Re: [math-fun] A Scientist Takes On Gravity
Read the paper, then Google the physics blogs for "Verlinde" & download Verlinde's (~1 hour) audio & PDF slides from a lecture that he gave. In the audio file, there are questions from the audience that are interesting. I've listened to it once & will listen to it several more times. Apparently, he does handle Lorentz & GR & even provides some explanation of dark matter (!). I didn't follow much of this, but apparently much of what you're asking about is the "easy" part, as it has already been done before for other models, including holographic & string theory models. At 07:34 AM 7/17/2010, Fred lunnon wrote:
I've always found cosmology intriguing --- though not alas enough to actually learn any properly. Much out there in the field seems solidly based (if too detailed for a casual enquirer to grasp properly), and I'm pretty sure I could get to grips with it if sufficiently motivated --- the Standard Model being a case in point. Much else is patently crank, generated by individuals with impaired judgement --- we might not always agree about individual cases here --- String Theory, anyone?
Very occasionally though I encounter something genuinely shocking --- so improbable and outrageous that I become aware of an emotional reaction, attempting to suppress it from consciousness --- general relativity and quantum mechanics come to mind here, when first met long ago. And perhaps more recently, the original (quaternion) formulation of the Maxwell equations.
But now Jacobson, Verlinde & Co. are rattling the bars of my comfortable worldview again, and folks, I'm reeling somewhat.
Tell me it ain't so --- space just the grin on another Cheshire cat?
How can Lorentz transformations occur --- space and time axes finally interchanging in the proximity of the Schwarzschild radius --- if spacetime is asymmetrical?
Do these ideas explain why space has just three dimensions --- never mind about a single time?
Have they any relevance to the missing mass problem?
Somebody, help! Fred Lunnon
On 7/16/10, Henry Baker <hbaker1@pipeline.com> wrote:
The paper: http://arxiv.org/abs/1001.0785
I read over the paper, and it is surprisingly readable for mere mortals.
I don't know enough physics to comment on its accuracy as a model of the "real" world, but even as an abstract model it is very beautiful.
Basically, Verlinde turns Bekenstein on his head. Verlinde rearranges the world so that gravity falls out of information/entropy instead of the other way around.
Bekenstein showed that the universe is "holographic", meaning that _all_ the information about what is going on within a simple region of space is encoded in bits on its surface, and the _amount_ of such information is proportional to its surface area.
Verlinde goes backwards and shows that gravity is an emergent concept from the statistics of microstates. The closest high school physics analog is an osmotic force across a membrane: the force arises because it is far more probable that the more concentrated fluid becomes less concentrated than the other way around.
Interestingly, the Heisenberg constant h plays very little part in Verlinde's derivation, which treats entropy, temperature, etc. as continuous variables. This makes a lot of sense, as gravity itself is a macroscopic phenomenon.
From a blog about Verlinde's paper:
http://motls.blogspot.com/2010/01/erik-verlinde-comments-about-entropic.html ...
On Sat, Jul 17, 2010 at 11:26 AM, Henry Baker <hbaker1@pipeline.com> wrote:
Read the paper, then Google the physics blogs for "Verlinde" & download Verlinde's (~1 hour) audio & PDF slides from a lecture that he gave. In the audio file, there are questions from the audience that are interesting. I've listened to it once & will listen to it several more times.
I'd appreciate a link--I haven't been able to find the video you're referring to. The very core of the argument goes like this. Say we have two boxes, one inside the other: +---------------+ | | | +----------+ | | | | | | | | | | | | | | +----------+ | +---------------+ Say the inner box has room for ten bits on its surface and the outer one room for twenty. Each box can use as many "1"s as there are particles inside it: +---------------+ | X | | +----------+ | | | | | | | X | | | | | | | +----------+ | +---------------+ In this case, the inner box has only one particle inside, so there are 10 choose 1 = 10 ways to choose a labeling of the inner box; the outer box has two particles inside, so there are 20 choose 2 = 380 ways. Thus there are 3800 ways to label the system in all. If both particles are in the inner box, though, the number of ways to label the system increases: +---------------+ | | | +----------+ | | | | | | | X X | | | | | | | +----------+ | +---------------+ The inner box now has 10 choose 2 ways = 90, while the outer box still has 380. So using the standard assumption that all labelings are equally accessible, it's 9 times as likely to find both particles in the inner box, and we get an entropic force drawing them together. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
What a beautiful argument! And the "gravitational constant" takes different values, according to whether particles are distinguishable or not. However, the available "space" (= number of bits in the label?) still seems to be given, rather than emergent ... WFL On 7/19/10, Mike Stay <metaweta@gmail.com> wrote:
On Sat, Jul 17, 2010 at 11:26 AM, Henry Baker <hbaker1@pipeline.com> wrote:
Read the paper, then Google the physics blogs for "Verlinde" & download Verlinde's (~1 hour) audio & PDF slides from a lecture that he gave. In the audio file, there are questions from the audience that are interesting. I've listened to it once & will listen to it several more times.
