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Adam Funk
Jan 24, 2012, 8:01:55 AM1/24/12
to
ISTR reading somewhere a while back that the "inverse square law" ---
blah blah is proportional to 1 / (r^2) --- in things like the
universal gravitation formula is a side effect of the trilogy of
spatial dimensions, so that the area subtended by a given solid angle
at distance r is proportional to r^2. So supposedly if we lived in
Flatland, these laws would have 1 / r instead of 1 / (r^2), because
the equivalent of subtended area would be proportional to r.
Comments?
--
The three-martini lunch is the epitome of American efficiency.
Where else can you get an earful, a bellyful and a snootful at
the same time? [Gerald Ford, 1978]
blah blah is proportional to 1 / (r^2) --- in things like the
universal gravitation formula is a side effect of the trilogy of
spatial dimensions, so that the area subtended by a given solid angle
at distance r is proportional to r^2. So supposedly if we lived in
Flatland, these laws would have 1 / r instead of 1 / (r^2), because
the equivalent of subtended area would be proportional to r.
Comments?
--
The three-martini lunch is the epitome of American efficiency.
Where else can you get an earful, a bellyful and a snootful at
the same time? [Gerald Ford, 1978]
Dr. HotSalt
Jan 24, 2012, 9:39:20 AM1/24/12
to
On Jan 24, 5:01 am, Adam Funk <a24...@ducksburg.com> wrote:
> ISTR reading somewhere a while back that the "inverse square law" ---
> blah blah is proportional to 1 / (r^2) --- in things like the
> universal gravitation formula is a side effect of the trilogy of
> spatial dimensions, so that the area subtended by a given solid angle
> at distance r is proportional to r^2. So supposedly if we lived in
> Flatland, these laws would have 1 / r instead of 1 / (r^2), because
> the equivalent of subtended area would be proportional to r.
>
> Comments?
Yep.
> ISTR reading somewhere a while back that the "inverse square law" ---
> blah blah is proportional to 1 / (r^2) --- in things like the
> universal gravitation formula is a side effect of the trilogy of
> spatial dimensions, so that the area subtended by a given solid angle
> at distance r is proportional to r^2. So supposedly if we lived in
> Flatland, these laws would have 1 / r instead of 1 / (r^2), because
> the equivalent of subtended area would be proportional to r.
>
> Comments?
http://blazelabs.com/f-p-hds.asp
"What's the evidence for the existence of higher dimensions?"
(about 2/3 of the way down)
Also, other weird stuff like "the ultimate time independent
dimension". W00t!
Dr. HotSalt
Doctroid
Jan 24, 2012, 9:48:26 AM1/24/12
to
In article <3nm2v8x...@news.ducksburg.com>,
Conversely in a higher number of dimensions the gravitational force
falls off faster than 1/r^2. Which is one reason why physicists are
trying to improve measurements of gravity on microscopic scales: if
there are compactified extra dimensions then you'd expect deviation from
inverse square law behavior when you measure at distance scales
comparable to the compactification scale. Probably if there are
compactified extra dimensions that distance would be on the order of the
Planck length, 1.6x10^-35 m, whereas the inverse square law has been
tested only down to some tens of micrometers, so there is rather, ahem,
a big gap there. But there are theories in which the compactification
scale could be much larger than the Planck length.
Note that closed, stable 2-body orbits (if you disregard general
relativity and assume no perturbations from other bodies) are possible
only in 3 spatial dimensions; you don't get them with inverse linear,
inverse cube, or any other 1/r^n force law.
--
Sig available on request.
- Doctroid
Adam Funk <a24...@ducksburg.com> wrote:
> ISTR reading somewhere a while back that the "inverse square law" ---
> blah blah is proportional to 1 / (r^2) --- in things like the
> universal gravitation formula is a side effect of the trilogy of
> spatial dimensions, so that the area subtended by a given solid angle
> at distance r is proportional to r^2. So supposedly if we lived in
> Flatland, these laws would have 1 / r instead of 1 / (r^2), because
> the equivalent of subtended area would be proportional to r.
>
> Comments?
Yep.
> ISTR reading somewhere a while back that the "inverse square law" ---
> blah blah is proportional to 1 / (r^2) --- in things like the
> universal gravitation formula is a side effect of the trilogy of
> spatial dimensions, so that the area subtended by a given solid angle
> at distance r is proportional to r^2. So supposedly if we lived in
> Flatland, these laws would have 1 / r instead of 1 / (r^2), because
> the equivalent of subtended area would be proportional to r.
>
> Comments?
