# light has inertia?

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Light photons inertia? what is the relation of the three things?

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Well, they are all concepts in physics.

They are all words to describe concepts.

They all have vowels... oh, and also consonants.

Did you want to ask a more specific question, perhaps?

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Photons make light.

Neither of them have inertia.

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Inertia seems to be better applied to objects with mass. Light does have momentum.

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Inertia seems to be better applied to objects with mass. Light does have momentum.

I meant to ask this question last year in physics, but the prof. moved on too quickly. How can a photon have momentum without mass?

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I meant to ask this question last year in physics, but the prof. moved on too quickly. How can a photon have momentum without mass?

Because it moves really fast!

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No, that's a good question. I know it's massless by definition, so one would presume that since momentum is mass times velocity, the velocity part is irrelevant since it's being multiplied by zero.

So, what is it that we're missing?

I see that for a photon momentum is calculated a bit differently, with Plancks constant divided by wavelength, but a simple "new way to say it mathematically" doesn't help me grasp the "why" of it.

Does it have something to do with the wave nature of light, and the energy differences at the wave crests? I really don't know, I'm just shooting in the dark here.

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If you want an equation, a good one is $E^2 = p^2c^2 + m^2c^4$. A result of that is that if something has energy, it must have either momentum or mass or both. Given that a photon is massless, this equation requires that it have momentum $p=E/c$

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A photons momentum is defined by it's wavelength.

P=mv is a classical approximation.

Since everything is a wave now the only 'true' way to find momentum is p = h/(wavelength)

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this one is a really gud question actually we have assumed the rest mass of the photon is zero so wen its at rest the momentum is zero but its acclerated we don't know wat happens to it...........

like we donna wether a photon is a particle or a wave so v decided its both of them the momentum of the photon is not the p=mv but a lot different its defined in terms of itz wave length p=h/l l= wavelength of the photon

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If you want an equation, a good one is $E^2 = p^2c^2 + m^2c^4$. A result of that is that if something has energy, it must have either momentum or mass or both. Given that a photon is massless, this equation requires that it have momentum $p=E/c$

Thanks. I recognize that as the expanded form of E=mc^2, but this assertion that "anything with energy must have momentum or mass or both" isn't very satisfying to my numbskull brain. I get the energy/mass relationship, but not the energy/momentum one.

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Because of p = h/wavelength

To have wavelength you have to have energy, so if you have wavelength, you have momentum!

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Because of p = h/wavelength

To have wavelength you have to have energy, so if you have wavelength, you have momentum!

I don't think you've really answered the question here... you're just defining things circularly.

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That is like saying why do things have energy, or why when you push something does it move. It just does! We just have laws to define it.

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That is like saying why do things have energy, or why when you push something does it move. It just does! We just have laws to define it.

The relativistic energy equation given above can be derived. There will be websites that go threw this. The fact that massless particles (including photons) have momentum is a result of that equation when m is set to 0.

There may well (and from memory I can dimly recall doing one) other methods for deriving the photon momentum relationship.

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Thanks. I recognize that as the expanded form of E=mc^2, but this assertion that "anything with energy must have momentum or mass or both" isn't very satisfying to my numbskull brain. I get the energy/mass relationship, but not the energy/momentum one.

Are you more familiar with the other equation for relativistic mass? $E = \frac{1}{\sqrt{1-v^2/c^2}}mc^2$ is the same equation as $E^2 = p^2c^2 + m^2c^4$.

Another way to go about it is with quantum. Here you have the equation $\lambda = h/p$ or alternately, $p = h/\lambda$. Then you can say that the photon has momentum because it has a wavelength. And you also have the equation that the energy of a photon is $E = hf = hc/\lambda$ which with the above again implies that $p = E/c$.

If you are asking why these equations are true, I don't think I can help you there.

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As noted above, you don't need mass to have momentum, just energy. Photons can bounce off things somewhat like a ping pong ball bounces off a table, and impart momentum. As for the more exact "how" IIRC all momentum arises pretty much in the same way in QM, but I won't go there.

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I meant to ask this question last year in physics, but the prof. moved on too quickly. How can a photon have momentum without mass?

I think this is a product of looking at things incorrectly, or perhaps inappropriately, but you are constrained to do so because you learn classical physics first, and learn that p = mv

Let me turn the question around (it may sound snarky, but it's not meant to be)

Why should you need mass to have momentum?

