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Q & A: relative time

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Most recent answer: 10/22/2007
Q:
This question has been bugging me for a couple weeks now. Iíve googled it many, many times and went back and re-read some books I have, but can not find the answer. I believe I understand that the constant speed of light means that if I pass you at Ĺ the speed of light, and as I pass, you flip on a flashlight, the light will still reach me in the same time as if I were standing still. In other words, my passage through time would alter and the light would still reach me at 670 million miles per my new slower hour. I assume this to mean that the properties of light will also remain unchanged, as in the red wavelengths will be red, the blue wavelengths will be blue, and all the other visible portions will fall in where they belong. All traveling at the same speed they usually do. Is this correct? I understand the Doppler Effect to mean that as I rush toward sound, the sound waves get shorter in frequency because I meet up with the peaks of the waves faster than if I had stood still. This makes since to me. The speed of sound is not constant. I can travel faster than sound and leave it behind. My speed should have some effect on the wavelength. Is this correct? Now for whatís bothering me. How do we see a red shift or blue shift in a spectrograph made of light waves that are constant regardless of the motion of the observer? It is obvious I am missing something; if you could point me in the proper direction I would appreciate it. Is it something in the reaction time for the emission lines that slows that part of the light down?
- Steve (age 47)
Georgia
A:
Steve- It's always fun to try to answer a question that somebody's really been wondering about. This answer will be biref, so if you need more info you can try googling this site under 'relativity'. If the answer isn't good enough try again, because this question at least has definite answers, known now for 100 years.

" the light will still reach me in the same time as if I were standing still." That depends by what you mean by 'at the same time'. The person shining the flashlight sees the light travelling at c away from him. If you are traveling at c/2 away from him, he sees the light gaining on you at only c/2. So he says the light takes twice as long to reach you as it would take if you were standing still at the distance from him at which, according to him, you were when he turned on the light.

Now according to you, this guy is traveling away from you at c/2 and the light is traveling toward you at c. You say that the light take sthe same time to reavch you that it would have taken if the guy was stationary at the same distance he was when according to you he turned on the light.

How can that be? You and he disagree not only about who is moving but also about the distances and time intervals between various events. The rules for calculating what coordinates one of you sees in terms of the other guy's coordinates are called the Lorentz transforms, and were figured out by Lorentz before they were nicely explained by Einstein.

The colors of light from the bulb of course are unchanged according to the guy holding the light. However, according to you they HAVE changed. They are Doppler shifted, toward lower frequencies. Wait, you ask: the Doppler formula gives different results for sound depending on if the source is moving away from the listener or vice versa (x2/3 or x1/2 for the frequency reduction factor when the relative speed is 1/2 the sound speed.) But here we're saying that there is no air to use as the stationary medium, so which of those results is right? It turns out that the answer is just the square root of their product, or sqrt(1/3) in this case. So this is called the 'relativistic Doppler shift'.

Mike W.

(published on 10/22/2007)

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