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Re: The Necessity Alternate Theories

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Natalina Nazvarova wrote:

> Thomas 'PointedEars' Lahn wrote:
>> Thomas 'PointedEars' Lahn wrote:
>>> Natalina Nazvarova wrote:
>>>> But does not imply that so many have to be zeroed.
>>> 
>>> But it does; that is how you write the metric tensor for Minkowski
>>> spacetime.  Otherwise the spacetime would not be a Minkowski one, it
>>> would not be flat (measuring distances would depend on the
>>> four-position).
>>> 
>>> And if you replace the components with their values in the expansion
>>> above, you can see that only the summands where µ = ν remain as the
>>> coefficients of those where µ ≠ ν are all 0.  (That is what multiplying
>>> with a diagonal matrix left-hand side does.)
>>> 
>>> Leaving only
>>> ds² = g_µν dx^µ dx^ν = g_00 dx^0 dx^0 + g_11 dx^1 dx^1
>>> + g_22 dx^2 dx^2 + g_33 dx^3 dx^3
> 
> What is this??

This is the metric partially expanded (on the g_µν where µ ≠ ν) by writing 
what Einstein summation notation (in which the general metric is expressed) 
actually means.

When you expand it completely, by replacing g_00, g_11, g_22 and g_33 (the 
g_µν where µ = ν) with the corresponding values of the components of the 
metric tensor, you will see that the result is precisely what I used as 
basis of deriving the equation for calculating the proper time interval in 
Minkowski spacetime.
 
>> Sorry for the confusion, of course it is
>> = g_00 dx^0 dx^0 − g_11 dx^1 dx^1 − g_22 dx^2 dx^2 − g_33 dx^3 dx^3.
>> instead.
> 
> Which is still incorrect of course.

It is _not_ “*still* incorrect”, but it *is* incorrect because the minus 
sign comes from the tensor’s components, in particular g_11, g_22, and g_33, 
instead.  Which is why I had canceled and deleted that posting 8 minutes 
before you replied to it.

> […] [as] you postulated already, as that being "a vector" (without having
> the demanded UNIT vectors attached at it).

So you have not done your homework (#1) yet.

> Then your another blunder,

Unfortunately, despite my sincere efforts, you still have no clue what you 
are talking about.

> that those terms should stand for "values".

They do:

  g_00 = c²

  g_11 = −1

  g_22 = −1

  g_33 = −1

All the other components of the metric tensor/matrix are 0, which means that 
the summands vanish when the tensor/matrix is multiplied with the vectors.

Homework assignment #2: Write in explicit matrix/vector form, using 
variables for the component values only, the equation for muliplying a 4 × 4 
matrix with a 4-vector.


PointedEars
-- 
Q: Who's on the case when the electricity goes out?  
A: Sherlock Ohms.

(from: WolframAlpha)

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The Necessity Alternate Theories kefischer <emoneyjoe@iglou.com> - 2015-10-08 13:01 -0400
  Re: The Necessity Alternate Theories Natalina Nazvarova <natana42@hotmail.com> - 2015-10-08 17:09 +0000
  Re: The Necessity Alternate Theories Odd Bodkin <bodkinodd@gmail.com> - 2015-10-08 13:30 -0500
    Re: The Necessity Alternate Theories Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-08 22:45 +0200
      Re: The Necessity Alternate Theories Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-08 22:58 +0200
        Re: The Necessity Alternate Theories Natalina Nazvarova <natana42@hotmail.com> - 2015-10-08 21:56 +0000
          Re: The Necessity Alternate Theories Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-09 06:39 +0200
            Re: The Necessity Alternate Theories Natalina Nazvarova <natana42@hotmail.com> - 2015-10-09 10:59 +0000
              Re: The Necessity Alternate Theories Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-09 20:29 +0200
                Re: The Necessity Alternate Theories Natalina Nazvarova <natana42@hotmail.com> - 2015-10-09 18:44 +0000
                Re: The Necessity Alternate Theories Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-10 09:40 +0200
                Re: The Necessity Alternate Theories Natalina Nazvarova <natana42@hotmail.com> - 2015-10-10 12:08 +0000
                Re: The Necessity Alternate Theories paparios <paparios@gmail.com> - 2015-10-10 05:25 -0700
                Re: The Necessity Alternate Theories Natalina Nazvarova <natana42@hotmail.com> - 2015-10-10 12:37 +0000
                Re: The Necessity Alternate Theories Maciej Woźniak <mlwozniak@wp.pl> - 2015-10-10 14:54 +0200
                Re: The Necessity Alternate Theories paparios <paparios@gmail.com> - 2015-10-10 06:02 -0700
                Re: The Necessity Alternate Theories Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-10 17:49 +0200
                Re: The Necessity Alternate Theories Natalina Nazvarova <natana42@hotmail.com> - 2015-10-10 16:08 +0000
                Re: The Necessity Alternate Theories Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-10 18:13 +0200
                Re: The Necessity Alternate Theories Natalina Nazvarova <natana42@hotmail.com> - 2015-10-10 16:16 +0000
                Re: The Necessity Alternate Theories Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-10 19:08 +0200
                Re: The Necessity Alternate Theories Natalina Nazvarova <natana42@hotmail.com> - 2015-10-10 18:02 +0000
                Re: The Necessity Alternate Theories Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-10 20:17 +0200
                Re: The Necessity Alternate Theories Natalina Nazvarova <natana42@hotmail.com> - 2015-10-10 18:37 +0000
                Re: The Necessity Alternate Theories Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-10 20:54 +0200
                Re: The Necessity Alternate Theories Natalina Nazvarova <natana42@hotmail.com> - 2015-10-10 19:00 +0000
                Re: The Necessity Alternate Theories benj <nobody@gmail.com> - 2015-10-10 16:40 -0400
                Re: The Necessity Alternate Theories underante <underante@yahoo.com> - 2015-10-09 15:31 -0700
  Re: The Necessity Alternate Theories kefischer <emoneyjoe@iglou.com> - 2015-10-09 02:42 -0400
    Re: The Necessity Alternate Theories Natalina Nazvarova <natana42@hotmail.com> - 2015-10-09 11:44 +0000
      Re: The Necessity Alternate Theories kefischer <emoneyjoe@iglou.com> - 2015-10-09 08:00 -0400

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