions (for exmple in quantm computation) or maximally probabilistic (for example in random number generator). This is where theory becomes an Art.
Entanglement is not a requirement of QM, rather is a feature inside of QM.
The phenomenon of Entanglement lies intrinsically within all Quantum Systems which hasn't been interacted with a "measurement apparatus" yet, whatever this term litterally means.
Entanglement is the "natural state" of all Quantum Systems.
Franklin Uriel Parás Hernández and Md. Tarek Hossain you two should discuss!
Dear Mario :
Well, there is not much to explain or discuss.
Your question doesn't make much sense.
I mean, QE is a fundamental feature of Quantum Mechanics, so it is a fundamental (at the most fundamental level) feature of the Nature itself.
The phenomenon of Quantum Mechanics doesn't have an underlying explanation.
But don't get me wrong.
There is a formal definition of Entanglement in QM, but it is a mathematical definition, in terms of Linear Algebra and Vector Spaces (Linear Transformations and so on).
The definition could be as follows:
An Entangled Quantum State is one wich cannot be written in any basis (not in a Schmidt basis nor other). You may know that a Pure Unentangled Separable State can be separated and written in a Schmidt's Basis, using the Tensor Product, however, you cannot do that with an Entangled State.
And the Entanglement between to Quantum States can be quantified by a special function, known as the Von Neumann Entropy. Which is a monotonous and continue function, which results in a value between 0 and 1. And the level (or grade) of Entanglement between two particles, or two bi-level states (a Qubit) can be measured by the Von Neumann's Entropy.
We know what Entanglement is, and we can state its definition, and quantify the level of entanglement.
But no one knows a fundamental explanation for why Entanglement is what it is. Or if you like... Why there is Entanglement? an opposed that there woudn't be such a feature in nature.
Another way of saying the same is: Where does Entanglement comes from? or What is the underlying mechanism (or explanation) of Entanglement? No one knows, because it is a fundamental feature of QM that doesn't have an underlying reason, or at least, we don't know what it is yet.
Best Regards my friend!
There is a simple explanation to entanglement, it is as follows:
Two photons are produced, shortly after each other. The two photons are accelerated, relative to the surrounding, reaching the light speed in a short time. But, during the time of acceleration, the two photons interact (if the time lapse between their creation wasn't too big). the two photons will get opposite directions and opposite handedness of their rotation. You can now do any manipulation (as long as they have the same number of reflections) and you will always find that the two photons have the opposite handedness in their rotation.
JES
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