If the speed of light is constant in any inertial frame

In summary: However, the direction of the shift is determined by the relative motion of the light source and detectors, not by the wavelength of the light.
  • #1
quincy harman
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If the speed of light is constant in any inertial frame then how do we measure a red shift or blue shift or why?
 
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  • #2
Sorry I didn't think the question through before I posted. I just remembered the wavelength has nothing to do with the speed.
 
  • #3
Imagine you have a light source at rest between two detectors which starts emitting light waves.

It would look something like this
doppler1.gif


Each light wave spreads out in a circle at c, with each wave front hitting each detector at a rate equal to the emission frequency.

Now consider what happens if the the light source is moving towards one detector and away for the other as seen from the frame of the detectors.

The light waves still spread out in a circle at c, but the origin point of each wave front is closer to one detector than it is from the other and the center of each circular wave front is displaced from the previous one. The wave fronts hitting the blue dot are closer together and the one hitting the red dot are further apart. since they are still traveling at c with respect to the detectors, the Blue dot see a higher frequency of light and the red dot a lower frequency.
doppler2.gif


As far as the light source is concerned, the waves still are moving outward from it at c in circles, but the red dot is running away from the wave fronts traveling in its direction and the blue dot is rushing towards the wave fronts in its direction. So according to the Light source frame we get the same result, wave fronts hit the blue dot at a faster rate than they hit the red dot.

So no matter which frame you pick, you expect the detectors to register Doppler shifts.
 
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Related to If the speed of light is constant in any inertial frame

What is the speed of light and why is it important?

The speed of light is a fundamental constant in physics, denoted by the letter "c". It is approximately 299,792,458 meters per second in a vacuum. It is important because it is the maximum speed at which all energy, matter, and information in the universe can travel. It plays a crucial role in many theories and equations in physics, including Einstein's theory of relativity.

What does it mean for the speed of light to be constant in any inertial frame?

This statement means that the speed of light is independent of the observer's motion or frame of reference. No matter how fast an observer is moving, they will always measure the speed of light to be the same value. This is one of the fundamental principles of Einstein's theory of special relativity.

What is meant by "inertial frame"?

An inertial frame is a reference frame in which Newton's first law of motion holds true. This law states that an object at rest will remain at rest, and an object in motion will continue in a straight line at a constant speed unless acted upon by an external force. In other words, an inertial frame is a non-accelerating frame of reference.

How was it discovered that the speed of light is constant in any inertial frame?

The constancy of the speed of light was first observed by the Danish astronomer Ole Rømer in the 17th century. He noticed that the timing of eclipses of Jupiter's moon, Io, appeared to vary depending on the Earth's position in its orbit. This led him to conclude that light must have a finite speed, and that it is the same for all observers regardless of their motion.

What are some implications of the constant speed of light?

The constancy of the speed of light has many important implications in physics. It allows for the concept of space and time to be relative, and for the famous equation E=mc² to hold true. It also plays a crucial role in modern technologies, such as GPS navigation and wireless communication. Additionally, it has led to the development of theories such as special and general relativity, which have revolutionized our understanding of the universe.

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