Três tentativas apenas, mas o eco de sua voz aponta, inevitalmente, para a única direção da seta do tempo: cada vez menos informação/energia útil pode ser utilizada. O poeta Robert Frost se perguntava ainda se o mundo terminaria em gelo ou fogo, mas, desde o Nobel de 2011, já não resta nenhuma dúvida de que tem o controle há 5 bilhôes de anos. São estes belos conceitos, digamos, "capitulativos" que nos ocupam com aquelas questões quase que "retóricas", já que o universo começou e terminará sem nosso aplauso, pois, depois do alvará da criação, seu engenheiro entrou em férias ou aposentadoria prematura, quem sabe, no ressort do nada e passou uma procuração para a entropia cuidar dos aspectos burocrárticos do longo processo, ou você teria alguma dúvida de que a natureza trabalha em favor do erro e que, no cerne de todos os encadeamentos catastróficos, parece sempre existir uma força amorosa secreta que investe na mesma direção mais improvável e, no balé macabro de suas simultaneidades, finalmente se encontram produzindo dano total. Por outro lado, existe, sim, uma possibilidade matemática remota de 50 chimpanzés digitarem, em velhas máquinas de escrever, num canto remoto do universo, todos os sonetos de Shakespeare, mas seria bom não esperar por isto, nem tentar atravessar a parede à sua frente.
Energia e materia escuras são enunciados que, no método científico, denominam-se, de acordo com a retórica aritotélica, "apofânticos", ou seja, a ciência descreve o que NÂO pode ser, como uma cerca mal ajambrada diante do precipício das significações. Conhecemos as propriedades e efeitos de ambas, isto é, a menos que você seja adepto de MOND, por exemplo, é como pedir a conta no restaurante e saber que a gorjeta é mais de 70%.
Duas velhinhas estão num asilo e uma diz para outra: Nossa, como comida por aqui é uma porcaria! E a outra retruca: Além disso, é pouca! Isto é a vida. Dura pouco, é tediosa e geramente é uma tremenda porcaria, salvo quando, do vácuo quântico, fulgura uma piada de Monty Python, ou uma melodia como a "Galaxy Song". Mas a vida enquanto auto-organização desafia esta entropia com sua matemática do caos. De maneira paradoxal, a vida, em sua tenacidade (apenas da perspectiva da geologia terrestre), parece ser um imperativo como febre auto-reflexiva da matéria para um dia cair em contradição e ser a contraparte da entropia, pois ela obedece a rigorosos padrões matemáticos, perfeitamente descritíveis. O velho Hegel afirmara uma vez que só é verdadeiro o que não produz contradiçâo, mas trata-se exatamente do contrário: somente pode ser verdadeiro aquilo que produz a contradição.
Pois seja o que for a "vida", e sua dignidade como pergunta e tentativa, ela não é e nem nunca foi apenas o produto da mera "adaptação" ao meio, ao contrário, ela sempre produziu um "excesso" de formas e padrões que os cientistas chamam quase que, por licença poética, "estéticos". Sabemos que existe vida apenas na terra. Sabemos também que existe vida com humor apenas na terra na busca permanente da piada definitiva. E sabemos também que a vida existe, porque o céu é escuro, apenas alguns kelvins acima do zero absoluto, caso contrário, seríamos assados naquele espeto universal da churrascaria da criação
Mas basta apenas olhar para o céu na distribuição uniforme de matéria visível e ver o absurdo, pois ele é uma imensa piada na forma de uma perfeita curva de corpo negro e somente poderia haver uma explicação plausível para que nossos vários modelos inflacionários encontrem um denominador comum com essa pequena jóia criogênica chamada sonda Max Planck e, bravamente, com nosso método "apofântico", chutaremos a cerca apenas alguns metros um pouco mais para longe.
No final do XIX, o fantasma da entropia e sua morte pelo gelo assombrou e também incediou a imaginação artística como diagnóstico da decâdencia da civilização européia. Se a própria história é um "motor", ela também deverá estar submetida às mesmas leis que organizam os processos físicos e químicos. O dramaturgo Alfred Jarry esboçou na figura do pai Ubu uma nova ciência que chamou de "Patafísica", justamente aquela que faz as perguntas que nenhum departamento ou instituição pode formular com dinheiro público. A Patafísica se define como a "ciência das soluções imaginárias e das leis que regulam as exceções" Por exemplo, qual seria a superfície de Deus. Não parece tão aburdo assim quando imaginamos que o tamanho do universo real, em relação ao seu horizonte de visibilidade no campo profundo do Hubble, seria, numa estimativa modesta em ordem de grandeza, equivalente à distância do núcleo à nuvem eletrônica que o circunda. Um ser humano andando é uma bolsa de água instável com um capacitor elétrico que produz contra-imagens e sonhos difusos, cujo centro de gravidade mal pode ser calculado no seu andar desengonçado. Como ele aprende a ficar de pé é uma história de amor a cada nova criança. Mas antes que as luzes se apaguem, finalmente, talvez você queira saber as respostas àquelas perguntas "definitivas" que o History e o Discovery Channels prometem responder depois do intervalo: Afinal, o que existe na área 51, quem assassinou J.F.Kennedy, e o que fizeram, enfim, com os cadáveres da autópsia de Roswell, pois o desejo de tudo não passe de um conto de fadas que a mamãe nos contou antes do beijo de boa noite será a imagem final antes que seus olhos se fechem. Será que alguém se lembrará de que você esteve na superfície do planeta, Brother, pois, certamente, a seta do tempo aponta que não haverá outra vida, nem ilha, e que não existe nenhuma possibilidade de você nascer de novo com a cara do Sawyer e, mais ainda, já que todos os sinais eletromagnéticos de vestígio humano a alguns anos luz em nossa vizinhança ainda são pura estática da qual não se pode extrair qualquer informação útil e se confundem com o ruído de fundo, eu não colocaria mais nenhum centavo no Setti, pois isto não é mesmo, definitivamente, ciência, Brother, a Grande Ciência não se baseia em "sustos" e "wishful thinking"
e o que você fará, então, esperar o último próton decair e suspirar, "ah, já estava mais do que na hora" e agora posso "não existir" mais em paz, o último apague as luzes. Haveria outras perguntas mais técnicas, que obcecam a maioria dos cientistas na tristeza burocrática de suas carreiras sem brilho, enfim, como é possivel existir num universo que literalmente "desconstroi" as evidências de seu desenvolvimento, sua própria historicidade material, pois sua acelerada expansão tornará nossa vizinhança cada vez mais solitária e, para este observador de um futuro remoto, não haveria mais a possibilidade sequer de reconstruir o que nós ainda podemos com a CMB e as supernovas 1A. Literalmente, o horizonte estaria "vazio" e seu "paradoxo" atual, que nos leva necessariamente à curvatura quase zero em grandes escalas (K 0) deixaria de ser um problema. Mas certamente a pergunta mais solitária e desesperada é que, nesse tempo remoto, não existira nenhuma "ilha de calor" para os nossos sonhos colonizarem, enfim, para onde iriam os nossos sonhos, memórias, o que amamos e odiamos, o último vestígio de informação útil daquilo que já foi certa vez seu "corpo" e a ilusão de "alma" que ele engendrou como um espasmo no abismo frio e escuro da noite eterna.
In the beginning was the void.
But the void was not nothing.
And there was light.
And the light changed.
And so the void brought forth the world.
And the world was good for it endured until men could comprehend it.
But it will come to pass that one day the energy of the void will have pushed all things away leaving nothing but the void.
But the void is not nothing.
At the dawn of a new century, a new theory is being born. It threatens to demolish the foundations of 20th century physics. Its authors are two of the world's leading cosmologists. If they're right, Einstein was wrong. It all began when Andy Albrecht and Joao Magueijo met at a conference in America in 1996.
This program began from Newtonian view of the universe then takes you through the General Relativity and the Flatness problem. This leads to the Horizon problem and its solution, the Inflation theory. However modern astronomy doesn't stop here, the Inflation theory has its flaw too, and what happened before the big bang? This can all be answered by changing one thing, the one thing no body dare to question until now.
