Galileo Did Do Experiments

After finding an old book of mine, The Ten Most Beautiful Experiments, over winter break, I wanted to follow up on my last post. I’ll say that this post is based almost entirely on that book’s chapter on Galileo, but since I don’t see it summarized in many places, I thought it was worth writing up. It is somewhat in vogue to claim that Galileo didn’t actually perform his experiments on falling bodies, and his writings just describe thought experiments. However, this actually confuses two different experiments attributed to Galileo. Most historians do believe stories of Galileo dropping weights from the Leaning Tower of Pisa are apocryphal and come from people confusing what is a thought experiment that Salviati, one of the fictional conversationalists in Two New Sciences, describes doing there, or a relatively unsourced claim by Galileo’s secretary in a biography after his death.

However, Salviati also describes an experiment that Galileo is recognized as having done: measuring the descent of balls of different weights down ramps, which also follow the same basic equation as bodies in free fall, but modified by the angle of slope. I think a few people may doubt Galileo actually completed the ramp experiment, based on criticisms by Alexandre Koyré in the 1950s that Galileo’s methods seemed too vague or imprecise to measure the acceleration. However, many researchers (like the Rice team in an above link) have found it possible to get data close to Galileo’s using the method Salviati describes. Additionally, another historian, Stillman Drake, who had access to more of Galileo’s manuscripts found what appears to be records of raw experimental data that show reasonable error. Drake also suggests that Galileo may have originally kept time through the use of musical tempo before moving on the water clock. Wikipedia (I know, but I don’t have much to go on) also suggests Drake does believe in the Leaning Tower of Pisa experiment. While he may not have done it at that tower, evidently Galileo’s accounts include a description that corresponds to an observed tic that happens if people try to freely drop objects of different sizes at the same time, which suggest he tried free fall somewhere.

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What to do if you’re inside a scientific revolution

A LesserWrong user (LesserWrong-er?) has a thought-provoking post on The Copernican Revolution from the Inside, with two questions in mind: (1) if you lived in 17th century Europe, would you have accepted heliocentrism on an epistemic level, and (2) how do you become the kind of person who would say yes to question 1? It’s interesting in the sense the often-asked question of  “What would you be doing during the Civil Rights Movement/Holocaust/Other Time of Great Societal Change” is, in that most people realize they probably would not be a great crusader against the norm of another time. But as someone in Charlottesville in the year 2017, asking about what you’d be doing in scientific arguments is less terrifying relevant than asking people about how they’d deal with Nazism, so we’ll just focus on that.

Cover of Kuhn's The Structure of Scientific Revolutions showing a whirlpool behind the title text.

Look, you’re probably in at least one.

For once on the internet, I recommend reading the comments, in that I think they help flesh out the argument a lot more and correct some strawmanning of the heliocentrists by the OP. Interestingly, OP actually says he thinks

In fact, one my key motivations for writing it — and a point where I strongly disagree with people like Kuhn and Feyerabend — is that I think heliocentrism was more plausible during that time. It’s not that Copernicus, Kepler Descartes and Galileo were lucky enough to be overconfident in the right direction, and really should just have remained undecided. Rather, I think they did something very right (and very Bayesian). And I want to know what that was.

and seems surprised that commenters think he went too pro-geocentrist. I recommend the following if you want the detailed correction, but I’ll also summarize the main points so you don’t have to:

  • Thomas Kehrenberg’s comment as it corrects factual errors in the OP regarding sunspots and Jupiter’s moon
  • MakerOfErrors for suggesting the methodological point should be that both geo- and heliocentric systems should have been treated with more uncertainty around the time of Galileo until more evidence came in
  • Douglas_Knight for pointing out a factual error regarding Venus and an argument I’m sympathetic to regarding the Coriolis effect but evidently am wrong on, which I’ll get to below. I do think it’s important to acknowledge that Galilean relativity is a thing, though, and that reduces the potential error a lot.
  • Ilverin for sort of continuing MakerOfError’s point and suggesting the true rationalist lesson should be looking at how do you deal with competing theories that both have high uncertainties

It’s also worth pointing out that even the Tychonic system didn’t resolve Galileo’s argument for heliocentrism based on sun spots. (A modification to Tycho’s system by one of his students that allows for the rotation of the Earth supposedly resolves the sunspot issue, but I haven’t heard many people mention it yet.)

