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As I understand it, there are a few different massless particles. Is there anything that differentiates these from each other besides frequency/wavelength?

My definition of speed would be the time it takes to get from one place to another. If we say nothing moves faster than light, we therefore mean that light will go from here to there (the Sun to the Earth for instance) in less time than any other particle.

When thinking about speed related to wavelength, I picture two people. The first person is running on a flat surface, the second is running up hills, and there is a set finish line. If both people run at the same speed, at the end of a certain time frame both will have run the same distance, but the person running on a flat surface will be closer to the finish line. In a race from the Sun to the Earth, the person (massless particle) with the flatter path (smaller wavelength) would arrive first. Is this a misunderstanding on my part?

Is the reason we use light as the limit that light has the shortest wavelength of the massless particles? If so, is it possible we could discover a massless particle with a shorter wavelength that would be faster? If not, what differentiates these massless particles?

Qmechanic
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Our standard particle physics model contains three massless particles:

  1. the photon, which is possesses spin 1, and which is the mediator of the electromagnetic interaction,
  2. the gluon, which also possesses spin 1, and which is the mediator of the strong interaction, and
  3. the graviton, which possesses spin 2, and which is the mediator of the gravitational interaction.

As each of these particles mediates a completely different force, it should be clear that they differ a lot -- "their frequency" is not their key difference. As they are all massless, they all travel with the speed of light and it is impossible to slow them down (in vacuum).

NotMe
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There is some excellent discussion already about how photons do not interact with the component of the Higgs Field whose excitations are Higgs Bosons.

Gluons, the other significant massless particle, do not interact with the higgs field directly. However gluons are actually responsible for most of the mass of particles confined by the strong force via their kinetic energy (meaning most of the ordinary mass in the universe is actually the strongly confined kinetic energy of massless gluons).

So in short, under current theory, mass arises either through interaction with the higgs boson component of the higgs field, or through some constrained amount of pure momentum via the strong force.

Frequency and wavelength in ordinary electromagnetic theory plays no part in particle velocity, it is always constant (e.g. the speed of light). In the case of particles that obey the strong force, they do increase their mass as their velocity increases as dictacted by special relativity. This can partially be described as a situation where relativistic effects cause the particle to contract in the direction of travel thereby decreasing the wavelength of the gluons internal to the particle (or alternatively increasing the frequency of the gluons). This compression can be thought of being partially responsible for the increase in particle mass (example being a proton being accelerated in a particle collider).

So it really is a question of whether you are talking about confined massless particles or free massless particles as to whether there is some relationship between velocity and frequency.