“Você é a manhã que se aproxima
e eu a tênue chama desta vela que se esvai.
Conserve esse sorriso até a aurora
Veja, meu amor, como me consumo ao sabor do vento,
Brilhando diante de ti até o último suspiro
Assim como meu coração que arde apaixonado.”
Hafez, de Sheraz
Por Goethe
poeta persa 1320-1389/90
Lied:
Vejam a média exótica
Desfilar de Maiorca a Düsseldorf.
Ela se afoga no próprio tédio e irrelevância
A duras penas recuperaremos as lágrimas, suspiram com cinismo e prepotência ariana.
Karl e seu bando passam da teoria à práxis
A pena é clara: motivo fútil e tratamento especia.l
No manicômio estadual, são obrigados pelo diretor social-democrata Kluge, todos os sábados, diante dos internos, a encenar um novo manuscrito para o próximo festival regional, do Kluge ** qual é e recordista em prêmios e indicações.
Dois enfermeiros armados conduzem Karl ao centro da arena. Algazarra, palmas e assobios. Fundo árcade, campinas floridas, animais compatíveis com ecossistemas auto-sustentáveis, salão lotado de velhinhos, vovós e vovôs punks, ex-combatentes do África Korps uniformizados e condecorados, alguns com o retrato de Erwin Rommel, enfermeiros guardam as saídas.
Latas de cerveja são jogadas no tablado-arena. Com exceção de Karl, os demais os demais permanecem ajoelhados em formação de choque, contemplando o conteúdo de diversos livros de Jurgen Habermas, empunhando espadas de papelão.
Karl ajoelha-se diante de Kluge : Dedicamos o nosso humilde empenho ao Magnânimo Diretor Kluge que nos conduz pela luminosa trilha segura da Ciência neste exercício do Esclarecimento em ato. Algazarra, palmas e assobios.
Kluge (Gesto para que comecem)
Algazarra, palmas e assobios
Karl segura uma rosa branca Durante anos, no silencio de Academias, nós, os puros de coração, perseguimos pelo deserto da abstração, o cálice sagrado do consenso desta generosa República.
Somos culpados sim, nos alemães assumimos de joelhos todas as culpas do milênio. Algazarra, palmas e assobios. Cada um Parsifal em busca do cálice do consenso, onde bebemos ainda o sangue de todas as vitimas, que é pouco diante desta renovada sede.
Já não me lembro mais daqueles anos em que fazia mestrado em Sociologia. Eu era apenas um rapaz de boas intenções a quem as palavras dos compêndios escorriam pelos ouvidos como mel neste oásis entre tâmaras. Sim, o consenso, dizíamos, o consenso normativo daqueles que nos impuseram esta máscara democrática e nos corromperam com os valores ocidentais, jeans e coca-cola
Algazarra, palmas e assobios Foi quando Serap**
surgiu em minha vida. Lembro-me de seu fulgurar, vestindo luto e majestosa com seus cabelos e olhos negros como o leite negro da madrugada. Serap era uma princesa à sombra da qual todos os exércitos marchariam para o inferno de gelo do coração da Groenlândia, sinistra e confusa, o mundo parecia mais simples à sua sombra,
e com Serap avançávamos em linha reta como leigos da alegria em pura ação algazarra, palmas e assobios tão abstrata, sem pudor na tolice que exalava e quando maio chegava Serap
era a mascote de nosso bando, nossa pastora, Serap para o bando, nas campinas verdejantes desta amada Republica! Um dia, em meio às nossas infrutíferas discussões, Serap pôs uma automática sobre a mesa e nos disse que o banco da esquina andava relaxando na segurança nestes tempos bicudos para nossos amados banqueiros, que financiam o ócio de pastorais pensamentos. Foi só saque, como dissemos.
Eu usava a máscara de Adorno e meu fiel companheiro Jens de Horhkeimer, e Matthias resolveu se vestir de policial californiano, só para garantir nossa própria segurança algazarra, palmas e assobios, licença poética de Serap diante das aporias no fronte da dialética.
Serap nos dissera que ainda surfaríamos, leigos da alegria, sob o sol de Maiorca e que estaria no carro, mas o único carro que nos esperava na porta era a viatura de nossa democrática Polícia, que nos recebeu em júbilo com a imprensa local.
Foi nos olhos de Serap que reconheci todos os inimigos do Esclarecimento, mas foi nesses olhos que eu me reconheci como meu verdadeiro inimigo. Cada um sua propria República e Serap libertou a serpente adormecida em meu coração com seu alemão de mestiça.
Algazarra, palmas e assobios Agora acabou, o consenso acabou (rasgam volumes de Habermas e da “Teoria da Ação Comunicativa”). (êxtase na audiência). Somos a vanguarda do ódio pela qual cada cidadão de nosso generosa Republica se orgulha e transformaremos novamente o mundo inteiro numa imensa prisão.
(Júbilo na audiência, enfermeiros de prontidão a um sinal de Kluge) A língua é um sistema compulsório. Morte a todos os inimigos do Esclarecimento! Choro convulsivo, joga a rosa branca no chão. Mordem os livros como cachorros enfurecidos. Enfermeiros chutam todos no chão, morfina.
Kluge No próximo sábado, retomamos os ensaios.
Internos aplaudem efusivamente, carregam Kluge nos ombros e cantam
a velha canção do fronte: “In der Heimat, in der Heimat, da gibt s ein Wiedersehen...”
*O ator que desempenhar Kluge deverá estudar as fotos de Foucault e, se possível, passar na calva produtos que realcem a iluminação.
** Serap: nome feminino em turco para “miragem”, “fantasma do deserto” Há muitos anos venho escrevendo minha versão pop de "Tommy", mas feminina, com minha persona feminina. Este é um texto terrivelmente dolorido para mim. Abomino todos os falsos profetas, todos aqueles que desprezam a herança de Compaixão (Mitleid) e Graça (Gnade) pela fragilidade do humano no deserto mineral da barbárie, e desprezo, particularmente, a figura de Michel Foucault e seu apoio cego à Revolução Islâmica, seus escritos INFAMES publicados na Itália, que pavimentaram o caminho do novo Imã à tirania, pois acredito e vou defender com todos os meios a sociedade aberta contra todos os seus inimigos internos e externos. Os piores tiranos sempre vêm sempre do exterior
From left, Adam Riess, Saul Perlmutter and Brian Schmidt shared the Nobel Prize in physics
"Meu único desejo é um pouco mais de respeito para o mundo, que começou sem o ser humano e vai terminar sem ele - isso é algo que sempre deveríamos ter presente". - Aos 97 anos, em 2005, quando recebeu o 17º Prêmio Internacional Catalunha, na Espanha.Claude Lévi-Strauss
The scientist is not a person who gives the right answers, he is one who asks the right questions.
Claude Levi-Strauss
The scientific mind does not so much provide the right answers as ask the right questions.
Claude Levi-Strauss
The world began without man, and it will complete itself without him.
Claude Levi-Strauss
This was another great lecture that cleared up a lot of personal confusion I had in the subject. Once again, particle physics is now my favorite topic! Sean also cleared up his promised use of small cycles to go over and over material in order to make it really sink in. Alternating between the experimental, observational lectures and the theoretical lectures is exactly what he meant, as we have been doing since the start. Lecture two's observations of a smooth universe led to two lectures on theories of curvature and expansion in a smooth universe. Observations of a lumpy universe then led to its theory. And now the observations of particle physics will lead to theories of the universe and ultimately composition of dark matter and dark energy. The larger cycles of knowing how we got here, why we believe in our theories, and speculations are yet to be fleshed out.
The clear presentations of fermions and bosons really sets the stage for the rest of the lecture. Sean tells the great story of how professor Bose, the namesake of bosons, had to get Einstein's recommendation in order to have his mistake turned discovery published. Unlike fermions, bosons actually prefer to pile on top of each other, although the story is not exactly clear on how the mistake implies this!
The atomic force fields and their associated carrier particles are presented nicely. Although the name of the force carried by the pion that holds the neutrons and protons together is not explicitly stated. Maybe a version of the strong force carried by the gluon?
