Why 'Change without Change' Is One of the Fundamental Principles of the Universe
Symmetry is about way more than splitting circles: It's change without change, and it has applications throughout mathematics, physics, and nature.
Frank Wilczek is an American theoretical physicist, mathematician and a Nobel laureate. He is currently the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology (MIT). Wilczek, along with David Gross and H. David Politzer, was awarded the Nobel Prize in Physics in 2004 for their discovery of asymptotic freedom in the theory of the strong interaction. He is on the Scientific Advisory Board for the Future of Life Institute. His new book is titled A Beautiful Question: Finding Nature's Deep Design.
Frank Wilczek: Symmetry in common usage is a kind of vague term like most terms in common usage. We use it flexibly. The idea of symmetry that has turned out to be extremely fruitful in mathematics and physics and in the fundamental description of nature is a precise distillation of some aspects of the common usage. So it’s not unnatural to call it symmetry, but it’s something very precise that we can describe.
When I say what it is it’ll sound kind of mystical, but it’s actually — I’ll spell it out and you’ll see what I mean. So symmetry in the sense that’s turned out to be fruitful in mathematics and physics and fundamental investigations is change without change. Now you might be puzzled. What does that have to do with symmetry? Well consider a circle. A circle is a very symmetric object. You can rotate it around its center by any angle and although every point on the circle may move, the circle as a whole doesn’t change. And that’s what makes it symmetric in the intuitive sense. You can change it. You can make changes on it which might have changed it, but although they transformed each part of it, don’t transform the thing as a whole. So that’s what makes a circle a symmetric object.
An equilateral triangle, for instance, you can’t rotate through any angle and get the same thing. It’ll change. If you rotate it one-third of the way around though by 120 degrees, it goes over into itself. If you rotate around the center by 120 degrees, it’s the same equilateral triangle. Whereas if you take some lopsided triangle, it’ll never go back to itself until you come all the way back to a trivial transformation. That doesn’t change anything. So change — so a triangle has less symmetry than a circle according to this concept, but some symmetry.
And so you start to see how this concept of change without change matches the intuitive notion of symmetry. The great advantage of that definition is that you can apply it in very broad context not only to describing the symmetry of objects, but to describing the symmetry of physical laws or the symmetry of equations. So, for instance, the theory of relativity is a statement of symmetry that if you change the way the world looks by moving past it at a constant velocity, you change the appearance of everything that’s happening. But the underlying laws are still valid. That’s the assumption of the theory of relativity that drives it and makes it powerful.
The idea that the laws of physics don’t change as a function of time is also a symmetry because it means you can change when you start your clocks and although the time stamps you’ll give to each event look different, the underlying equations will be the same. That’s the way of staying, that the laws of physics don’t change. And similarly with that the fact that the same physical laws apply at different places is a symmetry because you can change your position without changing the way the laws work. So symmetry is a very powerful constraint on our description of the world that nature seems to respect in many ways. Now the kind of symmetry that leads to quantum chromodynamics or general relativity or quantum electrodynamics is, mathematically, considerably more complex but it’s the same idea.
So there are transformations of the equations that change the different terms in them. So they might change an electric field into a magnetic field or a magnetic field into a combination of electric and magnetic that change the way the equations look, but don’t change their consequences. So the equations look quite different — some parts have moved over to the left and some parts have moved over to the right and some things have been multiplied in funny ways. But their consequences, their content is exactly the same. That’s the kind of equations that are like the circles among equations — are ones that have this symmetry property and those are the kinds of equations that turn out to be the ones that appear most prominently in our fundamental description of nature. It’s an extraordinary thing — but that’s not only true, but that’s how we got to the equations in the first place.
In his new book A Beautiful Question, theoretical physicist and Nobel laureate Frank Wilczek marries the age-old human quest for beauty and the age-old human quest for truth into a thrilling synthesis: The universe wants to be beautiful. In this video interview, Wilczek delves deep into the fundamental idea of symmetry. Did you know symmetry is much more complex than what we were taught in school? The possible and plausible abstractions of symmetry throughout physics and nature are plenty. The world is full of instances of change without changing.
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Could muons point to new physics?
New data have set the particle physics community abuzz.
- The first question ever asked in Western philosophy, "What's the world made of?" continues to inspire high energy physicists.
- New experimental results probing the magnetic properties of the muon, a heavier cousin of the electron, seem to indicate that new particles of nature may exist, potentially shedding light on the mystery of dark matter.
- The results are a celebration of the human spirit and our insatiable curiosity to understand the world and our place in it.
