dimensions [Archive] - Physics Forums

Thomas Cuny

Nov2-04, 12:38 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\nAre dimensions fundamental?\nDimensions don\'t seem to exist when the universe is in the big bang\nstate,the big crunch state, or in black holes.\nPerhaps dimensions don\'t really exist.\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>Are dimensions fundamental?
Dimensions don't seem to exist when the universe is in the big bang
state,the big crunch state, or in black holes.
Perhaps dimensions don't really exist.

Uncle Al

Nov5-04, 08:20 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\n\n\nThomas Cuny wrote:\n>\n> Are dimensions fundamental?\n> Dimensions don\'t seem to exist when the universe is in the big bang\n> state,the big crunch state, or in black holes.\n> Perhaps dimensions don\'t really exist.\n\nGiven: Dimensions do not exit.\n\nProblem 1: Assemble four rods so that each is perpendicular to the\nother three.\n\nProblem 2: Explain the success of physical theory assuming dimensions\ndo exist,\n\n<http://relativity.livingreviews.org/Articles/lrr-2003-1/>\nhttp://arXiv.org/abs/gr-qc/0311039\n<http://www.weburbia.demon.co.uk/physics/experiments.html>\nExperimental constraints on General Relativity\n\n<http://relativity.livingreviews.org/Articles/lrr-2003-1/>\nhttp://www.eftaylor.com/pub/projecta.pdf\n<http://www.public.asu.edu/~rjjacob/Lecture16.pdf>\nRelativity in the GPS system\n\nScience 303(5661) 1143;1153 (2004)\nhttp://arXiv.org/abs/astro-ph/0401086\nhttp://arxiv.org/abs/astro-ph/0312071\nDeeply relativistic neutron star binaries\n\n--\nUncle Al\nhttp://www.mazepath.com/uncleal/\n(Toxic URL! Unsafe for children and most mammals)\nhttp://www.mazepath.com/uncleal/qz.pdf\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>Thomas Cuny wrote:
>
> Are dimensions fundamental?
> Dimensions don't seem to exist when the universe is in the big bang
> state,the big crunch state, or in black holes.
> Perhaps dimensions don't really exist.

Given: Dimensions do not exit.

Problem 1: Assemble four rods so that each is perpendicular to the
other three.

Problem 2: Explain the success of physical theory assuming dimensions
do exist,

<http://relativity.livingreviews.org/Articles/lrr-2003-1/>
http://arXiv.org/abs/http://www.arxiv.org/abs/gr-qc/0311039
<http://www.weburbia.demon.co.uk/physics/experiments.html>
Experimental constraints on General Relativity

<http://relativity.livingreviews.org/Articles/lrr-2003-1/>
http://www.eftaylor.com/pub/projecta.pdf
<http://www.public.asu.edu/~rjjacob/Lecture16.pdf>
Relativity in the GPS system

Science 303(5661) 1143;1153 (2004)
http://arXiv.org/abs/http://www.arxiv.org/abs/astro-ph/0401086
http://arxiv.org/abs/http://www.arxiv.org/abs/astro-ph/0312071
Deeply relativistic neutron star binaries

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf

Dirk Van de moortel

Nov5-04, 08:20 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\n\n"Thomas Cuny" <tec@highstream.net> wrote in message news:10o7m48pnh03296@corp.supernews.com...\n>\n>\n >\n>\n>\n> Are dimensions fundamental?\n> Dimensions don\'t seem to exist when the universe is in the big bang\n> state,the big crunch state, or in black holes.\n> Perhaps dimensions don\'t really exist.\n\nI already posted this on sci.physics\nhttp://groups.google.com/groups?&threadm=IfIsc.2208\\$ea1.1678@news.cpqcorp.net\n\n Dimension is merely a handy mathematical concept.\nWe call a line "one dimensional" because you need\none number to unambiguously specify where a certain\npoint is with respect to an agreed upon starting point\nand unity marker.\nThe surface of the Earth is called "two dimensional"\nbecause we need two numbers to fix a place.\nOur \'ordinary space\' is called "three dimensional"\nbecause we need 3 numbers.\nIf we want a framework where we can unambiguously\nspecify where *and* when some event takes place, we\nwill need 4 numbers: 3 for the location, and one for\nthat number that we read on our clock. The latter we call\n"the time". Since we need 4 numbers to describe the\nevents, we say that this framework is "four dimensional"\n(and we call this framework "Spacetime").\n\nIf you scale sweetness, bitterness and acidity as numbers\nbetween (for instance) 0 and 100, then you can say that\n(the taste of) red wine is "three dimensional" and that (the\ntaste of) white wine is "two dimensional" because the\n"dimension of bitterness" is usually not present or at best\nto be neglected in the latter.\n\nWe can conceive "spaces" with as many dimensions as\nwe need to adequately describe what happens in them.\nFor instance, you can easily imagine an "infinite dimensional"\nspace: think of the set of all the polynomials in x, like for\ninstance -9x^3 -3x^2 + 6. Every such polynomial can be\nwritten as a combination of the following basis-polynomials:\n{ 1, x, x^2, x^3, x^4, x^5, ...}\nThe numbers we need for the example polynomial are\n{ 6, 0, -3, -9, 0, 0, .... }\nSince this is an "infinite set", we call our set of polynomials\n"infinite dimensional".\n\nNo mystery. Just names that we attach to concepts and\nactivities.\n\nhth\n\nDirk Vdm\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>"Thomas Cuny" <tec@highstream.net> wrote in message news:10o7m48pnh03296@corp.supernews.com...
>
>
>
>
>
> Are dimensions fundamental?
> Dimensions don't seem to exist when the universe is in the big bang
> state,the big crunch state, or in black holes.
> Perhaps dimensions don't really exist.

I already posted this on sci.physics
http://groups.google.com/groups?&threadm=IfIsc.2208$ea1.1678@news.cpqcorp.net

Dimension is merely a handy mathematical concept.
We call a line "one dimensional" because you need
one number to unambiguously specify where a certain
point is with respect to an agreed upon starting point
and unity marker.
The surface of the Earth is called "two dimensional"
because we need two numbers to fix a place.
Our 'ordinary space' is called "three dimensional"
because we need 3 numbers.
If we want a framework where we can unambiguously
specify where *and* when some event takes place, we
will need 4 numbers: 3 for the location, and one for
that number that we read on our clock. The latter we call
"the time". Since we need 4 numbers to describe the
events, we say that this framework is "four dimensional"
(and we call this framework "Spacetime").

If you scale sweetness, bitterness and acidity as numbers
between (for instance) and 100, then you can say that
(the taste of) red wine is "three dimensional" and that (the
taste of) white wine is "two dimensional" because the
"dimension of bitterness" is usually not present or at best
to be neglected in the latter.

We can conceive "spaces" with as many dimensions as
we need to adequately describe what happens in them.
For instance, you can easily imagine an "infinite dimensional"
space: think of the set of all the polynomials in x, like for
instance -9x^3 -3x^2 + 6. Every such polynomial can be
written as a combination of the following basis-polynomials:
{ 1, x, x^2, x^3, x^4, x^5, ...}
The numbers we need for the example polynomial are
{ 6, 0, -3, -9, 0, 0, .... }
Since this is an "infinite set", we call our set of polynomials
"infinite dimensional".

No mystery. Just names that we attach to concepts and
activities.

hth

Dirk Vdm