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Originally Posted by Sam5
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Originally Posted by swansont
What, exactly is Doppler-shifting? If it's time itself that is changing, then the type of clock is immaterial, as long as mechanical effects are compensated for.
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A classical Doppler shift regarding space and spacecraft is when a moving radio on a spacecraft that is moving away from the earth transmits, let’s say, a 1,000 Hz per second tone signal,
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First, a nitpick. A 'Hz/s' is a meaningless unit. Frequency is measured in Hz. You also don't want to use tones - sound can't propagate througha vacuum - you want to use light.
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Originally Posted by Sam5
and on earth the signal come into a radio receiver at 999 Hz per second. This is an “illusional” time dilation. It is known as a “redshifted” signal. It’s not real at the clock or at the transmitter on the spacecraft. It is just an illusion that is perceived by the radio receiver on earth.
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Big problem here - you've mixed up your refrence frames and as aresult what you're saying is meaningless. You can't have a Doppler shift relative to yourself. If I'm in my car, barrelling down the highway at 80 miles/hour, my radio is going to sound normal to me because I'm moving with my speakers - they're comoving so there is no Doppler shift between the two. However, someone who hears my radio as I drive by will hear a frequency change and what he hears is not an illusion. There are no preferred reference frames so his observation that the relative motion of my car relative to himself causes a frequency change (a Doppler shift) is a physically valid, real observation.
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Originally Posted by Sam5
What causes this type of Doppler shift is because the transmitter on the spacecraft is sending out 1,000 Hz, but the distance between the earth and the spacecraft increases constantly, so the signal has further and further to travel. This stretches out the wavelength of the signal in space, so that the frequency that is received on earth is only 999 Hz per second. If the spacecraft could stop in space, so that the distance between it and the earth does not increase, then the earth would receive the full 1,000 Hz per second.
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Right, because there is no Doppler shift if there is no motion.
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Originally Posted by Sam5
If the spacecraft is moving toward the earth and is sending out a 1,000 Hz signal, then the radio wavelengths are compressed, because the distance between the radio and the earth is decreasing, and so the radio on earth receives something like a 1,001 Hz per second signal. This is called a “blueshifted” signal.
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Right.
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Originally Posted by Sam5
Based on classical Doppler shift alone, at no time does the transmitted signal change rates. But the receiver on earth perceived an illusion of the rates changing, because of the Doppler effect.
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Dead wrong. The speed of the signal - which I assume is what you mean by rate - is not changing. The light sent by the spacecraft will still be travelling at 2.998 x 10^8 m/s. The sound coming out of my radio will still be travelling at 331.5 m/s. Both observers will agree on that. The wavelength and the frequency change.
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Originally Posted by Sam5
As proof of this theory, we could also use a reflective mirror on a moving spacecraft, and we can have a light pulse signal sent from earth and reflected back from the moving mirror. This way we know that the 1,000 Hz signal never changes at the source, because the source is at the earth and is not moving.
But when the mirror moves away from the earth, and the signal is reflected back, the signal is redshifted and only a 999 Hz per second signal comes back to the earth. When the mirror starts back toward the earth, the reflected light signal becomes blueshifted and the earth receives 1,001 Hz per second.
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Right answer, wrong reason. We will measure the signal's frequency to be 1 kHz when it's emitted because we're not moving relative to the transmitter. However, that doesn't change the fact that the signal we receive has changed its frequency. Assume the spacecraft is moving away from Earth at a constant speed. As a result, the signal it receives is redshifted - the signal has a lower frequency than it did when it left Earth. The signal is then reflected off the mirror towards Earth. Because, from the spacecraft's point of view, the Earth is moving away from it, the Earth will receive a signal that's been redshifted again.
There are several Doppler equations involved in this whole process, to calculate the exact results. Also, note that the earth will receive the redshifted signals for a longer time than it will receive the blueshifted signals. That’s because the earth is still receiving the redshifted signals when the mirror turns around and heads back. The earth will continue to receive the previously emitted redshifted signals for a while, even when the mirror is moving back. Finally the blueshifted signals start being received on earth.
When all the total number of Hz signals that were sent out, and all the total number of Hz signals that were reflected back, are counted, the same number that were sent out are the same as the number that were received on earth. There are no missing or “lost” Hz. If 10 billion were transmitted, then 10 billion will be received back on earth.
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Originally Posted by Sam5
The “relativistic” Doppler shift is slightly different, and it includes both the illusion of the classical Doppler shift and a real shift in the rate of an atomic clock. I can explain that to you if you wish. Lorentz first described the relativistic Doppler shift in the frequencies of moving atoms in his book in 1895 and he published the first relativistic Doppler shift equations in that book. The relativistic shift actually does take place at an atomic clock, and it is not an illusion. So the “relativistic Doppler shift” is an observed combination of the classical Doppler shift (which is an illusion) and the real shift in the oscillation rate of an atomic clock signal (which is real and actually does take place at the clock).
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Wrong. As far as the actual atomic clock is conerened it's at rest. We only receive a Doppler shifted signal if we're moving relative to it. This is partly due to the fact that, if the two reference frames are moving relative to each other, time is passing at different rates in those two frames.