# Massless particles

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Correct me if i'm wrong but i have always understood the reason why we cannot reach the speed of light is because our energy is turned to mass to we become infinately heavy. If this is true then why cannot massless particals such as neutrinos reach the speed of light. Also how can massless particles be propeled as i thought kinetic energy required mass??

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neutrinos have a mass, though very small.

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Neutrinos have a mass.

Massless particles such as a photon can travel at c (the speed of light) but not faster.

Classically kinetic energy requires mass show in the equation

$KE = \frac{1}{2}mv^2$

however massless particles are not a classical thing and so classical equations such as this do not apply.

We use non-classical equations for the energy of a massless particle such as

$E = hf$

or

$E^2 = (pc)^2 + (m_0 c^2)^2$

which is the same as

$E^2 = p^2 c^2 + m_0^2 c^4$

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Correct me if i'm wrong but i have always understood the reason why we cannot reach the speed of light is because our energy is turned to mass to we become infinately heavy. If this is true then why cannot massless particals such as neutrinos reach the speed of light. Also how can massless particles be propeled as i thought kinetic energy required mass??

You need to say which definition of mass you are using. Using the standard definition - rest mass - your mass doesn't change. Neutrinos aren't massless - they oscillate between types and have mass. Mass energy and kinetic energy are separate. You can have either, you can have both.

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Neutrinos are not massless, so they can not travel at the speed of light.

Photons can travel at the speed of light, and other massless particles can too, but if anything has a tiny bit of mass, even something as small as a neutrino, its mass will grow infinate by the time it reaches the speed of light.

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Neutrinos are not massless' date=' so they can not travel at the speed of light.

Photons can travel at the speed of light, and other massless particles can too, but if anything has a tiny bit of mass, even something as small as a neutrino, its mass will grow infinate by the time it reaches the speed of light.[/quote']

Again, you have to define what you mean. If the mass referred to is the rest mass, which is invariant under a Lorentz transformation, it doesn't change with speed. And that is the usual use of mass. "Inertial mass" which is frame-dependent is more or less obsolete terminology.

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I've got some questions on neutrinos I've read that neutrinos are always left handed (or right handed forgot...) and the explanation is that neutrinos always travel in light speed so nothing can pass it and see it right handed

sorry if my statement is confusing but have anyone read about it?

thanks

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That is outdated. Since neutrinos have mass they must also have a right-handed component. This is for exactly the reason you suggest. Whether a particle is 'left' or 'right' handed is a statement about whether its spin vector is aligned ('right-handed') or in the opposite direction ('left-handed') with respect the the direction of motion. It a particle has mass, one can move to a frame of reference where the particle is going in the opposite direction (with respect to the observer, ie. the observer overtakes the particle), and if the direction changes, then the handedness changes.

So there is no denying that right handed neutrinos exist. The controversy is whether or not they are any different from the left handed ones. If the neutino is a Majorana particle, then the right handed component is the same as the left handed one.

(Often there is some confusion of notation in this regard. The SU(2) symmetry which gives rise to the weak interaction, if unbroken, would allow its bosons to act only on left-handed states. So often people say 'left-handed' to mean particles with an SU(2) coupling. But since the SU(2) symmetry is broken in nature, one can have 'right-handed' particles (in the sense of spin) which have a coupling to the SU(2) gauge bosons. When people talk about 'right-handed nuetrinos' they usually mean a neutrino with no SU(2) coupling. Since there is no symmetry (not even a broken one) to keep its mass small, it is naturally extremely heavy.)

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