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Posts Tagged ‘Einstein

“A nothing will serve just as well as a something about which nothing could be said”*…

Metaphysical debates in quantum physics don’t get at “truth,” physicist and mathematician Timothy Andersen argues; they’re nothing but a form of ritual activity and culture. After a thoughtful intellectual history of both quantum mechanics and Wittgenstein’s thought, he concludes…

If Wittgenstein were alive today, he might have couched his arguments in the vocabulary of cultural anthropology. For this shared grammar and these language games, in his view, form part of much larger ritualistic mechanisms that connect human activity with human knowledge, as deeply as DNA connects to human biology. It is also a perfect example of how evolution works by using pre-existing mechanisms to generate new behaviors.

The conclusion from all of this is that interpretation and representation in language and mathematics are little different than the supernatural explanations of ancient religions. Trying to resolve the debate between Bohr and Einstein is like trying to answer the Zen kōan about whether the tree falling in the forest makes a sound if no one can hear it. One cannot say definitely yes or no, because all human language must connect to human activity. And all human language and activity are ritual, signifying meaning by their interconnectedness. To ask what the wavefunction means without specifying an activity – and experiment – to extract that meaning is, therefore, as sensible as asking about the sound of the falling tree. It is nonsense.

As a scientist and mathematician, Wittgenstein has challenged my own tendency to seek out interpretations of phenomena that have no scientific value – and to see such explanations as nothing more than narratives. He taught that all that philosophy can do is remind us of what is evidently true. It’s evidently true that the wavefunction has a multiverse interpretation, but one must assume the multiverse first, since it cannot be measured. So the interpretation is a tautology, not a discovery.

I have humbled myself to the fact that we can’t justify clinging to one interpretation of reality over another. In place of my early enthusiastic Platonism, I have come to think of the world not as one filled with sharply defined truths, but rather as a place containing myriad possibilities – each of which, like the possibilities within the wavefunction itself, can be simultaneously true. Likewise, mathematics and its surrounding language don’t represent reality so much as serve as a trusty tool for helping people to navigate the world. They are of human origin and for human purposes.

To shut up and calculate, then, recognizes that there are limits to our pathways for understanding. Our only option as scientists is to look, predict and test. This might not be as glamorous an offering as the interpretations we can construct in our minds, but it is the royal road to real knowledge…

A provocative proposition: “Quantum Wittgenstein,” from @timcopia in @aeonmag.

* Ludwig Wittgenstein, Philosophical Investigations

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As we muse on meaning, we might recall that it was on this date in 1954 that the official ground-breaking for CERN (Conseil européen pour la recherche nucléaire) was held. Located in Switzerland, it is the largest particle physics laboratory in the world… that’s to say, a prime spot to do the observation and calculation that Andersen suggests. Indeed, it’s been the site of many breakthrough discoveries over the years, maybe most notably the 2012 observation of the Higgs Boson.

Because researchers need remote access to these facilities, the lab has historically been a major wide area network hub. Indeed, it was at CERN that Tim Berners-Lee developed the first “browser”– and effectively fomented the emergence of the web.

CERN’s main site, from Switzerland looking towards France

“Men knew better than they realized, when they placed the abode of the gods beyond the reach of gravity”*…

In search of a theory of everything…

Twenty-five particles and four forces. That description — the Standard Model of particle physics — constitutes physicists’ best current explanation for everything. It’s neat and it’s simple, but no one is entirely happy with it. What irritates physicists most is that one of the forces — gravity — sticks out like a sore thumb on a four-fingered hand. Gravity is different.

Unlike the electromagnetic force and the strong and weak nuclear forces, gravity is not a quantum theory. This isn’t only aesthetically unpleasing, it’s also a mathematical headache. We know that particles have both quantum properties and gravitational fields, so the gravitational field should have quantum properties like the particles that cause it. But a theory of quantum gravity has been hard to come by.

In the 1960s, Richard Feynman and Bryce DeWitt set out to quantize gravity using the same techniques that had successfully transformed electromagnetism into the quantum theory called quantum electrodynamics. Unfortunately, when applied to gravity, the known techniques resulted in a theory that, when extrapolated to high energies, was plagued by an infinite number of infinities. This quantization of gravity was thought incurably sick, an approximation useful only when gravity is weak.

Since then, physicists have made several other attempts at quantizing gravity in the hope of finding a theory that would also work when gravity is strong. String theory, loop quantum gravity, causal dynamical triangulation and a few others have been aimed toward that goal. So far, none of these theories has experimental evidence speaking for it. Each has mathematical pros and cons, and no convergence seems in sight. But while these approaches were competing for attention, an old rival has caught up.

