amra@ihlpa.UUCP (s. aldrich) (06/05/85)
{Your Traveling Through Another Dimension......}
Greetings,
With all the recent discussion on the "Center of the {Known} Universe,"
and/or 3D(+) Space-Time, I thought I'd pose a question of my own.
Namely WHAT, to the best of current knowledge, exactly is a dimension?
How are they defined, and what seperates them from the others? Is there
a "perceptable" border across dimensions, and if so what constitutes the
"barrier region" between them? Is it a "state of energy/matter" or am I
completely off base?
Please remember that I'M NOT an Expert in Astronomy and/or Cosmology.
If my questions are "meaningless" please excuse this lack of "expertise"
on my part.
Thanks in advance for any & all help!
From The Atoms Currently Associated As:
Steve Aldrich (ihnp4!ihlpa!amra)
.."My God, It's Full Of Stars!.."crm@duke.UUCP (Charlie Martin) (06/06/85)
In article <293@ihlpa.UUCP> amra@ihlpa.UUCP (s. aldrich) writes: >{Your Traveling Through Another Dimension......} > >With all the recent discussion on the "Center of the {Known} Universe," >and/or 3D(+) Space-Time, I thought I'd pose a question of my own. > > Namely WHAT, to the best of current knowledge, exactly is a dimension? Oh boy, another chance to play Isaac Asimov -- but take this with a grain of salt, as it is certainly possible that someone else understands this better than I. When we talk about the number of dimensions of space, those "dimensions" are things at all, in the sense that you can pick on up and hold it in your hand. They are instead a sort of conventional was of talking about the way we deal with a location mathematically. Essentially, when we talk about space having three dimensions, what we mean is that we cannot locate a point uniquely with fewer than three real numbers. This can also be thought of as the number of lines that can be put together so that each line is perpendicular to all the other lines. In the space that we talk about, this number is (usually) three. (If you've had linear algebra, this is the same as saying that a basis for our space must contain three vectors.) When we talk about four (or more) dimensions, we are really talking about making some kind of model that has these many dimensions, then using it to handle a problem. If we choose our model well, it may make it easier to handle some problem. When Einstein starting talking about time as the fourth dimension, he did so because that made the math work out better. Hope that helps. -- Charlie Martin (...mcnc!duke!crm)
ethan@utastro.UUCP (Ethan Vishniac) (06/07/85)
[] Steve Aldrich writes > With all the recent discussion on the "Center of the {Known} Universe," > and/or 3D(+) Space-Time, I thought I'd pose a question of my own. > > Namely WHAT, to the best of current knowledge, exactly is a dimension? > How are they defined, and what seperates them from the others? Is there > a "perceptable" border across dimensions, and if so what constitutes the > "barrier region" between them? Is it a "state of energy/matter" or am I > completely off base? A dimension is a continuous parameter necessary to uniquely define an event in space-time. "Space has three dimensions" means that on any spatial hypersurface three numbers are needed. A particular direction associated with a dimension is a matter of convention (in the above example). "Space-time has four dimensions" just means to add another number (the date). The direction of the time direction is not *completely* arbitrary, but is substantially so. Observers moving at different speeds will define different time "directions" in space-time. Science fiction writers have used the word in a slightly different sense. The idea is that space-time might have umpteen dimensions, only four of which are readily apparent. Then something that is near us *in an unusual direction* is referred to as another "dimension", (as in "The Giant Cockroach from the Twelfth Dimension that Ate Detroit"). -- "Don't argue with a fool. Ethan Vishniac Borrow his money." {charm,ut-sally,ut-ngp,noao}!utastro!ethan Department of Astronomy University of Texas
nather@utastro.UUCP (Ed Nather) (06/07/85)
