Sean Carroll in PI's cosmology workshop

Last morn­ing, I lis­tened to Prof. Carroll's talk: Infla­tion and the Arrow of Time, in which he showed to us his atti­tude and idea of tack­ling the prob­lem of time arrow, or more specif­i­cally the prob­lem why the entropy of our uni­verse is orig­i­nally small. Below is a brief sum­mary of my notes.

First of all, he prompted a prob­lem. The 2^nd law of ther­mo­dy­nam­ics defines an arrow of time, i.e. the entropy increases with time, whereas the micro­scopic laws of physics don't define such an arrow. Accord­ing to Boltz­mann, is equal to the logrithm of the num­ber of microstates that give the same macrostates. But then, why do we assume to be orig­i­nally small?

He wrote down some num­bers. If we ignore the con­tri­bu­tion of grav­ity to the total entropy of the uni­verse, we can obtain the following.

• When Infla­tion starts,
• Now,
• Later,

So, why was so low in the beg­gin­ing of our uni­verse? He thinks that infla­tion by its own does not solve the prob­lem. Dur­ing infla­tion, the num­ber of low energy degrees of free­dom increases, while the total num­ber of degrees of free­dom stays the same. He then told us four pos­si­bil­i­ties of answer­ing the question.

1. starts very small and then just keeps increas­ing with time. Three issues arise in this picu­ture: i) micro­scopic CPT vio­la­tion; 2) need a law of physics for bound­aries of uni­verse; and iii) wave­func­tion is time-symmetric, but clas­si­cal his­to­ries are not.
2. Gold/Hawking pic­ture, where first increases with time and then decrease after reach­ing its max­i­mum. How­ever, this pic­ture is not accept­able log­i­cally, since it has more fine tun­ing prob­lems then we already have, e.g. needs to be fine tuned in the begin­ning of the uni­verse. Besides, observations seem telling us that our uni­verse will expand for­ever and not rec­ol­lapse.
3. Boltz­mann pic­ture. is fluc­tu­at­ing around its max­i­mum equi­lib­rium value in a thermo bath. The prob­lem is that it is very "expen­sive" to have such a fluc­tu­a­tion and prob­a­bly an anthropic prin­ci­ple is demanded such that our uni­verse is in the right posi­tion.
4. This is the picu­ture Prof. Car­roll prefers. In this pic­ture, can go as large as pos­si­ble and a pre-Big Bang era is assumed where the time arrow was reverse. The Big Bang hap­pens some­where in the ascend­ing half of the curve that is close to the min­i­mum of the curve.

Now in order to make sense of the 4^th pos­si­bil­ity, Prof. Car­roll first tried to con­vince us that the max­i­mum entropy state is the empty space but not the black hole state, which is merely the one with high­est entropy den­sity. When grav­ity is taken into account, a space of dust can col­lapse into black­holes such that the total entropy appar­ently reaches its max­i­mum. How­ever, this is not true. Black holes can evap­o­rate and the space ends up being empty. Such an empty space has even larger entropy than the black­hole state. Right at this moment, for some rea­son I left and missed the final 15 min­utes of his talk, dur­ing which he addressed his point. I bor­rowed the notes from oth­ers for that part, and hence are not sure if my under­stand­ing is cor­ret for what I am gonna say from now on. He then argued that in an large empty de Sit­ter space with pos­i­tive vac­cum energy, baby bub­ble uni­verses can appear based on Planck mass black­holes due to quan­tum fluctuations. When a black­hole evap­o­rates out, the total entropy is again increased and a baby uni­verse becomes a dis­con­nected region. Because quan­tum fluc­tu­a­tions may set up the con­di­tions nec­es­sary for the baby uni­verses to begin inflation, a baby uni­verse may then inflate and evolve to our universe. In this sce­nario, the arrow of time is some­how local in the sense that time always evolves from the low value of entropy to the larger.

With­out show­ing any image, I don't know if I made things clear. If you are inter­ested, you may send me an email to ask for a PDF file of the notes. I like the idea he pre­sented, and will prob­a­bly look more into it to see if Loop Quan­tum Grav­ity applies.

Before fin­ish­ing, I'd like to say a bit more about Prof. Car­roll and his pre­sen­ta­tion. Prof. Car­roll looks a bit like (at least to me) a com­bi­na­tion of a pro­fes­sor, a banker on Wall street and a spokesman of White House. I really enjoyed his talk. His style of pre­sent­ing the mate­r­ial is very elegant. Although he did not speak very loudly and not fast, I still strongly felt his enthu­si­asm. He had a mild tone with vocal vari­ety that makes (I think) every audi­ence com­fort­able. He had always been gen­tle­manly dur­ing the whole ses­sion and even when he was sur­rounded by sharp ques­tions or com­ments. I wish I had ever been enrolled in any of his classes.

Sum­mary on Prof. Wilczek's talk will appear tomor­row, if I feel bet­ter then.

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