Concluding with Feynman diagrams, one wonders if they were included more due to Sean's Caltech office being formerly occupied by their famous namesake, or if we will use them later in the course. Either is fine, but I do hope its the latter.
In this lecture we take another turn of the hermeneutic circle that describes how science is done, going from experiments and observations, to theorizing, back to experiments and observations, back to theorizing, and so forth. In lecture 2 we looked at the universe and saw that it was smooth, more or less the same everywhere, big, filled with galaxies, and getting bigger. Then in lectures 3 and 4, we thought about that. We asked how we could fit that into a picture of a theory of the universe, and talked about General Relativity and the expansion of space as described by the Friedmann equation, the smooth expansion of space that could have a curvature all of its own.
Now in the last few lectures, we talked about observations again. We looked at the universe and we took seriously the fact that its not perfectly smooth. There are lumps in the universe, there are galaxies and clusters of galaxies. These imply that we can measure the amount of matter in the universe, and we find that it's much more than can be accounted for, we think, by ordinary matter.
So now we're going to go back to the theorizing again, and start thinking about what it could be. If there is dark matter out there, if there is more matter in the universe than can be accounted for by ordinary stuff, what candidates can we come up with for what the dark matter might be? So to start in this lecture, we'll have to think about what kinds of particles may exist, full stop. We'll classify the kinds of particles you can find in nature.
The next lecture will examine in detail the kinds of particles that actually do exist, that we know of so far. The Standard Model of Particle Physics, tells us enough to explain all the data that we have about particle physics experiments here on earth. Only then can we sensibly start talking about what new kinds of particles we might invent to be the dark matter.
So first thinking about ordinary matter in the universe, we want to think about the particles that we have, which arrange themselves into atoms. These were Democritus' word for the indivisible particles of which everything is made. Sadly, in the 19th century, scientists jumped the gun, and gave the word to atoms to something which are not quite indivisible, yet are collections of particles that form the basic building blocks of chemical elements.
We've already mentioned a little bit about what an atom really is, so let's review very quickly the structure of an atom, since we're going to dive into the center of that atom and figure out what it's really made of. Atoms consist of atomic nuclei surrounded by electrons. So electrons are very light elementary particles that as far as we know, or even in the context of our best theories, are indivisible. No one has a good model for how an electron can have stuff inside of it. We think it's a fundamental particle of nature, at least in our observable part of the universe.
These electrons are orbiting around a nucleus, which is much heavier than the electrons themselves. Almost all of the mass in ordinary matter, comes from the nucleus, not from the electrons. The atomic nucleus is a combination of protons and neutrons, which are both heavy particles and have about the same mass of some 2000 times the mass of the electron.
The protons are positively charged and the neutrons are neutral, so you can balance a positively charged center you can get from a collection of protons in the nucleus, with a negative electric charge you get from the electrons surrounding the nucleus, so that most atoms are electrically neutral. Most ordinary matter such as a table or us, has a very tiny, practically zero, electrical charge. There could be some stray fluctuations, but basically in bulk, ordinary matter is electrically neutral.
So in those protons and neutrons, which create most of the mass in ordinary matter, it turns out that they themselves do have constituents. Protons and neutrons are by themselves not elementary particles, but are made of smaller particles called quarks. This is only something that was worked out in the 1960s and 70s, and now it is very firmly established that there are quarks inside protons and neutrons, and it turns out there are two kinds of quarks that you need to explain how to make both protons and neutrons. They're imaginatively labeled up quarks and down quarks.
The up quarks have an electrical charge of +2/3, while the down quarks have a charge of -1/3. Both protons and neutrons have three quarks each, so you can more or less guess how it's going to go. The proton, which has a charge +1, is going to have two up quarks and one down quark. The neutron, which is neutral, is going to have one up quark with a charge +2/3, and two down quarks with a charge -1/3 each. So the neutron will have a net zero charge, while the proton is +1.
It's very nice and convenient, but not an accident that the charge of the proton is exactly minus the charge of the electron. So that's the basic structure that we have for atoms, which we've already talked about. You can take these protons, neutrons, and electrons, and arrange them in all the different combinations that fit, according to the laws of physics, and you get the entire periodic table, with which you can do all the chemistry and all the other sciences other than physics.
However it's not the end of the story. We need to tell why protons, neutrons, and electrons, or if you like, up quarks, down quarks, and electrons, arrange themselves in those particular combinations, rather than some other combinations. As we know, the reason why particles stick together is due to some force of nature. So on one hand, you have matter particles in nature, you have electrons and quarks, stuff that makes up stuff, but then there's also the forces of nature, the things that hold those particles together in the nucleus or in the atom.
The most obvious force we have of course, is gravity, the one we've been talking about already. Yet let's put that to the side for the moment. In the atom, the important force is the electromagnetic force. Again, about 200 years ago, you wouldn't even have used that word, but would have separately talked about the electricity and magnetism. These are two separate phenomena.
Yet in the 19th century, a series of two physicists working hard, culminating in the work of James Clerk Maxwell, managed to unify our understanding of electricity and magnetism, so that physicists now talk about a single force called electromagnetism. In fact, this unification of electricity and magnetism, is precisely analogous to the way that Einstein unified space and time together into spacetime. So just as the time that clicks off on a clock will depend on how you move through space, whether or not you observe a certain field to be electric or magnetic, also depends on how you move through space!
This unification of electricity and magnetism into electromagnetism, was the inspiration for Einstein's theory of relativity. So it's the electromagnetic force which takes charged particles and makes them match up. Oppositely charged particles attract each other, particles with the same charge will repel each other, and that's the rule of electromagnetism.
The way that such forces are carried in nature, is by fields. Yet there's an interesting thing that happens due to quantum mechanics. This is the replacement for the classical mechanics of Isaac Newton, that physicists developed by the 1920s. Quantum mechanics is a very rich and complicated subject, not anything we'll really give due justice in this course, and requires an entire set of lectures all by its own.
One of its features is that if you start with a field pervading the universe, like the electromagnetic field, and you look at it carefully, what you see is that you can resolve it into individual particles. This is the relationship between the electromagnetic field that we know about and Maxwell talks about, and the individual photons that are the particles that carry radiation.
Photons are the excitations, the individual bundles of electromagnetic energy, that quantum mechanics predicts. Yet that's only part of the story. What quantum mechanics applies to fields, works for everything in the universe! According to our current understanding of nature, the universe is made of fields, which when quantized, appear to us as particles. Not only is there an electromagnetic field that appears to us as photons, there is an electron field that appears to us as an electron. There is a gravitational field that appears to us as gravitons, as we'll discuss later.
So the particle that carries the force of electromagnetism, is called the photon. If you like, you can think of the reason why an electron is bound to an atomic nucleus, as the fact that this nucleus and that electron are exchanging photons back and forth, which carries a force that glues the negatively charged electrons to the positively charged protons in the atomic nucleus.
The same thing happens with all the other forces of nature. It's the same kind of story over and over again. The next obvious force we need to explain is why protons and neutrons are bound together in the nucleus, or for that matter, why quarks are bound together inside the protons and neutrons. The individual protons and neutrons by the way, are collectively known as nucleons. Protons and neutrons are so similar that sometimes it's useful to label them with a single thing. We call them nucleons and they're the things which make up the nucleus.
So what keeps those quarks together in the nucleons, is a new force of nature, not the electromagnetic force. It's a different force which again, very unimaginatively has been labeled the strong nuclear force. This is what binds together individual quarks inside protons and neutrons. So if there's a force, there's a force field. If there's a force field, there are particles. The particles associated with the strong nuclear force, are called gluons, which actually is a pretty good name when you think of it! They are gluing together the individual quarks inside the protons and neutrons.
So in the next lecture we'll be a lot more systematic with all the different forces of nature and the particles that are associated with them. For this lecture, what is more important to us is just to understand the basic distinction that exists in all of particle physics between on the one hand, matter particles, and on the other hand, force particles. These two kinds of particles account for everything we can observe in nature.
