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Archive for November 2nd, 2019

What’s everything made of?

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This overlaps a bit with the previous post. Charles Sebens, assistant professor of philosophy at the California Institute of Technology, is interested in the foundations of quantum mechanics, classical field theory, and quantum field theory. He writes in Aeon:

Long before philosophy and physics split into separate career paths, the natural philosophers of Ancient Greece speculated about the basic components from which all else is made. Plato entertained a theory on which everything on Earth is made from four fundamental particles. There are stable cube-shaped particles of earth, pointy and painful tetrahedron-shaped particles of fire, somewhat less pointy octahedron-shaped particles of air, and reasonably round icosahedron-shaped particles of water. Like the particles of contemporary physics, Plato thought it was possible for these particles to be created and destroyed. For example, an eight-sided air particle could be created by combining two four-sided fire particles (as one might imagine occurring when a campfire dies out).

Our understanding of nature has come a long way since Plato. We have learned that much of our world is made of the various atoms compiled in the periodic table of elements. We have also learned that atoms themselves are built from more fundamental pieces.

Today, philosophers who are interested in figuring out what everything is made of look to contemporary physics for answers. But, finding answers in physics is not simply a matter of reading textbooks. Physicists deftly shift between different pictures of reality as it suits the task at hand. The textbooks are written to teach you how to use the mathematical tools of physics most effectively, not to tell you what things the equations are describing. It takes hard work to distil a story about what’s really happening in nature from the mathematics. This kind of research is considered ‘philosophy of physics’ when done by philosophers and ‘foundations of physics’ when done by physicists.

Physicists have developed an improvement on the periodic table called ‘the standard model’. The standard model is missing something very important (gravity) and it might turn out that the pieces it describes are made of yet more fundamental things (such as vibrating strings). That being said, the standard model is not going anywhere. Like Isaac Newton’s theory of gravity or James Clerk Maxwell’s theory of electrodynamics, we expect that the standard model will remain an important part of physics no matter what happens next.

Unfortunately, it’s not immediately clear what replaces the atoms of the periodic table in the standard model. Are the fundamental building blocks of reality quantum particles, quantum fields, or some combination of the two? Before tackling this difficult question, let us consider the debate between particles and fields in the context of a classical (non-quantum) theory: Maxwell’s theory of electrodynamics.

Albert Einstein was led to his 1905 special theory of relativity by engaging in foundational research on electrodynamics. After developing special relativity, Einstein entered into a debate with Walther Ritz about the right way to formulate and understand classical electrodynamics. According to this theory, two electrons placed near one another will fly apart in opposite directions. They both have negative charge, and they will thus repel one another.

Ritz thought of this as an interaction directly between the two electrons – each one pushing the other, even though they are not touching. This interaction acts across the gap in space separating the two electrons. It also acts across a gap in time. Being precise, each electron responds to the other’s past behaviour (not its current state).

Einstein, who was averse to such action-at-a-distance, understood this interaction differently. For him, there are more players on the scene than just the particles. There are also fields. Each electron produces an electromagnetic field that extends throughout space. The electrons move away from one another not because they are directly interacting with each other across a gap, but because each one is feeling a force from the other’s field.

Do electrons feel forces from their own electromagnetic fields? Either answer leads to trouble. First, suppose the answer is yes. The electromagnetic field of an electron gets stronger as you get closer to the electron. If you think of the electron as a little ball, each piece of that ball would feel an enormous outward force from the very strong electromagnetic field at its location. It should explode. Henri Poincaré conjectured that there might be some other forces resisting this self-repulsion and holding the electron together – now called ‘Poincaré stresses’. If you think of the electron as point-size, the problem is worse. The field and the force would be infinite at the electron’s location.

So, let us instead suppose that the electron does not feel the field it produces. The problem here is that there is evidence that the electron is aware of its field. Charged particles such as electrons produce electromagnetic waves when they are accelerated. That takes energy. Indeed, we can observe electrons lose energy as they produce these waves. If electrons interact with their own fields, we can correctly calculate the rate at which they lose energy by examining the way these waves interact with the electron as they pass through it. But, if electrons don’t interact with their own fields, then it’s not clear why they would lose any energy at all.

In Ritz’s all-particles no-fields proposal, the electron will not interact with its own field because there is no such field for it to interact with. Each electron feels forces only from other particles. But, if the electron does not interact with itself, how can we explain the energy loss? Whether you believe, like Einstein, that there are both particles and fields, or you believe, like Ritz, that there are only particles, you face a problem of self-interaction.

