If photons have no mass, then how can they travel the speed of light?

[thomasxc]

im compfuzzled.

 

[CompuChip]

Short answer: Precisely because they have no mass

Long answer: By "no mass" you probably mean "no rest mass". Your question is almost a FAQ in these forums, I'm sure if you search you'll find loads of relevant threads (I recall in particular this recent one).
[edit]Also this and this thread may be useful.[/edit]

[edit (2)]I didn't know the word compfuzzled, but I like it. Does it actually exist?[/edit]

 

[thomasxc]

thnx...so ,because its moving, it has energy(kinetic energy)?

 

[CompuChip]

I don't think kinetic energy is the correct word, it's nothing like $\frac12 m v^2$ (of course, because there is a mass in there). The energy of a photon depends on its wave length. I added two more threads in an edit of my first post.

 

[thomasxc]

okay i saw that. so it has energy because e=mc2...?

 

[Fredrik]

Yes and no. Most of us prefer to write $E^2=\vec p^2c^2+m^2c^4$, where E is the energy, p is the momentum and m is the mass. Some people would write m₀ instead of m on the right-hand side, and define m (yes, define is the right word) by saying that this is equal to $m^2c^4$. They would call m the "mass" and m₀ the "rest mass".

 

[Hootenanny]

okay i saw that. so it has energy because e=mc2...?

$E=mc^2$ is often quoted as Einstein's energy equation, but it isn't really the full equation. The full relationship for the energy of a particle is given by:

$$E^2 = \left(m_0c^2\right)^2 + \left(pc\right)^2$$

Where $m_0$ is the invariant or "rest" mass of the particle and $p$ is it's momentum. The first term of the expression is sometimes called the "rest energy" of a particle, because that is the energy that the particle has as measured from a reference frame stationary relative to it.

Now, photons have zero mass and therefore the first term disappears, i.e. the photon has no "rest energy". We are now simply left with:

$$E = pc$$

So all the photon's energy is in fact due to the photon's motion, as you have said previously.

 

[thomasxc]

i realized that wasntthe entire equation. i just shortened it to make it easy. is that taboo around here?lol

 

[Hootenanny]

i realized that wasntthe entire equation. i just shortened it to make it easy. is that taboo around here?lol

No not at all, I just thought that the full equation clarified the explanation somewhat. In fact your equation $E=mc^2$ can be considered complete if one considers $m$ as relativistic mass rather than invariant mass.

 

[thomasxc]

okay...im only a high schooler who studies physics in their spare time, and ill be taking it as a classfor the first time next year. i hardly know calculus and all these equations.

 

[Kimmurial]

How to photons, that have no mass, travel in a wave?

Sorry if the question is a bit simple, I am not a physicist by profession. I seek to understand how a photon can move if it has 0 mass. Is it that photons acquire some sort of "mass" and thus can move (therefore fulfilling Newtons laws)? I understand that we don't know what "mass" really is but I am perplexed as to how a photon moves in spacetime. Any answers would be appreciated."Edit: How "do" photons, that have no mass, travel in a wave?

 

[Kimmurial]

$E=mc^2$ is often quoted as Einstein's energy equation, but it isn't really the full equation. The full relationship for the energy of a particle is given by:

$$E^2 = \left(m_0c^2\right)^2 + \left(pc\right)^2$$

Where $m_0$ is the invariant or "rest" mass of the particle and $p$ is it's momentum. The first term of the expression is sometimes called the "rest energy" of a particle, because that is the energy that the particle has as measured from a reference frame stationary relative to it.

Now, photons have zero mass and therefore the first term disappears, i.e. the photon has no "rest energy". We are now simply left with:

$$E = pc$$

So all the photon's energy is in fact due to the photon's motion, as you have said previously.

So photon movement is not bound to Newtons laws?

 

[Pengwuino]

So photon movement is not bound to Newtons laws?

No. Infact, because of how photons behave, we know Newton's Laws are incomplete/simply approximations.