There are even theorems in quantum field theory that say these are the only possibilities. Those theorems wouldn't work if space were two-dimensional for example, but in the world in which we actually live where space is three-dimensional, those are the only two kinds of particles we can have, matter particles and force particles.
Matter particles are named fermions, after Enrico Fermi, who is the physicist who has the most stuff named after him of all time! There are particles, fermions, there is an interaction, the Fermi interaction, there is a laboratory outside Chicago called Fermilab, there is a unit of length called the fermi, etc. He was a very influential physicist, both as a theorist and as experimenter. Fermi was the person in charge of the first self-sustained nuclear chain reaction that humans put together as part of the initial phases of the Manhattan project.
Yet before that he was a theorist thinking about what kind of particles that can exist in nature, and Fermions are named after Fermi. Fermions are the matter particles in nature. The characteristic feature that is important to us know, is that matter particles take up space. That means if we have two fermions we cannot take two identical fermions, two electrons lets say, and put them in exactly the same place, exactly the same quantum state of matter.
You take a bunch of electrons and you can only squeeze them so close to each other. Electrons being matter particles, being fermions, take up a certain amount of space. That is a good thing. It's very good that matter particles take up space! That's why a table doesn't collapse! It's made of atoms, which are made of electrons in their outer shells, which makes them able to be packed together only so close. The atoms take up space, and that's why the table is solid.
If electrons were not fermions, were not matter particles that took up space, there would be nothing to prevent the table from collapsing. This principle that electrons cannot be put in the same place, that no matter particles can be in the same location, is called the Pauli exclusion principle, after Wolfgang Pauli, another physicist. It just says that no two particles can be in the exact same place, doing the exact same thing, at exactly the same time.
Quarks are also matter particles, so when you put three quarks together, you form protons and neutrons, which are also matter particles. The fact that you can't put protons or neutrons too close together, because they take up space, is not really relevant to our everyday lives, because the electrons take up more space. So most of the space being taken up in an ordinary table or in us, is due to the electrons taking up space. Yet in principle at least, so do the protons and neutrons.
In contrast to this we have bosons, which are the force carrying particles of nature. The important thing about force carrying particles is that they can pile on top of each other. You can go from individual particles to coherent classical excitations of the field. That's the reason why, in the context of force fields, physicists were confused for hundreds of years as to whether or not light for example, was particles or waves. We now understand in the context of quantum mechanics, that it's both. The fact is, that light is a set of particles, but are force particles. So they are bosons and can pile up on top of each other to make a wave.
So the concept of bosons was invented in 1922 by Satyendra Nath Bose, an Indian physicist. Bose was actually literally giving a lecture to some of his students about a well-known problem in statistical mechanics. This was the fact that when you took a bunch of particles and added up the different ways they could combine, you didn't get the right answer! In the 1920s this was considered to be a real problem, so he was trying to explain it to his students. Yet by mistake, he solved the problem! This was because he had goofed, and made an error which is easy to understand.
Imagine you have two boxes and two balls. You try to ask the different ways you can put them into these two boxes? basically there's four different ways. If you have a red ball and a blue ball, they could both be in the left box, both in the right box, the ref could be in the left and the blue on the right, or the blue on the left and red on the right. So these are four different possibilities.
So according to conventional statistics, if we said we knew nothing about where the balls are, what is the chance that both balls are in the left-hand box? It would be one in four. Yet during his lecture, Bose made a mistake, and considered three possibilities. Both balls in the left, both in the right, or one ball each. He didn't distinguish between the two balls being in the two different boxes. He assigned a probability of 1/3 to each of these possibilities, and miraculously he derived a formula that was in agreement with observation!
So he realized that somehow, fundamental particles of the Bose kind, must be indistinguishable. It must not matter whether the particles are here and here, or vice verse. It counts as the same kind of thing. He realized that is you make that assumption, suddenly everything fits together. You can see what the consequences of that assumption are. He's saying there are two particles on the left, two on the right, one particle each, are three possibilities that should actually be weighted equally. So now if you ask what the chance is that the two particles are on the left, you used to think it was a 25% chance, yet now you think it's a 33% chance, a one in three chance.
When particles obey Bose's behavior, they're more likely to be in the same place, than if they behave like ordinary, classical particles. Bosons not only can pile up on top of each other, they like to pile up on each other. This fundamental insight is in charge of things like lasers and a whole bunch of technological applications. So when Bose realized this in 1922, he became very excited and realized he had just figured out a resolution to a long-lasting problem. So he wrote a paper and submitted it to a journal, only to have them laugh at him for doing so! They said, "What do you mean? You've made a mistake! We're not going to publish this, you're mistake!"
No one understood that by making a certain assumption, he was able to explain a long-standing problem. So in despair he sent his paper to Einstein, who did understand what was going on, and Einstein used his influence to get Bose's paper published. The statistics that come out of it are known as Bose-Einstein statistics.
So photons are one such example of bosons. They can pile on top of each other, such as when they make a classical electric or magnetic field, or an electromagnetic wave. Gluons are also bosons, so can pile up on top of each other inside the nucleons to bind the quarks together. So we then get something that is working very nicely as a system. We have matter particles that take up space, that give things extent throughout space, and we have force particles that bind them together. It's good for us that we have both kinds of particles, otherwise the world we know would be a very different place.
So there is another feature of bosons that distinguishes them from fermions, and a lot of times if you hear on street corners where people talk about bosons and fermions, this is the language they will use, which is that they have different kinds of spin. It turns out that every elementary particle has an intrinsic spin, just like the spin of a top or a spinning coin, except that for every kind of particle, that spin never changes. It's a fixed amount that is never going to become some different amount. A top can speed up or slow down, yet an electron is always spinning just as fast.
You can measure the amount of spin in a certain fundamental unit of spin, which for historical reasons, always assigns a spin of 1/2 to the electron. So you can have particles that have a spin of zero without any spin at all, or a spin of 1/2, 3/2, etc. It turns out that all bosons have an integer amount of spin. In other words a boson will have either zero spin, or be spin 1, or spin 2, 3 or 4, etc. Whereas all fermions, all matter particles, will have spin given by an integer plus 1/2. So a spin 1/2 particle can be a fermion, spin 3/2 or 5/2, all will be fermions, matter particles.
For our purposes, it's much more important to keep in mind that fermions take up space, and bosons pile on top of each other. That's what makes them matter particles and force particles respectively. Yet it's also true, due to something called the "spin statistics connection," that if you know something to be a force particle, you know that it's spin will be an integer. If you know it's a matter particle, it will be an integer plus 1/2. You'll hear people talking in that language, so we just thought to mention it.
So those are the two basic kinds of particles that we can get in nature. Matter particles, or fermions, and bose particles that carry forces in nature. Yet there are also anti-particles. There is something called anti-matter. The way it works is subtly different for bosons and fermions. Ordinary matter particles like electrons or quarks, all have their own specific kind of anti-particle. So you have the electron which is charge -1 and a certain mass, the anti-particle will always have exactly the same mass, but the opposite charge.
So the electron has charge -1, spin 1/2, and a certain mass. The anti-electron (positron) has a charge of +1, the same spin of 1/2, and the same mass. Everything is the same, except that the charges of the particles go to minus what they used to be. So the anti-electron, which was the first anti-particle ever discovered, is usually called the positron, which plays an important part in the early universe.
Yet every fermion has its own anti-particle. So you have an up quark, and a down quark. You also have an anti up quark, and an anti down quark, and so forth. For bosons the situation is a little bit different. Some bosons can be their own anti-particle, like the photon. The gluons come in a set of 8, within which you have a bunch of particles and their corresponding anti-particles. So it's a little more complicated, but also it doesn't matter as much, because it's the matter particles, the fermions, that take up space and could run into each other.
When matter particles and anti-matter particles run into each other, they annihilate. So you take an electron and a positron, bring them together, and they will turn into photons, or energy. That is why we know very well that anti-matter plays very little role in our current universe, which is full of stuff. Yet even though it's a very dilute place, in the past it was actually quite densely packed. If there were a lot of anti-matter in the universe, it would have annihilated with the ordinary matter a long time ago. In the early universe, particles were bumping into each other all the time, and when that occurs, they create photons, energy in the form of photons.
