The Biggest Ideas in the Universe Quotes

“* The graviton hasn’t been directly detected, and possibly never will be, because individual gravitons interact extremely weakly with other particles. We only notice the gravity of the Earth because we’re feeling the combined gravitational attraction of 1050 atoms. But the basic tenets of quantum field theory and general relativity all but guarantee that gravitons exist. It is unique in being a spin-2 particle.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“One of the reasons we can make such sweeping statements with such confidence is a feature of QFT known as crossing symmetry. This is not a symmetry of physical fields but of the Feynman diagrams we use to describe their interactions. Roughly it says we can rotate any diagram by 90 degrees—converting particles to antiparticles when their direction in time gets reversed—and get another diagram with an equal amplitude.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“But there is a regime in which the Core Theory is entirely successful. If we don’t have strong gravitational fields, and we only consider processes taking place well below some prudently chosen ultraviolet cutoff (say 10 GeV), the basic structure of quantum field theory assures us that the Core Theory is the complete story.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“The Core Theory is obviously not the final theory of physics. It doesn’t describe dark matter or conditions of strong gravitational fields, and it features various coincidences and fine-tunings that suggest a more complete explanation yet to come. People have had some ideas about what such a complete theory might be like, but as of right now we don’t know. Nor do we know how close we are; a paper might be published with the final answer tomorrow, or we might still be looking for it a thousand years from now.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“What we’re left with includes two kinds of particles making up “matter”: Electrons 250 stable nuclides And we also have two long-range forces that are relevant to macroscopic physics: Electromagnetism Gravity”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“If the fundamental parameters of particle physics had been just a little bit different, protons could have been heavier than neutrons and would decay into them, rather than the other way around. That would make for a very boring universe. Our universe is interestingly complex because there are many kinds of stable nuclei, which are positively charged and can capture electrons, leading to rich forms of chemistry. If nuclei were all neutrons, they would be electrically neutral and unable to capture electrons. There would be no atoms, no chemistry, and no life.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“an effective field theory for particles and processes below some ultraviolet cutoff. And if that’s what we’re interested in, there is no trouble including gravity. We can take the spacetime metric gμν and write it as the sum of a background metric plus a small perturbation, , where is the metric of flat Minkowski spacetime. Then the perturbation hμν can be treated as an ordinary field propagating in flat spacetime as long as we stay away from black holes and other extreme gravitational phenomena. Its associated particle is of course the graviton. The resulting model has been dubbed the Core Theory by Frank Wilczek.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“Physicists often speak of the “Standard Model,” which doesn’t include gravity, since the Standard Model is a renormalizable quantum field theory, and the quantum version of general relativity would not be renormalizable.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“The real demand of the exclusion principle is that any two electrons have to be in completely orthogonal quantum states. If you try to make two of them overlap in almost the same configuration, one or both will be pushed into a higher-energy state. This creates a repulsion between the electrons known as an exchange force or Pauli repulsion. It is this repulsive force that is responsible for atoms taking up space, and thus for the solidity of matter. (For bosons there is an analogous attractive force. If electrons had been bosons, the universe would have been an utterly different place.)”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“The fact that electrons are fermions explains why matter is solid. Because electrons obey Fermi-Dirac statistics, we know that no two of them can occupy the same quantum state—the Pauli exclusion principle.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“THE SPIN-STATISTICS THEOREM We’ve seen that exchanging two identical fermions multiplies the wave function by a minus sign, while rotating a single spin-½ particle by 2π also picks up a minus sign. The essence of the spin-statistics theorem—bosons all have integer spins, fermions have half-integer spins—is that these two minus signs are secretly the same minus sign. For the wave function of several identical particles, exchanging two of them is equivalent to rotating just one of them. Since fermions pick up a minus sign under interchange, it also has to be true that they pick up a minus sign when rotated by 2π.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“Two things to note about this simple demonstration. First, you might detect a family resemblance between the picture of the forces due to a passing gravitational wave and a possible oscillation of a circular loop of string. That’s no coincidence. The reason why string theory, which was originally envisioned as an approach to the strong interactions, always ends up as a theory of gravity is that this particular mode of a vibrating closed string acts as a massless spin-2 particle, which we interpret as the graviton. (There’s more to being a graviton than just having the right spin—most important, coupling to all forms of energy-momentum, to satisfy the equivalence principle—but string theory predicts those properties as well.)”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“In the special case where we are restricted to two spatial dimensions rather than the usual three, the rules are a bit looser, and a new kind of particle called anyons become allowed. They were hypothesized by Jon Leinaas and Jan Myrheim and colleagues in 1977, and their properties elucidated by Frank Wilczek in 1982. The fundamental particles of the Standard Model live in three dimensions and are strictly bosons or fermions, but there are materials that support collective excitations that effectively live in just two dimensions. The existence of anyons in such systems was only verified experimentally in 2020.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“The real reason why all electrons have the same mass and charge is that they are all excitations of a single underlying electron field. As a result, any two electrons are identical particles: they are indistinguishable from each other, even in principle. This, plus the magic of quantum entanglement, has crucial consequences for how they behave in nature.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“The real reason why matter is solid comes down to the fact that electrons are fermions, and fermions have a special property: no two of them can be in the same quantum state. That’s why you can’t pile them on top of each other.