Re: Incorrect mathematical integration

On 07/24/2024 05:47 AM, Paul.B.Andersen wrote:

Den 24.07.2024 00:19, skrev Richard Hachel:

Le 23/07/2024 à 23:29, "Paul.B.Andersen" a écrit :

Den 22.07.2024 23:37, skrev Richard Hachel:

Le 22/07/2024 à 21:34, "Paul.B.Andersen" a écrit :

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Let's look at the LHC again.
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The length of the circuit is L = 27 k, γ = 7460
The real speed of the proton in the lab frame is
v = 0.999999991·c
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>

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When calculating velocities the distance and time must be measured
in the same frame of reference.
The distance in one frame and the time in another frame is not
a speed of anything if the frames are moving relative to each other.

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I know it may seem very strange (relativistic physics is a bit strange
but unavoidable) but that's how it happens.
It is the observing frame of reference that has the right distance,
but it is the particle or rocket that has the right time.
Observable time being only an anisochronous illusion.

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It isn't only "strange", it is idiotic nonsense.
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Measured in the lab frame the proton is moving around
the L = 27 km long ring in T = 90.0623065140618 μs.
The very real speed of the proton relative to the lab is
v = L/T =  0.999999991·c
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γ = 7460
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Measured in the proton frame, the length of the ring is
L' = L/γ = 3.6193029490616624 m.
The proton is moving around the L' long ring in the time
  τ = T/γ = 12.072695243171824 ns
The very real speed of the lab relative to the proton is
v =  L'/τ = (L/γ)/(T/γ ) = L/T = 0.999999991·c
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This should be blazingly obvious for anybody but complete morons:
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If the proton is passing a point in the ring with the speed v
relative to the point, then the point in the ring is passing
the proton a the speed v relative to the proton.
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The proton is moving at the speed 0.999999991·c relative to the lab,
and the lab is moving at the speed 0.999999991·c relative to the
proton.

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Because the distance and time are measured
in the same frame of reference.
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That what I say.

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No, that is not what you say.
You say the proton is moving at the speed 6947c relative to the lab.

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Which is the "proper speed" L/τ.
But L/τ  is not the speed of anything because it is the distance
in the lab frame divided by the time in the rest frame of the proton.
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And you thought that the real speed speed of the proton in the lab
frame
was 6947c and therefore you "tell them [the physicists at CERN]  that
the proton rotates 78 million times per second".
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Which is 6933 times the real number,  ≈ 11.25 thousand times per
second.

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Give it up, Richard.
The physicists at CERN measures that the proton 'rotates'
11.25 thousand times per second, you "tell them that the proton
rotates 78 million times per second."

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Don't tell me you don't understand that the proton rotates 11.25
million times per second in the laboratory frame but 78 million times
per second in the proton frame.
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This is called time dilation.

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"The proton rotates 11.25 million times per second in the laboratory
frame but 78 million times per second in the proton frame"!
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Good grief, this is way toooo stupid!
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But it is funny! Hilarious! The involuntary jokes are often the best.
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ROFL (not really, but it was close!)
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Yeah, you might think so, then though to equip the model
where the frames, in the space, are space-frames and frame-spaces,
so that the particle's _space_ besides its _frame_ are moving,
what results that space-contraction in effect, is real, that
the particle brings its space with it.
The linear accelerators are mostly aggregates of quite a large
number of, abstractly, particles, as with regards to energy
input and energy arrived.
The linear accelerators, like SLAC, illustrate that space-contraction
can be observed, affecting the surrounds of the main beam-line as
it were, as if according to a space contraction, and indeed about
the Galilean, inputs and outputs.
In the cosmological setting, the larger body or system being
its own rotational frame altogether, illustrating again that
the space contraction is observable, the Lorentzian in the
rotational, helps explain why theories like MOND have a
physical explanation and not just an algebraic model.
I.e., MOND sort of answers why there is no dark matter,
then there's a sort of inverse-MOND also to explain why
there's no dark energy, that the effects otherwise are
quite simple and holistic, instead of the "missing link"
non-theory of non-science.