We believe that in the early universe there were a lot of anti-particles and a lot of ordinary particles. What happened was that almost all of them annihilated. Yet for some reason, there was a slight imbalance. Somehow in the early universe, there was slightly more matter than anti-matter. What we see today, all the ordinary particles we see today, are the residue, the left-over, slight asymmetry between the amount of matter and anti-matter. We don't know why and it's a mystery in current physics. We have plenty of theories to try to explain it, yet are not sure which is correct. There's an ongoing research program and we'll be alluding to it in future lectures occasionally, yet don't have time to get into any details on the specifics.
So we'll just have to believe Sean that there's not a lot of anti-matter in the universe. The anti-matter in the universe is certainly not the dark matter, since it's not dark. It runs into ordinary matter and shines very brightly. That's not what we want for dark matter to be. So now we have some knowledge of what exists and what can exist. We have matter particles (fermions), force particles (bosons), and they each have their own kinds of anti-particles.
Now let's go back into the atom and see what we have. Remember that we have a nucleus with electrons going around. The electrons are matter particles, fermions, and so are the nucleons, the protons and neutrons that make up the atomic nucleus. They are bound to the electrons by the exchange of photons, of those particular force particles, back and forth. If you dive into the individual protons and neutrons, you see three quarks in each one, and they are bound together by gluons going back and forth between the different particles.
You can then ask what is making the protons and neutrons stick together in the nucleus? There are different ways to answer this question actually, depending on how you want to think about what is going on. One simple way of answering it is to think about pions, which are a different kind of particle, made of quarks. A pion is an example of a meson, which is made of one quark and one anti-quark bound together. The exchange of pions between protons and neutrons provides the binding between them.
So the pion is a boson, with one quark and one anti-quark in it. The individual spin of +1/2 and -1/2 add up to zero, because they're pointing in opposite directions. So the pion is a boson of spin 0, and it's a force particle. They can bind protons and neutrons together in atomic nuclei. That's one way of thinking about what is going on, inside the nucleus.
And of course we have gravity, the most obvious force in all of nature. Quantum field theory tells us that if we quantize gravity, we will decompose the gravitational field into particles. We have not succeeded in doing this yet, and don't yet understand how to think about gravity on a quantum mechanical context. Someday we hope to be able to do so, and we think it's a very robust prediction of the framework of quantum mechanics itself, that when we finally do understand how it works, it will involve gravitons, individual particle-like excitations of the gravitational field. So we believe that gravitons exist, even though we don't currently know how to describe them in any full way.
So given the set of particles that we have, we can start thinking about what those particles do. In particle physics language, we talk about the interactions between different kinds of particles that can bump into each other, annihilate, create things, emit different particles, and absorb different particles. We have a language of describing these processes of interactions called Feynman diagrams.
Richard Feynman of course, was the famous physicist at Caltech, where Sean currently resides. He was sufficiently famous that Sean now sits at the same desk which he used, which means that tourists will occasionally come to Sean's office to look at Feynman's desk! They won't look at Sean's desk which he has had at various places around the US, but Feynman's desk is famous enough.
The thing that Feynman did that was most obvious to the life of a working physicist was to invent the concept of Feynman diagrams. It seems like a fairly trivial idea. You just draw little cartoons of what particles can do. In fact, to a working physicist, each one of these little diagrams is associated with a number that lets us calculate the likelihood that a given process is going to happen. So we're not going to talk about any of that in any detail, as there's a lot of math involved, etc. It's not a lot of fun and requires years of graduate education to figure it all out.
We'll just use these little diagrams to remind us of which interactions can happen. So we see one example of a Feynman diagram where an electron moves from left to right, which at some point emits a photon. So the fact that this is an allowed Feynman diagram is telling us that electrons can emit photons. The reason why, as we'll discuss a little bit more in the next lecture, is that an electron has an electrical charge. The things that photons respond to and interact with, is the electrical charge itself. So for electrically charged particles, they can emit and absorb photons. This Feynman diagram is an example of an electron interacting with a photon.
Then there are certain rules about how you can manipulate Feynman diagrams. There are rules that say if a certain diagram exists, and describes an allowed process, then you know for sure that another specific kind of diagram can exist. For example, if you have a diagram where a bunch of particles come in, interact and then go out again, there will be a new diagram which is also allowed, which you can get by taking one of the particles that came out, and move it to the other side, so that instead of going out, it came in.
So our diagram has the electron coming in, which spits out a photon and then goes away, still as an electron. We can take that photon and move it over to the other side. So there must be a diagram describing the absorption of a photon by an electron, a diagram that has an electron and photon coming together, joining, and then going off as a single electron. Indeed, this happens. So we have a different kind of Feynman diagram that describes a different example of the electromagnetic interaction at work.
Finally, we can also do this, yet not with the photon, but the outgoing electron as well. So we had an example where the electron comes in, spits off a photon and goes away as an electron. What if we moved the outgoing electron to the initial state? Then we would have two particles coming in and going out as a photon. However the rule says that when you take a fermion, or something that has an antiparticle, and move it from one side to the other, you need to exchange particles and anti-particles. For the photon, that didn't matter since a photon is its own anti-particle. Yet when you move an electron from one side of the Feynman diagram to the other, you need to exchange it with a positron, the anti-electron.
So the fact that there is a diagram where the electron comes in, spits off a photon and goes off as an electron, this implies that there's another diagram where a positron comes in, hits an electron, and they go off together as a photon. In other words, it must be the case that an electron and positron can annihilate into photons, just as we predicted. The fact that an electron can spit off a photon, implies that it must be able to annihilate. Of course this is seen in the data, being consistent with the physics that we observe.
So these are just a few simple examples of how we can understand the interactions of elementary particles in terms of Feynman diagrams. In the next lecture we'll be more systematic. We'll tell of all the elementary particles discovered in the laboratory, and all the interactions they have. The point will be to say that none of them can be the dark matter, so we need to invent more particles to explain that part of the universe.
This last lecture looks at the big picture, a historical overview, and extrapolations for future clues. But first a big pat on the back for everyone; to the scientists for their inspiration and perspiration, to the human race for pursuing such questions, and to the audience for finishing the course!
Yet scientists tend to rest on their laurels when things are quiet. Why do we have a concordance cosmology of 5/25/70? Or is it legitimate to even ask such a question? Most numbers in the universe don't seem finely tuned. Those that are create a Hierarchy Problem, such as the mass of the Higgs particle being 150x the proton mass. It could just as well be many orders of magnitude greater, so why is it so small? Supersymmetry may eventually provide an answer.
Situations in the universe also don't seem finely tuned. The classic gas in a box where all molecules are in one corner does not violate any laws, but just has low entropy. There must be some physical dynamical reason for this to not be a natural situation. Applying this to the situations of the universe such as the horizon and flatness problems, we found the reason to be inflation. This even provided the physical dynamical reason, the perturbation situation. Asking these questions was not just an exercise in philosophy, they were legitimate, as is asking about concordance cosmology.
Dark matter has a natural answer in WIMPs. They are not too difficult to get from the standard model, and we have built detectors for them in space, ground, and underground. Dark energy is not so natural. The vacuum energy fits the data, but has the unnatural value problem of 120 orders of magnitude and the unnatural coincidence of an energy density roughly equal to that of dark matter.
An interesting diagram is displayed with lines and arrows representing interactions between the three 5/25/70 of concordance cosmology. Gravity is at the center, interacting with everything. It is helpful to a certain extent, but in his last comment on it, Sean talks about the very specific interaction possible between axions interacting and photons. I would have liked more general comments such as how this represents our new and so far, best standard model for concordance cosmology. There are many confusing possibilities for more lines and arrows, but I liked Sean pointing out how that is a positive aspect. We are not just resting on our laurels in this respect.
