How physics lowered the value of mass
Modern physics teaches us that mass is not an internal property of matter.
Here you are sitting and reading this article. Perhaps on paper, perhaps in an e-book, on a tablet, or on a computer. It does not matter. Whatever reading device you use, you can be sure that it consists of some substance: paper, plastic, tiny electronic stuff, printed circuit boards. Whatever it is, we call it matter, material substance. He has strength, he has weight.
But what is matter? Imagine an ice cube with a 2.7 cm edge. Imagine holding it in your palm. It is cold and a bit slippery. He weighs little, but he does have some weight.
Let's clarify the question. What does an ice cube consist of? And the second important question: what is responsible for its mass?
To understand what the ice cube is made of, we need to turn to the knowledge gained by chemists. According to a long tradition founded by alchemists, these scientists distinguish individual chemical elements - hydrogen, carbon, oxygen. Studies of the relative weights of such elements and the combination of gas volumes led John Dalton and Louis Gay-Lussac to the conclusion that various chemical elements are composed of atoms of different weights, which are combined according to the rules, in which a whole number of atoms participate.
The riddle of combining gases such as hydrogen and oxygen to produce water was solved when they realized that hydrogen and oxygen are diatomic gases, that is, H 2 and O 2 . And water is a compound substance containing two hydrogen atoms and one oxygen atom, H 2 O.
This partially answers our first question. Our ice cube consists of periodically organized H 2 O molecules. We can already begin to answer the second question. The Avogadro law postulates that a mole of a chemical contains 6 × 10 23 individual “particles”. We can imagine a mole of a substance as a molecular weight scaled to a quantity comparable to a gram. Hydrogen in the form of H 2 has a relative molecular weight (or molecular weight ) of 2, which means that each atom has a relative atomic weight of 1. In oxygen O 2, the molecular weight is 32, which means that each atom has an atomic weight of 16 Therefore, H 2 O water has a molecular weight of 2 × 1 + 16 = 18
So it turns out that our ice cube weighs about 18 grams, which means that it represents one mole of water. According to the Avogadro law, in this case it should contain about 6 Ă— 10 23 H 2 O molecules. This would seem to give a definite answer to our second question. The mass of the ice cube is obtained from the mass of hydrogen and oxygen atoms contained in 6 Ă— 1023 H 2 O molecules.
But we, of course, can go further. JJ Thomson , Ernest Rutherford , Niels Bohr, and many other physicists at the beginning of the 20th century taught us that all atoms consist of a heavy central nucleus surrounded by light electrons in their orbits. Then we learned that the central nucleus consists of protons and neutrons. The number of protons in the nucleus determines the chemical identity of the element: the hydrogen atom has one proton, and the oxygen atom has eight (this is called the atomic number). But the total mass, or the weight of the nucleus, is determined by the total number of protons and neutrons.
Hydrogen is still a unit (its nucleus consists of one proton - without neutrons). At the most common oxygen isotope - guess? - 16 (eight protons and eight neutrons). Obviously, it will not be a coincidence at all that these protons and neutrons are counted in exactly the same way as the atomic mass mentioned.
If we ignore light electrons, then we will be tempted to state that the mass of the ice cube is contained in all protons and neutrons in the nuclei of its hydrogen and oxygen atoms. Each H 2 O molecule contributes 10 protons and 8 neutrons, so if the cube contains 6 Ă— 10 23 molecules, and we can ignore the small difference between the masses of the proton and the neutron, we can conclude that the cube contains 18 times more particles, i.e. , 108 Ă— 10 23 protons and neutrons.
It's okay for now. But we have not finished yet. Now we know that protons and neutrons are not elementary particles. They consist of quarks. The proton consists of two upper quarks and a lower quark, and a neutron consists of two lower quarks and a top one [ in fact, not quite so / approx. trans. ]. And the color interactions linking quarks together inside larger particles are carried by massless gluons.
Okay, so we just need to continue on. If we again take the masses of the upper and lower quarks to be approximately equal, we simply multiply our number by three, and turn 108 Ă— 10 23 protons and neutrons into 324 Ă— 10 23 upper and lower quarks. And we can conclude that this is where the whole mass is contained. Yes?