Ritz and Einstein staked out two sides of a three-sided debate. There is a third option: perhaps there are no particles, just fields. In 1844, Michael Faraday explored this option in an unpublished manuscript and a short published ‘speculation’. One could imagine describing the physics of hard, solid bodies of various shapes and sizes colliding and bouncing off one another. However, when two charged particles (such as electrons) interact by electric attraction or repulsion, they do not actually touch one another. Each just reacts to the other’s electromagnetic field. The sizes and shapes of the particles are thus irrelevant to the interaction, except in so much as they change the fields surrounding the particles. So, Faraday asked: ‘What real reason, then, is there for supposing that there is any such nucleus in a particle of matter?’ That is, why should we think that there is a hard core at the centre of a particle’s electromagnetic field? In modern terms, Faraday has been interpreted as proposing that we eliminate the particles and keep only the electromagnetic fields.

On 8 August, at the 2019 International Congress on Logic, Methodology and Philosophy of Science and Technology in Prague, I joined four other philosophers of physics for a debate – tersely titled ‘Particles, Fields, or Both?’ Mathias Frisch of the Leibniz University Hannover opened our session with a presentation of the debate between Einstein and Ritz (see his Aeon essay, ‘Why Things Happen’). Then, the remaining three speakers defended opposing views – updated versions of the positions held by Einstein, Ritz, and Faraday.

Our second speaker, Mario Hubert of Caltech, sought to rescue Einstein’s picture of point-size particles and fields from the problem of self-interaction. He discussed the current status of multiple ideas about how this might be done. One such idea came from Paul Dirac, a mathematical wizard who made tremendous contributions to early quantum physics. Dirac’s name appears in the part of the standard model that describes electrons.

In a 1938 paper, Dirac took a step back from quantum physics to study the problem of self-interaction in classical electrodynamics. He proposed a modification to the laws of electrodynamics, changing the way that fields exert forces on particles. For a point-size particle, his new equation eliminates any interaction of the particle with its own electromagnetic field, and includes a new term to mimic the kind of self-interaction that we actually observe – the kind that causes a particle to lose energy when it makes waves. However, the equation that Dirac proposed has some strange features. One oddity is ‘pre-acceleration’: a particle that you’re going to hit with a force might start moving before you hit it.

In the 1930s and ’40s, a different strategy was pursued by four notable physicists: Max Born (known for ‘the Born rule’ that tells you how to calculate probabilities in quantum physics), Leopold Infeld (who coauthored a popular book on modern physics with Einstein: The Evolution of Physics), Fritz Bopp (who was part of the German nuclear research programme during the Second World War and, after the war, cosigned a manifesto opposing nuclear weapons and advocating nuclear energy in West Germany), and Boris Podolsky (a coauthor of the paper that spurred Erwin Schrödinger to coin the term ‘entanglement’ and introduce his enigmatic cat). These physicists proposed ways of changing the laws that specify how particles produce electromagnetic fields so that the fields produced by point particles never become infinitely strong.

When you change these laws, you change a lot. As Hubert explained in his presentation, we don’t fully understand the consequences of these changes. In particular, it is not yet clear whether the Born-Infeld and Bopp-Podolsky proposals will be able to solve the self-interaction problem and make accurate predictions about the motions of particles.

You might feel that all of this talk of classical physics has gotten us very far off topic. Aren’t we supposed to be trying to understand what the standard model of quantum physics tells us about what everything is made of?

The part of the standard model that describes electrons and the electromagnetic field is called ‘quantum electrodynamics’, as it is the quantum version of classical electrodynamics. The foundations of the two subjects are closely linked. Here’s how Richard Feynman motivates a discussion of the modifications to classical electrodynamics made by Dirac, Born, Infeld, Bopp, and Podolsky in a chapter of his legendary lectures at Caltech:

There are difficulties associated with the ideas of Maxwell’s theory which are not solved by and not directly associated with quantum mechanics. You may say, ‘Perhaps there’s no use worrying about these difficulties. Since the quantum mechanics is going to change the laws of electrodynamics, we should wait to see what difficulties there are after the modification.’ However, when electromagnetism is joined to quantum mechanics, the difficulties remain. So it will not be a waste of our time now to look at what these difficulties are.

Indeed, Feynman thought these issues were of central importance. In the lecture that he gave upon receiving the Nobel Prize in 1965 for his work on quantum electrodynamics, he chose to spend much of his time discussing classical electrodynamics. In collaboration with his graduate advisor, John Wheeler (advisor to a number of other important figures, including Hugh Everett III, the inventor of the Many-Worlds interpretation of quantum mechanics, and Kip Thorne, a corecipient of the 2017 Nobel Prize for gravitational-wave detection), Feynman had proposed a radical reimagining of classical electrodynamics.