I'd appreciate a link--I haven't been able to find the video you're referring to.
The very core of the argument goes like this. Say we have two boxes, one inside the other:
+---------------+ | | | +----------+ | | | | | | | | | | | | | | +----------+ | +---------------+
Say the inner box has room for ten bits on its surface and the outer one room for twenty. Each box can use as many "1"s as there are particles inside it:
+---------------+ | X | | +----------+ | | | | | | | X | | | | | | | +----------+ | +---------------+
In this case, the inner box has only one particle inside, so there are 10 choose 1 = 10 ways to choose a labeling of the inner box; the outer box has two particles inside, so there are 20 choose 2 = 380 ways. Thus there are 3800 ways to label the system in all.
If both particles are in the inner box, though, the number of ways to label the system increases:
+---------------+ | | | +----------+ | | | | | | | X X | | | | | | | +----------+ | +---------------+
The inner box now has 10 choose 2 ways = 90, while the outer box still has 380. So using the standard assumption that all labelings are equally accessible, it's 9 times as likely to find both particles in the inner box, and we get an entropic force drawing them together.
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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On Mon, Jul 19, 2010 at 11:11 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
However, the available "space" (= number of bits in the label?) still seems to be given, rather than emergent ... WFL
Yes, the holographic principle is taken as a starting point: it's assumed that the entropy is proportional to the surface area. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
On Mon, Jul 19, 2010 at 11:28 AM, Mike Stay <metaweta@gmail.com> wrote:
On Mon, Jul 19, 2010 at 11:11 AM, Fred lunnon <fred.lunnon@gmail.com> wrote:
However, the available "space" (= number of bits in the label?) still seems to be given, rather than emergent ... WFL
Yes, the holographic principle is taken as a starting point: it's assumed that the entropy is proportional to the surface area.
Sorry, it's assumed that the number of bits is proportional to the surface area. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
On Mon, Jul 19, 2010 at 09:34, Mike Stay <metaweta@gmail.com> wrote:
On Sat, Jul 17, 2010 at 11:26 AM, Henry Baker <hbaker1@pipeline.com> wrote:
[...]Verlinde's (~1 hour) audio & PDF slides from a lecture that he gave. In the audio file, there are questions from the audience that are interesting. I've listened to it once & will listen to it several more times.
I'd appreciate a link--I haven't been able to find the video you're referring to.
The link seems to be http://pirsa.org/10050022/ For me the video has no sound, but the MP3 works and I could play both simultaneously using two different programs. Or just listen to the MP3 and try to follow along with the PDF slides. Based on the slides, it seems this lecture at least partly covers the outline of the paper at http://arxiv.org/abs/1001.0785 (I also found a 2005 string theory lecture at http://www.fields.utoronto.ca/audio/05-06/strings/verlinde/ for the really curious) [...] In this case, the inner box has only one particle inside, so there are
10 choose 1 = 10 ways to choose a labeling of the inner box; the outer box has two particles inside, so there are 20 choose 2 = 380 ways. Thus there are 3800 ways to label the system in all.
I thought "20 choose 2" was 20*19/2 = 190. Likewise, 10 choose 2 would be 45. So, a ratio of 4.5, not a ratio of 9. What did I miss? -- Robert Munafo -- mrob.com
On 7/20/10, Robert Munafo <mrob27@gmail.com> wrote:
On Mon, Jul 19, 2010 at 09:34, Mike Stay <metaweta@gmail.com> wrote:
On Sat, Jul 17, 2010 at 11:26 AM, Henry Baker <hbaker1@pipeline.com> wrote:
[...]Verlinde's (~1 hour) audio & PDF slides from a lecture
that he gave. In the audio file, there are questions from the audience that are interesting. I've listened to it once & will listen to it several more times.
I'd appreciate a link--I haven't been able to find the video you're referring to.