Not. At this stage, our naive prejudices associated with atoms are crumbling. We can see the masses of the upper and lower quarks on the site of the Particle Data Group [ international collaboration of physicists compiling the results obtained in the study of particles / approx. trans. ]. The upper and lower quark are so light that their masses cannot be measured precisely, therefore only ranges are given there. The following numbers are in MeV / s 2 . In these units, the mass of the upper quark is approximately equal to 2.3, in the range from 1.8 to 3.0. Lower Quark heavier, 4.8, with a range from 4.5 to 5.3. Compare these masses with the mass of an electron in the same units: 0.51.
And now the shocking news. In the same units, MeV / s 2 , the proton mass is 938.3, the neutron mass is 939.6. But the combination of two upper and one lower quark gives us only 9.4, only 1% of the mass of the proton. The combination of two lower and one upper quark gives us only 11.9, or 1.3% of the mass of the neutron. And 99% of the mass of the proton and neutron have gone somewhere. What went wrong?
To answer this question, you need to understand what we are dealing with. Quarks are not independent particles of this type, as the ancient Greeks or mechanical philosophers would imagine. These are quantum particle waves; fundamental vibrations, or fluctuations of elementary quantum fields. The upper and lower quark are only several times heavier than an electron, and we have demonstrated the wave-particle nature of an electron in countless laboratory experiments. We need to prepare for strange, if not to say, unnatural behavior.
And let's not forget about the massless gluons. And about the special theory of relativity and E = mc 2 . Or about the " naked " and "dressed" masses. And yet, last in order, but not least, let's not forget about the role of the Higgs field as a “source” of the mass of all elementary particles. To understand what is happening inside a proton or neutron, we need to turn to quantum chromodynamics, to quantum field theory of the color interaction of quarks.
Quarks and gluons have a “ color charge ”. But what is it really? We have no way of knowing this. We know that color is a property of quarks and gluons, that there are three types of it that physicists choose to call red, green, and blue. But just as no one has ever seen an isolated quark or gluon, so, by and large, by definition, no one has ever seen a bare color charge. In fact, quantum chromodynamics (QCD) states that if such a bare charge had appeared, its energy would be almost infinite. Aristotle's aphorism sounded like " nature does not tolerate emptiness ." Today we could say: “nature does not tolerate a bare color charge”.
So what happens if we somehow manage to create an isolated quark with a colored charge exposed to everyone? His energy will exceed all limits, it is enough to cause virtual gluons from the "empty" space. Just as an electron moving in its own self-generated electromagnetic field collects a crowd of virtual photons accompanying it, so a bare quark collects the virtual gluons accompanying it. But unlike photons, gluons transfer their color charge and are able to reduce energy through, in particular, masking an open color charge. Imagine it like this: a naked quark is very embarrassed, and quickly puts on a cape of gluons.
But this is not enough. This energy is high enough not just to cause virtual particles (resembling background noise or hissing), but also real elementary particles. In this fight for the right to cover a bare color charge, an antiquark appears, mating with a bare quark and forming a meson. So a quark is never — never is — seen without an accompanying person.
But this is not enough. In order to fully cover the color charge, we need to place the antiquark in exactly the same place and exactly at the same time as the quark. The Heisenberg uncertainty principle prohibits nature from specifying the location of a quark and an antiquark in this way. Recall that accurate position measurement leads to an infinite pulse, and the exact rate of change of energy over time leads to infinite energy. Nature has no choice but to compromise. She can not completely hide the color charge, but can disguise it with the help of antiquark and virtual gluons. Then the energy is at least reduced to a controlled level.
The same thing happens inside protons and neutrons. Within the limits imposed by their host particles, three quarks are relatively free to rush here and there. But their colored charges must also be covered up, or at least it is necessary to reduce the energy of the bare charges. Each quark leads to the appearance of a whole blizzard of virtual gluons, rushing between them, together with quark-antiquark pairs. Physicists sometimes call the three quarks that make up a proton or neutron, " valence " quarks, because inside these particles there is enough energy for a quark-antiquark pair to appear. Valence quarks are not the only quarks inside these particles.
This means that the mass of protons and neutrons can be mainly attributed to the energy of gluons and the sea of ​​quark-antiquark pairs caused from a colored field.
How do we know this? We have to admit that it is actually quite difficult to perform calculations using QCD. The color interaction is extremely strong, and the corresponding interaction energies are therefore very high. Remember that gluons also have a color charge, so everything interacts with everything else. Almost anything can happen, and it is rather difficult to take into account all possible transformations of virtual and elementary particles.
