In theories of relativity, physical quantities do not exist as intrinsic properties of "objects", but only as relative properties of pairs, which cannot be attributed to any of the members separately. For example, consider in empty space two identical classical bodies with relative motion. The velocity is a property belonging to neither of the individual bodies, only the inter-velocity between the bodies has a physical meaning. In fact, even energy and all conservative quantities, which are global invariants of systems, depend on the reference system and are not only non-local, but actually non-localized.

Since, in scale relativity, elementary "particles" are identified with a set of fractal geodesics, whose purely geometric properties give birth to the "particle's" conservative properties, entanglement can be understood as those properties of the set of geodesics, corresponding to the particle pair, which do not exist separately for the subset of geodesics corresponding the individual particles.
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AWT models space-time with water surface and the transverse waves correspond the waves of light. But the lightweight objects can interact even via underwater waves. These waves are weaker but they're much faster than the surface ripples, so it will propagate superluminaly in vacuum. They correspond the gravitational waves, which are soughed unsuccessfully, because the physicists didn't realize the indeterministic character of these waves. But gravitational waves are all around us - they do manifest itself with CMBR noise in similar way, like the underwater sound waves manifest itself with Brownian noise at the water surface.

The quantum entanglement is superluminal effect, but it actually doesn't violate the special relativity. Just one particle dissolves in the vacuum and the second one is emerging in the opposite way, because the quantum waves of both particles are synchronized through extradimensions of space-time. But no actual motion along deterministic path happens there. No motion = no violation of relativity. Special relativity is magical itself, so what is magical for magicians may appear quite normal for common people, who are familiar with real life phenomena.

We have no way to unintrusively measure properties on the atomic scale without affecting the object measured. Either this is the problem and the particles have the same properties before they are measured or there actually is instantaneous action at a distance which has profound implications. It would mean to me that FTL travel may be possible for one thing.

Einstein made the comment while criticizing quantum mechanics as incomplete—the phenomenon of quantum entanglement seems to be at odds with Einstein's theory of relativity.

Indeed, it is! Here is a more complete one...http://www.vacuum...19〈=en

What is new here. They have known about, and tested for, entanglement for ages. What did I miss?

instantaneous action at a distance which has profound implications. It would mean to me that FTL travel may be possible for one thing.

Not necessarily. A pattern can be faster than light but does not convey information. For example you may sweep a torch against the night sky. The light arc sweeps over billions of light years in a few seconds. Yet you have no means of employing that method for superluminal communication

Paired particles may fixate states instantaneously, but this does not violate laws of causality as a pattern is not a message

Note that my explanation could be used for demonstration of extradimensions of string theory easily. The main reason for why it isn't used so is, the string theory is based on Lorentz invariance, which gets violated with superluminal effects apparently. The string theorists (who are otherwise seeking evidence for extradimensions obstinately) therefore have no chance how to prove one of postulates of their theory without destruction of another one. The same controversy is responsible for infalsfiability of string theory, which leads into huge untestable landscape of formal solutions.

Relativity isn't etched in stone. Experimentation that is performed deliberately and strictly within the rules established by Einstein is just plain bad science. We should proceed on the premise that superluminal communication is possible, and take it from there.

Exactly AT the same time does not imply FTL. Just means at exactly the same time. Energy is everywhere, but at a different levels. Energy is THE main force that all 4 other forces take their cut from to act on matter. We use geometry, trigonometry and calculus to describe all the infinite things our universe does by addition (as shortcuts). A NEW math must be developed in order to pursue it any further.
So - all you smart guys out there - let's get crackin'...

If two events are coincident in one reference frame, they may not be coincident in another.

"Exactly AT the same time does not imply FTL. Just means at exactly the same time." - Whydening Gyre

That road seems to lead to a logical contradiction.

"We should proceed on the premise that superluminal communication is possible, and take it from there." - baudrunner

How do you propose it be resolved?

The problem of course, is that if you measure the position of one particle you scramble the momentum of the other.

"Just one particle dissolves in the vacuum and the second one is emerging in the opposite way, because the quantum waves of both particles are synchronized through extradimensions of space-time." - ValeriaT

Why doesn't the particle that dissolves into the vacuum re-emerge? What signal from the detected particle prevents it from doing so?

Why doesn't the particle that dissolves into the vacuum re-emerge? What signal from the detected particle prevents it from doing so?

The particles routinely reemerge when they dissolve in vacuum temporarily. The photons or neutrinos are unstable and they suffer with so-called decoherence and quantum oscillations. During this they simply dissolve in extradimensions of vacuum and reemerge again after while - whereas they continue in their original path in form of unobservable scalar waves. It can be illustrated with Falaco soliton vortex traveling along water surface - it repeatedly dissolves and reappears again (it's even loudly commented during video). Without it the distant photons traveling from distant stars could never approach the terrestrial observer. We should rather ask what keeps such a unstable particles together along their path, because it's more tricky business.

When doing this "spooky action at a distance" thing. They have two "captive" photons. How were they entangled before they were "captive"? Were these photons part of a bigger group of the same photons to start with? Did they have the same source?
And - why can't they just capture a third photon and then stop the spin on one to see if it affects just one or both of the other "captive" photons?
Or maybe even a 4th and 5th.
Just to see what happens...

When doing this "spooky action at a distance" thing. They have two "captive" photons. How were they entangled before they were "captive"? Were these photons part of a bigger group of the same photons to start with? Did they have the same source?
And - why can't they just capture a third photon and then stop the spin on one to see if it affects just one or both of the other "captive" photons?
Or maybe even a 4th and 5th.
Just to see what happens...

One way is called 'parametric down conversion' where a single photon is sent through a crystal, which may split the photon into two lower energy photons in a way that conserves energy. The two photons are correlated.

The question of entanglement is all really quite simple if one considers the math of Quantum Physics to be not only correct, but "real". That is to say, the math is not just a model of the Universe, but rather the Universe is our simplified perception of the math. It's simular to the Mathematical Universe Hypothesis. In that case, particles entangle by the math of QM and not by some super luminal communication. Of course, that means we ourselves are also just math constructs and all our perceptions of reality are a contrived method to understand things much too complex for our minds to handle. Simple. Problem solved. Let's move on.