Also, knowing that we didn’t have a good understanding of the Coriolis effect until, well, Coriolis in the 1800s (though there are some mathematical descriptions in the 1700s), I was curious to what extent people made this objection during the time of Galileo. It turns out Galileo also predicted it as a consequence of a rotating earth. Giovanni Riccioli, a Jesuit scientist, seems to have made the most rigorous qualitative argument against heliocentrism because cannon fire and falling objects are not notably deflected from straight line paths. I want to point out that Riccioli does virtually no math in his argument on the Coriolis effect (unless there’s a lot in the original text that I don’t see in the summary of his Almagestum Novum). This isn’t uncommon pre-Newton, and no one would have the exact tools to deal with Coriolis forces for almost 200 years. But one could reasonably try to make a scaling argument about whether or not the Coriolis effect matters based only on the length scale you’re measuring and the rotation speed of the Earth (which would literally just be taking the inverse of a day) and see that that heliocentrists aren’t insane.

It’s not a sexy answer to the second question, but I think “patience for new data” goes a long way towards making you the kind of person who can say yes to the first question. You hear the term “Copernican revolution” thrown around like a very specific event, and I think it’s pretty easy to forget the relative timeframes of major players unless this is your bread and butter. Copernicus’ De revolutionibus came out in 1543. Newton’s Principia came out in 1687, which gives a physical explanation for Kepler’s empirical laws and results in them becoming more greatly accepted, and so can be considered a decent (if oversimplified) endpoint for the debate. Galileo began to get vocal about heliocentrism in the early 1610s. The Almagestum Novum came out in 1651. For over a century, people on both sides were gathering and interpreting new data and refining their theories.

I also like this article for a related point, albeit one a bit removed from the author’s thesis. In considering the question of how should accept new theories, we see the historical development of one theory overtaking another as “scientific consensus”. Earlier this year, rationalist Scott Alexander in a post on Learning to Love Scientific Consensus concisely summarized why the typical “consensus is meaningless” trope of just listing times consensus has turned out to be wrong isn’t particularly useful in understanding science:

I knew some criticisms of a scientific paradigm. They seemed right. I concluded that scientists weren’t very smart and maybe I was smarter. I should have concluded that some cutting-edge scientists were making good criticisms of an old paradigm. I can still flatter myself by saying that it’s no small achievement to recognize a new paradigm early and bet on the winning horse. But the pattern I was seeing was part of the process of science, not a condemnation of it.

Most people understand this intuitively about past paradigm shifts. When a creationist says that we can’t trust science because it used to believe in phlogiston and now it believes in combustion, we correctly respond that this is exactly why we can trust science. But this lesson doesn’t always generalize when you’re in the middle of a paradigm shift right now and having trouble seeing the other side.

The notion of “trusting” scientific consensus I think gets to a larger point. There are way more non-scientists than scientists, so most people aren’t in a place to rigorously evaluate contemporary analogues to the Copernican revolution, so you often have to trust consensus at least a little. Also scientists aren’t scientists of every field, so even they can’t evaluate all disputes and will rely on the work of their colleagues in other departments. And given how many fields of science there are, there’s always probably at least one scientific revolution going on in your lifetime, if not several. Fortunately they don’t all take 150 years to resolve. (Though major cosmological ones can take a long time when we need new instruments and new data that can take a long time to acquire.)

But if you want to be the kind of person who can evaluate revolutions (or maybe attempts at revolutions), and I hope you are, then here’s a bit more advice for the second question à la Kuhn: try to understand the structure of competing theories. This doesn’t mean a detailed understanding of every equation or concept, but realize some things are more much important to how a theory functions than others, and some predictions are relatively minor (see point 4 below for an application to something that I thing pretty clearly doesn’t fall into a revolution today). To pure geocentrists, the phases of Venus were theory-breaking because geocentrism doesn’t allow mechanisms for a full range of phases for only some planets, and so they had to move to Tycho’s model. To both groups writ large, it didn’t break the scientific theories if orbits weren’t perfectly circular (partly that was because there wasn’t really a force driving motion in either theory until Kepler and he wasn’t sure what actually provided it, so we see how several scientific revolutions later, it gets hard to evaluate their theories 100% within the language of our current concepts), though people held on because of other attachments. Which leads to a second suggestion: be open-minded about theories and hypotheses, while still critical based on the structure. (And I think it’s pretty reasonable to argue that the Catholic Church was not open-minded in that sense, as De revolutionibus was restricted and Galileo published his future works in  Protestant jurisdictions.) In revolutions in progress, being open-minded means allowing for reasonable revision of competing theories (per the structure point) to accommodate new data and almost maybe more importantly allows for generating new predictions from these theories to guide more experiment and observation to determine what data needs to be gathered to finally declare a winning horse.