Wheeler and Feynman – like Ritz – do away with the electromagnetic field and keep only the particles. As I mentioned earlier, Ritz’s field-free theory has particles interact across gaps in space and time so that each particle responds to the past states of the others. In the Wheeler-Feynman theory, particles respond to both the past and the future behaviour of one another. As in a time-travel movie, the future can influence the past. That’s a wild idea, but it seems to work. In appropriate circumstances, this revision yields accurate predictions about the motions of particles without any true self-interaction.

In a talk titled ‘Why Field Theories are not Theories of Fields’, the third speaker in our debate, Dustin Lazarovici of the University of Lausanne, took the side of Ritz, Wheeler, and Feynman. In the action-at-a-distance theories put forward by these physicists, you can’t tell what a particle will do at a particular moment just by looking at what the other particles are doing at that moment. You also need to look at what they were doing in the past (and perhaps what they will do in the future). Lazarovici argued that the electromagnetic field is merely a useful mathematical bookkeeping device that encodes this information about the past and future, not a real thing out there in the world.

Lazarovici then moved from classical to quantum electrodynamics. Like many other philosophers of physics, he believes that standard formulations of quantum electrodynamics are unsatisfactory – in part because they don’t give a clear picture of what is happening in nature. His research programme for fixing up the theory has a number of non-standard elements.

First, Lazarovici is aware that quantum electrodynamics suffers from the quantum measurement problem, and thinks that we ought to adopt a solution proposed by David Bohm, positing the existence of point particles that are distinct from the quantum wave function. Second, he wants to build quantum electrodynamics from a version of classical electrodynamics without fields, where particles interact directly with one another (such as Wheeler and Feynman’s). Third, he adopts Dirac’s controversial idea that space is filled with a vast ‘sea’ of negative energy electrons. This Dirac sea was central to early research in quantum electrodynamics but has fallen out of favour in most contemporary presentations of the theory.

These ideas fit together well, and Lazarovici hopes that they will allow us to avoid certain unpleasant infinities that arise in quantum electrodynamics. I’m curious to see where this approach leads. In favour of research that deviates from the mainstream, Feynman said (at the end of his Nobel lecture) that progress in physics might well be made by someone who teaches himself ‘quantum electrodynamics from a peculiar and unusual point of view; one that he may have to invent for himself’.

In my contribution to the debate, I advocated a different point of view on quantum electrodynamics. . .

Continue reading.

Written by LeisureGuy

2 November 2019 at 11:20 am

Posted in Science

How to Understand the Universe When You’re Stuck Inside It

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Amanda Gefter interviews Lee Smolin in Quanta. This post overlaps a bit with the succeeding post. Gefter writes:

The universe is kind of an impossible object. It has an inside but no outside; it’s a one-sided coin. This Möbius architecture presents a unique challenge for cosmologists, who find themselves in the awkward position of being stuck inside the very system they’re trying to comprehend.

It’s a situation that Lee Smolin has been thinking about for most of his career. A physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada, Smolin works at the knotty intersection of quantum mechanics, relativity and cosmology. Don’t let his soft voice and quiet demeanor fool you — he’s known as a rebellious thinker and has always followed his own path. In the 1960s Smolin dropped out of high school, played in a rock band called Ideoplastos, and published an underground newspaper. Wanting to build geodesic domes like R. Buckminster Fuller, Smolin taught himself advanced mathematics — the same kind of math, it turned out, that you need to play with Einstein’s equations of general relativity. The moment he realized this was the moment he became a physicist. He studied at Harvard University and took a position at the Institute for Advanced Study in Princeton, New Jersey, eventually becoming a founding faculty member at the Perimeter Institute.

“Perimeter,” in fact, is the perfect word to describe Smolin’s place near the boundary of mainstream physics. When most physicists dived headfirst into string theory, Smolin played a key role in working out the competing theory of loop quantum gravity. When most physicists said that the laws of physics are immutable, he said they evolve according to a kind of cosmic Darwinism. When most physicists said that time is an illusion, Smolin insisted that it’s real.

Smolin often finds himself inspired by conversations with biologists, economists, sculptors, playwrights, musicians and political theorists. But he finds his biggest inspiration, perhaps, in philosophy — particularly in the work of the German philosopher Gottfried Leibniz, active in the 17th and 18th centuries, who along with Isaac Newton invented calculus. Leibniz argued (against Newton) that there’s no fixed backdrop to the universe, no “stuff” of space; space is just a handy way of describing relationships. This relational framework captured Smolin’s imagination, as did Leibniz’s enigmatic text The Monadology, in which Leibniz suggests that the world’s fundamental ingredient is the “monad,” a kind of atom of reality, with each monad representing a unique view of the whole universe. It’s a concept that informs Smolin’s latest work as he attempts to build reality out of viewpoints, each one a partial perspective on a dynamically evolving universe. A universe as seen from the inside.

