Now it's 2010 and the five Messenger Lectures were delivered by the world's leading particle phenomenologist, Nima Arkani-Hamed (IAS Princeton).

Here is the first one, from October 4th, 2010.

*Press play to play.*

All the lectures are available (5 times 90 minutes):

- Setting the stage: spacetime and quantum mechanics
- Our "Standard Models" of particle physics and cosmology
- Spacetime is doomed: what replaces it?
- Why is there a macroscopic universe?
- A new golden age of experiments: What might we know by 2020?

*radical conservatives*much like Nima himself. ;-) Nima borrowed the term from John Wheeler.

**Hat tip:**Nima ;-)

Hi Lubos, many thanks for the links.

ReplyDeleteIn his 3rd lecture, Nima talks about entropy and black holes - and I have few questions.

1. He said (~26:50), if we threw some "disorder" into a black hole then the entropy of the Universe will decrease. I find it confusing - aren't we instead just "moving" the entropy of the Universe from one place to another, without actually changing it?

2. He said (~28:30) that high entropy means hot. I'm confused as well - as our Universe is expanding, the entropy increases so the Universe should become hotter and hotter. Is this correct? What are the evidences?

Thanks in advance for your answers :)

Hi Andrew, thanks for your interest.

ReplyDelete1. This comment about decreasing entropy is clearly meant to be a result of a classical physics reasoning. In the real physics that takes quantum mechanics into account, the 2nd law of thermodynamics holds again, with or without black holes.

Classically, everything you throw into a black hole is gonna be completely destroyed almost immediately. And a black hole of mass M has no visible internal structure. Once its shape gets stabilized and spherical - which is very soon - it seems to have no "hair". Therefore, it can carry no information and no entropy.

Throwing your trash bin to the black hole would transform it into a piece of mass in a structureless object, so the entropy would drop to zero. That would contradict the 2nd law according to which the entropy never decreases.

In reality, the 2nd law holds because the black holes actually carry an entropy - a large one. In fact, they have the maximum entropy among all objects of the same radius or all bound objects of the same mass. The entropy of the black hole - proportional to the area of event horizon - always goes up more than by the entropy of the trash that disappeared. That's surely the ultimate conclusion of Nima, too.

2. The "hot equals higher entropy" is true for all realistic material objects of a fixed size and fixed volume (except for black holes).

For an expanding Universe, it is the entropy density that is decreasing, but because the volume of space is increasing, the total entropy goes up and the 2nd law holds, like it always does.

At cosmological distances, many types of matter are already in some equilibrium, so the total entropy doesn't change - the entropy density goes like 1/V. Of course, there is still an increase from all the "local" phenomena such as heat transfer on stars, radiation from burning, growth of black holes, etc.

Black holes actually have a negative heat capacity, so the higher entropy they have, the larger their surface has to be, the heavier and bigger there are, and the *lower* temperature they have as a consequence. But normal material objects have positive heat capacities, something needed for stability. The relative longevity of black holes is because the temperature is really really low, proportional to the Planck's constant, anyway.

Best wishes

Lubos

Hi Lubos,

ReplyDeleteThanks for thorough answers - I did some reading but looks like I have to get back to you again :)

Let's continue this "throwing matter into a black hole will decrease the entropy" classical paradox. Yes, the matter is no longer visible but why can't we say that it is still sitting there, archived inside the black hole? In this case the 2nd law of thermodynamics still holds.

Maybe an answer from the classical point of view is like, if we throw information into a black hole, it gets completely lost (accordingly to the "no hair" theorem) and thus the entropy of the Universe will decrease.

But I don't feel it's correct - and not because of quantum mechanics. To me, entropy had always been a level of disorder - like everything in a house starting to break up (entropy increases) unless you fix it (decrease the entropy). So, when I throw my laptop into a black hole, the black hole will destroy this ordered piece of matter and thus the entropy (disorder) of the overall Universe should

increase. But then, why you say "Throwing your trash bin to the black hole would transform it into a piece of mass in a structureless object, sothe entropy would drop to zero"? Shouldn't "structureless" mean the highest possible entropy? Looks like my understanding of entropy is flawed, and that's the source of my confusion!..I did read about the entropy on the internet, and I see that there's "thermodynamics entropy" which is "Heat"/"Temperature" and that there's "statistical mechanics" entropy which is probability of a particular state of a system (low entropy = less probable). But structureless object is something

highlyprobable inside a black hole, so it should imply high entropy... Uh oh, I still cannot get my head around it.Thanks,

Andrew

Dear Andrew,

ReplyDeletesure, from a bookkeeping viewpoint, you could say that the entropy was "stored" inside the black hole.