***
Stray thoughts

  1. Let me explain  how I corrected my view on the Coriolis effect. We mainly think of it as applying to motion parallel to the surface of the Earth, but on further thought, I realized it does also apply to vertical motion (something further from the center of the Earth is moving at a faster rotational velocity than something closer, though they do have the same angular velocity). Christopher Graney, a physics and astronomy professor at Jefferson Community and Technical College who I will now probably academically stalk to keep in mind for jobs back home, has a good summary of Riccioli’s arguments from the Almagestum Novum in an article on arXiv and also what looks like a good book that I’m adding to my history/philosophy of science wishlist on Amazon. The Coriolis effect arguments are Anti-Copernican Arguments III-VI, X-XXII, and XXVII-XXXIII. Riccioli also addresses the sunspots in Pro-Copernican Argument XLIII, though the argument is basically philosophical in determining what kind of motion is more sensible. It’s worth pointing out that in the Almagestum, Riccioli is collecting almost all arguments used on both sides in the mid-17th century, and he even points out which ones are wrong on both sides. This has led some historians to call it what Galileo’s Dialogue should have been, as Galileo pretty clearly favored heliocentrism in Dialogue but Riccioli remains relatively neutral in Almagestum.
  2. I’m concerned someone might play the annoying pedant by saying a) “But we know the sun isn’t the center of the Universe!” or b) “But relativity says you could think of the Earth as the center of the Universe!”. To a), well yeah, but it’s really hard to get to that point without thinking of us living in a solar system and thinking of other stars as like our sun. To b), look, you can totally shift the frames, but you’re basically changing the game at that point since no frame is special. Also, separate from that, if you’re really cranking out the general relativity equations, I still think you see more space-time deformation from the sun (unless something very weird happens in the non-inertial frame transform) so it still “dominates” the solar system, not the Earth.
  3. For a good example of the “consensus is dumb” listing of consensuses of the past, look at Michael Crichton’s rant from his “Aliens Cause Global Warming” 2003 Michelin Lecture at CalTech beginning around “In science consensus is irrelevant. What is relevant is reproducible results.” Crichton gets close to acknowledging that consensus does in fact seem to accommodate evidence in the plate tectonics example, but he writes it off. And to get to Crichton’s motivating point about climate science, it’s not like climate science always assumed man had a significant impact. The evolution of global warming theory goes back to Arrhenius who hypothesized around 1900 that the release of CO2 from coal burning might have an effect after studying CO2’s infrared spectrum, and it wasn’t until the 60s and 70s that people thought it might outweigh other human contributions (hence the oft-misunderstood “global cooling” stories about reports from the mid-20th century).
  4. Or to sum up something that a certain class of people would love to make a scientific revolution but isn’t, consider anthropogenic climate change. Honestly, specific local temperature predictions being wrong generally isn’t a big deal unless say most of them can’t be explained by other co-occurring phenomena (e.g. the oceans seem to have absorbed most of the heat instead of it leading to rising surface temperatures), since the central part of the theory is that emission of CO2 and certain other human-produced gases has a pretty effect due to radiative forcing which traps more heat in. Show that radiative forcing is wrong or significantly different from the current values, and that’s a really big deal. Or come up with evidence of something that might counter radiative forcing’s effect on temperature at almost the same scale, and while the concern would go away, I think it’s worth pointing out it wouldn’t actually mean research on greenhouse gases was wrong. I would also argue that you do open-mindedness in climate science, since people do still pursue the “iris hypothesis” and there are actually almost always studies on solar variability if you search NASA and NSF grants. 

