Action at a distance consists of affecting a distant body instantaneously. At the atomic level, this is known as "non-locality".
Examples of action at a distance in physics are:
- Newtonian gravity
- Electrostatics (before Maxwell's equations in the 1800s)
- Quantum entanglement within quantum mechanics (called "non-locality")
Some scientists have long resisted the possibility of action at at distance (non-locality), and the theory of relativity assumes that information traveling instantaneously, or faster than the speed of light, is somehow impossible. But quantum entanglement proves that one particle affects another particle instantaneously.
The classical case: gravitation
In Isaac Newton's time, his theory of gravity was a case of this. The idea that an object could exert a force on another object without touching it was hard to accept. And yet the Sun reached across space and attracted the planets. Newton famously said "Hypotheses non fingo", or "I feign no hypotheses." He was saying that his theory was observed to be true, but he couldn't explain why.
The classical case: electricity and magnetism
During the 17th and 18th centuries, research into electric and magnetic fields showed that charged or magnetized objects can indeed reach across space and exert a force. The work of Michael Faraday and James Clerk Maxwell, particularly the latter's Maxwell's Equations, put this on a sound theoretical footing, and showed that the speed of light has a profound significance in physics, and is the speed at which these forces propagate. Unlike the case of quantum entanglement, there was nothing "spooky" about this.
The "cosmic speed limit"
In both of the above cases it is impossible for information to propagate, gravitationally or electromagnetically, faster than the speed of light. With the advent of relativity in the 20th century, it became clear that this is not just a coincidence. There is a "cosmic speed limit" for information propagation. The reasoning is this: Suppose event A is the drawing of the winning powerball lottery number and the broadcast of that information, and event B is a person receiving that information. If information traveled from A to B faster than the speed of light, under the Lorentz transformation there would be another inertial frame of reference in which B happens before A. That would make it possible to purchase a winning ticket in advance.
In Newton's time scientists were just barely becoming aware that light travels at a finite speed, and no deeper ramifications of the speed of light were known, so whether the gravitational force propagates at the speed of light was not an issue.
The issue of the "speed of gravity" can be viewed as the question of whether the Earth is attracted to where the Sun is now or where it was 8 minutes ago. That it is the same as the speed of light follows, on a theoretical basis, from relativity, but, since scientists like to leave no stone unturned, it has also been measured experimentally. It is now known that gravity, like electromagnetism, does propagate at the speed of light.
The modern case—quantum entanglement
"Spooky action at a distance" reared its confusing head again, at a much more sophisticated level, in the early 20th century, with the advent of quantum mechanics. This takes the form of quantum entanglement, in which multiple particles seem to share some quantum-mechanical state information across distances, that could in theory be considerable, and in which those particles "simultaneously" exhibit that information. This began with the formulation of the "Copenhagen interpretation" of Quantum mechanics in the 1930's. This is still the reigning paradigm, even though it leads to consequences that are difficult to grapple with. It implies the notion that reality doesn't exist until someone observes it. At the microscopic experimentally verifiable level it leads to the notion that the state of a particle exists only as a probability density, but not as reality, until someone observes it. At the extreme and fanciful level, it could be taken as the question "Does the moon exist if no one is looking at it?"
The consequences of the Copenhagen interpretation did not sit well (and still don't sit well) with the scientists of the day. This was brought into sharp focus with the "Einstein–Podolsky–Rosen paradox" (EPR paradox) of the mid 1930's. Einstein was one of the many scientists (and perhaps the most famous) who objected to "Spooky action at a distance".
In the 1960's Bell's inequality and Bell's theorem (after John Stewart Bell) put these issues on a more formal and straightforward mathematical basis.
The paradigm that people would much prefer is now called "local realism". However, experiments show that, when local realism conflicts with strict (Copenhagen) quantum mechanics, the latter is correct.
Articles about this, or articles about anything having to do with Einstein, often have eye-catching headlines, like "Einstein was wrong". This can be seen in the "biggest test yet" article, with its headline "Biggest Test Yet Shows Einstein Was Wrong About 'Spooky Action at a Distance'". Einstein disliked it, but he wasn't wrong. He was one of the co-authors of the Einstein–Podolsky–Rosen paradox, and that "paradoxical" result appears to be true. In any case, the action-at-a-distance issue came up decades after relativity.
What entanglement means
There are a number of experiments that can display entanglement. They generally involve two particles, originating in some apparatus and moving away from each other to detectors at different locations. These might be photons in measurable "spin up" and "spin down" configurations. After they have traveled to their detectors, each has its spin measured. The way they were emitted requires, by conservation of angular momentum, that the sum of the spins be zero, so one must be up and the other down.
Now the simplest explanation for this would be that they were given their spins right at the start. But that is not true. Experiments show that the spins could not have been in existence from the start. The "hidden variable" hypothesis posits that their spins were somehow latent, and, even though the spin states didn't actually exist, this hidden information would express itself when the particles were detected. The "hidden variable" hypothesis can be shown not to be correct. The photons are not thinking (to the extent that photons think) "I'm going to be spin up when I get to the detector." And yet the spins are different at the two detectors. This is entanglement. It's as if, when one particle gets to the detector, it sends a "thought message" to the other, instantaneously, "I've decided on spin up, so you'd better be spin down." This "message" has to be sent at a speed that might be greater than the speed of light.
Does that constitute supraluminal information transfer? No. This "information transfer" is not following local realism. It is not possible for someone at one detector to say "The winning lottery number is even, so I'm forcing you to be spin up and hence making the other be spin down", with someone at the other detector seeing that his photon is spin down and buying a lottery ticket accordingly. The information can travel only from the apparatus that emits the photons to the detectors, not from one detector to the other. The "cosmic speed limit" for information transfer still holds.
In quantum entanglement, it is not true that one particle affects another particle instantaneously. The affect or influence (in the sense of "cause and effect") does not go from one detector to the other. It goes from whatever created the particles in their entangled state to both detectors.
"The biggest test yet"
In May 2018 a "physics experiment" of a rather unusual kind was performed. No physical apparatus (particle accelerators, etc.) was involved. The experiment was performed by "crowdsourcing" internet users as sources of random numbers. These numbers were used in a large, purely mathematical, test of Bell's theorem, done entirely with computers. And yet it affects theoretical physics. The outcome of the test confirmed Bell's theorem. The EPR paradox, and "action at a distance", is true, and local realism is not.
Several theories have been developed as ways of denying action at a distance (non-locality). These include:
There are a number of videos on the internet that attempt to explain these concepts:
- https://www.forbes.com/sites/startswithabang/2016/04/28/why-does-gravity-move-at-the-speed-of-light/#5ee228976211 Why Does Gravity Move At The Speed Of Light?—Measurements of the binary pulsar PSR 1913+16 constrained the speed of gravity to within 0.2% of the speed of light.
- http://math.ucr.edu/home/baez/physics/Relativity/GR/grav_speed.html Does Gravity Travel at the Speed of Light?—Measurements of another binary pulsar system, PSR B1534+12, confirm this result, although so far with less precision.
- https://www.sciencealert.com/speed-of-gravitational-waves-and-light-same We've Finally Narrowed Down The Speed of Gravity And The Numbers Are Insane—Measurements of gravitational waves confirm this to about 7 decimal places.
- https://www.livescience.com/62523-physicists-crowdsource-a-reality-check.html Notwithstanding the headline "Einstein was wrong", the article does not disprove relativity. It says that local realism, a view advocated by Einstein and many others, is wrong.
- https://web.archive.org/web/20150117231730/http://curious.astro.cornell.edu/question.php?number=612 Does quantum entanglement imply faster than light communication?