The link seems to be http://pirsa.org/10050022/ For me the video has no sound, but the MP3 works and I could play both simultaneously using two different programs. Or just listen to the MP3 and try to follow along with the PDF slides. Based on the slides, it seems this lecture at least partly covers the outline of the paper at http://arxiv.org/abs/1001.0785 (I also found a 2005 string theory lecture at http://www.fields.utoronto.ca/audio/05-06/strings/verlinde/ for the really curious)
At times, I found the Flash (video's) audio fading badly ... Mind-expanding moment #1 --- instead of the customary hocus-pocus about what happens to an object falling through the event horizon, its information simply merges with the hologram at the surface (which expands to accommodate it). Mind-expanding moment #2 (in response to a listener who incautiously enquired how we know we are not at an event horizon) --- we _don't_ know that we are not at an event horizon. I'm suffering overload at this point --- time to take a break and start again later --- from the beginning, I think! Fred Lunnon
I agree, that's the coolest thing about it. A related statement is that, once the size of the screen shrinks to the size of the event horizon, the number of bit patterns becomes exactly 1 and it can shrink no further. (At least for the classical "uncharged, non-rotating" case) And yes, it's important to consider that we might be falling towards another much larger mass, or emerging from the other side of a wormhole (Einstein-Rosen bridge). I seem to recall that was put forth as a possible explanation of the "dark energy" mystery recently. Poplawski I think. On Tue, Jul 20, 2010 at 09:02, Fred lunnon <fred.lunnon@gmail.com> wrote:
Mind-expanding moment #1 --- instead of the customary hocus-pocus about what happens to an object falling through the event horizon, its information simply merges with the hologram at the surface (which expands to accommodate it).
Mind-expanding moment #2 (in response to a listener who incautiously enquired how we know we are not at an event horizon) --- we _don't_ know that we are not at an event horizon.
I'm suffering overload at this point --- time to take a break and start again later --- from the beginning, I think!
Fred Lunnon
-- Robert Munafo -- mrob.com
From: Fred lunnon <fred.lunnon@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Tue, July 20, 2010 6:02:18 AM Subject: Re: [math-fun] A Scientist Takes On Gravity Mind-expanding moment #1 --- instead of the customary hocus-pocus about what happens to an object falling through the event horizon, its information simply merges with the hologram at the surface (which expands to accommodate it). Mind-expanding moment #2 (in response to a listener who incautiously enquired how we know we are not at an event horizon) --- we _don't_ know that we are not at an event horizon. I'm suffering overload at this point --- time to take a break and start again later --- from the beginning, I think! Fred Lunnon _______________________________________________ This idea of merging with the hologram can only apply to the observation of an infalling body as made by an external observer. Signals from the body cease, an infinite red-shift as it approaches the event horizon, and information it contained becomes encoded in the quantum state of the surface, to be resurrected in the detailed state of the Hawking radiation as the black hole decays. To the infalling observer, nothing special happens when passing through the event horizon. This observer continues to receive signals from the external universe, even when trapped, until hitting the physical singularity. The spherical light-shell that reaches the singularity along with the observer is the final received signal. Extended backward to the external universe, it marks the boundary between events received by the infalling observer and those that arrive too late. Suitable observations may reveal that one is trapped inside an event horizon, but these cannot be entirely local, and could not be discerned from inside an opaque box. The question "how do we know we are not at an event horizon" might well be replaced by "how do we know we are not merged into the hologram". The answer again is "we don't know". Perhaps this can be made into a sequel to the "Matrix" movies. -- Gene
On Tue, Jul 20, 2010 at 12:05 AM, Robert Munafo <mrob27@gmail.com> wrote:
[...] In this case, the inner box has only one particle inside, so there are
10 choose 1 = 10 ways to choose a labeling of the inner box; the outer box has two particles inside, so there are 20 choose 2 = 380 ways. Thus there are 3800 ways to label the system in all.
I thought "20 choose 2" was 20*19/2 = 190. Likewise, 10 choose 2 would be 45. So, a ratio of 4.5, not a ratio of 9. What did I miss?
Nothing, of course. It was a dumb mistake. - Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Just checking, I wasn't trying to call anyone dumb. I haven't read much of the Verlinde paper and so I didn't know if you meant binomial coefficient, or perhaps an order-preserving definition of a "choose" function. On Tue, Jul 20, 2010 at 11:08, Mike Stay <metaweta@gmail.com> wrote:
On Tue, Jul 20, 2010 at 12:05 AM, Robert Munafo <mrob27@gmail.com> wrote:
[...] In this case, the inner box has only one particle inside, so there are
10 choose 1 = 10 ways to choose a labeling of the inner box; the outer box has two particles inside, so there are 20 choose 2 = 380 ways. Thus there are 3800 ways to label the system in all.
I thought "20 choose 2" was 20*19/2 = 190. Likewise, 10 choose 2 would be 45. So, a ratio of 4.5, not a ratio of 9. What did I miss?
Nothing, of course. It was a dumb mistake. - Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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-- Robert Munafo -- mrob.com
participants (5)
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Eugene Salamin -
Fred lunnon -
Henry Baker -
Mike Stay -
Robert Munafo