Quantum Waves are Still Physical, Regardless of Your Thoughts

Adam Frank, founder of NPR’s science and culture blog 13.7, recently published an essay on Aeon about materialism. It’s a bit confusing to get at what he’s trying to say because of the different focus its two titles have, as well as his own arguments. First, the titles. The title I saw first, which is what is displayed when shared on Facebook, is “Materialism alone cannot explain the riddle of consciousness”. But on Aeon, the title is “Minding matter”, with the sub-title or blurb of “The closer your look, the more the materialist position in physics appears to rest on shaky metaphysical ground.” The question of theories of mind is very different than philosophical interpretations of quantum mechanics.

This shows up in the article, where I found it confusing because Franks ties together several different arguments and confuses them with various ideas of “realism” and “materialism”. First, his conception of theories of mind is confusing. I’d say the average modern neuroscientist or other scholar of cognition is a materialist, but I’d be hesitant to say the average one is a reductionist who thinks thought depends very hard on the atoms in your brain. Computational theories of mind tend to be some of the most popular ones, and it’s hard to consider those reductionist. I would concede there may be too much of an experimental focus on reductionism (and that’s what has diffused into pop culture), but the debate over how to move from those experimental techniques to theoretical understanding is occurring: see the recent attempt at using neuroscience statistical techniques to understand Donkey Kong.

I also think he’s making a bit of an odd claim on reductionism in the other sciences in this passage:

A century of agnosticism about the true nature of matter hasn’t found its way deeply enough into other fields, where materialism still appears to be the most sensible way of dealing with the world and, most of all, with the mind. Some neuroscientists think that they’re being precise and grounded by holding tightly to materialist credentials. Molecular biologists, geneticists, and many other types of researchers – as well as the nonscientist public – have been similarly drawn to materialism’s seeming finality.

Yes, he technically calls it materialism, but he seems to basically equate it to reductionism by assuming the other sciences seem fine with being reducible to physics. But, first, Frank should know better from his own colleagues. The solid-state folks in his department work a lot with “emergentism” and point out that the supposedly more reductionist particle people now borrow concepts from them. And he should definitely know from his collaborators at 13.7 that the concept of reducibility is controversial across the sciences. Heck, even physical chemists take issue with being reducible to physics and will point out that QM models can’t fully reproduce aspects of the periodic table. Per the above, it’s worth pointing out that Jerry Fodor, a philosopher of mind and cognitive scientist, who does believe in a computational theory of mind disputes the idea of reductionism

purity

This is funny because this tends to be controversial, not because it’s widely accepted.

Frank’s view on the nature of matter is also confusing. Here he seems to be suggesting “materialism” can really only refer to particulate theories of matter, e.g. something an instrument could definitely touch (in theory). But modern fundamental physics does accept fields and waves as real entities. “Shut up and calculate” isn’t useful for ontology or epistemology, but his professor’s pithy response actually isn’t that. Quantum field theories would agree that “an electron is that we attribute the properties of the electron” since electrons (and any particles) can actually take on any value of mass, charge, spin, etc. as virtual particles (which actually do exist, but only temporarily). The conventional values are what one gets in the process of renormalization in the theory. (I might be misstating that here, since I never actually got to doing QFT myself.) I would say this doesn’t mean electrons aren’t “real” or understood, but it would suggest that quantum fields are ontologically more fundamental than the particles are. If it makes more physical sense for an electron to be a probability wave, that’s bully for probability waves, not a lack of understanding. (Also, aside from experiments showing wave-particle duality, we’re now learning that even biochemistry is dependent on the wave nature of matter.)

I’m also not sure the discussion of wave function collapse does much work here. I don’t get why it would inherently undermine materialism, unless a consciousness interpretation were to win out, and as Frank admits, there’s still not much to support one interpretation over the other. (And even then, again, this could still be solved by a materialist view of consciousness.) He’s also ignoring the development of theories of quantum decoherence to explain wavefunction collapse as quantum systems interact with classical environments, and to my understanding, those are relatively agnostic to interpretation. (Although I think there’s an issue with timescales in quantitative descriptions.)

