Re: time dilation

On Apr 11, 5:37�am, "harry" <harald.vanlintelButNotT...@xxxxxxx>
wrote:
"rbwinn" <rbwi...@xxxxxxxx> wrote in message

news:dd0d3b7a-58e7-48e4-b9ed-c269b00d1a88@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

The work of famous scientist Galileo Galilei provides us with a
question about time dilation and Dr. Albert Einstein's statement that
the laws of physics must remain the same in all frames of reference.
Galileo carried two lead weights of unequal sizes to the top of the
leaning tower of Pisa and dropped them at the same time, disproving
the idea of scientists of his time that the heavier of the two weights
would strike the ground first. �Of course, it took some time before
scientists accepted the results of his experiment. �They did not all
believe in the principle of equivalence the moment the two lead
weights hit the ground.
� � � �This brings us to another question about falling objects which
arises from the idea of dropping an object in a moving train car,
which writers of textbooks about relativity often use to show how the
Lorentz equations work.

Which one for example?

I do not have any in my possession. Einstein's book did not use this
example. However, a lot textbooks written by other scientists did.




If a weight is dropped from the top of a
train car to the floor, it falls a distance of y'. �In any
transformation equations this is always expressed as y'=y. � The
object travels the same distance vertically in S' as it does in S.
In Galileo's equations, it takes the same amount of time for the
object to travel from the roof of the train car to the floor in either
frame of reference. �t'=t.
� � In the Lorentz equations, a clock in S', the frame of reference
of the train car, is slower than a clock in S, the frame of reference
of the train tracks.
t'=(t-vx/c^)/sqrt(1-v2/c^2). �According to this equation, it takes
less time for the object to fall from the roof of the train car to the
floor in S' than it does in S. �So how are the laws of physics the
same in both frames of reference?
� � �If a clock in S ticks once while an object is falling in the
train car, it will not tick in S' until after the object has hit the
floor. �This means that the object is falling with a faster velocity
in S' than in S.
� � �I am sure that some of our scientific friends who believe in a
distance contraction will be anxious to explain this phenomenon.
Robert B. Winn

Neat. :-)
First a precision: as measured in all inertial frames, processes of
completely moving systems appear to be slower by the Lorentz factor.
However, your falling weight process is about a mixed system - thus (as
Einstein also briefly pointed out in 1905) your train better not use
pendulum clocks. ;-)
Well, I don't need to use pendulum clocks. I can use two weights as
clocks. If we put an identical train car beside the track and take
pictures of two weights as they fall in the two train cars, according
to experiment, the two weights will strike the floors of the train
cars at the same time as photographed from either frame of reference
if they are released at the tops of the train cars at the same time.
This is not some imaginary experiment. It has been done numerous
times. According to photographs, the two weights fall at the same
rate and strike the floors at the same time.
Now about laws of physics being the same: If there is another planet that is
at rest in S' with a moving train car that is at rest in S then the story
will be just the same, with S and S' exchanged.
That is wonderful, but it does not change anything. The two weights
will hit the floors at the same time on that planet also. So what
about the clock that scientists say is running slower? How is that
supposed to enter into this particular experiment?
Robert B. Winn


.

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