This means that although the QCD equations can be written relatively simply, they cannot be solved analytically, on paper. In addition, mathematical manual dexterity, so successfully used in quantum electrodynamics, is no longer applicable - because the interaction energies are so high that we cannot apply the renormalization . Physicists have no choice but to solve these equations on a computer.
Greater progress has been achieved with the help of the “lightweight” version of QCD [QCD-lite]. It considers only massless gluons, upper and lower quarks, and assumes that the quarks themselves are also massless (that is, literally "lightweight"). Calculations carried out with such approximations gave a proton mass of only 10% less than the measured one.
Let's stop for a minute and think about it. A simplified version of QCD, in which we mean that particles do not have masses, still gives 90% of the correct mass of proton. It turns out an amazing conclusion. Most of the proton mass comes from the energy of the interactions of its constituent quarks and gluons.
John Wheeler used the phrase “mass without mass” to describe the effects of superpositions of gravitational waves, capable of concentrating and localizing energy so that a black hole appears. If this happened, it would mean that the black hole - the ultimate manifestation of superdense matter - was created not from the matter of a collapsing star, but from the fluctuations of space-time. What Wheeler really wanted to say was that such a case would be an example of the creation of a black hole (mass) from gravitational energy.
But the phrase Wheeler and we are great. Frank Wilczek , one of the founders of QCD, used it in connection with the discussion of the results of calculations of lightweight QCD. If a large part of the proton and neutron mass comes from the energy of the interactions occurring inside these particles, then it really turns out to be “mass without mass”, which means that we have on our hands a behavior that we assign to mass, which does not require mass as properties .
Sounds familiar? Recall that in his fruitful addition to the work of 1905 on the special theory of relativity, Einstein’s equation actually looks like m = E / c 2 . And this is a great idea (not E = mc 2 ). And Einstein, in fact, prophetically wrote: “body mass is a measure of its energy content” [Einstein, A.] Annalen der Physik 18 (1905)]. The way it is. In his book, Lightness of Being [Wilczek, F. The Lightness of Being, Basic Books, New York, NY (2008)], Wilczek wrote:
The splitting of the uranium-235 nucleus releases some of the energy of the colored fields contained within protons and neutrons, with potentially explosive consequences. In the proton-proton chain, which includes the synthesis of four protons, the transformation of the two upper quarks into two lower quarks, which form two neutrons in the process, leads to the release of the excess energy of their color fields. Mass does not turn into energy. Energy is transferred from one type of quantum field to another.
And what do we get? We, of course, have come a long way since the atomists of ancient Greece talked about the nature of material matter 2500 years ago. But most of the time, we were convinced that matter is a fundamental part of our physical universe. We were convinced that energy is contained in matter. And, although matter can be reduced to microscopic constituents, for a long time we thought that they would still be matter, and possess such a basic quality as mass.
Modern physics teaches us something completely different, completely counterintuitive. Paving our way deeper inside - decomposing matter into atoms, atoms into subatomic particles, subatomic particles into quantum fields and interactions - we completely lost sight of matter. Matter has lost touch. It lost its superiority, and mass became a secondary property, the result of interactions between intangible quantum fields. What we consider to be mass is the behavior of these quantum fields; it is not a property belonging to them or necessarily inherent.
Despite the fact that our world is filled with hard and heavy things, the energy of quantum fields rules the ball. Mass becomes just a physical manifestation of this energy, and not vice versa.
Conceptually, it looks shocking, but at the same time extremely attractive. The great unifying property of the Universe is the energy of quantum fields, not rigid, impenetrable atoms. Perhaps this is not exactly the dream that philosophers could hold on to, but it is still a dream.
Jim Beggot is a freelance journalist and writer who lectured in chemistry, then worked for Shell, and now works as an independent business consultant and trainer. Among his many books are: The Scientific Story of Creation, The Higgs: The Invention and the Discovery of the God Particle, The Quantum History: The Story of Creation moments “[A Quantum Story: A History in 40 Moments] and“ A Beginner's Guide to Reality].
An adapted excerpt from the book: “Mass: in search of understanding of matter from Greek atoms to quantum fields” [Mass: The quest to understand matter from Greek atoms to quantum fields].