From there, Frank says we should be open to things beyond “materialism” in describing mind. But like my complaint with the title differences, those arguments don’t really follow from the bulk of the article focusing on philosophical issues in quantum mechanics. Also, he seems open to emergentism in the second to last paragraph. Actually, here I think Frank missed out on a great discussion. I think there are some great philosophy of science questions to be had at the level of QFT, especially with regards to epistemology, and especially directed to popular audiences. Even as a physics major, my main understanding of specific aspects of the framework like renormalization are accepted because “the math works”, which is different than other observables we measure. For instance, the anomalous magnetic moment is a very high precision test of quantum electrodynamics, the quantum field theory of electromagnetism, and our calculation is based on renormalization. But the “unreasonable effectiveness of mathematics” can sometimes be wrong and we might lucky in converging to something close. (Though at this point I might be pulling dangerously close to the Duhem-Quine thesis without knowing much of the technical details.) Instead, we got a mediocre crossover between the question of consciousness and interpretations of quantum mechanics, even though Frank tried hard to avoid turning into “woo”.

Why Can’t You Reach the Speed of Light?

A friend from high school had a good question that I wanted to share:
I have a science question!!! Why can’t we travel the speed of light? We know what it is, and that its constant. We’ve even seen footage of it moving along a path (it was a video clip I saw somewhere [Edit to add: there are now two different experiments that have done this. One that requires multiple repeats of the light pulse and a newer technique that can work with just one). So, what is keeping us from moving at that speed? Is it simply an issue of materials not being able to withstand those speeds, or is it that we can’t even propel ourselves or any object fast enough to reach those speeds? And if its the latter, is it an issue of available space/distance required is unattainable, or is it an issue of the payload needed to propel us is simply too high to calculate/unfeasable (is that even a word?) for the project? Does my question even make sense? I got a strange look when I asked someone else…
 This question makes a lot of sense actually, because when we talk about space travel, people often use light-years to discuss vast distances involved and point out how slow our own methods are in comparison. But it actually turns out the road block is fundamental, not just practical. We can’t reach the speed of light, at least in our current understanding of physics, because relativity says this is impossible.

To put it simply, anything with mass can’t reach the speed of light. This is because E=mc2 works in both directions. This equation means that the energy of something is its mass times the speed of light squared. In chemistry (or a more advanced physics class), you may have talked about the mass defect of some radioactive compounds. The mass defect is the difference in mass before and after certain nuclear reactions, which was actually converted into energy. (This energy is what is exploited in nuclear power and nuclear weapons. Multiplying by the speed of light square means even a little mass equals a lot of energy. The Little Boy bomb dropped on Hiroshima had 140 pounds of uranium, and no more than two pounds of that are believed to have undergone fission to produce the nearly 16 kiloton blast.)

But it also turns out that as something with mass goes faster, its kinetic energy also turns into extra mass. This “relativistic mass” greatly increases as you approach the speed of light. So the faster something gets, the heavier it becomes and the more energy you need to accelerate it. It’s worth pointing out that the accelerating object hasn’t actually gained material – if your spaceship was initially say 20 moles of unobtanium, it is still 20 moles of material even at 99% the speed of light. Instead, the increase in “mass” is due to the geometry of spacetime as the object moves through it. In fact, this is why some physicists don’t like using the term “relativistic mass” and would prefer to focus on the relativistic descriptions of energy and momentum. What’s also really interesting is that the math underlying this in special relativity also implies that anything that doesn’t have mass HAS to travel at the speed of light.

A graph with X-axis showing speed relative to light and Y-axis showing energy. A line representing the kinetic energy the object expoentially increases it approach light speed.

The kinetic energy of a 1 kg object at various fractions of the speed of light. For reference, 10^18 J is about a tenth of United States’ annual electrical energy consumption.

The graph above represents  the (relativistically corrected) kinetic energy of an 1 kilogram (2.2 pound) object at different speeds. You can basically think of it as representing how much energy you need to impart into the object to reach that speed. In the graph, I started at one ten thousandth the speed of light, which is about twice the speed the New Horizons probe was launched at. I ended it at 99.99% of the speed of light. Just to get to 99.999% of the speed of light would have brought the maximum up another order of magnitude.
Edit to add (9/12/2017): A good video from Fermilab argues against relativistic mass, but concedes it helps introduce relativity to more people.

