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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.

06 August, 2015

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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Japanese researchers discovered that the whale shark has "tiny teeth"—dermal denticles—protecting its eyes from abrasion.
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A massive star has mysteriously vanished, confusing astronomers

A gigantic star makes off during an eight-year gap in observations.

Image source: ESO/L. Calçada

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The massive star in the Kinsman Dwarf Galaxy seems to have disappeared between 2011 and 2019.
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Maybe it's still there, but much less luminous and/or covered by dust.

A "very massive star" in the Kinman Dwarf galaxy caught the attention of astronomers in the early years of the 2000s: It seemed to be reaching a late-ish chapter in its life story and offered a rare chance to observe the death of a large star in a region low in metallicity. However, by the time scientists had the chance to turn the European Southern Observatory's (ESO) Very Large Telescope (VLT) in Paranal, Chile back around to it in 2019 — it's not a slow-turner, just an in-demand device — it was utterly gone without a trace. But how?

The two leading theories about what happened are that either it's still there, still erupting its way through its death throes, with less luminosity and perhaps obscured by dust, or it just up and collapsed into a black hole without going through a supernova stage. "If true, this would be the first direct detection of such a monster star ending its life in this manner," says Andrew Allan of Trinity College Dublin, Ireland, leader of the observation team whose study is published in Monthly Notices of the Royal Astronomical Society.

So, em...

Between astronomers' last look in 2011 and 2019 is a large enough interval of time for something to happen. Not that 2001 (when it was first observed) or 2019 have much meaning, since we're always watching the past out there and the Kinman Dwarf Galaxy is 75 million light years away. We often think of cosmic events as slow-moving phenomena because so often their follow-on effects are massive and unfold to us over time. But things happen just as fast big as small. The number of things that happened in the first 10 millionth of a trillionth of a trillionth of a trillionth of a second after the Big Bang, for example, is insane.

In any event, the Kinsman Dwarf Galaxy, or PHL 293B, is far way, too far for astronomers to directly observe its stars. Their presence can be inferred from spectroscopic signatures — specifically, PHL 293B between 2001 and 2011 consistently featured strong signatures of hydrogen that indicated the presence of a massive "luminous blue variable" (LBV) star about 2.5 times more brilliant than our Sun. Astronomers suspect that some very large stars may spend their final years as LBVs.

Though LBVs are known to experience radical shifts in spectra and brightness, they reliably leave specific traces that help confirm their ongoing presence. In 2019 the hydrogen signatures, and such traces, were gone. Allan says, "It would be highly unusual for such a massive star to disappear without producing a bright supernova explosion."

The Kinsman Dwarf Galaxy, or PHL 293B, is one of the most metal-poor galaxies known. Explosive, massive, Wolf-Rayet stars are seldom seen in such environments — NASA refers to such stars as those that "live fast, die hard." Red supergiants are also rare to low Z environments. The now-missing star was looked to as a rare opportunity to observe a massive star's late stages in such an environment.

Celestial sleuthing

In August 2019, the team pointed the four eight-meter telescopes of ESO's ESPRESSO array simultaneously toward the LBV's former location: nothing. They also gave the VLT's X-shooter instrument a shot a few months later: also nothing.

Still pursuing the missing star, the scientists acquired access to older data for comparison to what they already felt they knew. "The ESO Science Archive Facility enabled us to find and use data of the same object obtained in 2002 and 2009," says Andrea Mehner, an ESO staff member who worked on the study. "The comparison of the 2002 high-resolution UVES spectra with our observations obtained in 2019 with ESO's newest high-resolution spectrograph ESPRESSO was especially revealing, from both an astronomical and an instrumentation point of view."

Examination of this data suggested that the LBV may have indeed been winding up to a grand final sometime after 2011.

Team member Jose Groh, also of Trinity College, says "We may have detected one of the most massive stars of the local Universe going gently into the night. Our discovery would not have been made without using the powerful ESO 8-meter telescopes, their unique instrumentation, and the prompt access to those capabilities following the recent agreement of Ireland to join ESO."

Combining the 2019 data with contemporaneous Hubble Space Telescope (HST) imagery leaves the authors of the reports with the sense that "the LBV was in an eruptive state at least between 2001 and 2011, which then ended, and may have been followed by a collapse into a massive BH without the production of an SN. This scenario is consistent with the available HST and ground-based photometry."

Or...

A star collapsing into a black hole without a supernova would be a rare event, and that argues against the idea. The paper also notes that we may simply have missed the star's supernova during the eight-year observation gap.

LBVs are known to be highly unstable, so the star dropping to a state of less luminosity or producing a dust cover would be much more in the realm of expected behavior.

Says the paper: "A combination of a slightly reduced luminosity and a thick dusty shell could result in the star being obscured. While the lack of variability between the 2009 and 2019 near-infrared continuum from our X-shooter spectra eliminates the possibility of formation of hot dust (⪆1500 K), mid-infrared observations are necessary to rule out a slowly expanding cooler dust shell."

The authors of the report are pretty confident the star experienced a dramatic eruption after 2011. Beyond that, though:

"Based on our observations and models, we suggest that PHL 293B hosted an LBV with an eruption that ended sometime after 2011. This could have been followed by
(1) a surviving star or
(2) a collapse of the LBV to a BH [black hole] without the production of a bright SN, but possibly with a weak transient."

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NASA releases first sounds ever captured on Mars

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