Photons, of course, all travel at the same speed of light (~300k km/s in a vacuum), however at different frequencies corresponding to their energy level.
If you were to “trace” two photon’s paths with a string from point A to point B, you would expect said string to be longer for a photon with a shorter wavelength, compared to the one with a longer wavelength once pulled taught.
Thus, considering that the two photons presumably travelled from point A to point B in the same amount time, the photon with the higher energy and shorter wavelength must have travelled further, and thus at a higher velocity compared to the lower energy photon.
Why isn’t this the case? Do the lower energy photons have a higher amplitude to make up this extra “distance”?
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Photons of differing energy levels only travel at the same speed when in a vacuum. While in a medium, less energetic photons are a bit slower.
But, while in a vacuum, they all travel at the same speed because they lack mass, regardless as to their energy level.
You’re making assumptions that aren’t necessarily accurate.
The way you describe it, you’re thinking of the photon as a little marble travelling up and down the wave’s shape as if it were a road.
That’s not the case. The energy is moving along the X axis, for example, with a certain forward speed… it’s just the wave shape that’s changing. The value of the electromagnetic field is oscillating faster when there’s more energy, but the total system is still moving through space at the same speed.
try thinking of it from the photons point of view. there is no time, it was emitted and absorbed in the same instant. the path or length of the line between determine what the wavelength is.
>If you were to “trace” two photon’s paths with a string from point A to
point B, you would expect said string to be longer for a photon with a
shorter wavelength, compared to the one with a longer wavelength once
pulled taught
This assumption is what’s tripping you up, because it’s not correct. Light isn’t little balls that are physically traveling up and down light they’re going up hills and down valleys, that’s just a representation of oscillations in the electric and magnetic fields. Also light travels at just under *300,000*km/s in a vacuum, not 300.
From a simple perspective, the photon isn’t travelling along that wave. The photon is that wave. Light is essentially a propagating electric and magnetic field. The wave is the fluctuation of the strength of the electric and magnetic field.
As for why all photons travel at the speed of light and the speed of light is the speed limit of the universe isn’t because of light. The other name for it is the speed of causality, which is to say how fast anything in the universe can affect anything else in the universe. The fluctuating electric and magnetic field of a photon is instantaneous. But, for it to move from one point in space to the next it has to follow the speed of causality. You can think of it as sort of the framerate of the universe. One frame has it at one location and it can’t move to the next location until the next frame. Every frame, all photons in the universe move the same distance, the Planck constant.
Keep in mind that when we’re talking about things like photons and electrons, we’re in the realm of quantum mechanics. Normal human reasoning and experiences do not apply. Human language in fundamentally incapable of accurately describing quantum mechanics in its entirety, you can only do that with math. For example, the Heisenberg uncertainty principle exists not because it’s impossible for us to physically measure both position and velocity of things like electrons. Rather, it’s because the mathematical description of an electron literally says that the more you know about the position of the particle, the less you know about the velocity and vice versa. It’s an artifact of the math.
You can either think of a photon as a massless particle which moves in a straight line (usually) at the speed of light (in a vacuum), or you can think of the wave interpretation of light, in which light is an electric and magnetic field which propagates outward at the speed of light. In the latter case, there is oscillation of the electromagnetic field in the directions that are perpendicular to the motion of the wave, and we often think of this as a sinusoidal wave because that’s one of the simplest waveforms to describe, but the light itself is not traveling in a sinusoidal path.
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