Riemann's interest in physics [Archive]

John Baez

Aug13-04, 07:36 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nIn article <mathman.18u4z8@physicsforums.com>,\nmathman <mathnucl@optonline.net> wrote:\n\n>Riemann\'s work was mathematics, not physics.\n\nRiemann was definitely interested in physics. As a student\nat Goettingen, he worked with Weber on electromagnetism\nstarting around 1849. Like Riemann, Weber was a student of\nGauss, but at this time Weber then had a chair in physics,\nand had proposed a theory of electromagnetism which was\neventually superseded by Maxwell\'s. Gauss is also famous\nfor his work on electromagnetism.\n\n>Where did you get the idea he was trying to unify gravity and\n>electricity? In Riemann\'s day electricity was barely understood.\n>Einstein was trying to unify, not Riemann.\n\nNot clear. In November 1850, Riemann came out with an essay in\nwhich he demanded:\n\na completely self-contained mathematical theory [...], which\nleads from the elementary laws up to the actions in an\nactually given filled space, without making a difference between\ngravity, electricity, magnetism or the equilibrium of temperature.\n\nIt might be fun to read this for more information:\n\nM. Monastyrsky, Riemann, Topology, and Physics, 2nd ed.\nNew York: Springer-Verlag, 1999.\n\nor even this:\n\nH. Weber and B. Riemann, Die partiellen Differential-Gleichungen\nder mathematischen Physik nach Riemanns Vorlesungen, 6. unveranderte\nAufl., 2 vols. Braunschweig, Germany: Vieweg, 1919.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>In article <mathman.18u4z8@physicsforums.com>,
mathman <mathnucl@optonline.net> wrote:

>Riemann's work was mathematics, not physics.

Riemann was definitely interested in physics. As a student
at Goettingen, he worked with Weber on electromagnetism
starting around 1849. Like Riemann, Weber was a student of
Gauss, but at this time Weber then had a chair in physics,
and had proposed a theory of electromagnetism which was
eventually superseded by Maxwell's. Gauss is also famous
for his work on electromagnetism.

>Where did you get the idea he was trying to unify gravity and
>electricity? In Riemann's day electricity was barely understood.
>Einstein was trying to unify, not Riemann.

Not clear. In November 1850, Riemann came out with an essay in
which he demanded:

a completely self-contained mathematical theory [...], which
leads from the elementary laws up to the actions in an
actually given filled space, without making a difference between
gravity, electricity, magnetism or the equilibrium of temperature.

It might be fun to read this for more information:

M. Monastyrsky, Riemann, Topology, and Physics, 2nd ed.
New York: Springer-Verlag, 1999.

or even this:

H. Weber and B. Riemann, Die partiellen Differential-Gleichungen
der mathematischen Physik nach Riemanns Vorlesungen, 6. unveranderte
Aufl., 2 vols. Braunschweig, Germany: Vieweg, 1919.

