Did Stephen Hawking fix his numerical mistake?

[mad mathematician]

I am reading Hawking's and Penrose's joint book called:" The Nature Of Space and Time".
And on page 98 it's written the following:"I have tried to show that the entropy of such a universe would be quarter of the area of the event horizon at the time of maximum expansion (fig. 5.12). However, at the moment I seem to be getting a factor of 3/16 rather than a 1/4."

Did he find where he had gone wrong in his calculations since the appearance of the book?

 

[PeterDonis]

Did he find where he had gone wrong in his calculations since the appearance of the book?

Without a reference to the actual scientific literature, we have no way of knowing.

 

[Jaime Rudas]

Without a reference to the actual scientific literature, we have no way of knowing.

Isn't what Hawking wrote considered actual scientific literature?

 

[PeterDonis]

Isn't what Hawking wrote considered actual scientific literature?

Not the book referred to in the OP. That's a pop science book, not a textbook or peer-reviewed paper.

 

[Jaime Rudas]

Not the book referred to in the OP. That's a pop science book, not a textbook or peer-reviewed paper.

I disagree. This text is certainly not a textbook or a peer-reviewed paper, but it can't be considered a pop science book or anything other than actual scientific literature.

 

[PeterDonis]

I disagree.

Please note that in my previous post, I was not giving my personal opinion. I was telling you (and the OP of this thread) the PF rules.

This text is certainly not a textbook or a peer-reviewed paper

Then as far as the PF rules are concerned, it's not scientific literature.

That said, if you want my personal opinion (as distinct from the PF rules), here it is:

it can't be considered a pop science book or anything other than actual scientific literature.

I don't think any actual practicing scientist would agree with you. The reason it's pop science is precisely that it is not peer-reviewed--which means that its authors cannot be compelled to stay within the bounds of what the actual science in the field under discussion says. The fact that they are both extremely distinguished scientists is irrelevant; they still are simply saying what they want, and nobody is going to call them on it if they say something that isn't actual science, but their personal opinion, or some line of research that they would like to be actual science, but which isn't yet.

Note that this does not mean such a book can't be very informative. It can. Kip Thorne's Black Holes and Time Warps, for example, while it is also a pop science book by the criterion I have given, is hugely informative (and has loads of references to actual textbooks and peer-reviewed papers, to which you can go to learn more about the actual science Thorne is describing for lay people). I learned a lot from it. But I still wouldn't use it here on PF as a reference to actual scientific literature. It's not.

 

[PeterDonis]

This text is certainly not a textbook or a peer-reviewed paper, but it can't be considered a pop science book

If you want to call it "lectures giving the speakers' opinions" instead of "pop science", go ahead. That's a matter of choice of words, not substance.

As for the substance, from the very first paragraph:

"In these lectures Roger Penrose and I will put forward our related but rather different viewpoints on the nature of space and time."

Emphasis mine. Hawking is saying it straight out: he and Penrose aren't talking about established science, or even making definite proposals about new science to be considered and tested. They're talking about their personal viewpoints.

 

[PeterDonis]

This text

And to bring this subthread back to the OP's question, since the paper you reference gives no references to actual scientific papers, it does not help us at all in answering the OP's question about Hawking's math. We need to see the actual papers in which he published the calculations in question--but we have no references to them here. And Hawking was not obliging enough to give us any in the lectures (which was characteristic of him, however unfortunate).

 

[martinbn]

Does he say why he expects it to be a quarter of the area and not 3/16?

 

[PeterDonis]

Does he say why he expects it to be a quarter of the area and not 3/16?

I believe the factor of $1/4$ is what appears in the formula Bekenstein derived for the entropy of a black hole in terms of the area of its horizon in Planck units.

 

[Jaime Rudas]

Please note that in my previous post, I was not giving my personal opinion. I was telling you (and the OP of this thread) the PF rules.

Understood. Hawking's viewpoints on the nature of space and time are not considered actual scientific literature. I add this point to the already long list of (to me) strange interpretations of the PF rules.

 

[PeterDonis]

Hawking's viewpoints on the nature of space and time are not considered actual scientific literature.

When they appear in a series of lectures that aren't peer reviewed, and by his own admission, as I've already shown with a direct quote, are just his personal viewpoint, not expounding any actual science, yes.

Contrast this with, for example, the classic textbook by Hawking & Ellis, which, while it covers similar material, is an actual textbook. There is much information in there about "the nature of space and time" as far as we know it from General Relativity, but it's not Hawking's personal opinions.

 

[Jaime Rudas]

When they appear in a series of lectures that aren't peer reviewed, and by his own admission, as I've already shown with a direct quote, are just his personal viewpoint, not expounding any actual science, yes.

Contrast this with, for example, the classic textbook by Hawking & Ellis, which, while it covers similar material, is an actual textbook. There is much information in there about "the nature of space and time" as far as we know it from General Relativity, but it's not Hawking's personal opinions.

Yes, yes. I understand.

 

[martinbn]

I believe the factor of $1/4$ is what appears in the formula Bekenstein derived for the entropy of a black hole in terms of the area of its horizon in Planck units.

Right, but this is about a cosmological model, not a black hole. Is there a reason or is it obvious that the factor should be the same.

 

[PeterDonis]

this is about a cosmological model, not a black hole

Yes, but in that model, at least according to Hawking, there is an event horizon because of the recollapse of the universe. (I'm not sure the universe would actually have to recollapse in the model he appears to be using--yes, it's spatially closed, but it also has a positive cosmological constant, and in such a model I don't think there's a recollapse--it's basically de Sitter in the closed slicing. But de Sitter also has an event horizon--normally called the cosmological horizon, but it's the same sort of thing.)

Of course Hawking is vague about all this in his lecture, which is why we need to look at an actual peer-reviewed paper, if anyone can find one, to see what the actual model is that he's using and what actual calculation he's making for entropy.