Quick Thoughts on Diversity in Physics

Earlier this month, during oral arguments for Fisher v. University of Texas, Chief Justice John Roberts asked what perspective an African-American student would offer in physics classrooms. The group Equity and Inclusion in Physics and Astronomy has written an open letter about why this line of questioning may miss the point about diversity in the classroom. But it also seems worth pointing out why culture does matter in physics (and science more broadly).

So nature is nature and people can develop theoretical understanding of it anywhere and it should be similar (I think. This is actually glossing over what I imagine is a deep philosophy of science question.) But nature is also incredibly vast. People approach studies of nature in ways that can reflect their culture. Someone may choose to study a phenomenon because it is one they see often in their lives. Or they may develop an analogy between theory and some aspect of culture that helps them better understand a concept. You can’t wax philosphical about Kekule thinking of ouroboros when he was studying the structure of benzene without admitting that culture has some influence on how people approach science. There are literally entire books and articles about Einstein and Poincare being influenced by sociotechnical issues of late 19th/early 20th century Europe as they developed concepts that would lead to Einstein’s theories of relativity. A physics community that is a monoculture then misses out on other influences and perspectives. So yes, physics should be diverse, and more importantly, physics should be welcoming to all kinds of people.

It’s also worth pointing out this becomes immensely important in engineering and technology, where the problems people choose to study are often immensely influenced by their life experiences. For instance, I have heard people say that India does a great deal of research on speech recognition as a user interface because India still has a large population that cannot read or write, and even then, they may not all use the same language.

The Coolest Part of that Potentially New State of Matter

So we’ve discussed states of matter. And the reason they’re in the news. But the idea that this is a new state of matter isn’t particularly ground-breaking. If we’re counting electron states alone as new states of matter, then those are practically a dime a dozen. Solid-state physicists spend a lot of time creating materials with weird electron behaviors: under this defintion, lots of the newer superconductors are their own states of matter, as are topological insulators.

What is a big deal is the way this behaves as a superconductor. “Typical” superconductors include basically any metal. When you cool them to a few degrees above absolute zero, they lose all electrical resistance and become superconductive. These are described by BCS theory, a key part of which says that at low temperatures, the few remaining atomic vibrations of a metal will actually cause electrons to pair up and all drop to a low energy. In the 1970s, though, people discovered that some metal oxides could also become superconductive, and they did at temperatures above 30 K. Some go as high as 130 K, which, while still cold to us (room temperature is about 300 K), is warm enough to use liquid nitrogen instead of incredibly expensivve liquid helium for cooling. However, BCS theory doesn’t describe superconductivity in these materials, which also means we don’t really have a guide to develop ones with properties we want. The dream of a lot of superconductor researchers is that we could one day make a material that is superconducting at room temperature, and use that to make things like power transmission lines that don’t lose any energy.

This paper focused on an interesting material: a crystal of buckyballs (molcules of 60 carbon atoms arranged like a soccer ball) modified to have some rubidium and cesium atoms. Depending on the concentration of rubidium versus cesium in the crystal, it can behave like a regular metal or the new state of matter they call a “Jahn-Teller metal” because it is conductive but also has a distortion of the soccer ball shape from something called the Jahn-Teller effect. What’s particularly interesting is that these also correspond to different superconductive behaviors. At a concentration where the crystal is a regular metal at room temperatures, it becomes a typical superconductor at low temperatures. If the crystal is a Jahn-Teller metal, it behaves a lot like a high-temperature superconductor, albeit at low temperatures.

This is the first time scientists have ever seen a single material that can behave like both kinds of superconductor. This is exciting becasue this offers a unique testing ground to figure out what drives unconventional superconductors. By changing the composition, researchers change the behavior of electrons in the material, and can study their behavior, and see what makes them go through the phase transition to a superconductor.

What is a State of Matter?

This Vice article excitedly talking about the discovery of a new state of matter has been making the rounds a lot lately. (Or maybe it’s because I just started following Motherboard on Twitter after a friend pointed this article out) Which lead to two good questions: What is a state of matter? And how do we know we’ve found a new one? We’ll consider that second one another time.