Sean concludes the course with a dramatic speculation and a cautionary tale. Seeking the naturalness in the overall configurations of the universe has worked very well in the dynamical process of inflation. The entropy of the universe is medium sized. Our example of gas in one corner of a box was low, when spread out it was high. The second law of thermodynamics says entropy will increase, so our current medium size would have been quite small long ago. Why would the universe start with such a low entropy? Inflation begs the question with an even smaller patch that becomes dominated by dark energy, with even lower entropy than the big bang. This could mean that in the future, dark energy would not be so quiet. The distant future may even have the quantum jiggles making new baby universes. Or are we a baby universe in yet some other parent universe? We need to examine such configurations as if they are plausible.
Some think we recently we were finished with discovering laws of physics. The early puzzles with electromagnetism and the orbit of Mercury were solved by quantum mechanics and relativity. But today we have the same types of puzzles with vacuum energy, the conflict between quantum mechanics and general relativity, and between dark matter and dark energy. Will there be whole new theories to solve them, or revolutions in our existing theories? The next century promises to be just as interesting and surprising as previous.
At this point in the final lecture of the course, we have a great deal to be proud of. By "we," Sean means scientists who have been trying their best, and put together a picture of what the universe is made of over the last 100 years. Yet he also means the human race, who have been wondering about these questions for the last several thousand years. Also of course, all of us who have been watching these lectures!
We've put together a pretty good picture of everything. Not only do we know that 95% of the universe is this dark sector, where 70% is dark energy that's smoothly distributed through space and time, and 25% is dark matter made of some heavy particle that settles into galaxies and clusters, but we also have good reason to believe that we're not missing anything. There may be 1% or more, here or there, but basically we know everything in the universe. Measuring the total ρ of stuff, through the curvature of space, convinces us that what we know right now, comprises everything there is to know.
However, scientists are notoriously bad at resting on their laurels. We really want to focus on the questions to which we don't know the answer, the puzzles that we're left with from this very successful picture. Fortunately, even though the picture we have of the universe today is very successful, it leaves us with tremendous questions and offers us clues as to where we might find the answers.
The clues reside in the fact that the picture which fits the data so well, is nevertheless extremely unnatural from certain points of view. It's perfectly fair to say that our picture of the universe with 5% ordinary matter, 25% dark matter, and 70% dark energy, makes no sense! Or at the very least, we could have done better if asked to design a simple and elegant universe! So there's something we don't understand about why our universe is like this, versus like something else.
So for this lecture, we'll step back a bit, looking at an historical overview of how we got here, and try to go from there to extrapolate where we might go next. We'll try to understand that given what we have learned about the universe, where might we be looking for clues as to what underlies particular configurations in which we find the universe in which we live.
So lets start with how we got here. Just 100 years ago, we knew next to nothing correct about what the universe was like on very large scales. We did know that there were stars, which were different than the sun, that they were further away, but the same basic kind of thing.
We didn't know what those stars were, or how they made their nuclear fuel, the stars or the sun. We didn't know there was such a thing as a nucleus. We knew there were atoms and different chemical elements, yet we hadn't yet decomposed atoms into electrons moving around nuclei. So the basic energy source for these stars was unknown to us.
We believed that the stars were distributed in an island universe configuration. We thought that the stars were moving around each other, in what we now call the Milky Way galaxy, yet we didn't know that there were other galaxies. We knew that there were little fuzzy patches on the sky that were called nebulae, yet we didn't know many of them were in fact galaxies in their own right,with hundreds of billions of stars, all by themselves.
We certainly didn't know about the expansion of the universe. We didn't know that galaxies had an apparent velocity moving away from us, or anything about Einstein's Theory of General Relativity, so we didn't know that space and time could expand. We believed in an absolute Newtonian universe in which space and time were fixed, not changing as a function of time. The dynamic nature of spacetime itself is something we didn't have access to.
So the modern story really begins in 1915 when Einstein puts the finishing touches on his General Theory of Relativity, which says that spacetime can be curved and have a dynamics all of its own. That dynamics is manifested to us as gravity. He very soon thereafter started thinking about cosmology and realized that if the universe was evenly spread all over the place, it would have to be dynamical, either expanding or contracting. Yet as far as he knew in 1917, it wasn't. So he changed his ideas by adding a new term to his equation for General Relativity, called the cosmological constant, something that would keep the universe static, at least in principle.
Then of course, in the late 1920s, it was realized that the universe is not static. Hubble talked about some of the nebulae being separate galaxies all by themselves, and that the universe is expanding. Einstein then tossed away his cosmological constant and realized it was a dynamical universe in which we live.
Very soon thereafter, Fritz Zwicky was looking at clusters of galaxies and found the first evidence for dark matter. He looked in the Coma cluster and realized there was more stuff there than we can possibly account for, just be what we saw. He didn't know at the time, that this stuff, the dark matter, couldn't be explained by ordinary atoms, and that was going to come down the road.
By the 1940s and 50s, we only first realized how the early universe worked. George Gamow had his student, Ralph Alpher and Robert Herman, figured out how to make light elements by nucleosynthesis in the early universe. As a spinoff, they got the CMB, the leftover radiation what we now know provides us a snapshot of what the universe looked like 400,000 years after the Big Bang. This CMB was discovered by accident in the 1960s by Penzias and Wilson. They were very careful radio astronomers who kept on getting these microwaves spread uniformly across the sky, yet didn't realize there was another group down the street in Princeton who were looking for these intentionally. They won the Nobel Prize in the 1970s for their work.
Then in the 70s, physicists put together the standard model of particle physics. So the "cosmological" standard model, crept up on us only gradually! Yet the "particle physics" standard model was put together over the space of only a few years. It's been extremely successful since then. Since the mid-1970s, no particle physics experiment has truly surprised us. Everything we've done has fit together into what we already knew as the standard model.
Also in the 1970s, Vera Rubin found the even better evidence for dark matter, by measuring the masses of individual galaxies by determining their rotation curves. She found that not only are galaxies heavier than they should be, given only the stars, gas, and dust that were in them, but that there was mass out beyond any of the visible matter. So eventually we realized that this dark matter was not able to be accommodated in what we understood about particle physics, so that it had to be a new particle.
By 1980, Alan Guth invents inflation. There were puzzles about the early universe we didn't understand. How was it so smooth? How was the spatial geometry of the early universe so close to being flat? Inflation made all that snap into place, and even though we're still not absolutely sure it's true, it's still the leading candidate to explain why the overall geometry of the universe is what it seems to be.
Then by the 1990s, observational cosmology became a precision science. The one watershed moment was the discovery in 1992 of the tiny fluctuations in temperature of the CMB. This was the result of the COBE satellite of NASA, which enabled us to begin linking the earliest moments of the universe's history, to what we observe today. At early times, the universe was extremely smooth, when only 1 part in 100,000 was the only deviation you could see. Under the force of gravity, those deviations have grown into the galaxies and clusters that we observe today.
Technology has now evolved enough to allow us to observe those galaxies and clusters to exquisite precision. We can compare what we see, with the predictions we get from the CMB extrapolated in time, and then put together the ingredients of the cosmological model that is so successful.
The final ingredient we needed was found in 1998, when supernovae used as standard candles allowed discovery of an accelerating universe that can only be explained by dark energy. This is some form of stuff whose ρ doesn't go away as the universe expands. That made up the extra 70% that was predicted by inflation if you wanted to live in a flat universe. Then by 2000, observations of the CMB confirmed that we indeed do live in a flat universe. The fact that 70% of the universe is dark energy, 30% is matter, simultaneously fit the dynamical measurements of galaxies and clusters, the supernovae data that shows the universe is accelerating, and the CMB that shows the universe to be spatially flat.
Since the year 2000, we've been confirming this picture in even more elaborate ways. The WMAP satellite has given us extra information that in fact the ordinary matter is only 5%, that you need some form of dark matter, and that the evolution of structure from then to now is consistent to what we think it would be, in this model where the universe is 70% dark energy.
So we land here at a place where we have a very successful model of everything in the universe. If you think about it, this model has three basic features, not just the three basic ingredients in the inventory, but three aspects that are important to its success. First is the fact that the universe is expanding, and the understanding of it within the context of General Relativity. In the 1915-1917 era, Einstein was realizing that the universe had to be expanding, and we now know that it's true. We can then use his equation to extrapolate all the way back to within a minute of the Big Bang and we get the right answer, as is confirmed by Big Bang nucleosynthesis.
