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Re: GPS Off Course

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Followups directed to: sci.physics.relativity

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hanson wrote:

> […] Thomas 'PointedEars' Lahn" [insult] wrote:
>> hanson wrote:
>>> ds^2 = dx^2 + dy^2 + dz^2 - c^2dt^2    ..... [1].
>>>
>>> Some say ds^2 is "space-time", others say that
>>> ds is "space-time", other still insist that ds^2 or
>>> ds are "space-time intervals", while others are
>>> adamant that "s" happens to be "space-time"
>> Who, according to your research, says either one, and where?
>
> The 1-liner of yours above does show, off the bat,
> that you don't know what you are talking about […]

No, it shows instead that you make unsubstantiated claims.

>>> Just tell me the MLT dimensions of "space-time"
>>> as shown in [1]
>>
>> There are no “MLT dimensions of space-time”.
> 
> So Space-time has no mass, no lenght, no area,
> no space and no time.

No, AISB it has three spatial dimensions (that can be compacted into one 
dimension, space) and one temporal dimension (time).  But those are 
*mathematical* dimensions, ways of how the *coordinates* of an object can 
change.

By contrast, mass and length, and by extension of length, area ([area] = 
[length]²), are *physical* dimensions of *quantities*.

> but you say it exists.

It exists insofar as that we can indeed observe the effects that would 
follow if the theories using it would be correct.  IOW, the predictions of 
the theories have been confirmed by observation again and again.

As you are probably aware, recently predictions that followed from assuming 
the correctness of the general theory of relativity, in particular a curved 
spacetime, curved according to the energy–momentum in a location, had been 
confirmed once again by the experimental observation of gravitational waves.

> ROTFMAO!

Simple minds are easily amused.

> In  [1] there is dx^2 + dy^2 + dz^2  which are ranges
> of x,y,z

No, they are not.

> that are ORDINARY **Length** items

Not really.  “x”, “y”, and “z” in the referred equation are appropriately 
chosen labels for the spatial *coordinates* of an event, a position, in 
spacetime.  “t” then is its one temporal coordinate, time.

The referred equation means that if you make the differences between 
corresponding coordinates of two points infinitely small, you can arrive at 
a way to measure distances between all possible two points in that flat 
manifold.

> and x^2,y^2,z^2 are their respective AREAS;

Only in an overly simplified sense.  “dx²” must be read “(dx)²”; _not_ 
“d(x²)”.

>> <snip> You must realize that there are
>> different definitions for the term “dimension”
>
> hansoon wrote

If you start quoting properly, as suggested by a proper newsreader, you will 
probably not embarrass yourself again by failing to spell your own (nick) 
name properly.

> So name some different definitions for length
> & name some different definitions for an area.

You misunderstand.  I said that there are different definitions of the term 
“dimension” in physics.  One of them is borrowed from mathematics, from 
geometry.  The one you are referring to is not borrowed from mathematics, 
and you are confusing it with the former.
 
>> there are different contexts in which it is used, if
>> you are going to understand “space-time” in physics.
>
> So, Lahn, show what those different contexts are
> and why they do need to be different for the one
> and same theory.

Because one (the mathematical one) concerns position only, and the other one 
concerns all physical quantities.  There are, of course, physical quantities 
in the theories of relativity as well (they are physical theories after 
all), and they do have dimensions there in the quantitative sense.

But spacetime *itself* does not have *that* kind of dimensions; it has the 
mathematical kind instead.  So your question regarding “the MLT dimensions” 
of spacetime does not make sense; it betrays a fundamental lack of 
understanding what spacetime is.

> Show what YOUR understanding of Space-time is,

My understanding, which is equal to what is being taught in mathematics and 
physics classes since more than a century, is that spacetime is a 3+1-
dimensional manifold.

>> On the other hand there are dimensions in physics, of physical quantities
>> which can be described in terms of combinations of the quantities mass
>> (M),
>> length (L), and time (T).
>>
> hanson wrote:
> On the other hand you just said again that Space-time does
> NOT exist in the real world

No, I did not say that.  I said that there are the dimensions with which 
you determine position and distance, and there are dimensions which which 
you *can* define the form of physical quantities.  Those are *separate* 
concepts.  You are committing the fallacy of equivocation here.

> which makes it as USELESS to real physics

On the contrary.  The mathematical dimensions of spacetime are fundamental 
to describing how physical quantities change when objects are in motion 
relative to one another.

Why?  Well, one quantity important in motion is speed.  Speed is 
the magnitude of velocity, and velocity is the change of *position* per 
unit time.  A position has *coordinates*.  Which coordinates determine 
position is the subject of geometry, of mathematics.  

If speed is measured relative to another object, it is important how 
distances to that object and times on that object are measured.  So
you see that there really is no contradiction in applying in physics 
*both* definitions of “dimension”, but in different contexts.

