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anticorncob28
Post  Post subject: Does red light travel faster than blue light?  |  Posted: Tue Feb 28, 2017 3:52 am
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If not, then please explain what is wrong with the following reasoning.
Blue light has a shorter wavelength than red light. Therefore to make the same displacement the blue light has to curve more and travel a greater total distance.
For example, the curve y = sin(3x) from x = 0 to x = 10 is longer than the curve y = sin(x) from 0 to 10, so a beam of light with shorter wavelength needs more time to go 10 units.

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marnixR
Post  Post subject: Re: Does red light travel faster than blue light?  |  Posted: Tue Feb 28, 2017 8:41 am
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tell me: why should speed have anything to do with wave length ?
it's almost like saying that the vibration on your steering wheel determines the speed of your car

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anticorncob28
Post  Post subject: Re: Does red light travel faster than blue light?  |  Posted: Tue Feb 28, 2017 9:17 pm
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So the answer is no. But I don't think you understand why I thought the answer might be yes.
marnixR wrote:
tell me: why should speed have anything to do with wave length ?
it's almost like saying that the vibration on your steering wheel determines the speed of your car

About the car. Let x represent the horizontal velocity and y vertical velocity. Say x is 60 (mph). Then most of the car has vertical velocity 0, so the total velocity is sqrt(60^2 + 0^2) = 60.
Now about the steering wheel. If it's vibrating up and down, at some points its vertical velocity will be some non-zero number y. The total velocity of the steering wheel is sqrt(60^2 + y^2) > 60 while it is moving up and down.
With a beam of light, its horizontal speed in a vacuum is c, right?
But if light has a wavelength and bobs up and down, it also has a non-zero vertical velocity y. The total speed is sqrt(c^2 + y^2) > c, which is a problem.
I'd figure that a photon must travel at a speed less than c horizontally so its total speed remains c. For shorter wavelengths the photon moves faster up and down and thus must move slower horizontally so its total speed is c.

So how is this wrong?

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PhDemon
Post  Post subject: Re: Does red light travel faster than blue light?  |  Posted: Tue Feb 28, 2017 9:42 pm

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I'm a bit drunk and haven't analysed your thought experiment in detail but how would your thought experiment apply to photons? Could the issue be with treating light purely as a classical wave? It isn't. It's a bit more complicated than that...

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Chrispen Evan
Post  Post subject: Re: Does red light travel faster than blue light?  |  Posted: Tue Feb 28, 2017 11:10 pm
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Photons don't travel with a sinusoidal motion.


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PhDemon
Post  Post subject: Re: Does red light travel faster than blue light?  |  Posted: Tue Feb 28, 2017 11:20 pm

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That's why I asked the question in my above post... But after rereading the OP I'm not convinced that
Quote:
Blue light has a shorter wavelength than red light. Therefore to make the same displacement the blue light has to curve more and travel a greater total distance


is correct. Can you explain why you think more curvature equates with more distance? Surely the distance travelled by the wave is the same regardless of how many peaks and troughs there are in that distance. In QM and classical physics the curvature of a wave(function) is related to its energy not the distance travelled.

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marnixR
Post  Post subject: Re: Does red light travel faster than blue light?  |  Posted: Tue Feb 28, 2017 11:47 pm
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I think I have some idea of the thinking behind the OP - if you were driving your car in a series of big S-curves, then you would cover more miles for the same amount of straight distance covered than if you did smaller S-curves

imo that's a faulty analogy

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PhDemon
Post  Post subject: Re: Does red light travel faster than blue light?  |  Posted: Wed Mar 01, 2017 12:06 am

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I agree, there's no hypothetical particle moving up and down through the peaks and troughs of the wave, you cannot equate the length of the path such a particle would make to the distance travelled by the wave.

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marnixR
Post  Post subject: Re: Does red light travel faster than blue light?  |  Posted: Wed Mar 01, 2017 8:55 am
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tbh, I have the suspicion that entities like the photon or the electron, since they exhibit properties of both particle and wave, are neither

hence we can't predict their behaviour by comparing them with other entities that are clearly pure particle or wave

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PhDemon
Post  Post subject: Re: Does red light travel faster than blue light?  |  Posted: Wed Mar 01, 2017 9:06 am

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marnixR wrote:
tbh, I have the suspicion that entities like the photon or the electron, since they exhibit properties of both particle and wave, are neither

hence we can't predict their behaviour by comparing them with other entities that are clearly pure particle or wave


This is true (and a point I've made a few times here), treating or describing a quantum object as a classical wave or a classical particle is sometimes fine as an approximation but it often (usually!) gives the wrong answer! I've used the invented term "wavicle" before to emphasize quantum objects are neither particles or waves but something completely different that has properties associated with both...

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anticorncob28
Post  Post subject: Re: Does red light travel faster than blue light?  |  Posted: Wed Mar 01, 2017 7:49 pm
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My question has been answered; thank-you to all.

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