Brian J Flanagan

Aug16-04, 12:56 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n\n> mathman wrote:\n>\n> >Riemann\'s work was mathematics, not physics.\n\n"The starting point is Hilbert\'s claim that the invariance of the\naction integral allows one to interpret the electromagnetic field\nequations as implicit in the gravitational field equations. Hilbert\nhere reiterates the claim of his first note that this fact would\nprovide the solution to a problem that he traces back to Riemann,\nnamely the problem of the connection between gravitation and light. He\ngoes on to observe that since then many investigators had tried to\narrive at a deeper understanding of this connection by merging the\ngravitational and electromagnetic potentials into a unity. The one\nexample Hilbert mentions explicitly is Weyl\'s unification of the two\nfields in a "unified world metric," as he calls it, by means of Weyl\'s\nnotion of gauge invariance."\n\nhttp://arxiv.org/PS_cache/physics/pdf/0405/0405110.pdf\n\n(For a very nice bit of summer reading, see Reid\'s masterful biography\nof \'Hilbert.\')\n\n\n"One reason why the discovery of noneuclidean geometry took so long\nmight have been the fact that there was universal belief that\neuclidean geometry was special because it described the space we live\nin. Stemming from this uncritical acceptance of the view that the\ngeometry of space is euclidean was the conviction that there was no\nother geometry. Philosophers like Kant argued that the euclidean\nnature of space was a fact of nature and the weight of their authority\nwas very powerful. From our perspective we know of course that the\nquestion of the geometry of space is of course entirely different from\nthe question of the existence of geometries which are not euclidean.\nGauss was the first person who clearly understood the difference\nbetween these two questions. In Gauss\'s Nachlass one can find his\ncomputations of the sums of angles of each of the triangles that\noccured in his triangulation of the Hanover region; and his conclusion\nwas that the sum was always two right angles within the limits of\nobservational errors. Nevertheless, quite early in his scientific\ncareer Gauss became convinced of the possibility of constructing\nnoneuclidean geometries, and in fact constructed the theory of\nparallels, but because of the fact that the general belief in\neuclidean geometry was deeply ingrained, Gauss decided not to publish\nhis researches in the theory of parallels and the construction of\nnoneuclidean geometries for fear that there would be criticisms of\nsuch investigations by people who did not understand these things\n(\'the outcry of the Boeotians\').\n\nRiemann took this entire circle of ideas to a completely different\nlevel. In his famous inaugural lecture of 1854 he touched on all of\nthe aspects we have mentioned above. He pointed out to start with that\na space does not have any structure except that it is a continuum in\nwhich points are specified by the values of n coordinates, n being the\ndimension of the space; on such a space one can then impose many\ngeometrical structures. His great insight was that a geometry should\nbe built from the infinitesimal parts. He treated in depth geometries\nwhere the distance between pairs of infinitely near points is\npythagorean, formulated the central questions about such geometries,\nand discovered the set of functions, the sectional curvatures, whose\nvanishing characterized the geometries which are euclidean, namely\nthose whose distance function is pythagorean not only for infinitely\nnear points but even for points which are a finite but small distance\napart. If the space is the one we live in, he stated the principle\nthat its geometrical structure could only be determined empirically.\nIn fact he stated explicitly that the question of the geometry of\nphysical space does not make sense independently of physical\nphenomena, i.e., that space has no geometrical structure until we take\ninto account the physical properties of matter in it, and that this\nstructure can be determined only by measurement. Indeed, he went so\nfar as to say that the physical matter determined the geometrical\nstructure of space.\n\nRiemann\'s ideas constituted a profound departure from the perceptions\nthat had prevailed until that time. In fact no less an authority than\nNewton had asserted that space by itself is an absolute entity endowed\nwith euclidean geometric structure, and built his entire theory of\nmotion and celestial gravitation on that premise. Riemann went\ncompletely away from this point of view. Thus, for Riemann, space\nderived its properties from the matter that occupied it, and that the\nonly question that can be studied is whether the physics of the world\nmade its geometry euclidean. It followed from this that only a mixture\nof geometry and physics could be tested against experience. For\ninstance measurements of the distance between remote points clearly\ndepend on the assumption that a light ray would travel along shortest\npaths. This merging of geometry and physics, which is a central and\ndominating theme of modern physics, may be thus traced back to\nRiemann\'s inaugural lecture."\n\nhttp://www.math.ucla.edu/~vsv/papers/ch2.pdf\n\nhttp://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/WKCGeom.html\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>mathman wrote:
>
> >Riemann's work was mathematics, not physics.

"The starting point is Hilbert's claim that the invariance of the
action integral allows one to interpret the electromagnetic field
equations as implicit in the gravitational field equations. Hilbert
here reiterates the claim of his first note that this fact would
provide the solution to a problem that he traces back to Riemann,
namely the problem of the connection between gravitation and light. He
goes on to observe that since then many investigators had tried to
arrive at a deeper understanding of this connection by merging the
gravitational and electromagnetic potentials into a unity. The one
example Hilbert mentions explicitly is Weyl's unification of the two
fields in a "unified world metric," as he calls it, by means of Weyl's
notion of gauge invariance."

http://arxiv.org/PS_cache/physics/pdf/0405/0405110.pdf

(For a very nice bit of summer reading, see Reid's masterful biography
of 'Hilbert.')

"One reason why the discovery of noneuclidean geometry took so long
might have been the fact that there was universal belief that
euclidean geometry was special because it described the space we live
in. Stemming from this uncritical acceptance of the view that the
geometry of space is euclidean was the conviction that there was no
other geometry. Philosophers like Kant argued that the euclidean
nature of space was a fact of nature and the weight of their authority
was very powerful. From our perspective we know of course that the
question of the geometry of space is of course entirely different from
the question of the existence of geometries which are not euclidean.
Gauss was the first person who clearly understood the difference
between these two questions. In Gauss's Nachlass one can find his
computations of the sums of angles of each of the triangles that
occured in his triangulation of the Hanover region; and his conclusion
was that the sum was always two right angles within the limits of
observational errors. Nevertheless, quite early in his scientific
career Gauss became convinced of the possibility of constructing
noneuclidean geometries, and in fact constructed the theory of
parallels, but because of the fact that the general belief in
euclidean geometry was deeply ingrained, Gauss decided not to publish
his researches in the theory of parallels and the construction of
noneuclidean geometries for fear that there would be criticisms of
such investigations by people who did not understand these things
('the outcry of the Boeotians').

