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### Author Topic: If photons have no mass, how do they have momentum?  (Read 6784 times)

#### @megzican

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##### If photons have no mass, how do they have momentum?
« on: 27/03/2011 02:30:03 »

If photons have no mass, how do they have momentum?

What do you think?
« Last Edit: 27/03/2011 02:30:03 by _system »

#### Phractality

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##### If photons have no mass, how do they have momentum?
« Reply #1 on: 27/03/2011 08:53:07 »

If photons have no mass, how do they have momentum?

The mainstream dogma is that photons have no mass. I am well outside the mainstream, so don't quote my answer on your homework unless your teacher is unusually openminded. I believe photons have mass in Euclidean space, but perhaps not in Minkowski space-time.

In Euclidean space, when a photon passes close to a star, it feels a gravitational force of attraction to the star, and the star feels an equal and opposite force of attraction to the photon.

The formula f = ma is not applicable at the speed of light, or even a significant fraction of the speed of light. So to talk about the force of attraction between a photon and a star, you must use the formula, f = dp/dt; force is the rate of change of momentum. This formula works for photons as well as for particles with rest mass. At relativistic speeds, F = ma does not work for particles with rest mass because the mass is increasing, and dp = mdv + vdm, so dp/dt ≠ ma.

Due to the attractive force acting on the photon, the photon changes direction. Since momentum is a vector, a change of direction is a change of momentum. For momentum to be conserved, an equal and opposite momentum must be imparted to the star. So the photon has gravitational mass and its own very weak gravitational field−in Euclidean space.

The path of a photon passing a star is a curve in Euclidean space. When you see a diagram showing light following a curved path, that is in fact drawn in Euclidean space, even when it is meant to illustrate Minkowski space-time. Unfortunately, it is impossible to draw warped space-time. Computers like warped space-time, but the human brain can't visualize it.

In Minkowski space-time, the path of a photon in a vacuum is the definition of a straight line. So the photon does not change direction in Minkowski space-time. Straightening the path of light by definition is what causes the warp of Minkowski space-time due to gravity. The sum of internal angles of a triangle no longer equals 180°, and two straight lines may cross more than once.

Consequently, mass doesn't have the same meaning in Einstein's general relativity that it has in Newtonian physics. For that matter, the meanings of all the old familiar parameters, like force, energy, momentum, etc., are tacitly altered by redefining what a straight line is. When one person is says, (Newtonian) mass, and the other person hears, "(Einsteinian) mass", arguments are sure to ensue.

Please don't think that I disagree with Einstein's general relativity. It computes correct answers efficiently over a very wide range of times, distances and speeds. The same problems can be solved numerically in Euclidean space using only the formulas of special relativity, but this will probably take much more computer time. The answers obtained by the two methods probably won't appear to be the same because one gives answers in Euclidean space, and the other in Minkowski space-time. But they should agree on whether two objects will collide or not.

#### yor_on

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##### If photons have no mass, how do they have momentum?
« Reply #2 on: 27/03/2011 13:29:34 »
Nice one Phractality. You need to explain your Euclidean space though and the conclusions you draw from it. The policy here, as I see it, okay :) Is that we might present stuff that are not main stream here, but only if also stating that this isn't mainstream, and only as relevant to the question. That also mean that if I find my ideas to need more than, phiiew, well, let's say about your post above, then I may consider moving it to 'new theories'.

And that's where you need to build up this Euclidean space methinks. Use Euclid's postulates and from there explain as simple as you can where, and how, you see photons getting a mass through the new geometry. You may have a point, but I have difficulties following how the change redefines a photon?

Maybe you will like this one Euclid's Elements. Eh, it needs java (to become interactive)

I will look forward to see you explaining your ideas. But don't lift in everything at once please.  That will make it hard to comment, and ask if one needs clarifications. :) And I don't think you have to worry. I expect those commenting to be civil and factual. We usually are here, well, except me then :)

#### lightarrow

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##### If photons have no mass, how do they have momentum?
« Reply #3 on: 27/03/2011 18:53:32 »
If photons have no mass, how do they have momentum?
Because at high speeds the formula p = m*v is not valid anylonger;

for massive particles the formula becomes:

p = m*v*γ   where γ = 1/sqrt[1 - (v/c)2]   v is the particle' speed.

for particles in general (massive or massless as photons):

p = sqrt[(E/c)2 - (mc)2]
where E = total energy of the particle.