Quanta Magazine spoke with Smolin about his approach to cosmology and quantum mechanics, which he details in his recent book, Einstein’s Unfinished Revolution. The interview has been condensed and edited for clarity.

You have a slogan: “The first principle of cosmology must be: There is nothing outside the universe.”

In different formulations of the laws of physics, like Newtonian mechanics or quantum mechanics, there is background structure — structure which has to be specified and is fixed. It’s not subject to evolution, it’s not influenced by anything that happens. It’s structure outside the system being modeled. It’s the framework on which we hang observables — the observer, a clock and so forth. The statement that there’s nothing outside the universe — there’s no observer outside the universe — implies that we need a formulation of physics without background structure. All the theories of physics we have, in one way or another, apply only to subsystems of the universe. They don’t apply to the universe as a whole, because they require this background structure.

If we want to make a cosmological theory, to understand nature on the cosmological scale, we have to avoid what the philosopher Roberto Unger and I called “the cosmological fallacy,” the mistaken belief that we can take theories that apply to subsystems and scale them up to the universe as a whole. We need a formulation of dynamics that doesn’t refer to an observer or measuring instrument or anything outside the system. That means we need a different kind of theory.

You’ve recently proposed such a theory — one in which, as you put it, “the history of the universe is constituted of different views of itself.” What does that mean?

It’s a theory about processes, about the sequences and causal relations among things that happen, not the inherent properties of things that are. The fundamental ingredient is what we call an “event.” Events are things that happen at a single place and time; at each event there’s some momentum, energy, charge or other various physical quantity that’s measurable. The event has relations with the rest of the universe, and that set of relations constitutes its “view” of the universe. Rather than describing an isolated system in terms of things that are measured from the outside, we’re taking the universe as constituted of relations among events. The idea is to try to reformulate physics in terms of these views from the inside, what it looks like from inside the universe.

How do you do that?

There are many views, and each one has only partial information about the rest of the universe. We propose as a principle of dynamics that each view should be unique. That idea comes from Leibniz’s principle of the identity of indiscernibles. Two events whose views are exactly mappable onto each other are the same event, by definition. So each view is unique, and you can measure how distinct one is from another by defining a quantity called the “variety.” If you think of a node on a graph, you can go one step out, two steps out, three steps out. Each step gives you a neighborhood — the one-step neighborhood, the two-step neighborhood, the three-step neighborhood. So for any two events you can ask: How many steps do you have to go out until their views diverge? In what neighborhood are they different? The fewer steps you have to go, the more distinguishable the views are from one another. The idea in this theory is that the laws of physics — the dynamics of the system — work to maximize variety. That principle — that nature wants to maximize variety — actually leads, within the framework I’ve been describing, to the Schrödinger equation, and hence to a recovery, in an appropriate limit, of quantum mechanics.

I know from your book that you’re a realist at heart — you believe strongly in a reality independent of our knowledge of it — and therefore, like Einstein, you think quantum mechanics is incomplete. Does this theory of views help complete what you think is missing in quantum theory?

Einstein — as well as someone called Leslie Ballentine — advocated an “ensemble interpretation” of the wave function [the mathematical object that represents a quantum system]. The idea was that the wave function describes an ensemble of possible states. But one day, I was sitting in a cafe working and suddenly I thought: What if the ensemble is real? What if, when you have a wave function describing a single water molecule, it’s actually describing the ensemble of every water molecule in the universe?

So whereas normally we would think that there’s one water molecule but an uncertainty of states, you’re saying that the uncertainty of states is actually the ensemble of all the water molecules in the universe?

Yes. They form an ensemble because they have very similar views. They all interact with one another, because the probability of interaction is determined by the similarity of views, not necessarily their proximity in space.

Things don’t have to be near each other to interact?

In this theory, the similarity of views is more fundamental than space. Often, two events have similar views because they’re close in space. If two people stand next to each other, they have very similar, overlapping views of the universe. But two atoms have many fewer relational properties than big, complex objects like people. So two atoms far apart in space can still have very similar views. That means that at the smallest scale, there should be highly nonlocal interactions, which is exactly what you get with entanglement in quantum mechanics. That’s where quantum mechanics comes from, according to the real-ensemble formulation.

It reminds me of a lot of work that’s going on now in physics that’s finding surprising connections between entanglement and the geometry of space-time.