The second source is of course the inventory, the (5%)(25%)(70%) split between ordinary matter, dark matter, and dark energy, which has been tested in multiple ways, and is overdetermined be the observations we have now.
The final aspect is the evolution of structure in the universe. The first two aspects deal with a universe that is spatially smooth, more or less the same everywhere, which is an extremely accurate picture, either at early times or on large scales today. Yet on smaller scales, we see that there are galaxies, there are clusters, there are stars and planets. Unfortunately we're unable to understand where they came from, going from the early universe to now.
So that's an incredibly successful picture. Using data, we can go from one second after the Big Bang, to 14 billion years after the Big Bang. We can sensibly extrapolate with our theories, back to times like 10 to the -30th power seconds after the Big Bang, when we talk about inflation. This inflation acts as a way to generate the perturbations we see today.
So when we are hypothesizing and speculating about what the universe was like at 10 to the -30th power seconds after the Big Bang, we can actually connect those speculations to observations we are making today. We're not absolutely sure of what the universe was like, earlier than one second old, but the very fact that we're trying to go back from one second, to some tiny fraction of a second, is indicative of the progress we've made, compared to 100 years ago when we didn't know the universe was even getting any bigger.
Yet let's step back and ask, given our extremely successful picture, why is it like this? Why is the universe smooth and homogeneous? Why is it that 70% of the universe is dark energy, versus the 30% that is matter? You can ask yourself if this is even a respectable question to be pondering? Should we be people who just look at the universe, describe what it's doing, and think that is our duty as scientists, so that it's not our job to ask why it is like that?
Yet of course as scientists, we are not satisfied with the current state of affairs. We always want a more complete picture. One of the ways to reach that, is to perform more experiments, to collect more data, to take more observations, to find out more about the universe, and we're certainly going to be doing that. In the previous lecture, we got this very diverse smorgasbord of experiments that will be done, a portfolio of different things, both highly speculative and guaranteed to get good results.
Yet in the meantime, there is another way to think about how we can go beyond our current understanding. That's to try and reflect upon whether our current picture of the universe makes sense to us at a deep level, whether it is somehow natural to us. There are no absolutely strong contradictions between the different elements of the standard model of cosmology, like Einstein was lucky enough to have a deep contradiction between Newtonian gravity and Special Relativity, when he was developing General Relativity.
Yet there are tensions between the different elements. So we're going to try and ask if it's somehow a natural universe in which we live, and if not, is the fact that the universe appears natural or unnatural to us, the sign that there's some deeper underlying forces with respect to what it would seem much more natural? So we as scientists have ways to think about this concept of naturalness, ways to take this more or less fuzzy human idea and turn it into something a little bit more quantitative. Both for theories that we have and for situations that we find in the world, science can tell you whether or not that particular thing sounds natural to us. For a theory like the standard model of particle physics for example, we say it's natural if everything that might be happening in that theory, is happening and doing so with the right strength?
OK, that didn't seem much less fuzzier than the original idea of naturalness, but what we mean quantitatively is that when we look at the numbers that appear afterward, the numbers that characterize the strength of different forces, and the frequency of different interactions, those numbers don't seem very finely tuned. In other words, if we were to change those numbers just a little bit, you would get the same basic kind of physics within your theory. Well when we look at some of the different aspects of the standard model, we see that there are fine tunings there.
One example is what particle physicists call the hierarchy problem. They look at the mass of the Higgs boson. We haven't detected it yet, but it's probably something like 100-150 times the mass of the proton. Yet if you look at it, there's no reason why that number, the mass of the Higgs boson, shouldn't be very much larger, shouldn't be up there near the Planck scale, some 10 to the 18th power times the mass of the proton.
Why is the mass of the Higgs boson so small compared to the natural scale it would like to have? That's an example of the kind of naturalness argument that the particle physicists use. What they will then do, is to try to find some underlying reason. In fact, in the form of supersymmertry, there is an underlying dynamic explanation for why the Higgs boson might be so much lighter than the much heavier scales characterized by the rest of particle physics.
For situations in the universe, it's a slightly different aspect of naturalness that we are concerned about. A configuration of stuff in the universe is natural if it's robust. If you move some particles around, you get the same basic idea. This is the kind of thing you might have been exposed to in some physics class, some time ago. If you have a box full of gas, and all that gas happens to be stuck in one corner of the box, that's not a very natural configuration. You let it go, and it begins to fill the box. We say that all the air molecules being stuck in one corner has a very low entropy, and as you let it go, it's going to naturally fill the box.
If you start with a gas filling the box, it will not naturally curl up in one corner. The configuration in which stuff is all spread out, is just much more robust. We can move a few particles around, yet it's still gas spread out smoothly throughout the box. So we have these notions of naturalness and unnaturalness. It is not that is you observe a gas with all the particles in one corner of a box, you would say that it violates the laws of physics. That is completely consistent with the laws of physics, but it's unnatural. We say there must be some reason why it's there. There must be some dynamical physics mechanism for why it looks like that.
So we want to apply that same kind of reasoning to the whole universe. This is a successful strategy that has been pursued before. For example, the horizon and flatness problems were inspirations for the development of the model of inflation. These problems were first, the idea that the universe is smooth on scales larger than it has any right to be. If we look at the universe in the CMB era, there were points with almost the same ρ and temperature, yet they shared no common points in their pasts. There was no way for them to know to be the same temperature, and yet they are. That's a naturalness problem.
Space, meanwhile, is very close to geometrically flat, yet tends to become less and less so, as time goes on. Why was it so close to flat in the early universe? That's another naturalness problem. By thinking about these problems, scientists were able to invent the model of inflation, which not only solves these problems, but as a bonus provides and explanation for the perturbations that we now think, grow into large-scale structure.
So this kind of reasoning is not just philosophizing, but it can lead us to very explicit scenarios that help us explain something that we don't otherwise understand. Well what can we do? What is our current universe like? Does it seem natural to us? Do we have possible mechanisms that make it fit into a bigger picture?
Well the two things we're concerned about in these lectures are dark matter and dark energy. For these two cases, the situation is actually very different. The dark matter case has scenarios that make it seem very natural to us. We have first and foremost the WIMP scenario, where if there exists in nature, some particle that is heavy, electrically neutral so we can't observe it very easy, yet that feels the weak nuclear force. As long as that particle is stable, it will naturally give rise to a density of particles that is very similar to what we observe in dark matter today.
In other words, you don't have to work very hard to extend the standard model of particle physics, so that naturally a dark matter candidate appears, with naturally the right amount of stuff in the universe. We don't necessarily know that this is the right scenario. Yet it's one that fits in with our understanding of what probably would make sense to us. Therefor, we take seriously this idea that the dark matter is a WIMP, seriously enough that we build very expensive experiments to go look for it, on the basis of that hypothesis. We build particle accelerators to try to produce it directly, we build satellites to try and look for the annihilation of WIMPs and anti-WIMPs in space, and we build underground detectors to find it directly in our own labs.
Meanwhile, the dark energy case does not have any model that would pass the naturalness test. The simplest model for dark energy, since we know it to be smoothly distributed through space and nearly constant as a function of time, is vacuum energy. This is something that is absolutely the same ρ in every cm³ of space and time. An absolutely minimum energy that doesn't evolve or fluctuate in any way, through time or space.
It's a simple model, yet it's not natural in terms of what we know about dark energy, because it doesn't have the right value. You can estimate how big the vacuum energy should be, according to our current understanding of gravitation and particle physics, the vacuum energy should be enormously larger than what we observe. it should be 10 to the 120 times what you actually get. So we don't know what is going on. We have a theory that fits, yet only at the cost of an extremely unnatural parameter.
The other thing that we know about the vacuum energy, is that it's victim to something called the coincidence scandal. If you'll notice, in the current universe the dark energy is bout 70% of the total energy budget, while matter is about 30%. Now by cosmology standards, 70% and 30% are equal. Those are very similar numbers. The reason why this is a little bit of a surprise, is because dark energy and matter evolve very differently with respect to each other. Matter dilutes away as the universe expands, so the ρ in matter when the CMB was formed, was a billion times bigger than the ρ of matter now. In the early universe when things squeezed together, the densities are much higher.
