Special & General Relativity Questions and Answers
If a blue shifted clock runs fast, why do fast moving particles decay slowly?
First of all, for moving particles ,the time dilation effect has nothing to do with the direction of travel. It is an absolute quantity. The issues of redshift and blue shift are appropriate only to electromagnetic waves traveling at the speed of light, and for them the time dilation effect is infinite since they travel at the speed of light.
There are two clocks in this problem. The one you are using and the one traveling. Mu mesons, if left to themselves and not in motion, decay in a fraction of a second. If the mu meson is traveling near the speed of light, special relativity says that if we were to look at the clock carried by the mu meson, we would see it run more slowly no matter what direction it is moving relative to us along the line-of-sight. The measurable effect is that, although mu mesons have a fixed decay rate, we would see these particles 'live' a longer lifetime as measured by OUR clock which is at rest with respect to us. As measured by the mu mesons's clock, however, it would decay after the usual number of seconds.
If the mu meson were to send us a light signal with a well defined frequency, we would see the wavelength of the light decrease as the mu meson was approaching us. The time interval between wave crests can be related to the lifetime of the mu meson on the clock carried by the mu meson. This also corresponds to a specific distance in the rest frame of the mu meson. Now, as viewed by the observer on the earth, the wavelength is shortened (or lengthened in the case of the mu meson moving away from us) by an amount equal to the relativistic factor determined from the relative speed of the mu meson. The fact that it is redshifted or blue shifted has nothing to do with the mu meson, and only with the way that light travel and is detected. BUT the factor by which this shifting occurs can be related to the difference in the times registered on your clock, and the mu mesons clock.
For example: If the mu meson is moving at 95 percent the speed of light then the time dilation factor will be 3.2 This means that Time(your clock) = 3.2 x Time( mu meson) and so the decay time you see for the mu meson is LENGTHENED by 3.2 times what it normally is when the mu meson is at rest in your reference frame. The red or blue shift of the received light pulses can be used to determine the relativistic factor since:
change in wavelength .................... = ( (1 - beta)/(1 + beta) )^1/2 rest wavelengthwhere beta = velocity/speed of light. For a body emitting light traveling at 95 percent the speed of light towards you, the doppler factor would be 0.16 so that for a light source emitting light at a wavelength of 6500 Angstroms, it would appear to be emitting the light at a wavelength of 6500 - 0.16*6500 = 5460 Angstroms; a blue shift.
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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.