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Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39

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fuller.david@hotmail.com wrote:

> How much do the protons weigh in the LHC at 7Tev?
>  
> The energy of a proton is 7 TeV.

No, it is not.  That is the *collision* energy coming from at least *two* 
colliding protons.  You want to read page 3 and following of the 2009 
edition of the LHC Guide:

<http://cds.cern.ch/record/1165534/files/CERN-Brochure-2009-003-Eng.pdf#page-3>

> Via E = mc2 the mass is simply 7 TeV/c2 -
> and these are the units usually used.

["mc2" and "c2" are not proper notations.  If you cannot use Unicode -- 
"mc²" and "c²", respectively -- you have to find an ASCII-compatible way to 
express powers.  The usual way is to use the circumflex/caret character, so 
it would be "mc^2" and "c^2", respectively.]

As has been explained here many times before (including several times by 
me), E = m c² (E = m c^2) is only true for the energy at relative rest,
E = E(v = 0) = E(p = 0) =: E₀.

The full equation for energy, and thereby the mass–energy equivalence, that 
can be derived from the norm of the four-momentum is

  E = √((m c²)² + (p c)²)                                               (1)

 [E = sqrt((m c^2)^2 + (p c)^2)],

with momentum

  p = γ m v                                                             (2)

 [p = gamma m v],

and the Lorentz factor

  γ = 1∕√(1 – (v∕c)²)                                                   (3)

 [gamma = 1/sqrt(1 - (v/c)^2)],

therefore, applying (3) to (2),

  p = m v∕√(1 – (v∕c)²)                                                 (4)

 [p = m v/sqrt(1 - (v/c)^2)],

and finally, applying (4) to (1),

  E = m c³ √(1/(c² − v²))

 [E = m c^3 sqrt(1/(c^2 - v^2))],

assuming m > 0, c > 0, and v ≥ 0 (v >= 0).

As you can read in the LHC Guide, the protons in the LHC, when they reach 
their greatest relative velocity, move with 99.9999991 % of the speed of 
light in vacuum, or 0.999999991 c.  So it is very important not to ignore 
the part of their energy that comes from their relative motion.  In fact, 
that is why we need particle *accelerators* for achieving high particle 
energies, therefore the chance for producing heavy particles like the 
discovered Higgs boson, in the first place.
 
> 7 TeV/c^2 divided by the rest mass 0.938272029 GeV/c^2 gives us 7460.52
> times the rest mass

Ex falso quodlibet.
 

PointedEars
-- 
Q: What happens when electrons lose their energy?  
A: They get Bohr'ed.

(from: WolframAlpha)

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(((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-26 20:34 -0700
  Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-27 08:33 -0700
    Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-27 08:44 -0700
      Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-27 08:46 -0700
      Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-27 08:53 -0700
        Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-28 07:34 -0700
          Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-28 07:46 -0700
            Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-28 09:42 -0700
              Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-28 10:17 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-28 10:25 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-28 10:51 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-28 10:54 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-28 19:29 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-28 19:59 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-29 10:43 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-29 10:44 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-29 11:03 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 kefischer <emoneyjoe@iglou.com> - 2015-10-28 17:29 -0400
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-28 15:37 -0700
            Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-28 09:51 -0700
        Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-30 18:31 +0100
          Something related to the Collision of Protons Bobby Sifuentes <bobsif@academicinstitute.org> - 2015-10-30 17:44 +0000
            Re: Something related to the Collision of Protons Odd Bodkin <bodkinodd@gmail.com> - 2015-10-30 14:11 -0500
              Re: Something related to the Collision of Protons Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-30 21:06 +0100
                Re: Something related to the Collision of Protons Bobby Sifuentes <bobsif@academicinstitute.org> - 2015-10-30 20:47 +0000
                Re: Something related to the Collision of Protons Bobby Sifuentes <bobsif@academicinstitute.org> - 2015-10-30 20:49 +0000
                Re: Something related to the Collision of Protons Bobby Sifuentes <bobsif@academicinstitute.org> - 2015-10-30 20:54 +0000
                Re: Something related to the Collision of Protons Bobby Sifuentes <bobsif@academicinstitute.org> - 2015-10-30 21:52 +0000
                Re: Something related to the Collision of Protons Bobby Sifuentes <bobsif@academicinstitute.org> - 2015-10-30 21:59 +0000
                Re: Something related to the Collision of Protons fuller.david@hotmail.com - 2015-10-30 22:20 -0700
          Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 John Heath <heathjohn2@gmail.com> - 2015-10-30 16:10 -0700
            Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-30 21:34 -0700
          Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-30 21:32 -0700
            Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-31 06:50 +0100
              Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 Jack Weidner <jackwd@webportal.au> - 2015-10-31 11:20 +0000
              Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-31 05:48 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-31 16:16 +0100
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-31 08:32 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-31 08:35 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2015-10-31 17:18 +0100
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 Hyperbolic.cc@outlook.com - 2015-10-31 09:30 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 Hyperbolic.cc@outlook.com - 2015-10-31 09:38 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 kefischer <emoneyjoe@iglou.com> - 2015-10-31 13:42 -0400
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 Hyperbolic.cc@outlook.com - 2015-10-31 09:58 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-31 12:15 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-11-04 07:58 -0800
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 Hyperbolic.cc@outlook.com - 2015-11-05 08:49 -0800
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 kefischer <emoneyjoe@iglou.com> - 2015-11-05 12:08 -0500
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 Poutnik <Poutnik4NNTP@gmail.com> - 2015-11-05 19:23 +0100
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 fuller.david@hotmail.com - 2015-10-31 12:11 -0700
                Re: (((4 * pi * (10^(-7)))^2) / 2)^pi = 9.5176229e-39 Hyperbolic.cc@outlook.com - 2015-10-31 09:59 -0700

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