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”.

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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.

Going over the Critique of Cosmos part 1 and a brief review of part 2

Like I said before, Hank Campbell’s had some interesting critiques of the first episode of Cosmos. I thought nearly all of them missed the mark, and to be honest, it seems like he’s being a bit of a science hipster here. I want to go more in depth, and I’ll do that here. Let’s go through his points

1. Venus was not caused by global warming

Let’s look at what Campbell says:  “We have to ask why he thinks Venus is the way it is due to the greenhouse effect — which is another way of saying global warming. Venus is almost 900 degrees Fahrenheit and the clouds are sulfuric acid. Even the most aggressive climate change models and their 20-foot ocean rises don’t predict that for Earth… If this sequel to Cosmos had been made in 1989 the screenwriters of Cosmos would have invoked acid rain on Venus instead of global warming. Regardless, CO2 did not cause the poisonous conditions on Venus; instead, CO2 is an effect of the poisonous conditions on Venus. Invoking the greenhouse effect when talking about Venus is like blaming ocean liners for inventing barnacles.

Okay, but global warming isn’t the same as the greenhouse effect.  If it weren’t for the CO2, SO2, and H2O, Earth’s surface temperature would be significantly lower. That is the definition of the greenhouse effect. More technically, the greenhouse effect is when a gas in an atmosphere can absorb heat radiated from a planet surface, which then redirects some of the heat escaping from the planet back towards the surface. This shift the temperature equilibrium to higher than it would without the greenhosue gas. In an exchange on a follow-up on his website, Science 2.0, Campbell says the real culprit is hydrogen escape. (Note: I’m the “Matt” participating in the comment section.) “On Venus gravity, hydrogen is already light so a lack of gravity causes the water problem to go nuts. No water, CO2 goes crazy – but CO2 did not cause the atmosphere of Venus, Tyson knows it, anyone who knows high school atmospheric science knows it…”

Campbell probably overestimates hydrogen escape by itself. Hydrogen escapes from Earth too (we’re predicted to lose our all water due to hydrogen escape within the next billion years). Also, Venus’ surface gravity is about 90% that of Earth’s, so hydrogen shouldn’t experience that much weaker of a pull to the planet that it does here.  The chain of cause and effect leading to atmospheric changes on Venus doesn’t mean the greenhouse effect doesn’t describe the current temperature, or ever played an effect in the evolution of Venus’ climate. Even planetary scientists describe Venus’ history as the result of a “runaway greenhouse effect”. Once most of Venus’ water was in the atmosphere, it stayed that way because water vapor is also a greenhouse gas and raised the temperature enough to prevent condensation into massive oceans that could have held on to the water longer. (It’s easier to strip hydrogen from molecules in the atmosphere.) This is also why I don’t buy the idea that this segment relates at all to climate change debates. CO2 is not the only greenhouse gas, and this is typically mentioned in modern discussions about methane, and Tyson didn’t actually mention the concentration of CO2 in Venus’ atmosphere. Campbell takes his concern of framing too far here.

2. The Multiverse is Not Science

Campbell: “Any time a scientist begins a sentence with “Many of us suspect,” it is codespeak for “we sit around and discuss it at the bar.”

Why not just let that go as artistic license? When Carl Sagan was filming the originalCosmos program, physicists Alan Guth and Andrei Linde had not even come up with “inflation” for the Big Bang that Tyson mentions casually. Thus, it would not have made it into the original Cosmos as fact. Too much speculation makes the audience wonder if scientists are going to be trusted guides or another version of Dr. Oz and his Miracle Vegetable of the week. Science doesn’t need to toss in speculation to be interesting, because what we know and therefore don’t know is fascinating enough.”

“The multiverse is not science. It is more like an anthropic secular alternative to a divine origin. It’s not science because it can’t be proved or disproved — it’s just postmodernism with some math. And it’s invoked shortly after the introduction where Tyson tells us to test everything.”

I also kind of cringed when Tyson mentioned a multiverse and it even had a visualization with the spaceship of the imagination. But if you pay attention to the language of the episode, you’ll see that the writers were actually being pretty deliberate. Tyson used “suspect” here. But for the rest of the episode, Tyson never describes a scientific theory as anything less than a fact (which is how scientists treat theories). This means Cosmos is not elevating the idea of a multiverse to the level of accepted scientific theory. And it is true that many physicists and cosmologists “suspect” a multiverse.  Also, Campbell seems to only be thinking of a string theory multiverse in his critique. Tyson’s description didn’t specify the “kind” of multiverse, but the description and visualization seemed to suggest one resulting from “chaotic inflation”. That kind of multiverse actually may be testable if we see an “imprint”, and the new gravitational wave measurements suggest chaotic inflation is the inflation model that more closely matches our universe.