Riemann took this entire circle of ideas to a completely different
level. In his famous inaugural lecture of 1854 he touched on all of
the aspects we have mentioned above. He pointed out to start with that
a space does not have any structure except that it is a continuum in
which points are specified by the values of n coordinates, n being the
dimension of the space; on such a space one can then impose many
geometrical structures. His great insight was that a geometry should
be built from the infinitesimal parts. He treated in depth geometries
where the distance between pairs of infinitely near points is
pythagorean, formulated the central questions about such geometries,
and discovered the set of functions, the sectional curvatures, whose
vanishing characterized the geometries which are euclidean, namely
those whose distance function is pythagorean not only for infinitely
near points but even for points which are a finite but small distance
apart. If the space is the one we live in, he stated the principle
that its geometrical structure could only be determined empirically.
In fact he stated explicitly that the question of the geometry of
physical space does not make sense independently of physical
phenomena, i.e., that space has no geometrical structure until we take
into account the physical properties of matter in it, and that this
structure can be determined only by measurement. Indeed, he went so
far as to say that the physical matter determined the geometrical
structure of space.

Riemann's ideas constituted a profound departure from the perceptions
that had prevailed until that time. In fact no less an authority than
Newton had asserted that space by itself is an absolute entity endowed
with euclidean geometric structure, and built his entire theory of
motion and celestial gravitation on that premise. Riemann went
completely away from this point of view. Thus, for Riemann, space
derived its properties from the matter that occupied it, and that the
only question that can be studied is whether the physics of the world
made its geometry euclidean. It followed from this that only a mixture
of geometry and physics could be tested against experience. For
instance measurements of the distance between remote points clearly
depend on the assumption that a light ray would travel along shortest
paths. This merging of geometry and physics, which is a central and
dominating theme of modern physics, may be thus traced back to
Riemann's inaugural lecture."

http://www.math.ucla.edu/~vsv/papers/ch2.pdf

http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/WKCGeom.html

greywolf42

Aug17-04, 11:26 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n"Brian J Flanagan" <worda1@wordassociation1.net> wrote in message\nnews:7260698f.0408141006.58a38e33@posting .google.com...\n>\n> > mathman wrote:\n> >\n> > >Riemann\'s work was mathematics, not physics.\n>\n> "The starting point is Hilbert\'s claim that the invariance of the\n> action integral allows one to interpret the electromagnetic field\n> equations as implicit in the gravitational field equations. Hilbert\n> here reiterates the claim of his first note that this fact would\n> provide the solution to a problem that he traces back to Riemann,\n> namely the problem of the connection between gravitation and light. He\n> goes on to observe that since then many investigators had tried to\n> arrive at a deeper understanding of this connection by merging the\n> gravitational and electromagnetic potentials into a unity.\n\nMaxwell beat Riemann to the effort. But Reimann did a more complete job on\ngravity. Neither was satisifed with their results.\n\n{snip}\n--\ngreywolf42\nubi dubium ibi libertas\n{remove planet for e-mail}\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Brian J Flanagan" <worda1@wordassociation1.net> wrote in message
news:7260698f.0408141006.58a38e33@posting.google.c om...
>
> > mathman wrote:
> >
> > >Riemann's work was mathematics, not physics.
>
> "The starting point is Hilbert's claim that the invariance of the
> action integral allows one to interpret the electromagnetic field
> equations as implicit in the gravitational field equations. Hilbert
> here reiterates the claim of his first note that this fact would
> provide the solution to a problem that he traces back to Riemann,
> namely the problem of the connection between gravitation and light. He
> goes on to observe that since then many investigators had tried to
> arrive at a deeper understanding of this connection by merging the
> gravitational and electromagnetic potentials into a unity.

Maxwell beat Riemann to the effort. But Reimann did a more complete job on
gravity. Neither was satisifed with their results.

{snip}
--
greywolf42
ubi dubium ibi libertas
{remove planet for e-mail}