The theory called asymptotically (as-em-TOT-ick-lee) safe gravity was proposed in 1978 by Steven Weinberg. Weinberg, who would only a year later share the Nobel Prize with Sheldon Lee Glashow and Abdus Salam for unifying the electromagnetic and weak nuclear force, realized that the troubles with the naive quantization of gravity are not a death knell for the theory. Even though it looks like the theory breaks down when extrapolated to high energies, this breakdown might never come to pass. But to be able to tell just what happens, researchers had to wait for new mathematical methods that have only recently become available…

For decades, physicists have struggled to create a quantum theory of gravity. Now an approach that dates to the 1970s is attracting newfound attention: “Why an Old Theory of Everything Is Gaining New Life,” from @QuantaMagazine.

* Arthur C. Clarke, 2010: Odyssey Two

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As we unify, we might pause to remember Sir Arthur Stanley Eddington, OM, FRS; he died in this date in 1944.  An astrophysicist, mathematician, and philosopher of science known for his work on the motion, distribution, evolution and structure of stars, Eddington is probably best remembered for his relationship to Einstein:  he was, via a series of widely-published articles, the primary “explainer” of Einstein’s Theory of General Relativity to the English-speaking world; and he was, in 1919, the leader of the experimental team that used observations of a solar eclipse to confirm the theory.

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“It can be argued that in trying to see behind the formal predictions of quantum theory we are just making trouble for ourselves”*…

Context, it seems, is everthing…

… What is reality? Nope. There’s no way we are going through that philosophical minefield. Let’s focus instead on scientific realism, the idea that a world of things exists independent of the minds that might perceive it and it is the world slowly revealed by progress in science. Scientific realism is the belief that the true nature of reality is the subject of scientific investigation and while we may not completely understand it at any given moment, each experiment gets us a little bit closer. This is a popular philosophical position among scientists and science enthusiasts.

A typical scientific realist might believe, for example, that fundamental particles exist even though we cannot perceive them directly with our senses. Particles are real and their properties — whatever they may be — form part of the state of the world. A slightly more extreme view is that this state of the world can be specified with mathematical quantities and these, in turn, obey equations we call physical laws. In this view, the ultimate goal of science is to discover these laws. So what are the consequences of quantum physics on these views?

As I mentioned above, quantum physics is not a realistic model of the world — that is, it does not specify quantities for states of the world. An obvious question is then can we supplement or otherwise replace quantum physics with a deeper set of laws about real states of the world? This is the question Einstein first asked with colleagues Podolski and Rosen, making headlines in 1935. The hypothetical real states of the world came to be called hidden variables since an experiment does not reveal them — at least not yet.

In the decades that followed quantum physics rapidly turned into applied science and the textbooks which became canon demonstrated only how to use the recipes of quantum physics. In textbooks that are still used today, no mention is made of the progress in the foundational aspects of quantum physics since the mathematics was cemented almost one hundred years ago. But, in the 1960s, the most important and fundamental aspect of quantum physics was discovered and it put serious restrictions on scientific realism. Some go as far as to say the entire nature of independent reality is questionable due to it. What was discovered is now called contextuality, and its inevitability is referred to as the Bell-Kochen-Specker theorem.

John Bell is the most famous of the trio Bell, Kochen, and Specker, and is credited with proving that quantum physics contained so-called nonlocal correlations, a consequence of quantum entanglement. Feel free to read about those over here.

It was Bell’s ideas and notions that stuck and eventually led to popular quantum phenomena such as teleportation. Nonlocality itself is wildly popular these days in science magazines with reported testing of the concept in delicately engineered experiments that span continents and sometimes involve research satellites. But nonlocality is just one type of contextuality, which is the real game in town.

In the most succinct sentence possible, contextuality is the name for the fact that any real states of the world giving rise to the rules of quantum physics must depend on contexts that no experiment can distinguish. That’s a lot to unpack. Remember that there are lots of ways to prepare the same experiment — and by the same experiment, I mean many different experiments with completely indistinguishable results. Doing the exact same thing as yesterday in the lab, but having had a different breakfast, will give the same experimental results. But there are things in the lab and very close to the system under investigation that don’t seem to affect the results either. An example might be mixing laser light in two different ways.

There are different types of laser light that, once mixed together, are completely indistinguishable from one another no matter what experiments are performed on the mixtures. You could spend a trillion dollars on scientific equipment and never be able to tell the two mixtures apart. Moreover, knowing only the resultant mixture — and not the way it was mixed — is sufficient to accurately predict the outcomes of any experiment performed with the light. So, in quantum physics, the mathematical theory has a variable that refers to the mixture and not the way the mixture was made — it’s Occam’s razor in practice.