Here you are sitting and reading this article. Perhaps on paper, perhaps in an e-book, on a tablet, or on a computer. It does not matter. Whatever reading device you use, you can be sure that it consists of some substance: paper, plastic, tiny electronic stuff, printed circuit boards. Whatever it is, we call it matter, material substance. He has strength, he has weight.
But what is matter? Imagine an ice cube with a 2.7 cm edge. Imagine holding it in your palm. It is cold and a bit slippery. He weighs little, but he does have some weight.
Let's clarify the question. What does an ice cube consist of? And the second important question: what is responsible for its mass?
To understand what the ice cube is made of, we need to turn to the knowledge gained by chemists. According to a long tradition founded by alchemists, these scientists distinguish individual chemical elements - hydrogen, carbon, oxygen. Studies of the relative weights of such elements and the combination of gas volumes led John Dalton and Louis Gay-Lussac to the conclusion that various chemical elements are composed of atoms of different weights, which are combined according to the rules, in which a whole number of atoms participate.
The riddle of combining gases such as hydrogen and oxygen to produce water was solved when they realized that hydrogen and oxygen are diatomic gases, that is, H 2 and O 2 . And water is a compound substance containing two hydrogen atoms and one oxygen atom, H 2 O.
This partially answers our first question. Our ice cube consists of periodically organized H 2 O molecules. We can already begin to answer the second question. The Avogadro law postulates that a mole of a chemical contains 6 × 10 23 individual “particles”. We can imagine a mole of a substance as a molecular weight scaled to a quantity comparable to a gram. Hydrogen in the form of H 2 has a relative molecular weight (or molecular weight ) of 2, which means that each atom has a relative atomic weight of 1. In oxygen O 2, the molecular weight is 32, which means that each atom has an atomic weight of 16 Therefore, H 2 O water has a molecular weight of 2 × 1 + 16 = 18
So it turns out that our ice cube weighs about 18 grams, which means that it represents one mole of water. According to the Avogadro law, in this case it should contain about 6 Ă— 10 23 H 2 O molecules. This would seem to give a definite answer to our second question. The mass of the ice cube is obtained from the mass of hydrogen and oxygen atoms contained in 6 Ă— 1023 H 2 O molecules.
But we, of course, can go further. JJ Thomson , Ernest Rutherford , Niels Bohr, and many other physicists at the beginning of the 20th century taught us that all atoms consist of a heavy central nucleus surrounded by light electrons in their orbits. Then we learned that the central nucleus consists of protons and neutrons. The number of protons in the nucleus determines the chemical identity of the element: the hydrogen atom has one proton, and the oxygen atom has eight (this is called the atomic number). But the total mass, or the weight of the nucleus, is determined by the total number of protons and neutrons.
Hydrogen is still a unit (its nucleus consists of one proton - without neutrons). At the most common oxygen isotope - guess? - 16 (eight protons and eight neutrons). Obviously, it will not be a coincidence at all that these protons and neutrons are counted in exactly the same way as the atomic mass mentioned.
If we ignore light electrons, then we will be tempted to state that the mass of the ice cube is contained in all protons and neutrons in the nuclei of its hydrogen and oxygen atoms. Each H 2 O molecule contributes 10 protons and 8 neutrons, so if the cube contains 6 Ă— 10 23 molecules, and we can ignore the small difference between the masses of the proton and the neutron, we can conclude that the cube contains 18 times more particles, i.e. , 108 Ă— 10 23 protons and neutrons.
It's okay for now. But we have not finished yet. Now we know that protons and neutrons are not elementary particles. They consist of quarks. The proton consists of two upper quarks and a lower quark, and a neutron consists of two lower quarks and a top one [ in fact, not quite so / approx. trans. ]. And the color interactions linking quarks together inside larger particles are carried by massless gluons.
Okay, so we just need to continue on. If we again take the masses of the upper and lower quarks to be approximately equal, we simply multiply our number by three, and turn 108 Ă— 10 23 protons and neutrons into 324 Ă— 10 23 upper and lower quarks. And we can conclude that this is where the whole mass is contained. Yes?