Conversely in a higher number of dimensions the gravitational force
falls off faster than 1/r^2. Which is one reason why physicists are
trying to improve measurements of gravity on microscopic scales: if
there are compactified extra dimensions then you'd expect deviation from
inverse square law behavior when you measure at distance scales
comparable to the compactification scale. Probably if there are
compactified extra dimensions that distance would be on the order of the
Planck length, 1.6x10^-35 m, whereas the inverse square law has been
tested only down to some tens of micrometers, so there is rather, ahem,
a big gap there. But there are theories in which the compactification
scale could be much larger than the Planck length.
Note that closed, stable 2-body orbits (if you disregard general
relativity and assume no perturbations from other bodies) are possible
only in 3 spatial dimensions; you don't get them with inverse linear,
inverse cube, or any other 1/r^n force law.
--
Sig available on request.
- Doctroid
Adam Funk
Jan 24, 2012, 3:01:34 PM1/24/12
to
On 2012-01-24, Doctroid wrote:
> In article <3nm2v8x...@news.ducksburg.com>,
> Adam Funk <a24...@ducksburg.com> wrote:
>
>> ISTR reading somewhere a while back that the "inverse square law" ---
>> blah blah is proportional to 1 / (r^2) --- in things like the
>> universal gravitation formula is a side effect of the trilogy of
>> spatial dimensions, so that the area subtended by a given solid angle
>> at distance r is proportional to r^2. So supposedly if we lived in
>> Flatland, these laws would have 1 / r instead of 1 / (r^2), because
>> the equivalent of subtended area would be proportional to r.
>>
>> Comments?
>
> Yep.
OK, I thought it seemed fairly obviously right for things like
> In article <3nm2v8x...@news.ducksburg.com>,
> Adam Funk <a24...@ducksburg.com> wrote:
>
>> ISTR reading somewhere a while back that the "inverse square law" ---
>> blah blah is proportional to 1 / (r^2) --- in things like the
>> universal gravitation formula is a side effect of the trilogy of
>> spatial dimensions, so that the area subtended by a given solid angle
>> at distance r is proportional to r^2. So supposedly if we lived in
>> Flatland, these laws would have 1 / r instead of 1 / (r^2), because
>> the equivalent of subtended area would be proportional to r.
>>
>> Comments?
>
> Yep.
radiation --- there's a certain amount of light or heat power coming
out of the source, so the amount hitting a given surface should vary
with the subtended solid angle, which in turn varies with 1/r^2 ---
but I wasn't sure if extending the analogy to gravity was a bit flakey
or not.
> Conversely in a higher number of dimensions the gravitational force
> falls off faster than 1/r^2. Which is one reason why physicists are
> trying to improve measurements of gravity on microscopic scales: if
> there are compactified extra dimensions then you'd expect deviation from
> inverse square law behavior when you measure at distance scales
> comparable to the compactification scale. Probably if there are
> compactified extra dimensions that distance would be on the order of the
> Planck length, 1.6x10^-35 m, whereas the inverse square law has been
> tested only down to some tens of micrometers, so there is rather, ahem,
> a big gap there. But there are theories in which the compactification
> scale could be much larger than the Planck length.
>
> Note that closed, stable 2-body orbits (if you disregard general
> relativity and assume no perturbations from other bodies) are possible
> only in 3 spatial dimensions; you don't get them with inverse linear,
> inverse cube, or any other 1/r^n force law.
--
English has perfect phonetic spelling. It just doesn't have phonetic
pronunciation. [Peter Moylan]
David DeLaney
Jan 24, 2012, 6:01:50 PM1/24/12
to
On Tue, 24 Jan 2012 13:01:55 +0000, Adam Funk <a24...@ducksburg.com> wrote:
>ISTR reading somewhere a while back that the "inverse square law" ---
>blah blah is proportional to 1 / (r^2) --- in things like the
>universal gravitation formula is a side effect of the trilogy of
>spatial dimensions, so that the area subtended by a given solid angle
>at distance r is proportional to r^2. So supposedly if we lived in
>Flatland, these laws would have 1 / r instead of 1 / (r^2), because
>the equivalent of subtended area would be proportional to r.
Correct. Think of it as "the amount of light the Sun has emitted doesn't
>ISTR reading somewhere a while back that the "inverse square law" ---
>blah blah is proportional to 1 / (r^2) --- in things like the
>universal gravitation formula is a side effect of the trilogy of
>spatial dimensions, so that the area subtended by a given solid angle
>at distance r is proportional to r^2. So supposedly if we lived in
>Flatland, these laws would have 1 / r instead of 1 / (r^2), because
>the equivalent of subtended area would be proportional to r.
change as it goes out and out and out. But the area it's spread across grows
as 1/r^2. So the light intensity dims as 1/r^2"; similar considerations for
other such things give the same sort of answer. And yes, 2-D people would
get 1/r gravity, and 4-D people would get 1/r^3, and neither one would have
stable orbits...
