May I briefly tidy up just one misconception. To specify an EVENT (within a given frame of reference) you need three spatial measurements (e.g., metric coordinates x, y, z) and one temporal measurement (time t). So, EVENT = Where and When. Whence the whole set of events forms a (3+1)-dimensional entity: (x, y, z, t). When mathematicians talk about dimension, we simply mean the number of 'parameters' needed to specify an object in a particular set. There's nothing 'spooky' about multi-dimensional (greater than our familiar 3 spatial dimensions) sets. If I'm inclined, I can define the set (or space) of all Nabokovians. This could have, say, six dimensions (a, h, g, hn, n, np), representing age, height, gender, hashed-name, nationality and number of publications. (Hilbert spaces can have an infinite number of dimensions, so there! Fractal spaces can have 2.5 or 10.654 or whatever dimensions.)
Treating an event as an object in a 4-dimensional space-time continuum does NOT imply that time is 'space-like' or that space is 'time-like.' SOME of the arithmetic manipulations are similar for all four elements (you can add the (x, y, z)s as lengths; you can add the ts to get durations) but spatial and temporal measurements remain distinct. In fact, one of Einstein's slick-tricks was to redefine the event as e = (x, y, z, it) where i is that strange (well, strange to non-mathematicians) square-root of minus 1. This neat trick serves to ISOLATE the spatial and temporal parts of an event when we evaluate complex expressions. (Here the term "complex" has an extra technical meaning -- mathematicians can enjoy private word-play as much as the novelists). So, ponder the irony: VN "accuses" Einstein of lumping space and time together, while, in fact, our Nutty Professor's slick equations keep them separate.
To supplement JR's (Jerry Friedman's) percipient response to JA (Joseph Aisenberg):
It's really an amazing achievement of HomSap to construct a theory with elegant formulae that PREDICTED (to 16 decimal places) actual physical events that seemed totally daft (impossible) under Newtonian mechanics. ECLIPSING the finest, wildest fictional works of Shakespeare and Nabokov. Forget all those pallid-fire fairy-tale flights-of-fancy, mad kings escaping chess-board traps ... Here we have the ultimate in flexing the muscles of the mind: imagining a new fabric of reality, with sums allowing predictive verification. ALSO, allowing possible falsification! This aspect of the (Popperian) Scientific Method seems to elude VN, at least in those passages where he mocks the notion of "theories turning out to be false."
The relativistic formulae for changes in mass, length and time (relative to frames moving with velocity v) all involve the fraction F = (v-squared) divided by (c-squared) where c is the velocity of light. c, you'll know is 300,000 km/sec (beyond which only tachyons travel -- another scientist's joke). F is therefore incredibly small for everyday velocities. Back in the 1920s it was thought that these tiny changes predicted by SR and GR (Special and General Relativity) would NEVER EVER be verifiable by human instruments. (Luckily, there were other measurable relativistic effects available, such as the gravitational bending of light.) As JR points out, precise verification of the "v-squared/c-squared" equations had to wait until we had particle-accelerators (boosting v to 0.99 c!) and accurate atomic clocks.
You can certainly argue that a few nano-seconds have no everyday, commonsense meaning in relation to human "rejuvenation." BUT BUT, in particle physics, a nano-second (1/1, 000, 000, 000th sec) is a bleeding ETERNITY! Mesons with a life-span of a pico-second (1/1,000, 000, 000, 000th sec) are considered eminently STABLE! We can now measure in atto-seconds (1/1, 000, 000, 000, 000, 000, 000th sec) yet this itself is unbelievably HUGE in terms of what is considered the "smallest meaningful" unit of time, viz., the PLANCK TIME. I won't waste space: it has 1/1, 000 ... with 44 zeroes. (There are corresponding Planck units of mass and length, below which meaurement is in theory impossible). How many Planck-times in an atto-second?: 1, 000 ... with 26 zeroes. So we are incredibly far away from what you might call ultimately accurate clocks.
