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A paradox arises when our accepted scientific principles and mathematical logic seem self-contradictory.
Zeno’s paradox is a prime example. Zeno imagined Achilles racing a tortoise that I’ll call Yertle. Since Achilles is much faster, Yertle is given a generous head start. Zeno said Achilles would never pass Yertle, because by the time Achilles reaches Yertle’s starting point, Yertle has crawled forward some distance. By the time Achilles covers that distance, Yertle has crawled forward yet again. Zeno argued this would continue ad infinitum, and Achilles would never pass Yertle. But we all know the faster Achilles must eventually pass the slower Yertle.
There are no true paradoxes in science, only apparent ones. Nature is never conflicted; “paradoxes” always arise from failures of human logic. Can you resolve Zeno’s paradox? Check your answer with mine in Part 2 of this newsletter.
Quantum mechanics (QM) has spawned many amusing paradoxes, including Schrödinger’s Cat and its recent reincarnation that replaces the hapless feline with two physicists in separate boxes.
While the predictions of QM are all experimentally confirmed, considerable angst remains regarding exactly how these occur.
Carlo Rovelli, an Italian theoretical physicist, has an intriguing solution to all these paradoxes.
Let’s explore the most important QM paradox: the EPR Paradox, named for its authors: Albert Einstein and his students Podolsky and Rosen.
Einstein is famous for his penetrating thought experiments — imaginary situations that focus on key principles, avoid messy practical details, and reveal nature’s deepest secrets. Thought experiments were the only experiments Einstein ever did. He thereby avoided the hazards of real experiments, such as high-voltage shocks, liquid nitrogen burns, and exposure to ionizing radiation — all the things that made me the man I am today.
In his 1935 EPR paper, Einstein describes a thought experiment that he said proves QM is an incomplete theory of nature, because it fails to explain how the bizarre behaviors it predicts actually happen. Einstein and some others believed nature follows definitive laws with none of the uncertainties of QM. He felt there were hidden variables — key properties of particles as yet unobserved — that decisively control the outcomes that QM says are unpredictable.
Let’s consider an incisive example: the decay of a positronium “atom” comprised of one electron and one positron (the electron’s anti-particle). A stationary positronium atom has zero linear and angular momenta. When it decays to two photons, conservation of momentum requires the photons to have exactly opposite linear and angular momenta. In this case, the only angular momenta are the photons’ intrinsic spin, a uniquely quantum property whose only values along any measurement axis are UP and DOWN.
Now, imagine a source that produces one stationary positronium atom each second that promptly decays to two photons. Let Alice be 15m to the left of the source, and let Bob be 15m to the right, as shown below. Both physicists measure the spins of photons coming their way.
QM says two photons from positronium decay exist in one entangled quantum state. When their spins are measured, each photon is 50% likely to be UP and 50% likely to be DOWN. But, to conserve angular momentum, entanglement ensures the two photons always have opposite spins — either the blue or red combinations above.
Before a measurement, QM says it is impossible to predict which photon of any pair will be UP. Niels Bohr said: “nothing exists until it is measured.”
Classical physics says all particle properties, including spin, are real, meaning they always have definite values whether the particles are isolated or are interacting with other particles (as occurs when we measure their properties).
The EPR paradox starkly contrasts quantum and classical physics by posing two existential conundrums:
A) Are the photons spins real — do they have definite values — before they are measured? This is the subject of Part 2 of this newsletter.
B) If the spins do not have definite values before being measured (as QM claims), how can the two separated photons “know” which will be UP and which will be DOWN? We will address this now.
In the decay reference frame, Alice and Bob are 30m apart, and their measurements occur at the same time. Neither photon can “know” the other’s spin until at least 100 nanoseconds (30m divided by c, the speed of light) after its own spin is measured. So, how can the photons always have opposite spins? (For experts on relativity, the two events are space-like separated in all reference frames, so they cannot have a cause-and-effect relationship.)
Einstein called this “spooky” action-at-a-distance.
This experiment has actually been performed several times, with separations as large as 147 km. The results are always Alice and Bob both measure 50% UP and 50% DOWN, but for each entangled pair, Alice and Bob always measure opposite spins.
Proponents of QM claim these experiments prove nature violates locality, allowing separated objects to interact instantaneously. This violates special relativity, which says no thing can move through space faster than c, as is confirmed by thousands of other experiments.
Rovelli has a clever solution. He says all these paradoxes disappear, if we accept that everything is a quantum system, including us.
When Alice measures an entangled photon, Rovelli says she and the photon become a new entangled quantum state, in which it is 50% likely that Alice measured UP and 50% likely that Alice measured DOWN. At the instant of her measurement, no one anywhere else in the universe can know what she observed. Similarly, Bob and his photon become another entangled state.
Rovelli says the observations themselves must be observed before they become real.
The new entangled states spread out through space, but not faster than the speed of light. In time, Alice’s entangled state and Bob’s entangled state arrive at a common point, where the states interact and collapse. As stipulated by QM, the collapse yields a single, definite, allowed value of the spin measurements. In this case, angular momentum conservation allows only two outcomes: Alice-UP;Bob-DOWN or Alice-DOWN;Bob-UP. Both outcomes are equally probable, and the spins are always opposite.
In Rovelli’s solution, everything works out perfectly without faster-than-light communications.
Rovelli says everything is a quantum system, and relationships are the only reality — all we can hope to know are the relationships between quantum systems.
For your amusement, I add a personal story. In the last few years of my father’s life, he became obsessed with the EPR paradox — a more benign obsession than many others. He and I spent countless, but fruitless, hours debating the EPR. After he died, I read Rovelli’s excellent but challenging book Quantum Gravity. I was riveted by a footnote on page 217, where Rovelli says his Relational Interpretation of QM resolves the apparent EPR paradox.
That footnote was too brief for me to digest, so I emailed Rovelli requesting a more thorough explanation. Scientists with public profiles often receive myriad contacts from a certain fringe of the general public. To avoid getting promptly “filed”, my email began by mentioning my famous father and his keen interest in the EPR.
Carlo sent me a very kind and detailed explanation of his EPR ideas, and added that he certainly knew of the great Italian physicist Oreste Piccioni — “we all study his work”. I thanked him for his generous reply, praised his wonderful solution to the EPR paradox, and suggested he publish his solution.
Nine months later, I received a copy of Carlo’s EPR paper that ended with a dedication to the memory of Oreste Piccioni. I was deeply touched.
For more about quantum mechanics and the EPR paradox see my books Feynman Simplified Part 3 (paperback) or Feynman Simplified 3C (ebook).
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