In elementary school, we all learned that solid, liquid, and gas were different states of matter (and maybe if you’re science class was ahead of the curve, you talked about plasma). And recent scientific research has focused a lot on two other states of matter: the exotic Bose-Einstein condensate, which is looked at for many experiments to slow down light, and the quark-gluon plasma, which closely resembles the first few milliseconds of the universe after the Big Bang. What makes all of these different things states? Essentially a state of matter is the set behavior of the collection of particles that makes up your object of interest, and each state behaves so differently you can’t apply the description one to another. A crucial point here is that we can only consider multiple partcies to be states, and typically a large number of particles. If you somehow have only one molecule of water, it doesn’t really work to say whether it is solid, liquid, or gas because there’s no other water for it to interact with to develop collective properties.

So room temperature gold and ice are solids because they’re described by regular crystal lattices that repeat. Molten gold and water are no longer solids because they’re no longer described by a regular crystal structure but still have relatively strong forces between molecules. The key property of a Bose-Einstein condensate is that most of its constituent particles are in the lowest possible energy. You can tell when you switched states (a phase transition) because there was a discontinuous change in energy or a property related to energy. In everyday life, this shows up as the latent heat of melting and the latent heat of vaporization (or evaporation).

The latent heat of melting is what makes ice so good at keeping drinks cold. It’s not just the fact that ice is colder than the liquid; the discontinuous “jump” of energy required to actually melt 32°F  ice into 32°F water also absorbs a lot of heat. You can see this jump in the heating curve below. You also see this when you boil water. Just heating water to 212 degrees Fahrenheit doesn’t cause it all to boil away; your kettle/stove also has to provide enough heat to overcome the heat of vaporization. And that heating is discontinuous because it doesn’t raise the temperature until the phase transition is complete. You can try this for yourself in the kitchen with a candy thermometer: ice will always measure 32 F, even if  you threw it in the oven, and boiling water will always measure 212 F.

A graph with the horizontal axis labelled "Q (heat added}" and the veritcal axis labelled "temperature (in Celsius)". It shows three sloped segments, that are labelled, going from the left, ice, heating of water, and heating of water vapor. The sloped line for "ice" and "heating of water" are connected by a flat line representing heat used to melt ice to water. The "heating of water" and "heating of water vapor" sloped lines are connected by a flat line labelled "heat used to vaporize water to water vapor".

The heating curve of water. The horizontal axis represents how much heat has been added to a sample of water. The vertical axis shows the temperature. The flat lines are where heat is going into the latent heat of the phase transition instead of raising the temperature of the sample.

There’s also something neat about another common material related to phase transitions. The transition between a liquid and a glass state does not have a latent heat. This is the one thing that makes me really sympathetic to the “glasses are just supercooled liquids” views. Interestingly, this also means that there’s really no such thing as a single melting temperature for a given glass, because the heating/cooling rate becomes very important.

But then the latter bit of the article confused me, because to me it points out that “state of matter” seems kind of arbitrary compared to “phase”, which we talk about all the time in materials science (and as you can see, we say both go through “phase” transitions). A phase is some object with consistent properties throughout it, and a material with the same composition can be in different phases but still in the same state. For instance, there actually is a phase of ice called ice IX, and the arrangement of the water molecules in it is different from that in conventional ice, but we would definitely still consider both to be solids. Switching between these phases, even though they’re in the same state, also requires some kind of energy change.

Or if you heat a permanent magnet above its critical temperature and caused it to lose its magnetization, that’s the second kind of phase transition. That is, while the heat and magnetization may have changed continuously, the ease of magnetizing it (which is the second derivative of the energy with respect to strength of the magnetic field) had a jump at that point. Your material is still in a solid state and the atoms are still in the same positions, but it changed its magnetic state from permanent to paramagnetic. So part of me is wondering whether we can consider that underlying electron behavior to be a definition of a state of matter or a phase. The article makes it sound we’re fine saying they’re basically the same thing. This Wikipedia description of “fermionic condensates” as a means to describe superconductivity also supports this idea.

Going by this description then means we’re surrounded by way more states of matter than the usual four we consider. With solids alone, you interact with magnetic metals, conductors (metals or the semiconductors in your electronics), insulating solids, insulating glasses, and magnetic glasses (amorphous metals are used in most of those theft-prevention tags you see) on a regular basis, which all have different electron behaviors. It might seem slightly unsatisfying for something that sounds as fundamental as “states of matter” to end up having so many different categories, but it just reflects an increasing understanding of the natural world.