# speed of light ?

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#### ramparts

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And the Wiki article makes that somewhat clear, I think. The last sentence is the kicker: the question of neutrino masses can't be decided (right now) based on our measurements of neutrino speeds because (apparently) the measured speed of neutrinos is consistent with the speed of light - meaning it could be the speed of light, or it could be less than it, within experimental error. The relation to the neutrino mass is that if neutrinos are massless (which we're now pretty certain they're not) then they'd travel at c, but if they're massive then they can't travel at c.

C

#### csmyth3025

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ramparts":1dfygtzf said:
And the Wiki article makes that somewhat clear, I think. The last sentence is the kicker: the question of neutrino masses can't be decided (right now) based on our measurements of neutrino speeds because (apparently) the measured speed of neutrinos is consistent with the speed of light - meaning it could be the speed of light, or it could be less than it, within experimental error. The relation to the neutrino mass is that if neutrinos are massless (which we're now pretty certain they're not) then they'd travel at c, but if they're massive then they can't travel at c.

Just to be clear on this question, I think that when photons or neutrinos are described as having mass, the reference is usually interpreted by laymen such as myself as meaning rest mass as opposed to relativistic mass. This distinction is somewhat confusing to me but I rely on explanations like the following (exerpted from the Wikipedia article on mass-energy equivalence):

The concept of mass–energy equivalence connects the concepts of conservation of mass and conservation of energy, which continue to hold separately. The theory of relativity allows particles which have rest mass to be converted to other forms of mass which require motion, such as kinetic energy, heat, or light. However, the mass remains. Kinetic energy or light can also be converted to new kinds of particles which have rest mass, but again the energy remains. Both the total mass and the total energy inside a totally closed system remain constant over time, as seen by any single observer in a given inertial frame. In other words, energy cannot be created or destroyed, and energy, in all of its forms, has mass. Mass also cannot be created or destroyed, and in all of its forms, has energy. According to the theory of relativity, mass and energy as commonly understood, are two names for the same thing, and neither one is changed or transformed into the other. Rather, neither one appears without the other. Rather than mass being changed into energy, the view of relativity is that rest mass has been changed to a more mobile form of mass, but remains mass. In this process, neither the amount of mass nor the amount of energy changes. Thus, if energy changes type and leaves a system, it simply takes its mass with it. If either mass or energy disappears from a system, it will always be found that both have simply moved off to another place.

To me, this passage says that if an electron falls from a more energetic orbital state (in an atom) to a less energetic state and emits a photon in the process, the mass of the electron will be diminished ever so slightly by an amount represented by the energy content of the photon (in accordance with the relationship E=mc^2). Likewise, the photon will have that same amount of mass - due to its energy content - in accordance with the same relationship.

This same Wikipedia article goes on to describe what is meant by "massless" particles (photons, for instance):

If you run away from a photon in the direction it travels, having it chase you, when the photon catches up to you the photon will be seen as having less energy. The faster you were traveling when it catches you, the less energy it will have. As you approach the speed of light, the photon looks redder and redder, by Doppler shift (the Doppler shift is the relativistic formula), and the energy of a very long-wavelength photon approaches zero. This is why a photon is massless; this means that the rest mass of a photon is zero.

Can I rely on these narrative explanations to get a mental picture (from a layman's perspective) of how light or other forms of energy can both have mass and be "massless" at the same time?

Chris

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