Now let’s try to invent a deeper theory of reality underpinning quantum physics. Surely, if we are going to respect Occam’s razor, the states in our model should only depend on contexts with observable consequences, right? If there is no possible experiment that can distinguish how the laser light is mixed, then the underlying state of reality should only depend on the mixture and not the context in which it was made, which, remember, might include my breakfast choices. Alas, this is just not possible in quantum physics — it’s a mathematical impossibility in the theory and has been confirmed by many experiments.

So, does this mean the universe cares about what I have for breakfast? Not necessarily. But, to believe the universe doesn’t care what I had for breakfast means you must also give up reality. You may be inclined to believe that when you observe something in the world, you are passively looking at it just the way it would have been had you not been there. But quantum contextuality rules this out. There is no way to define a reality that is independent of the way we choose to look at it…

Why is no one taught the one concept in quantum physics which denies reality?” It’s called contextuality and it is the essence of quantum physics. From Chris Ferrie (@csferrie).

* “It can be argued that in trying to see behind the formal predictions of quantum theory we are just making trouble for ourselves. Was not precisely this the lesson that had to be learned before quantum mechanics could be constructed, that it is futile to try to see behind the observed phenomena?” – John Stewart Bell

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As still we try, we might relatively hearty birthday greetings to Sir Marcus Laurence Elwin “Mark” Oliphant; he was born on this date in 1901. An Australian physicist who trained and did much of his work in England (where he studied under Sir Ernest Rutherford at the University of Cambridge’s Cavendish Laboratory), Oliphant was deeply involved in the Allied war effort during World War II. He helped develop microwave radar, and– by helping to start the Manhattan Project and then working with his friend Ernest Lawrence at the Radiation Laboratory in Berkeley, California, helped develop the atomic bomb.

After the war, Oliphant returned to Australia as the first director of the Research School of Physical Sciences and Engineering at the new Australian National University (ANU); on his retirement, he became Governor of South Australia and helped found the Australian Democrats political party.

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“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.”*…

No scripture is as old as mathematics is. All the other sciences are younger, most by thousands of years. More than history, mathematics is the record that humanity is keeping of itself. History can be revised or manipulated or erased or lost. Mathematics is permanent. A² + B² = C² was true before Pythagoras had his name attached to it, and will be true when the sun goes out and no one is left to think of it. It is true for any alien life that might think of it, and true whether they think of it or not. It cannot be changed. So long as there is a world with a horizontal and a vertical axis, a sky and a horizon, it is inviolable and as true as anything that can be thought.

As precise as mathematics is, it is also the most explicit language we have for the description of mysteries. Being the language of physics, it describes actual mysteries—things we can’t see clearly in the natural world but suspect are true and later confirm—and imaginary mysteries, things that exist only in the minds of mathematicians. A question is where these abstract mysteries exist, what their home range is. Some people would say that they reside in the human mind, that only the human mind has the capacity to conceive of what are called mathematical objects, meaning numbers and equations and formulas and so on—the whole glossary and apparatus of mathematics—and to bring these into being, and that such things arrive as they do because of the way our minds are structured. We are led to examine the world in a way that agrees with the tools that we have for examining it. (We see colors as we do, for example, because of how our brains are structured to receive the reflection of light from surfaces.) This is a minority view, held mainly by neuroscientists and a certain number of mathematicians disinclined toward speculation. The more widely held view is that no one knows where math resides. There is no mathematician/naturalist who can point somewhere and say, “That is where math comes from” or “Mathematics lives over there,” say, while maybe gesturing toward magnetic north and the Arctic, which I think would suit such a contrary and coldly specifying discipline.

The belief that mathematics exists somewhere else than within us, that it is discovered more than created, is called Platonism, after Plato’s belief in a non-spatiotemporal realm that is the region of the perfect forms of which the objects on earth are imperfect reproductions. By definition, the non-spatiotemporal realm is outside time and space. It is not the creation of any deity; it simply is. To say that it is eternal or that it has always existed is to make a temporal remark, which does not apply. It is the timeless nowhere that never has and never will exist anywhere but that nevertheless is. The physical world is temporal and declines; the non-spatiotemporal one is ideal and doesn’t.