I think a lot of that work is really interesting. The hypothesis that’s motivating it is that entanglement is fundamental in quantum mechanics, and the geometry of space or space-time emerges from structures of entanglement. It’s a very positive development.

You’ve said that these ideas were inspired by Leibniz’s Monadology. Did you just happen to pull out your Monadology and reread it?

I first read Leibniz at the instigation of Julian Barbour, when I was just out of graduate school. First I read the correspondence between Leibniz and Samuel Clarke, who was a follower of Newton, in which Leibniz criticized Newton’s notion of absolute space and absolute time and argued that observables in physics should be relational. They should describe the relations of one system with another, resulting from their interaction. Later I read the Monadology. I read it as a sketch for how to make a background-independent theory of physics. I do look at my copy from time to time. There is a beautiful quote in there, where Leibniz says, “Just as the same city viewed from different directions appears entirely different … there are, as it were, just as many different universes, which are, nevertheless, only perspectives on a single one, corresponding to the different points of view of each monad.” That, to me, evokes why these ideas are very suitable, not just in physics but for a whole range of things from social policy and postmodernism to art to what it feels like to be an individual in a diverse society. But that’s another discussion!

Your work has been very influenced by philosophy. Looking back historically, people like Einstein and Bohr and John Wheeler all took philosophy very seriously; it directly influenced their physics. It seems to be a trait of great physicists and yet —

And also of not-great physicists.

OK, fair! It just seems that it’s become almost taboo to talk about philosophy in physics today. Has that been your experience? . . .

Continue reading.

Written by LeisureGuy

2 November 2019 at 11:13 am

Posted in Science

Time to talk of toilets

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Toilets have not been a common blogging topic, but we have one that’s definitely worth mentioning. We live in an apartment building, and recently the building owners replaced all the toilets in the building with Hennessy & Hinchcliffe toilets. I thought the toilets we had were perfectly good—but wow! this new toilet is amazing. It’s a low-flush toilet (3 liters (or 0.8 gallons) per flush), and the flush is totally efficient. When you take the lid off the reservoir, you can see that it’s not your run-of-the-mill toilet:

I tried to find out more about it, and I did find this post. From that post:

Many dual flush toilets on the market use 4.0 Lpf for liquid “product” and 6.0 Lpf for solid “product”.

Some toilets use only 4.8 Lpf.

This toilet uses only 3.0 litres per flush, for both liquid and solid “products”.

If you are interested by high-efficiency toilets, you should read this article:

A new test method provided a big push. Introduced in 2002, the Maximum Performance (MaP) Test used simulated human waste made from a soybean mixture that duplicated real world conditions, unlike previous tests.

There are now toilets that are able to flush 1,000 grams of solid waste with only 4.8 litre flushes.

The only widely available three-litre toilets on the market are the Proficiency line from Hennessy & Hinchcliffe in Mississauga, Ont. Launched in 2009, all models flush 800 grams in MaP testing

It uses a unique passive air pressurized trap-way that starts an immediate siphon without depending on water entering the bowl.

“Three litres of water are effectively used to clean and scour the bowl since our tests have shown that the vacuum created by our BSB flush system alone will flush the toilet contents without any additional water,” said [Jerrad] Hennessy.

If you ever have to replace a toilet, I highly recommend the Hennessy & Hinchcliffe 3-liter-per-flush toilet. Quite apart from water saving, the flush just does a better job.

Here are the detailed specs (PDF) for one model.

You can find specs on a variety of models on this page if you click “Proficiency Products” under “Henessy & Hinchcliffe 3.0 Litre.”

Written by LeisureGuy

2 November 2019 at 10:10 am

Posted in Daily life, Technology

My boar brushes, beginning with the amazing Omega 21762

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Yesterday’s brush was half boar, but today we go all in on boar. The Omega 21762 boar brush (here in the Razor & Brush special edition of a few years back) is an astonishingly soft boar brush. I believe the knot is made using the natural ends of the bristles rather than bristles trimmed to length. At any rate it feels very soft on the face and the knot is quite soft as well. Most people like this softness, possibly because they expected it from reviews (see link), while others prefer a brush that is stiffer and scrubbier. For me, it depends on my mood, and this morning I loved using the brush: its light touch was just what I needed, and it can readily whip up and hold a ton of good lather, from Zi’ Peppino this morning: rich, thick, soft, fragrant—just what I needed.

The Baby Smooth always delivers a great shave, and by the time I splashed on a good amount of Zi’ Peppino aftershave, I was ready for the weekend.

Written by LeisureGuy

2 November 2019 at 9:48 am

Posted in Shaving

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