Except that from a microscopic or statistical viewpoint using classical GR, it was clear that there was no entropy. One knows that the black hole is quickly gonna be empty, it has no structure, so it has no bits to remember the entropy. Such an empty black hole is completely clean and *ordered*. There can't be any disorder somewhere if something is completely empty. If you don't see why this was what a classical physicist would have to conclude, then your understanding of entropy is indeed flawed.

Quantum gravity changes the conclusion but the "place" where the entropy is stored (or the degrees of freedom) has no simple intuitive interpretation. Effectively, the black hole horizon is made out of "QG atoms" that carry the huge entropy but they're completely invisible to a GR observer. Also, from some viewpoint, the bits may be imagined to be stored inside, in the details of the fuzzball configurations, but one still has to explain why the black hole (with the microscopically complicated interior) looks empty to all long-distance observers.

Best wishes

Lubos

Hi Lubos,

ReplyDeleteYeah, now it's more clear. I incorrectly thought that there was matter from the event horizon all the way down. But since a black hole is a singularity point in the center of a completely empty sphere - so it's clear that black holes don't have entropy (from classical point of view).

From quantum gravity viewpoint, however, they do have entropy and it's Hawking radiation that carries the entropy.

...If I understand all that correctly :)

But still we have problem with lost information - and Nima mentions in his 3rd lecture (~52:30) about the information being "kept" at the boundary of a black hole. Whoa! Do I get that right? So I still can somehow "recognize" my laptop I had thrown into the black hole, by looking at the boundary??

And one more question - does that picture describes our whole universe, so that our 3+1 dimensional world is a boundary of a 5-dimensional tin can?

Thanks for taking time answering my questions!

--Andrew

Dear Andrew, a full harmony now achieved concerning the classical entropy of a BH.

ReplyDeleteNow, the laptop.

From the viewpoint of the external observer outside the black hole, the interior of the black hole doesn't exist. You can't get the information out of the interior - classically - at most from the horizon.

That's where the Hawking radiation is coming from, so at least in some geometric sense, you may imagine that the Hawking radiation carries the information about the laptop from the horizon - look at the Penrose diagram - so that's where the information had to hide all the time.

This is a somewhat ambiguous statement because alternatively, one may also imagine that the information is inside and it tunneled outside because of QG nonlocalities. These two interpretations, while sounding directly opposite, may actually be matematically equivalent to each other because of complementarity etc.

Yes, this picture - if I understand what you wanted to take from it - describes the whole Universe. That's what holography and AdS/CFT is all about. However, you have went in the wrong direction with the dimensions. Our 3+1D world has gravity, so it's equivalent to a 2+1D - not 4+1D - information on the horizon.

Our 3+1D world may also be "physically" a 4+1D world, like in Randall-Sundrum models, but the the extra dimension is completely "real" and "ordinary" to start with, even though the dynamics of the RS (AdS) space makes it invisible.

Best wishes

Lubos

Hi Lubos,

ReplyDeleteThanks for the answer, though I can't keep up the conversation about extra dimensions :) so instead would ask again about the black holes.

Last night I thought: ok, maybe it's an empty nothing with singularity in the center - but when my laptop would cross the horizon, shouldn't it still be the same laptop just moving faster and faster towards the singularity point (where it would get destroyed)?

So I tried to calculate the acceleration, and um, got weird results. Here's my train of thought:

a = F/m, where the only force is F=GMm/r^2 ('M' is for mass of the black hole and 'm' is mass of the laptop).

So, a = GM/r^2

Let's take Sagittarius A* as our black hole (accordingly to wikipedia it's radius is ~6.25 light hours and mass is ~4.31*10^6 solar masses)

Plugging in the numbers, we get

a = 6.67*10^-11 * 4.31*10^6*1.9*10^30 / (6.25 * 3*10^6)^2

which is cca 0.16*10^12 (!) which is obviously incorrect as it's faster than light. Where's my mistake?

Thanks,

Andrew

Dear Andrew,

ReplyDeletesurely you're joking. Of course, if you apply the 17th century laws of Newtonian physics to motion inside black holes, you will get nonsense.

You have missed all relativistic effects - not just the curved spacetime inside the black hole (general relativity) but also special relativity (mass increases as you approach the speed of light, and it will never allow a massive object to reach the speed of light).

Clearly, you must either start to learn proper relativity, or you must realize that everything you "know" about the black holes now are just naive stories for children in the kindergarten that can't be used to properly calculate any additional detail.

Best wishes

Lubos

Hmm, true. Hopefully the question didn't offend you :S

ReplyDeleteI will start learning relativity.