<https://en.wikipedia.org/wiki/Special_relativity#Physics_in_spacetime>

> So, tell why the motion of bodies _in_ space & -in_ time is
> not sufficient but needs […] space-time […]?

There are several ways to explain it.  I prefer to start with the fact that 
all experiments have shown that the speed of light is constant in all frames 
of reference.  Spacetime then provides a convenient mathematical framework 
to describe the observed effects that follow from that.

> None of the agencies of the world's space faring nations
> do use SR or GR for determining the trajectories of their SVs

Because the speeds of those space vehicles (SV) are so low compared to the 
mindbogglingly huge speed of light that (what we know since more than a 
century) the *approximations* of classical mechanics suffice there:

  lim  γ(v) = lim 1∕√(1 − (v∕c)²) = 1
  v→0         v→0

    [γ(v) is the Lorentz factor for speed v which determines the degree of
     length contraction and time dilation.  As γ(v) approaches 1, it
     becomes increasingly harder to observable any length contraction and 
     time dilation.  If necessary, equations for both can be provided here
     *again* to demonstrate this.]

However, SR and GR become important where electromagnetic signals are 
involved, as those travel at the speed of light.  One such kind of signals 
are those of global navigation satellite systems (GNSSs).  The trilaterated 
position of the observer on the surface of this planet would be off if both 
SR and GR would not have been considered in the design of the hardware and 
the software of the satellites of those systems and the receivers on the 
ground:

<http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html>


BTW, when do you think will you have learned to post in a civilized manner, 
including *proper* quotation?

F'up2 sci.physics.relativity

-- 
PointedEars

Twitter: @PointedEars2
Please do not cc me. / Bitte keine Kopien per E-Mail.

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GPS Off Course The Starmaker <starmaker@ix.netcom.com> - 2016-04-01 12:21 -0800
  Re: GPS Off Course Sam Wormley <swormley1@gmail.com> - 2016-04-01 14:30 -0500
  Re: GPS Off Course jimp@specsol.spam.sux.com - 2016-04-01 22:15 +0000
  Re: GPS Off Course Sergio <invalid@invalid.com> - 2016-04-01 20:37 -0500
    Re: GPS Off Course The Starmaker <starmaker@ix.netcom.com> - 2016-04-01 19:26 -0800
      Re: GPS Off Course Sergio <invalid@invalid.com> - 2016-04-01 21:33 -0500
        Re: GPS Off Course Bimpy <pimp@pimp.com> - 2016-04-02 13:38 +0000
          Re: GPS Off Course Bimpy <pimp@pimp.com> - 2016-04-02 13:45 +0000
  Re: GPS Off Course Bimpy <pimp@pimp.com> - 2016-04-02 12:07 +0000
  Re: GPS Off Course Sam Wormley <swormley1@gmail.com> - 2016-04-02 08:49 -0500
    Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-02 08:10 -0700
      Re: GPS Off Course "Paul B. Andersen" <relativity@paulba.no> - 2016-04-02 23:22 +0200
        Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-02 16:20 -0700
          Re: GPS Off Course "Paul B. Andersen" <relativity@paulba.no> - 2016-04-03 13:37 +0200
            Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-03 10:25 -0700
              Re: GPS Off Course "Paul B. Andersen" <relativity@paulba.no> - 2016-04-04 19:39 +0200
                Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-04 13:34 -0700
                Re: GPS Off Course "Paul B. Andersen" <relativity@paulba.no> - 2016-04-05 09:41 +0200
                Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-05 01:17 -0700
                Re: GPS Off Course "Paul B. Andersen" <relativity@paulba.no> - 2016-04-05 20:00 +0200
                ORI Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-05 13:12 -0700
                Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-05 13:54 -0700
                Re: ORI Re: GPS Off Course The Starmaker <starmaker@ix.netcom.com> - 2016-04-05 17:07 -0700
                Re: ORI Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-05 17:26 -0700
                Re: GPS Off Course Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-04-07 04:40 +0200
                Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-06 22:56 -0700
                Re: GPS Off Course Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-04-07 22:54 +0200
                Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-07 17:02 -0700
                Re: GPS Off Course Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2016-04-08 05:36 +0200
                Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-08 01:26 -0700
                Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-08 22:16 -0700
                Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-08 22:18 -0700
                Re: GPS Off Course Helmut Wabnig <hwabnig@.- --- -.dotat> - 2016-04-09 08:17 +0200
                Re: GPS Off Course "hanson" <hanson@quick.net> - 2016-04-09 00:24 -0700
  Re: GPS Off Course The Starmaker <starmaker@ix.netcom.com> - 2016-04-02 13:36 -0800
    Re: GPS Off Course The Starmaker <starmaker@ix.netcom.com> - 2016-04-02 13:38 -0800
      Re: GPS Off Course The Starmaker <starmaker@ix.netcom.com> - 2016-04-02 21:46 -0800

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