ONE & THE SAME, ACROSS THE UNIVERSE.
Abstract: Why Quantum Physics violates locality. Twentieth-second century primary school version.
LOCALITY: What does locality mean? It means that what happens at a point is determined by what is happening in a neighborhood of that point within a small enough distance, as determined by light. Moreover, it means that the universe U is made of points: U = Union points. Points, by definition, are singletons (they have no elements in the sense of set theory), and they have dimension zero: nothing belongs to a point.
SPACETIME: Generally the universe is called “spacetime”. However, this concept, spacetime, introduces the assumptions of Einstein’s Special Relativity, as boosted by Minkowski, established before Quantum Physics.
In particular the spacetime hypothesis assumes that the universe is a product of what is called in mathematics the “real line”, which assumes, among other things, what is called a T2, Hausdorff topology. Two different points are separated by different neighborhoods (to use the appropriate concepts from general topology).
Quantum Physics violates both LOCALITY and SPACETIME.
How do we know this? When one analyzes the smallest processes, one finds that, in plenty of cases, the SMALLEST PROCESSES, THE INDIVISIBLE PROCESSES, SPREAD IN TIME OVER ARBITRARY BIG REGIONS, ON THEIR OWN (THAT IS WITHOUT ANY INTERACTION WITH THE REST OF THE UNIVERSE). Are they then big, or are they small? Verily, therein a mystery of the Quantum.
In this innocuous concept I just uttered, they spread as big as they want, although being as small as there is, one finds the entire origin of Quantum non locality. No need for fancy mathematics, or even any equation. The idea is as dramatic as can be.
Indeed, non locality boils down to a matter of definition. As the indivisible process spreads out, it stays one, well, by definition. It means that touching it anywhere is like touching it everywhere.
When two particles comes out of such an indivisible process, they are called “ENTANGLED”. The semantics gets in the way. What we do not have is actually two particles, but two possible experimental channels, which can be widely separated, where, if we experiment, two particles will show up, and widely separated, if the channels are so.
Thus we see that the two channels are entangled, and touching one is also touching the other.
What are some of these cases where the smallest, indivisible processes spread out macroscopically? Well, they are so common, that they seem to be the rule, not the exception:
Diffraction (the 1 slit experiment) is such a case: the slit is small, diffusion gets big. Arbitrarily big.
The famous 2 slit experiment is another case: the slits are close by, the interference screen is at a large distance. Hey, the 2-slit could be a galactic cluster. A cluster made of galaxies, each 200,000 light years across.
Any fundamental process where two particles separate after interacting. (In particular the simple set-up of the Einstein Podolski Rosen thought experiment, such as the Bohm total spin zero variant.)
It is highly likely that such an effect is used all over biology, to transport energy close to 100% efficiency over macroscopic distances (an allusion to the fact that this is not only about pure science, but the economic fall-out will be considerable, once this is so well understood that we can dominate the processes involved).
Not all Quantum processes spread all over space. Bohr got the Nobel for his patchy, haphazard atomic theory which worked, because electronic matter waves self interfere coherently onto themselves (these matters waves, the de Broglie waves, are called orbitals, and they make the body of atoms, what we call matter, and sharing orbitals is much of what we call chemistry).
Thus we have found the following, from the most basic set-up of Quantum theory:
A Fundamental Quantum Process, is one, until interacted with, even if it is spread over space. This is what Quantum Non Locality is all about.
Some crystals can make out of one photon, two photons with opposite polarizations, and they could then be sent in two different channels, a light year apart.
Parallel transporting along the two channels the polarization directions, we would always find them opposite. A more subtle relation between the polarizations holds, and was found to be true even when the polarization angles are moved randomly during the photons flight time (Aspect experiment, for which Alain Aspect got the Wolf Prize in 2010).
By making all sorts of supplementary hypotheses about local hidden parameters and local measurements of polarizations, though, on finds that should not be the case. This contradiction is called the Bell Inequality (I like Bell very much, and I approve of his quest, which is also my quest. I apologize for his many admirers, by presenting his efforts in an arguably demeaning light).
The preceding, most simple way to look at Non Locality, gives an excellent reason to not do that: the logic of the Quantum is as simple as it gets: as long as I am left alone, says the Quantum, I am one. And indivisible.
What does it all mean? First Einstein and company in their “EPR” paper, talked about “elements of reality”. They did NOT talk about ELEMENTS OF SPACE. They did not have the notion. I will argue they should have, but of course, the fact that they did not have it was central to their (erroneous) reasoning.
Einstein and company wondered how a particle could communicate with another, even across light years. Wrong amazement. Particles are not “communicating“. Actually, they are not “particles” to start with.
For decades I have advocated a radical solution, as exposed above, aligning the definition elementarily: the two particles are one and the same, they are in the same place at the time of the Quantum interaction, and stop being so, as a result. The topology used in physics, the same that the dinosaurs used, the T2, separated topology, is not appropriate to the real universe. OK, it was appropriate for pterosaurs. But it’s not appropriate, across the universe. BTW, the pterosaurs, the best fliers, by far, that this planet has known, went extinct, although they were obviously very smart.
Is this the end all, be all? Quantum Physics a la Bohr reigns, and nothing else can be said? No. If the bare bone theory above is true, the entire theory of spacetime is false: space is not made of points, and it is constructed interactively. The case of time is even more so. Imagine there are no heavens made of points, only the sky you make, etc. Thus more has been said.
Note 1: An enlightening analogy: The question of using the Quantum set-up to transmit information superluminally, or what Einstein called “Spooky Interaction At A Distance” has come up. The preceding, as it is, sticking to strict Quantum theory, demolishes both views, with crushing simplicity.
How? OK, let’s make an experimental metaphor. Suppose we have an infinitely rigid bar between the two entangled particles: each time we experiment with one, we turn the bar, and so it turns at the other end too. Simple. Some will say: ha ha ha, but then I can look at the bar, and I see the bar turn, and so information has been transmitted. Not so fast. We are dealing with as elementary a Quantum process as possible, which means the particle was not observed, before the bar turned. So we see the bar turn, but we do not know if it was, or not, turning before. To tell if a signal was sent, one has first to define a state where one can say no signal was received.
Note 2: I was a rough to the point of inaccuracy with the Bell Inequality above. There is a subtlety, which can be seen easily say in the case of spin. Spin measurements in various directions are not independent of each other. Thus, if one measures spin in the close channel, a measurement of spin in another, random direction in the distance channel will show that influence, and a local determination of spin in the distant channel by parallel transport will not exhibit this. BTW, introducing the notion of parallel transport in the conversation, which is the whole point of the “local hidden parameter” debate is from yours truly.
Note 3: And let’s not forget to smile about the naïve who developed frantically supersymmetric superstrings super budgeted super having-nothing-to-do-with reality… While forgetting to think about the fundamentals as described above.