1. ## Question about photons

Recently , I have been wondering if photons have rest mass . I ignorantly know that we can calculate a particles' rest mass by using m=E/c*2 , but if a particle has rest mass >0 , it will need an infinite amount of energy for this particle to approach to 299792458 m/s . My question was if photons have rest mass>0 , how it can travel at the speed of light.
My cousin who 's studying quantum mechanics gave me an answer . He said the reason why light have mass is because Einstein defined light is a stream of particle, which is photon and particle is matter, so light have mass. The reason why we don't feel that light have mass is because the mass of light is really small . Besides , he told me that we can use E=hf to calculate the energy that photon carry.For example, the red light frequency is 400nm, then use E=hf, the energy of red light is 2.6504*10^-40, then (2.6504*10-40)/(3*10^8)^2=2.94*10^-57, then the mass of photon is 2.94*10^...-57kg in 400nm light. 2.94*10^-57 is very close to 0,but it is >0 .
After our conversation , I became confused and start to wonder if E=mc*2 can REALLY be applied to calculate photon's mass . or it's better to use E=nhv? or is there any other method? Pardon for my ignorance .  Reply With Quote

2. ## Light speed is constant in any coordinate system, so you need just include the momentum to the full energy:
E^2 = (pc)^2 + m^2c^4.

The photon is massless. For m=0 we have E= pc, where p=hk (k is wave vector k=2pi/lambda and h is reduced Planck constant). In this case E= pc = hf and no problem with m=0.

Clear skies,
Valentin  Reply With Quote

3. ## The Following 2 Users Say Thank You to astroval For This Useful Post:

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4. ## so the photon which einstein has defined has an invariant mass of 0 ?  Reply With Quote

5. ## Calling a photon a particle is not quite correct. A photon is a quantum of light, the smallest indivisible amount possible. You can have 1 photon, or 2 photons, but not 0.5 or 1.5. That doesn't mean they are particles that have mass, per say. Listen to Valentin.   Reply With Quote

6. ## The rest mass of photon = 0. Invariant mass of photon also = 0
m^2c^4 = E^2 - (pc)^2 = 0

Einsteins theory says that even pure energy has to behave in some ways like mass. Therefore light could be bend by the gravitation force of the Sun.  Reply With Quote

7. ##  Originally Posted by throneoo Recently , I have been wondering if photons have rest mass . I ignorantly know that we can calculate a particles' rest mass by using m=E/c*2 , but if a particle has rest mass >0 , it will need an infinite amount of energy for this particle to approach to 299792458 m/s . My question was if photons have rest mass>0 , how it can travel at the speed of light.
My cousin who 's studying quantum mechanics gave me an answer . He said the reason why light have mass is because Einstein defined light is a stream of particle, which is photon and particle is matter, so light have mass. The reason why we don't feel that light have mass is because the mass of light is really small . Besides , he told me that we can use E=hf to calculate the energy that photon carry.For example, the red light frequency is 400nm, then use E=hf, the energy of red light is 2.6504*10^-40, then (2.6504*10-40)/(3*10^8)^2=2.94*10^-57, then the mass of photon is 2.94*10^...-57kg in 400nm light. 2.94*10^-57 is very close to 0,but it is >0 .
After our conversation , I became confused and start to wonder if E=mc*2 can REALLY be applied to calculate photon's mass . or it's better to use E=nhv? or is there any other method? Pardon for my ignorance .

Given the equation, even if the mass of light was really small, it would still need an infinite amount of energy to reach c! Even the mass values he says eg "then the mass of photon is 2.94*10^...-57kg in 400nm light" would still require an infinite amount of energy to reach c.

'really small' is a matter of comparison, not a measurement in a useful sense.

Last edited by Arny Moots; 10-29-2010 at 10:14 AM.  Reply With Quote

8. ## the momentum of photon is p=E/c.........then how is the momentum defined ? Does it have anything to do with the classical definition of momentum ?  Reply With Quote

9. ##  Originally Posted by throneoo the momentum of photon is p=E/c.........then how is the momentum defined ? Does it have anything to do with the classical definition of momentum ?

I will try - but it not so simple.

F = ma, right? Also, F = m(dv/dt), right? Therefore, F = d(mv)/dt = dp/dt, right?

F= dp/dt â it is original Newton law.

dp=Fdt
this is allow us find p for electromagnetic waves.

In electromagnetic waves we have two forces electric and magnetic.

For electric force F=qE where q is electric charge and E is electric field

For magnetic force F=q[v x B] where v is velocity of the particle with electric charge and B is magnetic field. The magnetic Lorentz force is always perpendicular to both the velocity of the particle and the magnetic field that created it

Let see now only electromagnetic waves in vacuum. E and B are perpendicular each other and both perpendicular to wave (Poynting vector). Because magnetic force perpendicular velocity â they not create any work (dW= Fds). So, the work (and energy e) in the wave is proportional only amplitude of electrical force (e~E).

Momentum is created only magnetic field (in average electric force is 0), so momentum is proportional only amplitude of magnetic field B (p~B). Relation between amplitude E and amplitude B
is E=cB and as result energy e is equal to pc (e=pc)

So p=e/c

I did maximum for me now. Hope it will help.  Reply With Quote

11. ## Photons have ZERO mass. They are not particles, per se. They are corpuscles of light. They carry the electromagnetic force but have no mass, whatsoever.  Reply With Quote

12. ## thank you so much for explaining that....now that at least I know the calculation of the momentum of light is completely different and independent from the classic equation p=mv  Reply With Quote

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