If brute force doesn't work, then look into the peculiarities of nothingness. This may sound like a Zen koan, but it's actually the strategy that particle physicists are using to find physics beyond the Standard Model, the current registry of all known particles and their interactions. Instead of the usual colliding experiments that smash particles against one another, exciting new results indicate that new vistas into exotic kinds of matter may be glimpsed by carefully measuring the properties of the quantum vacuum. There's a lot to unpack here, so let's go piecemeal.
It is fitting that the first question asked in Western philosophy concerned the material composition of the world. Writing around 350 BCE, Aristotle credited Thales of Miletus (circa 600 BCE) with the honor of being the first Western philosopher when he asked the question, "What is the world made of?" What modern high energy physicists do, albeit with very different methodology and equipment, is to follow along the same philosophical tradition of trying to answer this question, assuming that there are indivisible bricks of matter called elementary particles.
Deficits in the Standard Model
Jumping thousands of years of spectacular discoveries, we now have a very neat understanding of the material composition of the world at the subatomic level: a total of 12 particles and the Higgs boson. The 12 particles of matter are divided into two groups, six leptons and six quarks. The six quarks comprise all particles that interact via the strong nuclear force, like protons and neutrons. The leptons include the familiar electron and its two heavier cousins, the muon and the tau. The muon is the star of the new experiments.
The Standard ModelCredit: Cush via Wikimedia Commons licensed under CC0 1.0
For all its glory, the Standard Model described above is incomplete. The goal of fundamental physics is to answer the most questions with the least number of assumptions. As it stands, the values of the masses of all particles are parameters that we measure in the laboratory, related to how strongly they interact with the Higgs. We don't know why some interact much stronger than others (and, as a consequence, have larger masses), why there is a prevalence of matter over antimatter, or why the universe seems to be dominated by dark matter — a kind of matter we know nothing about, apart from the fact that it's not part of the recipe included in the Standard Model. We know dark matter has mass since its gravitational effects are felt in familiar matter, the matter that makes up galaxies and stars. But we don't know what it is.
Whatever happens, new science will be learned.
Physicists had hoped that the powerful Large Hadron Collider in Switzerland would shed light on the nature of dark matter, but nothing has come up there or in many direct searches, where detectors were mounted to collect dark matter that presumably would rain down from the skies and hit particles of ordinary matter.
Could muons fill in the gaps?
Enter the muons. The hope that these particles can help solve the shortcomings of the Standard Model has two parts to it. The first is that every particle, like a muon, that has an electric charge can be pictured simplistically as a spinning sphere. Spinning spheres and disks of charge create a magnetic field perpendicular to the direction of the spin. Picture the muon as a tiny spinning top. If it's rotating counterclockwise, its magnetic field would point vertically up. (Grab a glass of water with your right hand and turn it counterclockwise. Your thumb will be pointing up, the direction of the magnetic field.) The spinning muons will be placed into a doughnut-shaped tunnel and forced to go around and around. The tunnel will have its own magnetic field that will interact with the tiny magnetic field of the muons. As the muons circle the doughnut, they will wobble about, just like spinning-tops wobble on the ground due to their interaction with Earth's gravity. The amount of wobbling depends on the magnetic properties of the muon which, in turn, depend on what's going on with the muon in space.
Credit: Fabrice Coffrini / Getty Images
This is where the second idea comes in, the quantum vacuum. In physics, there is no empty space. The so-called vacuum is actually a bubbling soup of particles that appear and disappear in fractions of a second. Everything fluctuates, as encapsulated in Heisenberg's Uncertainty Principle. Energy fluctuates too, what we call zero-point energy. Since energy and mass are interconvertible (E=mc2, remember?), these tiny fluctuations of energy can be momentarily converted into particles that pop out and back into the busy nothingness of the quantum vacuum. Every particle of matter is cloaked with these particles emerging from vacuum fluctuations. Thus, a muon is not only a muon, but a muon dressed with these extra fleeting bits of stuff. That being the case, these extra particles affect a muon's magnetic field, and thus, its wobbling properties.
About 20 years ago, physicists at the Brookhaven National Laboratory detected anomalies in the muon's magnetic properties, larger than what theory predicted. This would mean that the quantum vacuum produces particles not accounted for by the Standard Model: new physics! Fast forward to 2017, and the experiment, at four times higher sensitivity, was repeated at the Fermi National Laboratory, where yours truly was a postdoctoral fellow a while back. The first results of the Muon g-2 experiment were unveiled on 7-April-2021 and not only confirmed the existence of a magnetic moment anomaly but greatly amplified it.