Not. At this stage, our naive prejudices associated with atoms are crumbling. We can see the masses of the upper and lower quarks on the site of the Particle Data Group [ international collaboration of physicists compiling the results obtained in the study of particles / approx. trans. ]. The upper and lower quark are so light that their masses cannot be measured precisely, therefore only ranges are given there. The following numbers are in MeV / s 2 . In these units, the mass of the upper quark is approximately equal to 2.3, in the range from 1.8 to 3.0. Lower Quark heavier, 4.8, with a range from 4.5 to 5.3. Compare these masses with the mass of an electron in the same units: 0.51.
And now the shocking news. In the same units, MeV / s 2 , the proton mass is 938.3, the neutron mass is 939.6. But the combination of two upper and one lower quark gives us only 9.4, only 1% of the mass of the proton. The combination of two lower and one upper quark gives us only 11.9, or 1.3% of the mass of the neutron. And 99% of the mass of the proton and neutron have gone somewhere. What went wrong?
To answer this question, you need to understand what we are dealing with. Quarks are not independent particles of this type, as the ancient Greeks or mechanical philosophers would imagine. These are quantum particle waves; fundamental vibrations, or fluctuations of elementary quantum fields. The upper and lower quark are only several times heavier than an electron, and we have demonstrated the wave-particle nature of an electron in countless laboratory experiments. We need to prepare for strange, if not to say, unnatural behavior.
And let's not forget about the massless gluons. And about the special theory of relativity and E = mc 2 . Or about the " naked " and "dressed" masses. And yet, last in order, but not least, let's not forget about the role of the Higgs field as a “source” of the mass of all elementary particles. To understand what is happening inside a proton or neutron, we need to turn to quantum chromodynamics, to quantum field theory of the color interaction of quarks.
Quarks and gluons have a “ color charge ”. But what is it really? We have no way of knowing this. We know that color is a property of quarks and gluons, that there are three types of it that physicists choose to call red, green, and blue. But just as no one has ever seen an isolated quark or gluon, so, by and large, by definition, no one has ever seen a bare color charge. In fact, quantum chromodynamics (QCD) states that if such a bare charge had appeared, its energy would be almost infinite. Aristotle's aphorism sounded like " nature does not tolerate emptiness ." Today we could say: “nature does not tolerate a bare color charge”.
So what happens if we somehow manage to create an isolated quark with a colored charge exposed to everyone? His energy will exceed all limits, it is enough to cause virtual gluons from the "empty" space. Just as an electron moving in its own self-generated electromagnetic field collects a crowd of virtual photons accompanying it, so a bare quark collects the virtual gluons accompanying it. But unlike photons, gluons transfer their color charge and are able to reduce energy through, in particular, masking an open color charge. Imagine it like this: a naked quark is very embarrassed, and quickly puts on a cape of gluons.
But this is not enough. This energy is high enough not just to cause virtual particles (resembling background noise or hissing), but also real elementary particles. In this fight for the right to cover a bare color charge, an antiquark appears, mating with a bare quark and forming a meson. So a quark is never — never is — seen without an accompanying person.
But this is not enough. In order to fully cover the color charge, we need to place the antiquark in exactly the same place and exactly at the same time as the quark. The Heisenberg uncertainty principle prohibits nature from specifying the location of a quark and an antiquark in this way. Recall that accurate position measurement leads to an infinite pulse, and the exact rate of change of energy over time leads to infinite energy. Nature has no choice but to compromise. She can not completely hide the color charge, but can disguise it with the help of antiquark and virtual gluons. Then the energy is at least reduced to a controlled level.
The same thing happens inside protons and neutrons. Within the limits imposed by their host particles, three quarks are relatively free to rush here and there. But their colored charges must also be covered up, or at least it is necessary to reduce the energy of the bare charges. Each quark leads to the appearance of a whole blizzard of virtual gluons, rushing between them, together with quark-antiquark pairs. Physicists sometimes call the three quarks that make up a proton or neutron, " valence " quarks, because inside these particles there is enough energy for a quark-antiquark pair to appear. Valence quarks are not the only quarks inside these particles.
This means that the mass of protons and neutrons can be mainly attributed to the energy of gluons and the sea of ​​quark-antiquark pairs caused from a colored field.
How do we know this? We have to admit that it is actually quite difficult to perform calculations using QCD. The color interaction is extremely strong, and the corresponding interaction energies are therefore very high. Remember that gluons also have a color charge, so everything interacts with everything else. Almost anything can happen, and it is rather difficult to take into account all possible transformations of virtual and elementary particles.
