"No mass electrons" What the heck is that?

http://phys.org/news/2016-02-graphene-superconductiveelectrons-mass-resistance.html#nRlv

Dirac-cone? How can electrons even ACT like they have no mass? What is going on here?

Originally posted by sonhouse
http://phys.org/news/2016-02-graphene-superconductiveelectrons-mass-resistance.html#nRlv

Dirac-cone? How can electrons even ACT like they have no mass? What is going on here?

Don't read too much into it. The electrons have mass, they just have a dispersion relation which is similar to what you would get for a free particle (which an electron in graphene is not) with no mass. The form of the dispersion relation is a cone, hence "Dirac cone."

Originally posted by KazetNagorra
Don't read too much into it. The electrons have mass, they just have a dispersion relation which is similar to what you would get for a free particle (which an electron in graphene is not) with no mass. The form of the dispersion relation is a cone, hence "Dirac cone."

Ok, so what is a 'dispersion relation'?

Originally posted by sonhouse
http://phys.org/news/2016-02-graphene-superconductiveelectrons-mass-resistance.html#nRlv

Dirac-cone? How can electrons even ACT like they have no mass? What is going on here?

Someone once suggested that massless particles have to travel at the speed of light. Electrons are a little slower than c because they do have mass, but very little.

How slow can a massless particle travel? How slow can an electron travel?

Originally posted by Metal Brain
Someone once suggested that massless particles have to travel at the speed of light. Electrons are a little slower than c because they do have mass, but very little.

How slow can a massless particle travel? How slow can an electron travel?

A massless particle can be at zero velocity in the right medium, an infinite refractive index material and it happens. An electron can be trapped to not move at all also since it is controlled by electric fields, if you shape the field right it will fit in an energy valley and not move away from it unless energy is added overcoming the energy valley it currently resides in.

Electrons CAN be a bit slower than c but only with the addition of a lot of energy. It cannot go exactly at c so photons will always outrun electrons in free space.

Both follow the curvature of space, in short, gravity fields, however. Electrons just get accelerated or decelerated by electric fields and deflected by magnetic fields which attempt to force said electron in a curved path and if the electron is going slowly enough
the magnetic field lines can cause said electron to spiral around the field pretty much forever, I think anyway, can't testify to that since it might also give off Cherenkov radiation from the spinning path it takes, if so it will lose energy and I don't know exactly what happens in that case.

Originally posted by sonhouse
A massless particle can be at zero velocity in the right medium, an infinite refractive index material and it happens. An electron can be trapped to not move at all also since it is controlled by electric fields, if you shape the field right it will fit in an energy valley and not move away from it unless energy is added overcoming the energy valley it curr ...[text shortened]... ing path it takes, if so it will lose energy and I don't know exactly what happens in that case.

"A massless particle can be at zero velocity in the right medium, an infinite refractive index material and it happens"

Here is an excerpt from the link below:
In vacuum, light travels at 300,000 kilometers/second. If it hits a refracting medium like water or glass, light is bent and travels slower.

Is it really traveling slower or just following a longer path within the medium?

http://www.zmescience.com/research/light-frequencies-travel-infinitely-fast-zero-refraction-index-041324/

Originally posted by Metal Brain
Is it really traveling slower or just following a longer path within the medium?/

It is a quantum particle, so its velocity should not be confused with that of a Newtonian system, but yes, it really travels slower.

Originally posted by sonhouse
Ok, so what is a 'dispersion relation'?

It's a relation between energy (or frequency) and momentum.

Originally posted by Metal Brain
Someone once suggested that massless particles have to travel at the speed of light. Electrons are a little slower than c because they do have mass, but very little.

How slow can a massless particle travel? How slow can an electron travel?

Massless particles will always travel at the speed of light in vacuum.

The lower limit for velocity is set by zero-point motion although it depends on what you define as "velocity" in this limit.

Originally posted by KazetNagorra
Massless particles will always travel at the speed of light in vacuum.

The lower limit for velocity is set by zero-point motion although it depends on what you define as "velocity" in this limit.

In a high refractive index, doesn't light going through it change wavelengths? Like get redder or something?

Originally posted by sonhouse
In a high refractive index, doesn't light going through it change wavelengths? Like get redder or something?

The speed of a wave is the frequency times the wavelength. Since, for a ray of light passing to a more optically dense material, the speed has dropped and the frequency is unchanged the wavelength has to have decreased as well.

The electrons behave as if they are massless because the part of the dispersion relation where they exhibit this behaviour locally looks like the dispersion relation for a massless electron, away from this region the electrons behave as if they are massive. I'm guessing on energy grounds that the "effective speed of light" - in other words the constant c in the effective Dirac equation - is much lower than the speed of light in a vacuum.

Originally posted by KazetNagorra
Massless particles will always travel at the speed of light in vacuum.

The lower limit for velocity is set by zero-point motion although it depends on what you define as "velocity" in this limit.

Velocity will always depend on the reference frame picked.

Everything not travelling at the speed of light is stationary for some reference frames
and travelling at near light speed in others.

So the answer to how fast/slow can electrons go, they can go any speed [S] from
0 <= S < C

Although an electron with zero velocity relative to you is going to be really really uncertain
about where it actually is... And the moment you find it, it will no longer be stationary relative
to you.

Because this happens at the fun intersection of SR and QM.