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Failures of the Galilean transformation (was: The Song of Lt. Cdr. Data)

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Arindam Banerjee wrote in <news:sci.physics>:

> On Wednesday, September 20, 2017 at 9:37:46 PM UTC+10, Thomas
> 'PointedEars' Lahn wrote:
>> Arindam Banerjee wrote:
>> > On Wednesday, September 13, 2017 at 2:06:56 PM UTC+10, sci.physics
>> > wrote:
>> >> How much energy will it take to get these spaceships to travel faster
>> >> than light?
>> >> 
>> >> Where does this energy come from?
>> > 
>> > If the acceleration of the ship is g or say 10m./sec^2 then from rest
>> > the ship will reach the speed of light
> 
> In 347 days

Argumentum ad nauseam.

No, it will not *ever* reach the speed of light using conventional 
propulsion.

> At 100m/s/s 34.7 days which is quite feasible with modern technology
> and with 1000m/s/s 3.47 days which should happen within 100 years

Newtonian mechanics does not work anymore when the relative speeds approach 
the speed of light (or masses are large, see GR).  For two theoretical 
objects moving at the speed of light, the error is *100 %*:

  u(v, u') = (v + u')∕(1 + v u'∕c²)    Relativistic speed composition

  u(c, c)  = (c + c)/(1 + c²/c²) = c

vs.

  v(v₁, v₂) = v₁ + v₂

  v(c,  c)  = c + c = 2 c              Galilean/Newtonian speed composition,

where u is the speed of K as observed by A, and u' is the speed of K as 
observed by B which is moving relative to A at speed v.

When the speeds are much less than the speed of light, then the 
Galilean/Newtonian speed composition also only works *approximately* as only

  lim      u(v, u') = v + u'.
  v u' → 0

<http://www.wolframalpha.com/input/?dataset=&i=plot+%7B2+v%7D,
+%7B2v%2F(1+%2B+v%5E2)%7D+for+v+%3D+0+to+1>
 
>> *You cannot reach the speed of light c using conventional propulsion*
>> (i.e. not based on dynamic spacetime), because the kinetic energy you
>> would need to generate approaches infinity.
> 
> Idiotic e=mcc babbling.

I did not write “e=mcc”.

> As c depends upon the velocity of the emitter,

It does not.  Experimentally confirmed a thousandfold, if that is even 
enough.

> the first postulate for deriving e=mcc is knocked out

Einstein defines the first postulate of special relativity as follows:

,-<http://einsteinpapers.press.princeton.edu/vol2-trans/154>
| 
| […] lead to the conjecture that not only in mechanics, but in
| electrodynamics as well, the phenomena do not have any properties 
| corresponding to the concept of absolute rest, but that in all coordinate 
| systems in which the mechanical equations are valid, also the same 
| electrodynamic and optical laws are valid, as has already been [3] shown 
| for quantities of the first order. We shall raise this conjecture [4] 
| (whose content will be called "the principle of relativity" hereafter) to 
| the status of a postulate […]

So you are claiming that not “in all coordinate systems in which the 
mechanical equations are valid, also the same electrodynamic and optical 
laws are valid”?

> so the whole theory is absolute bunkum.

If that is true, then, for example, why has the protons’ relative speed in 
the LHC not already surpassed the speed of light *by orders of magnitude*?

If the Galilean transformation would hold in all regimes, then the mass–
energy equivalence E₀ = m c² would be wrong, the protons would have no 
energy when at rest (E₀_{Galilean} = 0), so with the collision energy
(= Galilean kinetic energy) per beam of ca. 6.5 TeV [1], and a proton mass 
of ca. 938 MeV∕c² [2], a proton’s speed relative to the accelerator ring 
should be

  E_{Galilean} = m v²/2

             v = √(2 E_{Galilean}/m)

             v ≈ √((2 × 6.5 TeV)/(938 MeV∕c²) ≈ 118 c.

But it is _not_.

Instead, it is *measured* to be just

             E = γ m c²
             E = m c²/√(1 − u²/c²)
  √(1 − u²/c²) = m c²/E
    1 − u²/c²  = m²c⁴/E²
        u²/c²  = 1 − m²c⁴/E²
        u²     = c² − m²c⁶/E²
        u²     = (E²c² − m²c⁶)/E²
        u²     = c² (E² − m²c⁴)/E²
        u      = c √(E² − m²c⁴)/E
        u      = c √((6.5 TeV)² − (938 MeV∕c²)²c⁴)∕(6.5 TeV)

             u ≈ 0.9999999896 c,

*precisely* as special relativity predicts.

How do you explain that?

> As proven by the correct analysis of the MMI experiment which I did back
> in 2005, 

“MMI”?

> and evidenced by the Doppler effect.

On the contrary, the Doppler effect is striking evidence that the phase 
speed of *any* wave does _not_ change (i.e., is invariant) if the wave 
source is moving relative to the observer.  Because c = λ f = const., where 
c is phase speed, λ is wavelength, and f is frequency.  This applies even if 
you insist on pre-relativistic, even pre-Maxwellian, mechanics.

<https://en.wikipedia.org/wiki/Doppler_effect>

Conclusion: You have not the slightest clue what you are talking about.

_______
[1] <https://home.cern/about/updates/2015/05/protons-set-collide-13-tev-prepare-physics>
[2] <http://pdg.lbl.gov/2017/tables/rpp2017-sum-baryons.pdf>
-- 
PointedEars

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

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Thread

Re: The Song of Lt. Cdr. Data Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-20 13:37 +0200
  Re: The Song of Lt. Cdr. Data Arindam Banerjee <banerjeeadda1234@gmail.com> - 2017-09-20 06:26 -0700
    Failures of the Galilean transformation (was: The Song of Lt. Cdr. Data) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-20 17:23 +0200
      Re: Failures of the Galilean transformation (was: The Song of Lt. Cdr. Data) Arindam Banerjee <banerjeeadda1234@gmail.com> - 2017-09-20 16:19 -0700
        Re: Failures of the Galilean transformation Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2017-09-22 14:00 +0200
          Re: Failures of the Galilean transformation Arindam Banerjee <banerjeeadda1234@gmail.com> - 2017-09-22 05:10 -0700

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