Dave "the amount of lolcats stays constant per unit Internet volume, however.
And of course Internet volume only gets larger with rage" DeLaney
--
\/David DeLaney posting from d...@vic.com "It's not the pot that grows the flower
It's not the clock that slows the hour The definition's plain for anyone to see
Love is all it takes to make a family" - R&P. VISUALIZE HAPPYNET VRbeable<BLINK>
http://www.vic.com/~dbd/ - net.legends FAQ & Magic / I WUV you in all CAPS! --K.
Adam Funk
Jan 25, 2012, 3:59:26 PM1/25/12
to
On 2012-01-24, David DeLaney wrote:
> On Tue, 24 Jan 2012 13:01:55 +0000, Adam Funk <a24...@ducksburg.com> wrote:
>>ISTR reading somewhere a while back that the "inverse square law" ---
>>blah blah is proportional to 1 / (r^2) --- in things like the
>>universal gravitation formula is a side effect of the trilogy of
>>spatial dimensions, so that the area subtended by a given solid angle
>>at distance r is proportional to r^2. So supposedly if we lived in
>>Flatland, these laws would have 1 / r instead of 1 / (r^2), because
>>the equivalent of subtended area would be proportional to r.
>
> Correct. Think of it as "the amount of light the Sun has emitted doesn't
> change as it goes out and out and out. But the area it's spread across grows
> as 1/r^2. So the light intensity dims as 1/r^2"; similar considerations for
It seems obvious with radiation: the source is putting out n watts, so
> On Tue, 24 Jan 2012 13:01:55 +0000, Adam Funk <a24...@ducksburg.com> wrote:
>>ISTR reading somewhere a while back that the "inverse square law" ---
>>blah blah is proportional to 1 / (r^2) --- in things like the
>>universal gravitation formula is a side effect of the trilogy of
>>spatial dimensions, so that the area subtended by a given solid angle
>>at distance r is proportional to r^2. So supposedly if we lived in
>>Flatland, these laws would have 1 / r instead of 1 / (r^2), because
>>the equivalent of subtended area would be proportional to r.
>
> Correct. Think of it as "the amount of light the Sun has emitted doesn't
> change as it goes out and out and out. But the area it's spread across grows
> as 1/r^2. So the light intensity dims as 1/r^2"; similar considerations for
the target receives proportional to n/r^2 W/m^2. I wondered if the
extension to gravity was pushing it a bit.
(Oddly, I can't remember where I came across this, or why I was
suddenly wondering about the other day.)
> other such things give the same sort of answer. And yes, 2-D people would
> get 1/r gravity, and 4-D people would get 1/r^3, and neither one would have
> stable orbits...
> Dave "the amount of lolcats stays constant per unit Internet volume, however.
> And of course Internet volume only gets larger with rage" DeLaney
--
"It is the role of librarians to keep government running in difficult
times," replied Dramoren. "Librarians are the last line of defence
against chaos." (McMullen 2001)
David DeLaney
Jan 25, 2012, 11:09:44 PM1/25/12
to
Adam Funk <a24...@ducksburg.com> wrote:
>On 2012-01-24, David DeLaney wrote:
>> other such things give the same sort of answer. And yes, 2-D people would
>> get 1/r gravity, and 4-D people would get 1/r^3, and neither one would have
>> stable orbits...
>
>But (science for engineers) how would you get the units to work out?
Different units for G, obviously.
>On 2012-01-24, David DeLaney wrote:
>> other such things give the same sort of answer. And yes, 2-D people would
>> get 1/r gravity, and 4-D people would get 1/r^3, and neither one would have
>> stable orbits...
>
>But (science for engineers) how would you get the units to work out?
>> Dave "the amount of lolcats stays constant per unit Internet volume, however.
>> And of course Internet volume only gets larger with rage" DeLaney
>
>Well that's TOTALLY obvious.
Adam Funk
Jan 28, 2012, 9:32:15 AM1/28/12
to
On 2012-01-26, David DeLaney wrote:
> Adam Funk <a24...@ducksburg.com> wrote:
>>On 2012-01-24, David DeLaney wrote:
>>> other such things give the same sort of answer. And yes, 2-D people would
>>> get 1/r gravity, and 4-D people would get 1/r^3, and neither one would have
>>> stable orbits...
>>
>>But (science for engineers) how would you get the units to work out?
