Re: Are *observed* SR effects real?
- From: Darwin123 <drosen0000@xxxxxxxxx>
- Date: Fri, 8 Aug 2008 16:50:04 -0700 (PDT)
On Jul 11, 4:04 pm, "Sue..." <suzysewns...@xxxxxxxxxxxx> wrote:
On Jul 11, 2:27 pm, Darwin123 <drosen0...@xxxxxxxxx> wrote:
http://farside.ph.utexas.edu/teaching/em/lectures/node108.html
As was earlier stated inertial motion is without force.Sorry for the late reply on this issue. I am better informed now than
Therefore H&K is not a test of SR.
I was then.
The HK experiment really is a test of SR. The reason is that
during a single oscillation of the atom, the atomic clock is
effectively in free fall. I'll give a rough calculation with numbers
rounded off for numerical simplicity.
Let us assume the period of oscillation for the atom in the
atomic clock is 1 ns (=10^-9 s). Let the surface velocity of the earth
and airplane be 5x10^4 m/s. Let the free fall acceleration be 10 m/
s^2.
In the question of whether SR rules, the important time scale is
a single oscillation of the atom on the surface relative to a similar
atom at the center of the earth. The total effect is the sum of the
discrepency of these single oscillations. If the single atoms on the
surface consistently show the same time dilation factor relative to
the center of the earth, we have proven that the time dilation occurs
overall. Because all these delays add up over the trip of the
airplane.
Look at the airplane from the POV of the center of the earth
during a 1 ns oscillation. That is 1 ns at the center of the earth
(inertial frame at center, not the rotational frame). Make believe
that gravity disappears but the E and M forces remain the same. The
clock on the surface (in the airplane) is no longer in free fall. It
is accelerating away from the center at 10 m/s^2. However, it is still
moving horizontally at 5x104 m/s.
Is the clock on the surface effectively at free fall? The answer
can be found by calculating the components of displacement with the
gravity gone.
The vertical displacement is given by:
y=0.5gt^2.
Since g =t0m/s, and t=10-9 s, the displacement y is 5x10^-18 m. This
is much smaller than an atom, or even the effective radius of an
electron. This is small.
Now compare it to the horizontal displacement, x.
x=vt
where v is the horizontal velocity. Since v=5x104 m/s and t=10^-9 m
x=5x10-6 m.
So x>>y. However, y was caused by the cessation of gravity. The
motion has hardly been effected by the loss of gravity. Therefore,
gravity is unimportant in this problem.
Since gravity is unimportant to the problem, we can use SR instead
of GR with no problem. The HK experiment really was a test of SR, not
GR.
To finish the problem off, leaving the gravity off. Of the two
clocks, surface and center, which is a true inertial frame?
The clock on the surface is being acted on by the contact forces
(E&M) forces of the airplane. The air applies lift to the airplane,
which pushes on the seat, which pushes up the clock. The clock is
therefore accelerating upward at 10 m/s. The clock in the airplane is
not an inertial frame. We can not use the Lorentz time dilation
formula for a clock in this frame.
What forces are acting on the atomic force at the center of the
earth. Well, the clock is under a lot of pressure to be sure. If the
troglodytes at the center have satisfied proper protocols for time
measurement, they have built this clock to work at this pressure.
Furthermore, all the E&M forces on the clock in the center cancel out.
There is no net force on the clock, and so no acceleration. The clock
in the center of the earth is in a true inertial frame.
The troglodyte observer looks up at the clock on the surface and
sees it circle the earth, coming back to the same spot. Each
oscillation of the surface clock was slightly shorter than the
corresponding oscillation of the center clock, as given by the Lorentz
time dilation factor. The differences accumulate. Therefore, at the
end of the trip, where the clock is back in the same place, the time
measured by the surface clock is slightly shorter than that in the
center. The time dilation factor depends on the speed of the surface
clock relative to the center of earth clock.
The speed of travel of the three clocks are different relative
to the center. They ALL measure shorter relative to the center clock.
However, the east bound clock was moving the fastest. So it shows the
most delay. The west bound clock was moving slowest. So it shows the
least delay. When the two clocks on the surface get together, the west
bound clock is ahead of the east bound clock.
This is fully consistent with SR since neither the east or the
west bound clock are inertial frames. They are BOTH moving slower than
the center of earth clock. However, the center of earth clock is in an
inertial frame. It is supposed to see clocks in other frames move
slower.
Thus, the HK experiment is mostly a test of SR. The calculation
performed using GR shows very little difference from the SR
calculation. And it is all because the E&M forces can't move the
surface bound clock very far upwards in 1 ns.
Also, the answer to Spaceman's question is obvious. The physical
reason for the Lorentz time dilation in the HK experiment is the E&M
forces holding the atomic clock in the airplane up. It happens to be
that the magnitude of these EM forces are exactly the same as the
centripetal force in the Newtonian calculation. So one can roughly say
that it is the Newtonian centripetal force that is causing the Lorentz
time dilation.
The subtle point here is that inn a free fall frame, there are
only E&M forces. So from the standpoint of the free fall frame, where
SR is exactly true, the E&M forces are the centripetal forces that
exist in the accelerated frame of the surface.
So maybe a better answer to Spaceman's question is that the E&M
forces are indirectly causing the Lorentz time dilation. Whatever. The
HK experiment IS a test of SR.
.
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