Before outstaying my welcome, this Planck Time, being the theoretically smallest measurable interval, presents us with the QUANTUM view of time as DISCONTINUOUS. A much bigger strain on commonsense than SR or GR. Just as energy comes in little lumps, time goes by in little jumps. Quite a jolt if you enjoy singing the Hymn: TIME LIKE AN EVER-ROLLING STREAM, BEARS ALL ITS SONS AWAY!
Stan Kelly-Bootle
On 29/07/2008 19:38, "Nabokv-L" <nabokv-l@UTK.EDU> wrote:
-------- Original Message --------
Subject: Re: [NABOKV-L] Einstein and Langevin
Date: Tue, 29 Jul 2008 08:16:31 -0700 (PDT)
From: Jerry Friedman <jerry_friedman@yahoo.com> <mailto:jerry_friedman@yahoo.com>
Reply-To: jerry_friedman@yahoo.com
To: Vladimir Nabokov Forum <NABOKV-L@LISTSERV.UCSB.EDU> <mailto:NABOKV-L@LISTSERV.UCSB.EDU>
--- On Mon, 7/28/08, joseph Aisenberg <vanveen13@SBCGLOBAL.NET> <mailto:vanveen13@SBCGLOBAL.NET> wrote:
> S. K.-B.: It's a real challenge to separate the popular
> expositions of Relativity (and their impact on what you
> might call "lay [laid-back?] culture") from the
> hard (truly hard) applied mathematics involved in
> Einstein's "slick" formulae.
...
> Jansy mentioned in a recent post that she ponders setting
> off in an "imaginary" space-ship in order to test
> the Einstein "rejuvenation" formula. In fact,
> Jansy, it definitely works for REAL space-ships. REAL
> astronauts and atomic-clocks have made the journey and they
> do return YOUNGER.
>
> J.A.: This is quite fascinating! How did they know the
> astraunauts were younger? Since they would have been going
> at far far less than the speed of light it doesn't seem
> exactly measurable, unlike say, the loss of bone mass that
> occurs in zero gravity existence. I suppose their clocks
> were a little behind those they had originally been synced
> with? Couldn't have been by much I suspect.
Jerry Friedman: You've got the idea. According to
<http://en.wikipedia.org/wiki/Hafele-Keating_experiment>,
the time differences are in the hundreds of nanoseconds
(billionths of a second). Obviously this had no
measurable effect on the astronauts; it was measured only
by the cesium clocks. Also, the clocks run /faster/ in
lower gravity, and this effect is stronger than the slowing
due to their speed, so the net result was that the
astronauts were a tiny fraction of a second /older/ when
they returned than they would have been if they'd stayed
on Terra firma.
GPS satellites have to adjust their clocks for these
effects. However, as Stan pointed out, relativity is
far easier to measure at particle accelerators. Certain
of Einstein's "slick formulae"--not only time dilation
and E = mc^2, but also the latter's generalization for
energy as a function of momentum, and the relationship
of momentum to speed--simply can't be rejected, and I
don't think they could have been even in 1968 by anyone
who looked at what was going on at accelerators.
> J. A. I must admit as every inch a non physicist
> I've never understood notions of space-time continuums
J.F.: I'd say "space-time continuum" is a way of
understanding certain mathematical facts about the positions
and times of events as measured by observers moving at high
speeds. It's not a way of talking aobut how we perceive
space and time. If you're interested in some simple math,
feel free to e-mail me, or look around on the Web.
> or that time travel could exist in any real or perceivable
> way, since it doesn't seem like time exists. It is
> merely a reification of the clock device
> which we culturally use to measure changes in space: in
> other words the time is always now, with rearrangements of
> matter. How could one move around in "time" since
> this "stuff" isn't really anything at all?
J.F. In principle, we can alter the speed at which we go
toward the future. So if we knew a way to make
spaceships go at almost the speed of light (or to
suspend our lives and then revive ourselves), we could
see the Earth 1000 years from now after experiencing
a much shorter time ourselves. You may or may not
want to call that time travel. Most physicists would
say we can't revisit our pasts.
Jerry Friedman