To most people, the official results, published recently, don't seem so exciting: a "tension between theory and experiment of 4.2 standard deviations." The gold standard for a new discovery in particle physics is a 5-sigma variation, or one part in 3.5 million. (That is, running the experiment 3.5 million times and only observing the anomaly once.) However, that's enough for plenty of excitement in the particle physics community, given the remarkable precision of the experimental measurements.
A time for excitement?
Now, results must be reanalyzed very carefully to make sure that (1) there are no hidden experimental errors; and (2) the theoretical calculations are not off. There will be a frenzy of calculations and papers in the coming months, all trying to make sense of the results, both on the experimental and theoretical fronts. And this is exactly how it should be. Science is a community-based effort, and the work of many compete with and complete each other.
Whatever happens, new science will be learned, even if less exciting than new particles. Or maybe, new particles have been there all along, blipping in and out of existence from the quantum vacuum, waiting to be pulled out of this busy nothingness by our tenacious efforts to find out what the world is made of.
- Benjamin Franklin wrote essays on a whole range of subjects, but one of his finest was on how to be a nice, likable person.
- Franklin lists a whole series of common errors people make while in the company of others, like over-talking or storytelling.
- His simple recipe for being good company is to be genuinely interested in others and to accept them for who they are.
Think of the nicest person you know. The person who would fit into any group configuration, who no one can dislike, or who makes a room warmer and happier just by being there.
What makes them this way? Why are they so amiable, likeable, or good-natured? What is it, you think, that makes a person good company?
There are really only two things that make someone likable.
This is the kind of advice that comes from one of history's most famously good-natured thinkers: Benjamin Franklin. His essay "On Conversation" is full of practical, surprisingly modern tips about how to be a nice person.
Franklin begins by arguing that there are really only two things that make someone likable. First, they have to be genuinely interested in what others say. Second, they have to be willing "to overlook or excuse Foibles." In other words, being good company means listening to people and ignoring their faults. Being witty, well-read, intelligent, or incredibly handsome can all make a good impression, but they're nothing without these two simple rules.
The sort of person nobody likes
From here, Franklin goes on to give a list of the common errors people tend to make while in company. These are the things people do that makes us dislike them. We might even find, with a sinking feeling in our stomach, that we do some of these ourselves.
1) Talking too much and becoming a "chaos of noise and nonsense." These people invariably talk about themselves, but even if "they speak beautifully," it's still ultimately more a soliloquy than a real conversation. Franklin mentions how funny it can be to see these kinds of people come together. They "neither hear nor care what the other says; but both talk on at any rate, and never fail to part highly disgusted with each other."
2) Asking too many questions. Interrogators are those people who have an "impertinent Inquisitiveness… of ten thousand questions," and it can feel like you're caught between a psychoanalyst and a lawyer. In itself, this might not be a bad thing, but Franklin notes it's usually just from a sense of nosiness and gossip. The questions are only designed to "discover secrets…and expose the mistakes of others."
3) Storytelling. You know those people who always have a scripted story they tell at every single gathering? Utterly painful. They'll either be entirely oblivious to how little others care for their story, or they'll be aware and carry on regardless. Franklin notes, "Old Folks are most subject to this Error," which we might think is perhaps harsh, or comically honest, depending on our age.
4) Debating. Some people are always itching for a fight or debate. The "Wrangling and Disputing" types inevitably make everyone else feel like they need to watch what they say. If you give even the lightest or most modest opinion on something, "you throw them into Rage and Passion." For them, the conversation is a boxing fight, and words are punches to be thrown.
5) Misjudging. Ribbing or mocking someone should be a careful business. We must never mock "Misfortunes, Defects, or Deformities of any kind", and should always be 100% sure we won't upset anyone. If there's any doubt about how a "joke" will be taken, don't say it. Offense is easily taken and hard to forget.
Not following Benjamin Franklin's advice.Credit: Ronald Martinez via Getty Images
On practical philosophy
Franklin's essay is a trove of great advice, and this article only touches on the major themes. It really is worth your time to read it in its entirety. As you do, it's hard not to smile along or to think, "Yes! I've been in that situation." Though the world has changed dramatically in the 300 years since Franklin's essay, much is exactly the same. Basic etiquette doesn't change.
If there's only one thing to take away from Franklin's essay, it comes at the end, where he revises his simple recipe for being nice:
"Be ever ready to hear what others say… and do not censure others, nor expose their Failings, but kindly excuse or hide them"
So, all it takes to be good company is to listen and accept someone for who they are.
