Why Are Photons Massless in Quantum Field Theory?

[The_Thinker]

how come light does not have mass, we know e=mc^2, so what gives; why is it that light doesn't have mass or rather what is the explanation for light not having mass?

 

[dextercioby]

how come light does not have mass, we know e=mc^2, so what gives; why is it that light doesn't have mass or rather what is the explanation for light not having mass?

Physics does rather poorly into explaining WHY Nature behaves the way it does...In this case,it cannot tell WHY the photon is massless...Experiments indicate that they are massless...Theories of light have been constructed on this assumption.

But the question is unanswered...

Daniel.

 

[Chronos]

I realize this answer is not totally satisfying, but $$E^2 = m^2c^4 + p^2c^2$$. What it shows is that a 'particle' can have energy without a rest mass, and rest mass is not required under the rules of relativity. A photon cannot be at rest under relativity, nor can any other massless 'particle'. Massless 'particles' are forbidden to travel at any velocity other than 'c'. The term 'particle' often gets confusing. Physicists use it to represent an entity that behaves like an object until you torture it. It then becomes a waveform. Torture the waveform, and it reverts back to a particle. They don't call it quantum weirdness for no reason.

 

[da_willem]

As Chronos pointed out: the argument a photon has energy and via E=mc^2 must have mass as well is invalid, because in this context E=mc^2 is invalid! This only applies in the 'rest frame' of an object, where the only contribution to the energy is from the rest mass m: E=mc^2. When something moves relative to you you also have to take into acount it's kinetic energy. The general relation is:

$$E^2=m^2c^2+p^2c^2$$

With p the particles momentum. This indeed comes down to E=mc^2 in the rest frame of the particle weher it's momentum p is zero.

(In case you have had some quantum mechanics you know the energy and momentum of a photon are hv and hv/c with v the photons frequency. Inserting this in the above relation yields m=0. The mass of the photon is zero.)

 

[The_Thinker]

ahh... so basically, no one knows why photons don't have mass, they just don't... ok...

by the way, u mentioned some experiments that they did to determine it's mass, what were they, could u name them or give me a link to an article abt them,

but thanks for replying guyz...

 

[marlon]

Physics does rather poorly into explaining WHY Nature behaves the way it does..

This is a classical mistake in the way we need to look at physics. It is NOT the intention of physics to tell us why nature does what she does. Physics only describes nature it does NOT explain the behaiviour of nature. Physics does NOT teel us why there is gravity or why nature incorporated gravity (we only know massive objects interact via gravity, but we don't know why). Physics does not tell us why on the atomic scale, nature is probabilistic in "nature"...

So physics does not do a poor job in explaining why nature behaves the way it does. This is fundamentally wrong for the above reasons...

regards
marlon

 

[The_Thinker]

umm.. by the way marlon what exactly does ur signature mean, I've been trying to figure that out for some time now without much success... ;)

 

[marlon]

When the accursed have been confounded (Jesu)
And given over to the bitter flames.
Call me among the blessed...

marlon

it is a Latin text coming from the Requiem-mass

 

[Crosson]

Physics can give us the answer to "why?", it is a mistake to believe this is not its purpose. The problem is that each new physical theory answers old questions and raises new ones, so there are always more "why?"s.

Look at the great "why?"s that physics has solved in the past. "Why do the heavens move as they do?" got the answer "by the same force that gives you weight". "What is vision, what is light?" was settled as "Light is electromagnetic radiation".

Don't you see? One day the question "why is the photon massless?" will be answered in terms of a new theory that explains many things but also raises new questions.

 

[JesseM]

It seems to me that one reason it wouldn't make sense for photons to have nonzero rest mass is because the equation for relativistic momentum is $$mv/\sqrt{1 - v^2 / c^2}$$, and if m is some nonzero constant, then as v approaches c, the momentum will approach infinity. On the other hand, this equation has no well-defined limit as v approaches c if you also let m approach 0, so although this equation can't tell you the momentum of a photon, at least it's not inconsisent with this equation for a particle with zero rest mass moving at the speed of light to have finite momentum, while it would seem to be inconsistent if the particle was defined to have nonzero rest mass (of course one could just respond that the equation doesn't apply to photons, but it would seem inelegant if there was a well-defined limit for some property of particles approaching c yet photons didn't have that property).

 

[Gecko]

the E^2=m^2c^2+p^2c^2 is not valid because mass is used to find momentum (p) so it still all cancels out to 0.

edit:i didnt see the above answer, i think we posted around the same time.

 

[pmb_phy]

how come light does not have mass, we know e=mc^2, so what gives; why is it that light doesn't have mass or rather what is the explanation for light not having mass?

The answer to your question lies in the definition of the "m" in that expression. The definition of "m" is a much discussed topic in most physics forums, this one being no diffferent.

One can define the "m" of a particle as the "m" in p = mv where p is the particle's 3-momentum and v is the particle's 3-velocity. The inertial energy, E, of a particle is defined as the sum of the particle's rest energy, E₀, and the particle's kinetic energy, K. I.e. E = K + E₀. It can then be shown that E = mc². However, from the definition above, i.e. p = mv, it also follows that anything with momentum has a non-zero "m." If the particle is a tardyon (i.e. a particle that always travels at a speed less than the speed of light) then it can be shown that m is a function of speed, i.e. m = m(v). Let m₀ = m(0). Then it can be shown that

$$m = \gamma m_0 = \frac{m_0}{\sqrt{1-v^2/c^2}}$$

and thus

$$E = mc^2 = \gamma m_0c^2$$

It can easily be shown that

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

Since the magnitude of a photon's momentum is related to its energy as E = pc it follows that m₀ = 0.