Look at the last formula: if m = 0, p = E/c.

So, massless particles (as photons) have momentum if they have energy.
« Last Edit: 27/03/2011 18:56:09 by lightarrow »

#### Phractality

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##### If photons have no mass, how do they have momentum?
« Reply #4 on: 28/03/2011 00:27:51 »
... then I may consider moving it to 'new theories'.

Okay. Let's continue this in New Theories.

...Use Euclid's postulates and from there explain as simple as you can where, and how, you see photons getting a mass through the new geometry. You may have a point, but I have difficulties following how the change redefines a photon?

Euclidean geometry is the OLD geometry−−more than 2300 years old; Minkowski geometry has been around less than a century.

#### yor_on

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##### If photons have no mass, how do they have momentum?
« Reply #5 on: 28/03/2011 13:11:27 »
"If photons have no mass, how do they have momentum?" That's one of the really good questions to ask. Let us look at how we know they must have a momentum first. We know it from the way electrons behave. "Charged particles (here electrons) undergoing acceleration (slowing down or speeding up) experience radiant energy transfer with their 'surroundings'. Slowing down and speeding up are NOT to be exclusively associated with radiative energy loss and energy uptake, respectively. Each can entail either energy loss or gain for an electron."

This 'radiant energy' is described as photons. For them to be able to 'transfer' anything they need to interact with it, and that they do. This interaction is electrostatic and also considered to be a 'push', aka momentum. That we say it is a momentum is because it make the electron change its motion, a little like hitting a ball with another ball. But a photon is before all 'energy'. And its 'boundaries are not, as far as I know, physical. It has no real size, you would in theory be able to superimpose all photons there are, in one 'spot', without taking any place.

So a photon has no 'boundary', unlike our ball of matter. But it behaves as if it has.

#### JMLCarter

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##### If photons have no mass, how do they have momentum?
« Reply #6 on: 29/03/2011 00:44:28 »
"If photons have no mass, how do they have momentum?"

Agreed (I think) the key equation is

p = h / λ

h is plank's constant, λ is wavelength of the light.

So, the shorter the wavelength the more the momentum.

The "envelope" of the photon has the same spatial distribution regardless of wavelength. That means there are more waves in a short wavelength photon than a long one. Each wave gives a little electromagnetic push to a charge and imparts some momentum. That is one way of understanding this relation.

Objects with mass are actually the more complex case, as their interaction can still be considered to be via virtual force carriers like (and usually) photons, but generated by a "reservoir" from the velocity of the mass in some way.
I'd like to understand properly how that's supposed to work. What's going on that's different between a massive object and a large collection of photons when each imparts its momentum? I hope that question makes sense.

#### yor_on

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##### If photons have no mass, how do they have momentum?
« Reply #7 on: 29/03/2011 01:55:28 »
Heh, it all start to make sense now :)

Or maybe not? I say it is without size, you say it contain different wavelengths :) And it's all about how we choose to see it. If you think waves then a photon can be described as a wave packet, although ill-defined as its 'cutoff', where it starts and ends, becomes impossible to define, as I understands it? But as a photons energy can be translated into a waves frequency, well? Waves was the accepted definition before Max Planck defined black body radiation as discrete packets of energy, from which Einstein later made up those da*n 'photons' to explain the photoelectric effect.

I like to think of them as 'size less' photons myself, consisting of energy, but it's a matter of taste and what you think came 'first' I guess? :)
==

Are you thinking 'potential energy' there JML? Or 'relative mass'?

I see it as the invariant mass do not change in a motion, but as you can associate a different energy with something moving (relative something else), you can also count on it. And those two is what you usually count on. But as far as I know there are no more 'atom jiggling' due to motion, at least not a uniform one. An acceleration may be different but I don't really know there? All acceleration creates a gravity and gravity has the ability to compress objects caught in it, but I suspect that to get to this effect you will have too reach very high acceleration, too high to survive in fact. The compression should bring more energy into the particles making up the spacecraft which then will express itself as more invariant mass.