Dark energy meanwhile, has a ρ that is constant. The number of ergs per cm³ is a tiny number that is fixed, it's just as small in the early universe, as it is today, as it will be in the future. So back when the was formed, the ρ of dark energy is the same as it is today. In other words, it was a billionth of the ρ of matter. These two numbers, the ρ in dark energy and the ρ in matter, change rapidly with respect to each other as the universe expands. Yet today, when we happen to be here looking for them, they are approximately equal. Why is that?
We don't know the answer to this question, and it might be explained by environmental selection. It might be that most observers in some large ensemble of a multiverse, are going to be born at a time in their regions of space history when the ρ of dark energy is similar to the ρ of dark matter. That is a hypothesis, the kind of thing that we're driven to contemplate when thinking about these naturalness arguments. It may or may not be right, but these give us a clue for the directions in which to move next.
So here is a picture that we can return to, of where we might go in future years after we study the dark sector in greater detail. We right now have a very successful understanding of an ordinary model from the standard model of particle physics. We have dark matter and dark energy which are consistent with the data if they only interact with us through gravity. Yet that doesn't mean that this is the final word. It could be much more rich than that. So there's plenty of possibilities for new physics here that we're looking for in future experiments.
The dark energy could interact with itself. In other words, it might not be absolutely constant everywhere, but might evolve. It might change slowly with time in one way or another, yet might also change slowly with space. There could be perturbations in the ρ of dark energy. Likewise, the dark matter might interact with itself. In fact, in every realistic model of dark matter, there are some interactions between the dark matter and itself. There's some way for the dark matter to be produced in the first place.
More interestingly, there could be interactions between ordinary matter and the dark sector, in one way or another. There could be interactions between dark matter and ordinary matter, like the kinds we are looking for. It could very well be that the dark mater feels the weak interactions of the standard model of particle physics. That would enable us to create the dark matter in accelerator experiments, and in deep underground labs.
Even if not, even if the dark matter is not weakly interacting, it might interact through some other force. The axion is an example of a particle that is electrically neutral, yet indirectly interacts with photons. So we have separate experiments that are dedicated for looking for the interactions of axions with photons. It could be any day now that people begin to actually discover the dark matter directly, because of those interactions. We're looking for them because they make the dark matter theories more natural in the context of other things we understand about particle physics.
Best of all, maybe, would be if dark energy interacted with ordinary matter. If the dark energy is just vacuum energy, just a constant amount of stuff in every cm³, then it will not interact. It's just a background feature of spacetime, and all we'll ever be able to do, is measure its affects on the curvature of spacetime, on the expansion of the universe.
Yet if the dark energy is something different, if it's dynamical, something that changes from place to place, then dynamical fields tend to interact. We can look for interactions between the dark energy in photons, or the dark energy in nuclear matter, and experiments are ongoing to do exactly that. It could even be that the dark energy has similar kinds of interactions with the dark matter.
It could be that the dark sector all by itself, forms some interestingly interacting set of things, and we, the ordinary matter, sit off by the sides. So the dark matter could be affected by the dark energy, and have its mass change. Or it could have its interactions change in some interesting way. We don't know, yet it's not bad that we don't know. It's good that there are so many possibilities that we'll be pursuing, looking for observational evidence for anyone of these things happening.
So for the last part in this set of lectures, we'll end with one dramatic speculation, and one cautionary tale, just to bring us back to reality at the end. The dramatic speculation has to do with, one again, the naturalness of our picture of cosmology. In this case, we're not talking about the naturalness of the theory that we have, the theory with the parameters that describe dark matter and dark energy, but rather the configuration in which we find our universe today. Remember that this already worked once, this kind of reasoning where we said, "Why is the universe in this kind of situation in which we find it?"
This question worked with inflation. Inflation was able to successfully explain why the universe is homogeneous and isotropic, and why it's very close to spatially flat, invoking a dynamical mechanism based in physics, located in the early universe. It turns out that there is a deeper question that inflation doesn't quite answer. This is very closely related to the question of the gas in a box, the question of the entropy of the universe.
Our current universe has what you might call a medium sized entropy. This basically tells you how disordered things are. So if your gas in a box is stuck in one corner, that's a very low entropy. It's very highly ordered since someone cleaned it up and put it there. Yet if the gas is spread out all over the place, that's high entropy, and is disordered. We understand on the basis of physics, that stuff in the universe like to go from being low entropy, to being high entropy. Disorder tends to increase, just because there are many more ways of being disordered, than being ordered.
So this is a deep feature of fundamental physics, called the second law of thermodynamics. Things tend to become more disordered with time. Our current universe is semi-ordered. In the far past, things were much more highly ordered, so that entropy was lower. In the far future, it will be much more disordered, and the entropy will be much more higher. The entropy is growing with time, as the universe goes from the Big Bang, to the cold heat death, where everything is spread out and not radiating.
The question then is, why did the universe ever start out in some phase where the entropy was so low? You might, and many contemporary cosmologist do, think this has something to do with inflation. Yet in fact, inflation is begging the question. It imagines that a tiny patch of the universe was dominated by the dark energy, an even lower entropy state than the ordinary Big Bang. The truth is we don't yet now know, why the universe had such a low entropy.
It might, however, have something to do with dark energy. Dark energy is telling us that in the future of our universe, it will not be completely quiet. Dark energy means that even in empty space, there is some energy that keeps propelling the universe and keeps giving a little quantum jiggle to all the fields in the universe. If you wait long enough, much longer than the current age of the universe, It could be that those quantum jiggles come together in exactly the right configurations to make what is called a baby universe. To start a little patch with incredibly high ρ, ready to inflate and separate off from the universe that we know. Furthermore it could be that our universe is somebody else's baby, started off in some other universe that was cold and filled with nothing than dark energy.
In other words, the dark energy that we've discovered, though we're obviously just speculating here, might play some role in helping us understand why the configuration of our current universe looks so unnatural, looks like it started in such a low entropy state. That's the kind of thing we're led to think about, by thinking about dark matter and dark energy.
Finally, the cautionary tale is, how close are we to being done? In 1900, a lot of physicists though we were close to being done with the laws of physics. We had a really good understanding on the basis of Newtonian mechanics, of how matter and energy worked. There were just a few little things that were a tiny bit bothersome. For example, if you calculated the lifetime of an atom, you found it was an incredibly tiny fraction of a second. It should be the case that an electron zooming around a nucleus, should collapse really quickly.
Why was that number so much smaller than the observations said it was supposed to be? There was also an inconsistency in 1900 between successful theories of physics. Electromagnetism and Newtonian mechanics, didn't quite have the same set of symmetries, and that was a puzzle. Finally, if you looked at the sky, you saw that some celestial bodies weren't moving as they should. The orbit of Mercury was discrepant. It was moving in the wrong way, a different way than predicted by Newtonian mechanics.
So as it turns out that all of these tiny discrepancies led to revolutions. They led to quantum mechanics, the Special Theory of Relativity, and to General Relativity. It could have been that you just cleaned up something here and there, or it could have been a completely different picture of the universe.
The same thing is true today. We have a number that is wrong, and that number is the vacuum energy. Our number is much smaller than it has any right to be, since we observe a vacuum energy of 120 orders of magnitude smaller than we predict. We have an inconsistency between successful theories. We have General Relativity and quantum mechanics, both of which fit the data, but are mutually incompatible. Finally, we have celestial bodies moving in a way that doesn't make sense to us. We see things orbiting faster than they should, and attribute these to dark matter and dark energy.
It may be that we're almost done. It may be that a couple of things will fall into place, and we'll have a complete understanding of the fundamental laws of nature. Or it could be that a revolution is in the offing, similar to what we had 100 years ago. We don't know, and that's the fun of science. The only guarantee is that the next 100 years of exploration, will be equally interesting and surprising as the last 100 years have been.
