Hawking Radiation: Info vs Semanticity? - Hossenfelder

[gerald V]

TL;DR

As I know definitions, a thermal radiation like Hawkings carries a maximum of entropy, which is the same as information. Semanticity (what was the hole made from?) is something different.

In this video How we know that Einstein's General Relativity can't be quite right - YouTube , Hossenfelder says: "The [Hawking] radiation is entirely random and does not carry any information..."

I have heard and read this from a number of other sources, and never understood. Completly random (= thermal) is the maximum of entropy alias information. One needs a lot of bits for encoding.

It appears to me that physicists rather mean „we are unable to extract semanticity from Hawking radiation“, what is a trickily different thing. One has a huge pile of bits and is unable to reconstruct from those the history of the black hole. However, finding semanticity would mean that the information of the radiation is not maximum, since it has a non-random pattern. So Hawking radiation as currently understood does not carry too little information, rather too much.

Doesn’t this demonstrate that something is wrong with our concepts of information and semanticity? Or do I simply mess up definitions?

Many thanks in advance.

 

[haushofer]

Why do you say that "entropy is the same as information"? It seems like you're suggesting that a maximum entropy entails a maximum amount of information.

As I see it: if you have two black bodies (for which the radiation spectrum only depends on T), both emitting radiation at the same temperature T, these black bodies can be quite different from each other in shape, material, etc. So measuring the temperature doesn't contain any useful information about the body itself.

That the spectrum is black body follows from the usual calculation underlying Hawking radiation; see e.g. Winitzki's textbook/notes on quantum field theory on classical backgrounds.

 

[PeterDonis]

"The [Hawking] radiation is entirely random and does not carry any information..."

We don't know whether this is actually true. Hossenfelder is describing a common belief, but not everyone agrees with it, and we have no way of testing the question experimentally and no good theory of quantum gravity with which to investigate it theoretically. Which means we also do not have a good understanding of "information" when black holes are involved.

 

[gerald V]

Thank you both very much.

In particular @ haushofer: I have always had problems to understand what information shall mean. In fact, it appears to me as the same as entropy. Entropy is the logarithm of the phase space volume occupied. Say, if this phase space volume is 1000 in units of Planck's constant, to denote at which of these subvolumes the system actually is at a given instant of time, one has to reserve 3 digits (or an analogue of bits). So the entropy in decadic basis is 3. And information is just the number of digits (or bits or pixel or so) needed to encode something which always can be made analogous to a number (a photo of the Mars surface can be transformed into a - usually binary - number).
D'accord, the temperature encodes little about the radiating body. Thermal radiation only means that it looks random in a well defined way, what only is one comparably tiny characteristic. It is like the difference between knowing that the decimal digits of $\pi$ look random, and actually knowing them.

 

[vanhees71]

It's perhaps more intuitive to think of entropy as a measure of "surprise". Entropy is a measure for the missing information, which means that having a probabilities with higher entropy $S=-\sum_{i} p_i \ln p_i$ you are more surprised about the result of measuring the described random variable than if you have probabilities with lower entropy.

Take as an example a fair die. Then the probability to find a certain number when throwing it is $p_i=1/6$ and the entropy is $\ln 6$, and that's also the state of maximum entropy, because you have the greatest surprise, no matter which result you get when throwing the die.

Now take an extremely loaded die, always showing $6$. Then $p_i=0$ for $i \in \{1,\ldots,5 \}$ and $p_6=1$. The entropy now is 0. Indeed, with such a die there's not the slightest surprise that you get always a 6, given that probabilities.