> [] > Steve Aldrich writes > > > With all the recent discussion on the "Center of the {Known} Universe," > > and/or 3D(+) Space-Time, I thought I'd pose a question of my own. > > > > Namely WHAT, to the best of current knowledge, exactly is a dimension? > > How are they defined, and what seperates them from the others? Is there > > a "perceptable" border across dimensions, and if so what constitutes the > > "barrier region" between them? Is it a "state of energy/matter" or am I > > completely off base? > > A dimension is a continuous parameter necessary to uniquely define an > event in space-time. "Space has three dimensions" means that on > any spatial hypersurface three numbers are needed. A particular direction > associated with a dimension is a matter of convention (in the above example). > "Space-time has four dimensions" just means to add another number (the date). > The direction of the time direction is not *completely* arbitrary, but > is substantially so. Observers moving at different speeds will define > different time "directions" in space-time. > > Science fiction writers have used the word in a slightly different sense. > The idea is that space-time might have umpteen dimensions, only four of > which are readily apparent. Then something that is near us *in an > unusual direction* is referred to as another "dimension", (as in > "The Giant Cockroach from the Twelfth Dimension that Ate Detroit"). > > "Don't argue with a fool. Ethan Vishniac > Borrow his money." {charm,ut-sally,ut-ngp,noao}!utastro!ethan > Department of Astronomy > University of Texas > To put it in less abstract terms, to demonstrate we really *do* need four "dimensions" to specify things in our universe, suppose I say I'll meet you in the National Bank building, corner of 5th (1D) and main st (2D) on the 13th floor (3D). You might find it necessary to invoke the fourth dimension to be sure we'll meet: "When?" (4D). "It's a *beautiful* theory. I don't believe a word of it." -- Ed Nather Astronony Dept, U of Texas @ Austin {allegra,ihnp4}!{noao,ut-sally}!utastro!nather nather%utastro.UTEXAS@ut-sally.ARPA
mjs@eagle.UUCP (M.J.Shannon) (06/08/85)
Ethan Vishniac says: > Science fiction writers have used the word in a slightly different sense. > The idea is that space-time might have umpteen dimensions, only four of > which are readily apparent. Then something that is near us *in an > unusual direction* is referred to as another "dimension", (as in > "The Giant Cockroach from the Twelfth Dimension that Ate Detroit"). > An article in Scientific American (March, 1985) describes the universe as having at least 7 (I think; I don't have my copy handy) dimensions and at most 11 dimensions. Above 11 dimensions, a lot of math that physicists use to describe said universe breaks down. While I have no complaints on the article (or on Scientific American in general -- an excellent magazine!), due to the audience addressed, often some very interesting tidbits are lacking in articles like this one. Questions I have include: Are the N-4 dimensions named (and if so, what are their names)? Do the dimensions come in related groups (i.e., we perceive 3 dimensions of `space' and 1 of `time'; does time come in 3 directions maybe?)? Do we perceive the N-4 dimensions? If so, how? Why does `time' appear to be unidirectional? Are there dimensions other than `time' that appear to be unidirectional? I have often suspected (in my casually interested, but not highly educated in physics mind) that the number of dimensions must be prime, and am very gratified to hear that the likely number (11) is prime. Well, that's probably enough for now. Can any of you physicists shed any light on these questions to a mere dabbler in physics? -- Marty Shannon UUCP: ihnp4!eagle!mjs Phone: +1 201 522 6063
chrisa@azure.UUCP (Chris Andersen) (06/14/85)
> I have often suspected (in my casually interested, but not highly educated in > physics mind) that the number of dimensions must be prime, and am very > gratified to hear that the likely number (11) is prime. > Actually, I'm uncomfortable with the idea of a finite number of dimensions. If someone tells me that there are only eleven dimensions, I would turn to the Universe and ask it why *only* eleven? Why not 100? If there is some firm mathematical basis for only eleven, I'll have to look it up. Chris Andersen UUCP: tektronix!azure!chrisa
austin@nsc-pdc.UUCP (Austin Mack) (06/26/85)
> > Actually, I'm uncomfortable with the idea of a finite number of dimensions. > If someone tells me that there are only eleven dimensions, I would turn > to the Universe and ask it why *only* eleven? Why not 100? > > If there is some firm mathematical basis for only eleven, I'll have to look it > up. > I think it would have to be a physical basis since Hilbert has defined a very elegant mathematical space with infinitely many (aleph 0 level of infinity) dimensions. My question would be can Hilbert space be proven or disproven to exist in the *real* universe? Austin Mack