Think in more general terms about the concepts of force and energy. Energy means you can do work, and work means exerting a force. Forces cause changes in momentum. So anything with energy is going to have to have momentum

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I was WAY too caught up in classical thinking. The equations didn't help much (only they did make me realize that it's just they way nature behaves, and the equations describe nature, and the equations tell us that photons have momentum)... I was looking for something more intuitive.

When I stepped back and thought about the energy, and the little vibratory nature of the particles, I was okay with it (even if my mental picture is not a completely accurate description of the universe).

The sticking point was that I thought of momentum immediately and pretty solidly as mass x velocity, and anything multiplied by zero... Well, you get it. It has energy, and can impart momentum, much like the solar sail. I may not be able to write the equations, but I can grasp the idea.

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How many times do we need to have this discussion?

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This might be a useful picture to think about- completely classical (as in Maxwell):

Imagine a particle (say a proton) at rest at the origin (0,0,0). Along comes some radiation traveling in the +z direction with the electric field oscillating in the x-axis and the magnetic field oscillating in the y-axis.

Let's say when it reaches the proton the electric field is in the +x direction and the magnetic field is in the +y direction. The electric field pushes the proton in the +x direction and the vxB force is in the +z direction. 180 degrees later, the electric and magnetic field are in the -x and -y directions. Now the electric field pushes the proton in the -x direction, but the vxB force is still in the +z direction.

So the time average of the force in the x-axis is 0, but there is a net force in the +z direction. Now the proton which was initially at rest now has some momentum in the +z direction. Where did it come from? It can only be that the light was carrying some momentum and transferred is to the proton.

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Thanks NeonBlack. I've heard before that the classical EM had momentum, but never seen it explained.

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As noted above, you don't need mass to have momentum, just energy..

I fail to understand this. Isnt relativity in its most basic explination E = Mc2 used to explain that if you have mass you have energy and if you have energy you have mass. The way it is stated in the quote about it would violate M = c2/E (if i wrote that correctly) Which would be an alternate way of stating E=mc2 to state how much mass a givin amount of energy has? Am i wrong here?

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I fail to understand this. Isnt relativity in its most basic explination E = Mc2 used to explain that if you have mass you have energy and if you have energy you have mass. The way it is stated in the quote about it would violate M = c2/E (if i wrote that correctly) Which would be an alternate way of stating E=mc2 to state how much mass a givin amount of energy has? Am i wrong here?

$E^2 = m^2c^4 + p^2c^2$

$E = mc^2$ assumes a particle at rest.

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Light photons inertia? what is the relation of the three things?

Some people like to say that the photon has mass because the photon has energy $E=hf$, where $(h)$ is 'Planck’s constant' and $(f)$ is the frequency of the photon. Thus, they tend to assume that because it has energy $(E)$ it must have mass $(M)$ because of Einstien’s mass-energy equivalence equation $E=Mc^2$...

They also say that the photon has momentum, and momentum is related to mass $p = Mv$ where $(v)$ is velocity and $(p)$ is for momentum. Yet, you cannot justify it having mass using this argument. This is actually 'relativistic mass' - which is nothing but the measure of energy which will change with velocity.

It isn't actually mass, even though mass and energy are related. In physics jargon, the mass of an object is called its 'invariant mass,' and the photon has no invariant mass. Now, a massless particle can have energy and it can have momentum, simply because mass is related to these through the equation $M^2c^4 +p^2c^2 = E^2$, which is subsequently zero-mass for a photon because $E = pc$ for massless radiation (remember, c means the speed of light). So yes, the photon has momenta and energy, and can deliver a punch out of it when it hits a surface, but it doesn't have mass.

Now, one of Einstein's predictions in his General Version of Relativity, was linking mass and inertia together as one thing. Therefore, a photon cannot have an inertia related to mass, but could have an inertia related to momentum, since a photon does have a momentum.

Inertia is a property of matter which states that an object retains its motion in a particular speed and will never slow down or speed up, unless acted upon by an external force. A Photon is never at rest, and as far as we can tell, cannot be sped up or slowed down (unless by quantum tunelling),and therefore, it doesn't agree very well with experiment if it had a mass.

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