Re: time dilation
- From: PD <TheDraperFamily@xxxxxxxxx>
- Date: Fri, 11 Apr 2008 04:19:19 -0700 (PDT)
On Apr 10, 6:40 pm, rbwinn <rbwi...@xxxxxxxx> wrote:
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. 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
Just a few comments:
1. Galileo almost certainly did not drop balls from a tower in Pisa,
though it makes a lovely story.
2. The dropping of a ball in a train car teaches us something
completely different than y'=y. The fact that the ball drops the same
distance vertically in S and S' is not the physical law that is the
same in both S and S'. Falling a distance y or falling a distance y'
is not a physical law. Nor is doing so in time t or time t'.
3. Numerical answers being in agreement is not what the principle of
equivalence means. As an illustration of this, before it is dropped,
the velocity of the ball on the train is different in S and S', yet
the laws of physics are identical. Once you understand how the values
of the velocity can be different in two different frames, but the laws
of physics be identical, then you might have a better grip on what the
principle of equivalence says.
PD
.
- References:
- time dilation
- From: rbwinn
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