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“atoms are not empty space, at least not in our wave function–realist way of thinking. The electron wave function spreads out into a certain definite shape within each atom. You can try to deform that shape, but it will generally cost a lot of energy.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“The electroweak theory plus the QCD model of strong interactions has an overall gauge symmetry of SU(3)×SU(2)×U(1). Together with the specific set of fermionic particles (six quarks, six leptons) and of course the Higgs field, the overall theory is known by the underwhelming name of the Standard Model of particle physics. The finishing theoretical touches were put on the Standard Model in the 1970s, and experimentalists have continued to verify the existence of all of its various particles.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“Nowadays we are sufficiently constrained that we have to work a bit harder to explain where the electron mass comes from, and ultimately we attribute it to the Higgs field pervading all of space. It’s not that the very notion of “mass” requires a Higgs field, it’s just that the restrictive structure of the Standard Model would forbid fermion masses if it weren’t for the Higgs getting a vacuum-expectation value and breaking the SU(2)×U(1) symmetry. That scenario, hatched in the 1960s, has been spectacularly confirmed in a long series of experimental results from the 1970s all the way up to the discovery of the Higgs boson itself in 2012.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“That just about does it for the electromagnetic and strong interactions. Both forces are based on gauge symmetries, and the corresponding gauge bosons are massless. A similar story holds for gravitation, which is described by general relativity. Gravitons interact with each other, but only very weakly, so gravitons are not confined, and gravity is in the Coulomb phase.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“Before we knew about gluons or strongly interacting flux tubes, it was noticed that certain hadrons fell into patterns we might expect from the vibrational modes of a string. This led to the invention of something called string theory. The idea never really fit as a theory of just strong interactions, but it grew into a framework for quantum gravity as well as all the other interactions together, and it is still extremely popular among theoretical physicists.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“In many ways the basic structure of QCD is much like that of QED. In both cases we have a connection gauge field, which gives rise to photons in QED and gluons in QCD. In QED we have electric charge, which is just a number, while in QCD we have color charges that live in a three-dimensional red/green/blue vector space. In both cases the force-carrying particles are massless, ultimately because of restrictions imposed by gauge invariance. The form of the kinetic terms and the interactions are largely the same.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“Similar reasoning applies to gravity as described by general relativity. In both cases we get long-range forces carried by massless particles because there are symmetries prohibiting the particles from obtaining mass, leading to inverse-square force laws (Coulomb’s law for electromagnetism, Newton’s law of universal gravitation for gravity). That’s why it’s those two forces that are most evident in our macroscopic, human-scale lives. The energy of a particle is related to its momentum and mass by E2 = p2 + m2, so the minimum energy a particle can have (namely, when p = 0) is E = m. It takes a certain minimum energy to create a massive particle; in terms of the forces they transmit, that implies that those forces diminish rapidly with distance. Massless particles, meanwhile, can be as low-energy as we wish. It takes little effort for low-energy virtual photons or gravitons to journey across vast distances of space, making long-range forces possible.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“Symmetries aren’t just a convenient simplification or an attractive aesthetic feature of quantum fields. Implementing them consistently leads directly to forces between particles of matter. That idea is at the heart of the Standard Model of particle physics.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“It’s important to internalize the ideas that (1) a group is defined by both its set of elements and the binary operation defined on that set, and (2) two groups that look different are really “the same,” as far as their groupness is concerned, if there is an isomorphism between them.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“The very first chapter in Space, Time, and Motion was devoted to the idea of “conservation.” One of the things we mentioned was Noether’s theorem, according to which every continuous symmetry transformation of a system is associated with a conserved quantity. And we said that a symmetry is a transformation you can do to a system that leaves its essential features unchanged.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“means that if you try to squeeze a particle into a region smaller than λC = 1/m, the quantum state becomes a superposition of one or more particles—not a single particle at all. The Compton wavelength is the smallest length scale at which we can safely think about the system as just representing one particle. In practice, this means that the Compton wavelength can be thought of as the “size” of a particle, as far as QFT is concerned. And notice that it goes down as the mass goes up. In quantum field theory, heavier particles occupy less space. It’s a funny concept of size, however, not completely harmonious with our classical intuition. The wave function of a particle can easily be spread out over a distance greater than its Compton wavelength; it just can’t be squeezed into less.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“So a particle at rest, with p = 0, has E = m, which we recognize as a famous equation once we remember we’re setting c = 1.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“When Louis de Broglie first suggested that particles had wave-like properties back in 1924, he proposed the relevant wavelength to have in mind for a particle with momentum p, what we now call the de Broglie wavelength, (7.4)”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“We don’t know what the ultimate theory of everything is, or even whether it’s a quantum field theory at all, certainly not down to ultra-small scales and high energies. But an effective field theory that derives from that ultimate theory will generally look renormalizable, at least to a good approximation.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe

“EFFECTIVE FIELD THEORY The puzzle of infinities was dealt with by Tomonaga, Schwinger, Feynman, Dyson, and their colleagues, with the first three sharing the Nobel Prize in Physics in 1965 for their efforts. The procedure they invented was dubbed renormalization. It is essentially a method for subtracting off infinity in a particular way that allows us to express the final answer to a scattering calculation in terms of physically measurable, finite quantities.”
― Sean Carroll, Quanta and Fields: The Biggest Ideas in the Universe