 

[Feldoh]

okay...im only a high schooler who studies physics in their spare time, and ill be taking it as a classfor the first time next year. i hardly know calculus and all these equations.

That's fine. The take home point is that relativity tells us that objects without a rest mass (which is generally the mass you think of in Newtonian/classical physics) still have energy.

 

[tiny-tim]

Welcome to PF!

Hi Kimmurial! Welcome to PF!

… Is it that photons acquire some sort of "mass" and thus can move (therefore fulfilling Newtons laws)?

Newton's laws (and waves) require momentum, not mass (second law: force = rate of change of momentum).

Photons have energy and momentum (but no rest-mass).

Their momentum enables them to take part in collisions.

 

[Kimmurial]

Hi Kimmurial! Welcome to PF!


Newton's laws (and waves) require momentum, not mass (second law: force = rate of change of momentum).

Photons have energy and momentum (but no rest-mass).

Their momentum enables them to take part in collisions.

Thanks :)

So you are saying that a photons ability to travel at the speed of light is attributed to their momentum but Newtonian physics states p=mv.
If photons have no mass then isn't p=0?

 

[DaveC426913]

Thanks :)

So you are saying that a photons ability to travel at the speed of light is attributed to their momentum but Newtonian physics states p=mv.
If photons have no mass then isn't p=0?

Newton's laws are inadequate to apply to massless photons. That's what everyone's been saying.

 

[jhmar]

The root of the problem can be found in the closing line of The Nature of Mass by Max Jammer:

"Thus in spite of all the strenuous efforts of physicist and philosophers, the notion of mass, although fundamental in physics, is as we noted in the preface, still shrouded in mystery".

It follows that photon mass or any mathematical explanation using the term mass is an empirical explanation; it is the best known current explanation, but one that needs further work.

 

[tiny-tim]

I seek to understand how a photon can move if it has 0 mass. Is it that photons acquire some sort of "mass" and thus can move (therefore fulfilling Newtons laws)? I understand that we don't know what "mass" really is but I am perplexed as to how a photon moves in spacetime.

So you are saying that a photons ability to travel at the speed of light is attributed to their momentum but Newtonian physics states p=mv.
If photons have no mass then isn't p=0?

Newton's laws of collisions only require momentum.

Newton's laws of collisions are completely valid. They accord with reality.

Newtonian physics of space-time is wrong (or, if you prefer, inaccurate) … there is no point in trying to apply it to objects moving at or near the speed of light.

Newtonian physics of space-time states p=mv. That is wrong (but accurate enough for speeds nowhere near the speed of light). There is no point in asking how a photon can fulfil a law that is wrong: it can't and it doesn't!

The correct law for momentum is p = mv/√(1 - v²/c²) …

if m = 0, p doesn't have to be zero if v/√(1 - v²/c²) is infinite, ie if v = c.

 

[Rap]

Thanks :)

So you are saying that a photons ability to travel at the speed of light is attributed to their momentum but Newtonian physics states p=mv. If photons have no mass then isn't p=0?

Newtonian physics is not exactly correct. The momentum of a massive particle in special relativity is

$$p=\frac{mv}{\sqrt{1-v^2/c^2}}$$

if you make the velocity (v) get closer to c and keep the mass constant, then the term in the denominator gets smaller and smaller and the momentum gets larger and larger. If you know that the momentum when v=c is finite, then as v gets closer to c, you must have the mass get smaller and smaller. You can see that only a massless particle can travel at the speed of light without having infinite momentum. The problem is that when v=c you have for momentum 0/0 which is undefined. Newtonian mechanics is WAY wrong at or near the speed of light, so you cannot use Newtonian definitions to figure out what is happening at or near the speed of light.

 

[Mueiz]

im compfuzzled.

Why not ?

