zero rest mass?

[foofighter]

how is it that photons, to have mass, are bound to constant movement, and if they stop completely, they have no mass. isn't mass a property of everything that exists, whether it is in the form of energy or matter. if something has no mass then it doesn't exist. someone help me out here please lol

[swansont]

You are using mass and rest mass interchangeably, without having defined them. Rest mass is not a property of everything that exists. You appear to be defining mass to be E/c², which is different than rest mass.

[foofighter]

thx for the clearup - is there a way to explain the difference in a nutshell? thx

[timo]

A moving relativistic particle has momentum [math] \vec p [/math] and energy [math]E[/math]. The energy modulo c² (speed of light squared) is sometimes called "relativistic mass" [math] m_{\gamma} [/math], more precisely [math] m_{\gamma} = E/c^2 [/math] (note that this is the same as [math] E = m_{\gamma}c^2 [/math]).

 

Momentum and energy are related to each other via [math] E(\vec p) = \sqrt{|\vec p|^2 c^2 + m_0^2 c^4}[/math], where [math] m_0 [/math] is a constant that depends on the particle type. [math]m_0[/math] is called the "invariant mass" or "rest mass". In constrast to the relativistic mass which depends on the particle's momentum (remember that [math] m_{\gamma} = \sqrt{| \vec p | + m_0^2 c^2}/c [/math]), the rest mass is a property of the particle type (meaning e.g. all electrons have the same mass). The name rest mass can be understood from taking the special case in which the particle is at rest (meaning [math] \vec p =0 [/math]). In this case [math] E = \sqrt{0+ m_0^2 c^4} = m_0 c^2 [/math] meaning that for the frame at which the particle is at rest [math] m_{\gamma} = m_0 [/math].

 

In short:

- Relativistic mass is another word for energy.

- Invariant mass is a particle-type dependent term in the equation that relates energy and momentum (dispersion relation or energy-momentum relation).

- For particles at rest, invariant mass and relativistic mass are equal. Otherwise, relativistic mass is greater than invariant mass.

- When only speaking of "mass" without stating whether it's the invariant or the relativistic mass, you need to determine which one is meant from the context. If it's a particle property (someone saying "protons have a mass of ...") then it's the invariant mass.

 

EDIT: And when Swansont said "rest mass" is not a property of everything that exists he (hopefully) meant that it can be zero for some things (like the photons).

[foofighter]

thanks that helped clarify things. so the what is taken care. now the question is why, what about the nature of photons causes them to have no mass when still, whereas when they are moving they have mass. what happens when they stop? do they stop existing? if they don't stop existing, then how can we observe them if they have no rest mass/energy? i know we can because they recently stopped light dead in its tracks by cooling it down. thx

[foodchain]

Hey, on a side note if light had mass it would become a pretty destructive force maybe?

[swansont]

i know we can because they recently stopped light dead in its tracks by cooling it down.

 

If you read the details you'll see that that's not actually what they did.

[foofighter]

so what did they do exactly?

[swansont]

The light was absorbed and the energy stored in atoms. But when they released the energy, it retained the coherence.