>
> Different units for G, obviously.
Ah, of course. And R in the gas law must have a m taken off in
> Adam Funk <a24...@ducksburg.com> wrote:
>>On 2012-01-24, David DeLaney wrote:
>>> other such things give the same sort of answer. And yes, 2-D people would
>>> get 1/r gravity, and 4-D people would get 1/r^3, and neither one would have
>>> stable orbits...
>>
>>But (science for engineers) how would you get the units to work out?
>
> Different units for G, obviously.
Flatland because "volume" is "area".
>>> Dave "the amount of lolcats stays constant per unit Internet volume, however.
>>> And of course Internet volume only gets larger with rage" DeLaney
>>
>>Well that's TOTALLY obvious.
>
> Dave "experimentation is still indicated" DeLaney
--
I used to be better at logic problems, before I just dumped
them all into TeX and let Knuth pick out the survivors.
-- plorkwort
Adam Funk
Jan 28, 2012, 9:49:05 AM1/28/12
to
--
...the reason why so many professional artists drink a lot is not
necessarily very much to do with the artistic temperament, etc. It is
simply that they can afford to, because they can normally take a large
part of a day off to deal with the ravages. [Amis _On Drink_]
Adam Funk
Jan 28, 2012, 9:50:43 AM1/28/12
to
On 2012-01-24, Adam Funk wrote:
> On 2012-01-24, Doctroid wrote:
>
>> In article <3nm2v8x...@news.ducksburg.com>,
>> Adam Funk <a24...@ducksburg.com> wrote:
>>
>>> ISTR reading somewhere a while back that the "inverse square law" ---
>>> blah blah is proportional to 1 / (r^2) --- in things like the
>>> universal gravitation formula is a side effect of the trilogy of
>>> spatial dimensions, so that the area subtended by a given solid angle
>>> at distance r is proportional to r^2. So supposedly if we lived in
>>> Flatland, these laws would have 1 / r instead of 1 / (r^2), because
>>> the equivalent of subtended area would be proportional to r.
>>>
>>> Comments?
>>
>> Yep.
>
> OK, I thought it seemed fairly obviously right for things like
> radiation --- there's a certain amount of light or heat power coming
> out of the source, so the amount hitting a given surface should vary
> with the subtended solid angle, which in turn varies with 1/r^2 ---
> but I wasn't sure if extending the analogy to gravity was a bit flakey
> or not.
Well, duh: I just remembered that gravity has the effect of dispersing
> On 2012-01-24, Doctroid wrote:
>
>> In article <3nm2v8x...@news.ducksburg.com>,
>> Adam Funk <a24...@ducksburg.com> wrote:
>>
>>> ISTR reading somewhere a while back that the "inverse square law" ---
>>> blah blah is proportional to 1 / (r^2) --- in things like the
>>> universal gravitation formula is a side effect of the trilogy of
>>> spatial dimensions, so that the area subtended by a given solid angle
>>> at distance r is proportional to r^2. So supposedly if we lived in
>>> Flatland, these laws would have 1 / r instead of 1 / (r^2), because
>>> the equivalent of subtended area would be proportional to r.
>>>
>>> Comments?
>>
>> Yep.
>
> OK, I thought it seemed fairly obviously right for things like
> radiation --- there's a certain amount of light or heat power coming
> out of the source, so the amount hitting a given surface should vary
> with the subtended solid angle, which in turn varies with 1/r^2 ---
> but I wasn't sure if extending the analogy to gravity was a bit flakey
> or not.
*potential* energy over the subtended area, so the analogy with
radiated energy does work.
--
XML is like violence: if it doesn't solve the problem,
use more.
Adam Funk
Feb 1, 2012, 3:49:22 PM2/1/12
to
On 2012-01-26, David DeLaney wrote:
> Adam Funk <a24...@ducksburg.com> wrote:
>>On 2012-01-24, David DeLaney wrote:
>>> Dave "the amount of lolcats stays constant per unit Internet volume, however.
>>> And of course Internet volume only gets larger with rage" DeLaney
>>
>>Well that's TOTALLY obvious.
>
> Dave "experimentation is still indicated" DeLaney
To track down the elusive source of the bozons?
>>On 2012-01-24, David DeLaney wrote:
>>> Dave "the amount of lolcats stays constant per unit Internet volume, however.
>>> And of course Internet volume only gets larger with rage" DeLaney
>>
>>Well that's TOTALLY obvious.
>
> Dave "experimentation is still indicated" DeLaney
--
Physics is like sex. Sure, it may give some practical results,
but that's not why we do it. [Richard Feynman]
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