 

[accatagliato]

So you are saying that a photons ability to travel at the speed of light is attributed to their momentum but Newtonian physics states p=mv.
If photons have no mass then isn't p=0?

no, because what it's called the "photon momentum" is not connected with its velocity (mv), but with its wave-like behavor, in particularly with the wave vector k:
$$\vec{p}=\hbar \vec{k}$$
where k is defined:
$$\vec{k}=\frac{2\pi}{\lambda} \vec{n}$$
where n is the wave direction unit vector.

 

[JMS61]

Just out of curiosity, how do we know that a photon does not have any rest mass? Yes a rest mass is not necessary to study it's behavior, but does that mean that it does not have any rest mass?

 

[Rap]

Just out of curiosity, how do we know that a photon does not have any rest mass? Yes a rest mass is not necessary to study it's behavior, but does that mean that it does not have any rest mass?

If it does have rest mass then it must travel at less than c. That means that the "speed of light" is less than c, which means c should no longer be referred to as "the speed of light" but maybe just "Einstein's constant" or something. Its a valid question, tho, check out

http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html

 

[DaveC426913]

Just out of curiosity, how do we know that a photon does not have any rest mass?

Well, if it did, it would take an infinite amount of energy to accelerate it to c.

 

[JMS61]

Rap and Dave I understand the math behind what you are saying and the accelerator experiments that support that math. So at this point we are probably entering into the realm of theoretical physics and I not sure that this is the proper place or topic for that discussion. The problem before us is that faster than light travel is not possible according to today's physics unless we can find away for physics to explore the possibility of a photon having a rest mass. So may I ask this, "where do we discuss theoretical physics on this message board?"

 

[DaveC426913]

Rap and Dave I understand the math behind what you are saying and the accelerator experiments that support that math. So at this point we are probably entering into the realm of theoretical physics and I not sure that this is the proper place or topic for that discussion. The problem before us is that faster than light travel is not possible according to today's physics unless we can find away for physics to explore the possibility of a photon having a rest mass. So may I ask this, "where do we discuss theoretical physics on this message board?"

This is all theoretical physics.

I think what you're asking is "where do we discuss speculative physics on this message board?"

To which the answer is: ''on some other board".



PF is devoted to established, mainstream physics.

 

[JMS61]

Thank you Dave, your input is appreciated.

 

[Kimmurial]

Thanks guys. Insightful responses.

 

[torquil]

This is all theoretical physics.

I think what you're asking is "where do we discuss speculative physics on this message board?"

To which the answer is: ''on some other board".

Although, the "Beyond the Standard Model" and "Cosmology" sections on PF are quite devoted to speculative physics. As are large parts of the theoretical physics academic community

 

[Phrak]

This is all theoretical physics.

I think what you're asking is "where do we discuss speculative physics on this message board?"

To which the answer is: ''on some other board".



PF is devoted to established, mainstream physics.

Well, that sucks. But then again, it means I can both giveth and receiveth all the standard answers about what doesn't really work. I've gotten a lot of standard miles closing one eye, squinting through the other, and relaying what I see.

 

[tiny-tim]

Hi Phrak!

I've gotten a lot of standard miles closing one eye, squinting through the other, and relaying what I see.

Technically, you can't squint with one eye shut …

squinting is when the two eyes point in different directions … see http://en.wikipedia.org/wiki/Strabismus"

 

[Phrak]

Hi Phrak!


Technically, you can't squint with one eye shut …

squinting is when the two eyes point in different directions … see http://en.wikipedia.org/wiki/Strabismus"

/ Squints with one eye at Tiny across the pond. /

 

[A. Neumaier]

Just out of curiosity, how do we know that a photon does not have any rest mass? Yes a rest mass is not necessary to study it's behavior, but does that mean that it does not have any rest mass?

Astronomical observations only pose an upper bound of currently 2 10^{-25} eV (approx. 3.6 10^{-61} kg) on the photon mass, but all known experimental data seem to be in agreement with the assumption that the mass of the photon is exactly zero, as in the standard model.

See the entry ''Is the photon necessarily massless?'' in Chapter B2 of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html#photon