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Why did Einstein (and contemporary physicists) feel the speed of light is constant?
Since light can have different wavelengths, is it not possible that it can travel at different speeds?
6 Answers
Einstein never said that the speed of light was always the same, he said that it was the same from all observers. That is not the same thing.
c is a constant...or else the equation don't work... :)
They felt that the speed of light (in vacuum) is constant because it was measured that way. The Michelson–Morley experiment (first done in 1881) showed that 'c' is constant at all times of year, in all directions, at all times of the day, and all wavelengths.
I don't actually know how Einstein first came up with the idea that light was constant, but nowadays, many hundreds of experiments (the most well known one being the Michaelson-Morrey experiment) have all reached the conclusion that the speed of light in a vaccum is constant, regardless of one's frame of reference.

If wavelength changes while velocity remains constant, then all that means is the frequency of the wave is changing. This is what occurs with light: the speed of light = frequency times wavelength. I'm not sure how you figure that different wavelengths automatically equal different velocities.
I suspect that Michelson-Morley is relevant here - but I'm not in a position to explain - I recently asked a related question...
While the experimental evidence provided by Michelson and Morley certainly played a role in Einstein's convictions, the reason he was so clear about his conclusion is more fundamental to the way he approached science.

In Newtonian physics, it is a fundamental principle that you cannot, from any mechanical evidence, determine your speed; that you can only find your speed relative to another object.

That is, if you are on a train or a jet or a rocket ship that is not accelerating, every physical experiment - every experiment involving matter, would give identical results whatever your speed.

If there was some objective speed to electromagnetic radiation - which is energy with no mass at all - then one could use this lack of symmetry to determine an absolute speed in our universe. And Einstein was convinced that the universe was more orderly than that, and that if you could not determine absolute speed using matter, you could not do it with energy either.

it was an assumption that, really, took a lot of audacity. And of course, his ideas were not verified for many decades after his paper in 1905!
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