3. There is No Sound In Space

Like I said before, there actually isn’t a good defense of this. Tyson wouldn’t accept it in any other show, and I’m surprised he let that happen here.

4. Giordano Bruno Was Not More Important To Science Than Kepler And Galileo

Like I said before “The episode did not claim Bruno was more important than contemporary natural philosophers and empiricists and definitely pointed out that he wasn’t a scientist. Bruno’s ideas, though, do fit in well with the idea of understanding our place in the universe, which was the entire point of the first episode, as stated in like the first five minutes.”

5. The Universe Was Also Not Created in One Year

“On January 1st, we had the Big Bang and on December 31st, I am alive, less than a tiny fraction of a millisecond before midnight. That can’t be right — it took me a whole day just to write this article.

Oh, Cosmos is not being literal? Oddly, a number of religious critics, Tyson included, insist that too many religious people believe the Book of Genesis is taken literally by people who read the Bible. Unless we accept that figurative comparisons help make large ideas manageable, a year is no more accurate than six days — it is instead a completely arbitrary metric invented to show some context for how things evolved.”

Oh my God, seriously? Hank Campbell is trying so hard to not want to be in a culture war that he wound up back in it. First, Tyson is not nearly as involved in the science aspect of the “culture war” as, say, Richard Dawkins. Also, many Americans don’t take the Biblical account of Genesis figuratively. According to a 2012 Gallup poll, 46% of Americans think God created humans instantly in their present form within the last 10,000 years.

All these complaints just seem… odd. Like I said, “science hipster” is the best description I can think of. I was surprised to hear Campbell really liked the second episode. I actually liked that episode less. The description of the evolution of the eye seemed like a just-so story  in some steps, and probably would not win over the creationists who argue that “the eye is too complex to have evolved”. I thought the step showing the evolution of the lens seemed HUGE and it wasn’t associated with an organism like most of the other steps were. I feel like it would have been more straightforward to show the variety of eyes in the context of the tree of life, but maybe I say this because I’m not as familiar with evolutionary biology. The visualization of DNA seemed “too busy” at times, and they kept changing schematic representations without explaining it. I get that DNA doesn’t really look as pretty as it does in my old bio textbooks, but I was unsure of what was being represented at times. I thought the comparison of DNA sequences seemed a bit odd without a description of what base pairs are.

The Titan bit also seemed odd. I liked the description of Titan, but didn’t like the idea of the ship of the imagination visiting a hydrothermal vent (or its analogue) there. To me it seemed like the show was saying the hydrocarbon lakes on Titan are as deep as Earth’s oceans, and unless I’m really behind the times, I don’t think we know the depth that much. And we definitely don’t know if there are hydrothermal vents on Titan, and that visualization wasn’t accompanied by Tyson saying we “suspect” or some other phrase that would give it less of a weight than a theory/fact like the multiverse visualization was.

Are We Living in a Physicist’s Nightmare?

So about a year ago, physicists at CERN announced the discovery of the Higgs boson (or more technically, a “Higgs-like particle” that has now been confirmed to be the Higgs) in the LHC. And you probably haven’t heard much about the collider since then.  Part of that is because the the discovery (or non-discovery) of the Higgs at the energies the LHC was probing at was one of the biggest tests of the Standard Model of Particle Physics, which was one of the major selling points of building the LHC in the first place. And since February of this year, the LHC has been shut down to allow for technical improvements that will turn it into an even more energetic detector (and in particle physics, the more energetic you are, the more you can see). If you’re really tuned into CERN, you may know that in November of last year, researchers announced observations of a rare kind of meson decay into muons (which are like heavier electrons).

But part of the reason also seems to be that the results from before the shutdown don’t give physicists much new to theorize on. The Higgs boson was discovered to have the mass predicted by the Standard Model, and so served as a great test of that. But that also means it doesn’t really offer anything new for theorists. And though the muon decay hasn’t been verified yet to the statistical significance that particle physicists consider to mean a discovery, what has been found so far still fits into the Standard Model. Neither of these findings fit into most of the common models of supersymmetry, which is believed to be a necessary component of string theory, which is currently the dominant idea to go beyond the Standard Model to a “theory of everything”.

The stakes for various new physics that researchers hope to find at the LHC.

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