Philosophy doesn't always have to be about huge questions of truth, beauty, morality, art, or meaning. Sometimes it can teach us simply how to not be a jerk.
Weird science shows unseemly way beetles escape after being eaten
Certain water beetles can escape from frogs after being consumed.
- A Japanese scientist shows that some beetles can wiggle out of frog's butts after being eaten whole.
- The research suggests the beetle can get out in as little as 7 minutes.
- Most of the beetles swallowed in the experiment survived with no complications after being excreted.
In what is perhaps one of the weirdest experiments ever that comes from the category of "why did anyone need to know this?" scientists have proven that the Regimbartia attenuata beetle can climb out of a frog's butt after being eaten.
The research was carried out by Kobe University ecologist Shinji Sugiura. His team found that the majority of beetles swallowed by black-spotted pond frogs (Pelophylax nigromaculatus) used in their experiment managed to escape about 6 hours after and were perfectly fine.
"Here, I report active escape of the aquatic beetle R. attenuata from the vents of five frog species via the digestive tract," writes Sugiura in a new paper, adding "although adult beetles were easily eaten by frogs, 90 percent of swallowed beetles were excreted within six hours after being eaten and, surprisingly, were still alive."
One bug even got out in as little as 7 minutes.
Sugiura also tried putting wax on the legs of some of the beetles, preventing them from moving. These ones were not able to make it out alive, taking from 38 to 150 hours to be digested.
Naturally, as anyone would upon encountering such a story, you're wondering where's the video. Thankfully, the scientists recorded the proceedings:
The Regimbartia attenuata beetle can be found in the tropics, especially as pests in fish hatcheries. It's not the only kind of creature that can survive being swallowed. A recent study showed that snake eels are able to burrow out of the stomachs of fish using their sharp tails, only to become stuck, die, and be mummified in the gut cavity. Scientists are calling the beetle's ability the first documented "active prey escape." Usually, such travelers through the digestive tract have particular adaptations that make it possible for them to withstand extreme pH and lack of oxygen. The researchers think the beetle's trick is in inducing the frog to open a so-called "vent" controlled by the sphincter muscle.
"Individuals were always excreted head first from the frog vent, suggesting that R. attenuata stimulates the hind gut, urging the frog to defecate," explains Sugiura.
For more information, check out the study published in Current Biology.
Our ancestors first developed humanlike brains 1.7 million years ago
A recent study analyzed the skulls of early Homo species to learn more about the evolution of primate brains.
For nearly two centuries, scientists have known that humans descended from the great apes. But it's proven difficult to precisely map out the branches of that evolutionary tree, especially in terms of determining when and where early Homo species first developed brains similar to modern humans.
There are clear differences between ape and human brains. Compared to apes, the Homo sapiens brain is larger, and its frontal lobe is organized such that we can engage in toolmaking, planning, and language. Other Homo species also enjoyed some of these cognitive innovations, from the Neanderthals to Homo floresiensis, the hobbit-like people who once inhabited Indonesia.
One reason it's been difficult to discern the details of this cognitive evolution from apes to Homo species is that brains don't fossilize, so scientists can't directly study early primate brains. But primate skulls offer clues.
Brains of yore
In a new study published in Science, an international team of researchers analyzed impressions left on the skulls of Homo species to better understand the evolution of primate brains. Using computer tomography on fossil skulls, the team generated images of what the brain structures of early Homo species probably looked like, and then compared those structures to the brains of great apes and modern humans.
The results suggest that Homo species first developed humanlike brains approximately 1.7 to 1.5 million years ago in Africa. This cognitive evolution occurred at roughly the same time Homo species' technology and culture were becoming more complex, with these species developing more sophisticated stone tools and animal food resources.
The team hypothesized that "this pattern reflects interdependent processes of brain-culture coevolution, where cultural innovation triggered changes in cortical interconnectivity and ultimately in external frontal lobe topography."
The team also found that these structural changes occurred after Homo species migrated out of Africa for regions like modern-day Georgia and Southeast Asia, which is where the fossils in the study were discovered. In other words, Homo species still had ape-like brains when some groups first left Africa.
While the study sheds new light on the evolution of primate brains, the team said there's still much to learn about the history of early Homo species, particularly in terms of explaining the morphological diversity of Homo fossils discovered in Africa.
"Deciphering evolutionary process in early Homo remains a challenge that will be met only through the recovery of expanded fossil samples from well-controlled chronological contexts," the researchers wrote.
