Re: The Cosmic Muons Paradox

On Sep 7, 5:24 pm, mluttgens <mluttg...@xxxxxxxxx> wrote:
On 7 sep, 12:12, "Paul B. Andersen" <paul.b.ander...@xxxxxxxxxxxx>
wrote:



mluttgens wrote:
On 4 sep, 17:26, PD <thedraperfam...@xxxxxxxxx> wrote:
On Sep 4, 8:07 am, mluttgens <mluttg...@xxxxxxxxx> wrote:

<snip>

In the Universe, only the CMBR can be considered as
an absolute reference frame.
But you'll find there is nothing special about the CMBR frame.

Hereafter is an example:
Object A moves at vA wrt the CMBR,
Object B moves at vB wrt the CMBR.
Let's calculate the time dilations on A and B relative to the
CMBR clock. Let tA a time interval mesured on object A, tB a
time interval measured on object B, and tR a time interval
measured on an object at rest wrt the CMBR.
One gets tA = tR * sqrt(1-vA^2/c^2) and
              tB = tR * sqrt(1-vB/c^2), hence
tA/tB = sqrt(1-vA^2/c^2) / sqrt(1-vB/c^2), and
tA = tB * (sqrt(1-vA^2/c^2) / sqrt(1-vB/c^2)), or
tB = tA / (sqrt(1-vA^2/c^2) / sqrt(1-vB/c^2)).
Marcel, we talked about this in a different thread. Time dilation
reciprocity is exhibited in TWO different pairs of events, not ONE
pair of events. You've reverted back to your previous mistake, having
forgotten what was explained to you just a little bit ago.

I am referring to the demonstration by Paul B. Andersen
of the existence of mutual time dilation in the case of
the cosmic muons.

No, you are not!

Luttgens:

"The time dilation effect is *not* reciprocal in the case of
the cosmic muons."

Paul B. Andersen (message of Thu, 27 Aug 2009):

Sure it is:

   Let the origins of the muon frame (primed) and the ground
   frame (unprimed) be at the muon creation point at t = t' = 0.
   Let the ground be at x = 10km
   Let there be a clock at the ground showing coordinate time
   of the ground frame.
   Let the speed of the muon be 0.9987c, gamma = 19.6

   |------------------->x' -> 0.9987c
   |----------------|-->x
   0               10km

   The event E0  'clock at ground shows zero'  has the coordinates
   (t0,x0) = (0 s,10^4 m)
   Transformed to the muon frame:
   t0'= gamma(t0 - v*x0/c^2) = -19.6*0.9987*10^4/3*10^8
                                        = - 6.525*10^-4 = -652.5 us
   This means that the clock at ground will show zero at the muon
   frame time -652.5 us.

   The muon will hit the ground when the ground clock shows
   t1 = 10^4/0.9987*3*10^8 sek = 33.376 us

   The muon time will then be:
   t1' = gamma(t1 - x0*v/c^2)
       = 19.6(33.376us - 10^4*0.9987/3*10^8) sek = 1.70 us
   which is less than the muon's lifetime.

   What about the mutual time dilation?

   From the ground frame's point of view:
   The muon time has advanced 1.70 us while 33.376 us
   have passed.
   So the muon 'clock' is running slow by the factor
   1.70/33.376 = 0.051 = 1/gamma

   From the muon's point of view:
   The ground clock showed zero at the muon time -652.5 us
   The ground clock showed 33.376 us at the muon time 1.70 us
   The ground clock has advanced 33.376 us while 654.2 us
   have passed.
   So the ground clock is running slow by the factor
   33.376/654.2 = 0.051 = 1/gamma

Which show that your statement in your original post
(the first one in this thread):
  "The time dilation effect is *not* reciprocal in the case of
  the cosmic muons."
is plain wrong!

The following is definitely NOT a reference to my posting.

--
Paul

My comment:

One can consider that the Earth is at rest in the CMBR
because its velocity wrt the CMBR is is very small compared
to that of the muon wrt the CMBR.

The claim of Paul B. Anderson that from the muon's point
of view, the ground clock has advanced 33.376 us while 654.2 us
have passed is based on the muon's hypothesis that the
Earth is moving toward him at  0.9987c (gamma = 19.6).
Indeed,  33.376 ms = 654.2 ms / gamma

Such claim implies that the CMBR is moving toward
the muon at about  0.9987c, as the Earth is practically
linked with the CMBR.
But the idea of a moving CMBR makes no sense at all.

So, one has to conclude that there is no mutual time
dilation in the case of the cosmic muons.
As it predicts mutual time dilation, SR has to be false.

Marcel Luttgens

This is utter nonsense!

It is not because Muon the SRist decides that the Earth is
moving toward him at 0.9987 c, that the Earth's realist will
cease to observe in the CMBR a dipole corresponding to
a velocity of 370 km/s.
Of course, Einstein ignored the existence of the CMBR,

Especially since its existence wasn't even discovered until after his
death.

Marcel, you're a hoot.

but
today, his followers don't have that excuse.

Marcel Luttgens

<snip>

Paul

http://home.c2i.net/pb_andersen/



.

Relevant Pages

  • Re: The Cosmic Muons Paradox
    ... But you'll find there is nothing special about the CMBR frame. ... Object A moves at vA wrt the CMBR, ... Let the origins of the muon frame and the ground ... The muon will hit the ground when the ground clock shows ...
    (sci.physics.relativity)
  • Re: The Cosmic Muons Paradox
    ... But you'll find there is nothing special about the CMBR frame. ... Object B moves at vB wrt the CMBR. ... Let the origins of the muon frame and the ground ... Let there be a clock at the ground showing coordinate time ...
    (sci.physics.relativity)
  • Re: The Cosmic Muons Paradox
    ... But you'll find there is nothing special about the CMBR frame. ... Object A moves at vA wrt the CMBR, ...    of the ground frame. ...    This means that the clock at ground will show zero at the muon ...
    (sci.physics.relativity)
  • Re: The Cosmic Muons Paradox
    ... to that of the muon wrt the CMBR. ... as the Earth is practically ...
    (sci.physics.relativity)
  • Re: The Cosmic Muons Paradox
    ... It is special, because an object can move wrt it, but the CMBR ... of mass of the cars) and the road is different, ... We just don't expect the energy of impact in the interaction ...
    (sci.physics.relativity)