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The Fourth Dimension

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  The Fourth Dimension The Starmaker <starmaker@ix.netcom.com> - 2015-09-17 12:04 -0700
    Re: The Fourth Dimension gilber34 <invalid@invalid.com> - 2015-09-17 14:07 -0500
    Re: The Fourth Dimension The Starmaker <starmaker@ix.netcom.com> - 2015-09-17 13:31 -0700
      Re: The Fourth Dimension Rock Brentwood <federation2005@netzero.com> - 2015-09-18 13:07 -0700
        Re: The Fourth Dimension Rock Brentwood <federation2005@netzero.com> - 2015-09-18 13:13 -0700
    Re: The Fourth Dimension Sam Wormley <swormley1@gmail.com> - 2015-09-17 15:58 -0500
      Re: The Fourth Dimension The Starmaker <starmaker@ix.netcom.com> - 2015-09-17 14:40 -0700
        dimension sAm noTthaTguY <abu.kuanysh05@gmail.com> - 2015-09-17 16:30 -0700
        Re: The Fourth Dimension benj <nobody@gmail.com> - 2015-09-18 01:05 -0400
          Re: The Fourth Dimension The Starmaker <starmaker@ix.netcom.com> - 2015-09-17 22:42 -0700
          Re: The Fourth Dimension The Starmaker <starmaker@ix.netcom.com> - 2015-09-17 23:01 -0700
            Re: The Fourth Dimension Poutnik <poutnik4nntp@gmail.com> - 2015-09-18 08:40 +0200
              Re: The Fourth Dimension The Starmaker <starmaker@ix.netcom.com> - 2015-09-17 23:59 -0700
                Re: The Fourth Dimension Poutnik <Poutnik4NNTP@gmail.com> - 2015-09-18 10:28 +0200
                  free, but not neccesarily cheap noTthaTguY <abu.kuanysh05@gmail.com> - 2015-09-18 11:15 -0700
                Re: The Fourth Dimension Sam Wormley <swormley1@gmail.com> - 2015-09-18 08:23 -0500
                  Re: The Fourth Dimension Poutnik <Poutnik4NNTP@gmail.com> - 2015-09-18 15:41 +0200
                  Re: The Fourth Dimension The Starmaker <starmaker@ix.netcom.com> - 2015-09-18 10:56 -0700
        Re: The Fourth Dimension Sam Wormley <swormley1@gmail.com> - 2015-09-18 08:20 -0500
    Re: The Fourth Dimension Poutnik <poutnik4nntp@gmail.com> - 2015-09-18 08:20 +0200
      Re: The Fourth Dimension Poutnik <Poutnik4NNTP@gmail.com> - 2015-09-18 11:19 +0200

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#521791

On 09/18/2015 08:20 AM, Poutnik wrote:

P.S.:
Citizens in that weird city could not calculate general distances
as invariant wrt used surveyor system
as we can do

D = sqrt( (delta_x)2 + (delta_y)2 ) .

They could just calculate differences in N-S and E-W coordinates
that differ for different surveyor systems.

But with smart guy invention,
they could do it after using
D = sqrt((E-W-metres)2 + (N-S-sacred-units . meters_per_sacred_unit)2 )

---
Similarly, our space-intervals and time-intervals differs
in different surveyor systems of different inertial frames.

We are with our different inertial frames in the similar position
as the weird city with their metering and surveying systems.
the values do not match each other.

But if we recalculate sacred unit 1s to equivalent length 299 792 458 m
and if we define this length as the 4th dimension of now called
space-time, we can define space-time interval
sqrt ( delta_x^2 + delta_y^2 + delta_z^2 - c^2. delta_t^2 ).

This distance is invariant wrt Lorentz transformation,
and not depend on used inertial system.

Similarly as distance D is invariant
wrt to translation and rotation of used cartesian coordinates.



-- 
Poutnik ( the Czech word for a wanderer )

Knowledge makes a great man humble, but a small man arrogant.

Eventual Wikipedia articles are provided with intention
of a convenient reference, not as an evidence, argument,
and usually not as a primary source of my knowledge.

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