This means that although the QCD equations can be written relatively simply, they cannot be solved analytically, on paper. In addition, mathematical manual dexterity, so successfully used in quantum electrodynamics, is no longer applicable - because the interaction energies are so high that we cannot apply the renormalization . Physicists have no choice but to solve these equations on a computer.
Greater progress has been achieved with the help of the “lightweight” version of QCD [QCD-lite]. It considers only massless gluons, upper and lower quarks, and assumes that the quarks themselves are also massless (that is, literally "lightweight"). Calculations carried out with such approximations gave a proton mass of only 10% less than the measured one.
Let's stop for a minute and think about it. A simplified version of QCD, in which we mean that particles do not have masses, still gives 90% of the correct mass of proton. It turns out an amazing conclusion. Most of the proton mass comes from the energy of the interactions of its constituent quarks and gluons.
John Wheeler used the phrase “mass without mass” to describe the effects of superpositions of gravitational waves, capable of concentrating and localizing energy so that a black hole appears. If this happened, it would mean that the black hole - the ultimate manifestation of superdense matter - was created not from the matter of a collapsing star, but from the fluctuations of space-time. What Wheeler really wanted to say was that such a case would be an example of the creation of a black hole (mass) from gravitational energy.
But the phrase Wheeler and we are great. Frank Wilczek , one of the founders of QCD, used it in connection with the discussion of the results of calculations of lightweight QCD. If a large part of the proton and neutron mass comes from the energy of the interactions occurring inside these particles, then it really turns out to be “mass without mass”, which means that we have on our hands a behavior that we assign to mass, which does not require mass as properties .
Sounds familiar? Recall that in his fruitful addition to the work of 1905 on the special theory of relativity, Einstein’s equation actually looks like m = E / c 2 . And this is a great idea (not E = mc 2 ). And Einstein, in fact, prophetically wrote: “body mass is a measure of its energy content” [Einstein, A.] Annalen der Physik 18 (1905)]. The way it is. In his book, Lightness of Being [Wilczek, F. The Lightness of Being, Basic Books, New York, NY (2008)], Wilczek wrote:
If the mass of the human body mainly originates from the protons and neutrons contained in it, the answer is now clear and final. The inertia of this body with an accuracy of 95% relates to its energy content.
The splitting of the uranium-235 nucleus releases some of the energy of the colored fields contained within protons and neutrons, with potentially explosive consequences. In the proton-proton chain, which includes the synthesis of four protons, the transformation of the two upper quarks into two lower quarks, which form two neutrons in the process, leads to the release of the excess energy of their color fields. Mass does not turn into energy. Energy is transferred from one type of quantum field to another.
And what do we get? We, of course, have come a long way since the atomists of ancient Greece talked about the nature of material matter 2500 years ago. But most of the time, we were convinced that matter is a fundamental part of our physical universe. We were convinced that energy is contained in matter. And, although matter can be reduced to microscopic constituents, for a long time we thought that they would still be matter, and possess such a basic quality as mass.
Modern physics teaches us something completely different, completely counterintuitive. Paving our way deeper inside - decomposing matter into atoms, atoms into subatomic particles, subatomic particles into quantum fields and interactions - we completely lost sight of matter. Matter has lost touch. It lost its superiority, and mass became a secondary property, the result of interactions between intangible quantum fields. What we consider to be mass is the behavior of these quantum fields; it is not a property belonging to them or necessarily inherent.
Despite the fact that our world is filled with hard and heavy things, the energy of quantum fields rules the ball. Mass becomes just a physical manifestation of this energy, and not vice versa.
Conceptually, it looks shocking, but at the same time extremely attractive. The great unifying property of the Universe is the energy of quantum fields, not rigid, impenetrable atoms. Perhaps this is not exactly the dream that philosophers could hold on to, but it is still a dream.
Jim Beggot is a freelance journalist and writer who lectured in chemistry, then worked for Shell, and now works as an independent business consultant and trainer. Among his many books are: The Scientific Story of Creation, The Higgs: The Invention and the Discovery of the God Particle, The Quantum History: The Story of Creation moments “[A Quantum Story: A History in 40 Moments] and“ A Beginner's Guide to Reality].
An adapted excerpt from the book: “Mass: in search of understanding of matter from Greek atoms to quantum fields” [Mass: The quest to understand matter from Greek atoms to quantum fields].
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