A third point of view, historically and presently, for a small but not inconsequential number of mathematicians, is that the home of mathematics is in the mind of a higher being and that mathematicians are somehow engaged with Their thoughts. Georg Cantor, the creator of set theory—which in my childhood was taught as a part of the “new math”—said, “The highest perfection of God lies in the ability to create an infinite set, and its immense goodness leads Him to create it.” And the wildly inventive and self-taught mathematician Srinivasa Ramanujan, about whom the movie “The Man Who Knew Infinity” was made, in 2015, said, “An equation for me has no meaning unless it expresses a thought of God.”

In Book 7 of the Republic, Plato has Socrates say that mathematicians are people who dream that they are awake. I partly understand this, and I partly don’t.

Mathematics has been variously described as an ideal reality, a formal game, and the poetry of logical ideas… an excerpt from “What is Mathematics?” from Alec Wilkinson— eminently worthy of reading in full.

* Albert Einstein

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As we sum it up, we might send carefull-calcuated birthday greetings to Georgiy Antonovich Gamov; he was born on this date in 1904. Better known by the name he adopted on immigrating to the U.S., George Gamow, he was a physicist and cosmologist whose early work was instrumental in developing the Big Bang theory of the universe; he also developed the first mathematical model of the atomic nucleus.

But mid-career Gamow began to shift his energy to teaching and to writing popular books on science… one of which, One Two Three… Infinity, inspired legions of young scientists-to-be and kindled a life-long interest in science in an even larger number of other youngsters (like your correspondent).

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“A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it”*…

A curious thing happened at the end of the 19th century and the dawning of the 20th. As European and American industries became increasingly confident in their methods of invention and production, scientists made discovery after discovery that shook their understanding of the physical world to the core. “Researchers in the 19th century had thought they would soon describe all known physical processes using the equations of Isaac Newton and James Clerk Maxwell,” Adam Mann writes at Wired. But “the new and unexpected observations were destroying this rosy outlook.

These observations included X-rays, the photoelectric effect, nuclear radiation and electrons; “leading physicists, such as Max Planck and Walter Nernst believed circumstances were dire enough to warrant an international symposium that could attempt to resolve the situation.” Those scientists could not have known that over a century later, we would still be staring at what physicist Dominic Walliman calls the “Chasm of Ignorance” at the edge of quantum theory. But they did initiate “the quantum revolution” in the first Solvay Council, in Brussels, named for wealthy chemist and organizer Ernest Solvay.

“Reverberations from this meeting are still felt to this day… though physics may still sometimes seem to be in crisis” writes Mann (in a 2011 article just months before the discovery of the Higgs boson). The inaugural meeting kicked off a series of conferences on physics and chemistry that have continued into the 21st century. Included in the proceedings were Planck, “often called the father of quantum mechanics,” Ernest Rutherford, who discovered the proton, and Heike Kamerlingh-Onnes, who discovered superconductivity.

Also present were mathematician Henri Poincaré, chemist Marie Curie, and a 32-year-old Albert Einstein, the second youngest member of the group. Einstein described the first Solvay conference (1911) in a letter to a friend as “the lamentations on the ruins of Jerusalem. Nothing positive came out of it.” The ruined “temple,” in this case, were the theories of classical physics, “which had dominated scientific thinking in the previous century.” Einstein understood the dismay, but found his colleagues to be irrationally stubborn and conservative…

For more– and a complete list of attendees in the photo above: ““The Most Intelligent Photo Ever Taken”: The 1927 Solvay Council Conference, Featuring Einstein, Bohr, Curie, Heisenberg, Schrödinger & More.”

* Max Planck (second from the left in the first row of the photo above)

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As we ponder paradigms, we might send insightful birthday greetings to Edward Williams Morley; he was born on this date in 1838. A chemist who was first to precisely determine the atomic weight of oxygen, he is probably best remembered for his collaboration with the physicist Albert A. Michelson. In what we call the Michelson–Morley experiment (actually a number of experiments conducted between April and July in 1887), they attempted to detect the luminiferous aether, a supposed medium permeating space that was thought to be the carrier of light waves; their method was the very precise measurement of the speed of light (in various directions, and at different times of the year, as the Earth revolved in its orbit around the Sun). Michelson and Morley always found that the speed of light did not vary at all depending on the direction of measurement, or the position of the Earth in its orbit– the so-called “null result.”

Neither Morley nor Michelson ever considered that these null results disproved the hypothesis of the existence of “luminiferous aether.” But other scientists began to suspect that they did. Almost two decades later the results of the Michelson–Morley experiments supported Albert Einstein’s strong postulate (in 1905) that the speed of light is a constant in all inertial frames of reference as part of his Special Theory of Relativity.

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