02 Transverse Doppler Effect
Today, I
would like to introduce a way to check relativistic effects in a narrow
laboratory. Relativistic effects are usually hard to see in the lab. It is
difficult because it requires an incredibly fast speed. But there is a way.
Initially,
experiments were conducted using excited hydrogen atoms. What we are going to do today is look at
Walter Kündig's method. The basic method of Kündig is as
follows. [Walter Kündig, “Measurement
of the Transverse Doppler Effect in an Accelerated System”, Phys. Rev. 129,
2371(1963)]
Walt Kündig's Experimental Devices
It uses a
device that turns quickly like a centrifuge. It measures the frequency of light
emitted from the source by placing the source in the middle and the absorber at
the edge. The story of the experimental device is not important, but please read the literature if you are
interested in learning about that.
The
experimental
results are interesting. The Doppler Effect
was known before the theory of relativity was published. What is surprising,
however, is that when an object goes across an observer, it has a special
effect. This is a phenomenon that did not exist in the classical Doppler
effect.
The third
is the main character. This transverse Doppler effect has never been found
before.
Do you
admit that the speed of light is the product of wavelength and frequency? If
you do not admit this, I have nothing further to say. However, I think that you will acknowledge everything and
continue to write. The philosophy of relativity is that the speed of light in a
vacuum must be constant, regardless of the speed of the light source or the
observer. As long as it is an inertial system, the speed of the observer
does not matter at all.
Therefore, the speed of light should always be kept at c, no matter what state
it is in. But then there is a problem. If the length contraction is correct,
the speed of this light changes. The equation is shown below. Because the
wavelength is also the length dimension, the expression of length contraction
can be used.
We are ready now.
What is this? By applying length contraction to the transverse Doppler effect, the speed of light is not kept constant. How can this be? Is that what it is? Is it possible to become embarrassed in such rigorous relativity? In any case, the constancy of speed of light must be observed. Let's look at it a bit differently.
In this case, the constancy of speed of light is maintained. Transverse Doppler effect is applied from above. However, you can see that it contains unfamiliar equations. If you write down the expression, write it down as follows using this expression.
The
length that we have known so far is different from the contraction type. You
may
be seeing this expression for the first
time, but I am very familiar with it. This equation appears in many places of relativity.
I will
introduce it gradually, but when the length contraction intervenes, inconsistency always occurs, and when the expansion of
the length appears, it always resolves coolly. So the shape of the wave is as
follows.
The
horizontal Doppler effect is that the waveform is from left to right. On the
left, the frequency is high and the wavelength is short. However, when an
object moves across and
in front of me at a
fast pace, the
wavelength will
look like the one
on the right. So
the right side has a lower frequency and a longer wavelength. Here, the
wavelength is longer, so the expansion of the length is correct. Compared
with the shape of the object, it is as follows.
If there is an object between two crests, you can confirm that it has been stretched in the direction in which it progresses. You know that the light on the left or right waveform is all the same speed.
Therefore,
it can be confirmed that the relativistic length of the correct length is not
'length contraction' but 'length expansion'. I will continue to present more evidence in following posts.
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