Why do moving rulers shrink (length contraction) and moving clocks run slow (time dilation) such that everyone measures the same speed of light c, regardless of their relative motions? Einstein resolved this mystery at the turn of the 20th century in "principle fashion" by turning the question on its head. He invoked the relativity principle (AKA "no preferred reference frame") and argued that since c appears in the equations of physics, no preferred reference frame says that everyone must measure the same value for c regardless of their motions relative to the source (that is, regardless of their reference frames).
Length contraction and time dilation then follow as a result of this "light postulate." Ironically, he missed a chance to use the exact same principle to resolve the mystery of quantum entanglement, which he introduced in 1935, calling it "spooky actions at a distance." Indeed, he died believing that quantum entanglement was evidence that quantum mechanics was "incomplete" when his relativity principle would have told him that quantum mechanics is as complete as possible with respect to quantum entanglement.
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After 24 years of research and 2 years of writing and revising the paper, we have finally published an answer to Mermin's challenge that he issued in American Journal of Physics in 1981. Our answer to Mermin's "challenging exercise" has been accepted for publication in Scientific Reports.

This paper "Re-Thinking the World with Neutral Monism: Removing the Boundaries Between Mind, Matter, and Spacetime," was published in a special issue of Entropy, "Models of Consciousness." Therein, we show how all of physics follows from two axioms via neutral monism (see summary chart below).

While many physicists believe physics is fundamental to consciousness, we argue in this paper that "the purvey of physics is to model and explore regularities and patterns in the self-consistent collection of shared information between perceptual origins (POs)." We write: 

When POs exchange information about their perceptions, they realize that some of their disparate perceptions fit self-consistently into a single spacetime model with different reference frames for each PO. Thus, physicists' spacetime model of the "real external world" represents the self-consistent collection of shared perceptual information between POs, e.g., perceptions upon which Galilean or Lorentz transformations can be performed.

This idea is not unique to us. Here is how Weyl put it: Physics is the "Construction of objective reality out of the material of immediate experience." And, as Eddington said, "physics is about the world from the point of view of no one in particular." Thus, just as there is no dualism of the “inner” world of experience and the “outer” physical world, there is no dualism of psychology and physics.

Quantum mechanics is arguably our most successful and accurate physical theory, having been confirmed to one part in a billion. Max Tegmark and John Wheeler reported, for example, that “about 30% of the U.S. gross national product is now based on inventions made possible by quantum mechanics.” And David Mermin calls quantum mechanics, “The greatest intellectual achievement of the 20th century.” Yet, quantum mechanics is mysterious. Nobel Laureate Richard Feynman said, “I think I can safely say that nobody understands quantum mechanics.”
 
The mystery of quantum mechanics that we resolve in this paper was introduced in a famous 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen called, “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” The quantum property that led Einstein to believe quantum mechanics is incomplete is called “entanglement.” But, Einstein’s belief that entanglement could be accounted for by supplying its “missing elements” was shown to be false nine years after he died in a 1964 seminal paper by John Bell called, “On the Einstein Podolsky Rosen Paradox.” Bell showed that if reality contained hidden variables to account for quantum entanglement, then quantum mechanics was not only incomplete, but it was wrong. In his paper, Bell described an experiment that would reveal whether or not quantum mechanics was indeed incomplete. The experiment has since been performed many times in different forms and quantum mechanics has always been vindicated. 
 
While the formalism of quantum mechanics is clear in its prediction for Bell’s experiment, it does not provide any explanation for that prediction, just a mathematical description for the outcomes. A layman’s explanation of this mystery was provided by David Mermin in a famous 1981 paper titled, “Bringing home the atomic world: Quantum mysteries for anybody” that Richard Feynman called, “One of the most beautiful papers in physics that I know.” Therein, he presented the “Mermin device” that illustrates the mystery of entanglement for the “general reader.” He then challenged the “physicist reader” to explain the way the device works “in terms meaningful to a general reader struggling with the dilemma raised by the device.” 
 
Most researchers in foundations of physics believe that resolving the mystery of quantum mechanics will require an entirely new scientific worldview. In his 2004 book, Richard DeWitt writes:
 
New discoveries in the 1600’s, such as those involving Galileo and the telescope, eventually led to an entirely new way of thinking about the sort of universe we live in. Today, at the very least, the discovery of Bell-like influences forces us to give up the Newtonian view that the universe is entirely a mechanistic universe. And I suspect this is only the tip of the iceberg, and that this discovery, like those in the 1600s, will lead to a quite different view of the sort of universe in which we live.
 
In answering Mermin’s challenge we show that the principle of no preferred reference frame, which is responsible for the mysteries of time dilation and length contraction in special relativity, is also responsible for the mystery of Bell state entanglement in quantum mechanics. Specifically, the conservation of spin angular momentum following from the Bell spin states holds only on average in different reference frames, not on a trial-by-trial basis. Therefore, this “average-only” conservation constitutes an adynamical constraint with no overt evidence for an underlying dynamical mechanism, so we justify it via the principle of no preferred reference frame in direct analogy with the postulates of special relativity. Thus, we see a common theme in both relativistic and non-relativistic modern physics relating the fundamental constants c (the speed of light) and h (Planck’s constant) per adynamical explanation. All this implies that physical reality is based fundamentally on adynamical principles rather than the dynamical, causal mechanisms of Newton’s mechanistic universe.

In this paper, we argue that the mystery of Bell state entanglement should be resolved via principle explanation rather than constructive explanation. Specifically, the principle responsible is "conservation per no preferred reference frame." Thus, the mystery of Bell state entanglement stems from one and the same principle responsible for the mysteries of length contraction and time dilation in special relativity, i.e., no preferred reference frame.

In this Insight I explain how average-only conservation of spin angular momentum is responsible for the mystery of entanglement per the Bell spin states. 

This is Episode 10, "Conclusion: Modern Physics is Comprehensive and Coherent," of the video series, "Beyond the Dynamical Universe: Rising to Wilczek's Challenge."

This is Episode 9, "Quantum Mysteries for Anybody: Solved," of the video series, "Beyond the Dynamical Universe: Rising to Wilczek's Challenge."

This is Episode 8, "Quantum Mysteries for Anybody: The Mermin Device," of the video series, "Beyond the Dynamical Universe: Rising to Wilczek's Challenge."