Another way to define "m" is to assume the particle is a tardyon and assume that it's momentum can be expressed as p = M(v)v. Then we define "m" as m = M(0). Now we have to write

$$E = \gamma mc^2$$

and

$$E^2 - (pc)^2 = m^2c^2$$

In the particle's rest frame

$$E = mc^2$$

As for me? I don't like this whole "photon mass = zero" thingy. The relationship between E, p and for m₀ is derived on the basis that the particle is a tardyon. One then extrapolates for a luxon (particle that always travels at the speed of light) by letting E = pc, which holds for all luxons, in the expression

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

it follows that m₀ = 0.


Pete

 

[pmb_phy]

This is a classical mistake in the way we need to look at physics. It is NOT the intention of physics to tell us why nature does what she does.

I have to disagree on that point.

Recall the Foreword, written by Alan Lightman, from The Inflationary Universe, by Alan H. Guth. From page ix

...In other words, the nature of the questions changed. The questions became more fundamental. "Why?" was added to the "What?" and "How?" and "Where?". Alan Guth was one of the young pioneers of the new cosmology, asking the Whys, and his Inflationary Universe theory provided many answers.

Pete

 

[marlon]

Look at the great "why?"s that physics has solved in the past. "Why do the heavens move as they do?" got the answer "by the same force that gives you weight".

This is wrong. Indeed, physics describes the motion of heavens and the concept of "the same force that gives you weight" is necessary for the description. But this is not the point. The why at most fundamental level (which we are talking about, i mean like the photonmass) are NOT answered by physics. Can you tell me why gravity is mg, can you tell me where gravity comes from (and don't say from massive objects, because then i'll just ask why it comes from massive objects?).

Why do we need the probability-appraoch for QM, why is that any different then classical phenomena ?

You see, we can describe using physics but we cannot EXPLAIN the choices
of nature


regards
marlon

as to pmp : why you disagree ? the text you posted doesn't say anything in my eyes...

 

[pmb_phy]

as to pmp : why you disagree ? the text you posted doesn't say anything in my eyes...

Perhaps not in your eyes, but in mine.

You suggest that "It is NOT the intention of physics to tell us why nature does what she does."

In the first place the person did not ask why nature does what she does. They asked why light has no mass if E = mc^2. There is a legitimate answer to that question. The questioner knew that light has energy. They also know of E = mc^2. This suggested to the questioner that for all E there is a non-zero m. One answer to the question lied not in explaining why light has zero rest mass and why he can't use E = mc^2 for light. Howevever nobody asked the questioner what he meant by "m." I simply addressed that point. So I was able to say "Why" light has no mass if E = mc^2. The answer liked in clarification and definition etc.

In the second place one can always ask "Why?" in physics. We can get answers to those kind of questions. What we can't get answers to are those pertaining to postulates. However if we never ask ourselves "Why?" then we will never get an answer to our question.

The article I quoted addressed the second point. Guth started asking Why? regarding certain aspects of the universe are what they are. He got an answer - the answer was the inflationary model of the universe.

That is why I disagreed. However I assumed you disagreed with this philosophy. Is that correct?

Pete

 

[marlon]

That is why I disagreed. However I assumed you disagreed with this philosophy. Is that correct?

Pete

yes indeed i do...

marlon

 

[Newton]

some ppl here have chatted about how physics does not answer WHY the photon does not have mass. this is only half right.
it is true that physics will not be able to tell us why the most FUNDAMENTAL laws are as they are, but things that occur as a CONSEQUENCE of them are considered to be explanations for they WHY of this or that.
In the case of the photon, there is a DEEPER description of nature than that provided by Einstein's mass, energy equation which does provide the answer to this WHY.
In quantum field theory, underlies symmetries dictate the allowed mass of the gfauge bosons of the interacting theory. In the case of quantum electrodynamics; gauge invariane demands that the photon be massless!

now, that tells us why. you may say "why is electromagnetism a quantum field theory, etc etc". but that is a DEEPER question. at this point we do not have an answer to that.

 

[marlon]

In the case of quantum electrodynamics; gauge invariane demands that the photon be massless!

This is wrong. Photons are massless because they do not interact with the Higgs-field. Why ?, Well, because they exhibit the U(1)-symmetry which is the local symmetry of the EM-interactions and which is the general symmetry of the QED (or QCD)-vacuum. This has nothing to do with gauge-invariance. It is quite the opposite, as a matter of fact, gauge-symmetries are broken in the spontaneous breaking of symmetry.

This however is indeed an explanation in our physical terms as to why the photon has no mass. But, it does not tell us the real reason as to why nature decided that photons don't have mass. We observed that they don't and then we built all field theories and adapted them so they would fit this observation.

you may say "why is electromagnetism a quantum field theory, etc etc". but that is a DEEPER question. at this point we do not have an answer to that.

ha, that's a bit funny to be honest because we CAN answer that very clearly. Just read my journal (the "why fields"-entry) and you will find many explanations for that.

regards
marlon