It's a rather weird thought as the gravity-well in a accelerating spacecraft by definition will be outside it under its 'tail' so to speak so then you would have a motion directed one way with the gravity working the other. I don't think it's possible myself to make a 'black hole' from an acceleration as you always can imagine some other ship being at rest relative the one accelerating seeing it for what it is normally. But it's the same as what a Lorentz contraction might do the atoms, if it is real, compressing them in the axis of the motion.

Very weird stuff.

You can also define the energy as something belonging to whatever 'system' you define. Then I believe it to become a part of the so called stress energy tensor. But as all motion, accelerations included is measured as a 'speed' relative something else, so the truly 'real' new energy inside that accelerating ship should be equivalent to what gravity you experience. And there it won't matter what 'speed' your planet had when you left it, as I think now? It depends though upon if there is some objective way to define a uniform speed for SpaceTime. If there is such a way, it will matter, if there is not, I expect it not to matter. I don't know any 'zero speed' from where we can define all other speeds myself?

And now it becomes weirder :)

It won't matter what speed you started from relative something else as long as where you started was uniformly moving. All uniform speeds can be defined as being 'at rest' as I see it. That means that they, if anything, will be the universes definition of a 'zero speed'.

And now we are deep into werdiness, but it makes sense, although not from what we see on Earth :)
==

To see what I mean you can consider the velocity needed to get free from Earth. That velocity has nothing to do with any 'speed' measured relative the moon, the solar system, our galaxy, or the CBM (Cosmic background radiation). None of those potential energies or 'speeds' matter for that rocket. The only thing that matters is Earths invariant mass, and rotation possibly. We make Earth go double the 'speed' relative the ? CBM? It won't make a difference as long as we're talking 'uniform motion'. But It will matter when we discuss 'uniform acceleration' which in one sense is a uniform motion too, but one that as it is in this gravitational field will cost you more energy to resist when accelerating, well, depending on the direction of course. From or towards the gravitational potential. Considering this, the energy spent for breaking a geodesic, in a constant acceleration at one Gravity as defined inside the ship, will have to differ depending on from where you leave. So saying that one gravity in that ship is equivalent to the same energy expended everywhere is incorrect. That points to that the idea with the 'stress energy tensor' that somehow is a function of SpaceTime, relative your ship, is the better definition I think of how much energy you will spend.

But the universe seems to have its own definition for being 'at rest', if now my logic makes any sense. And even though you can be 'at rest' everywhere in space, infalling towards a black hole too, gravity will take its toll if you break your geodesics accelerating, or when tidal forces starts to tug at you.
« Last Edit: 29/03/2011 02:38:10 by yor_on »

#### lightarrow

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##### If photons have no mass, how do they have momentum?
« Reply #8 on: 29/03/2011 13:18:14 »
"If photons have no mass, how do they have momentum?"

Agreed (I think) the key equation is

p = h / λ

h is plank's constant, λ is wavelength of the light.

So, the shorter the wavelength the more the momentum.

The "envelope" of the photon has the same spatial distribution regardless of wavelength. That means there are more waves in a short wavelength photon than a long one. Each wave gives a little electromagnetic push to a charge and imparts some momentum. That is one way of understanding this relation.
I don't think it's a good idea to talk of a photon's "envelope" or of anything concerning photon's shape or dimensions. We know it's the quantum of excitation of the EM field and little more than this.

Quote
Objects with mass are actually the more complex case, as their interaction can still be considered to be via virtual force carriers
They interact with the "fields".

Quote
like (and usually) photons, but generated by a "reservoir" from the velocity of the mass in some way.
I'd like to understand properly how that's supposed to work. What's going on that's different between a massive object and a large collection of photons when each imparts its momentum? I hope that question makes sense.
It is always an interaction between matter (electrons, nucleons etc.) and fields.

#### JMLCarter

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##### If photons have no mass, how do they have momentum?
« Reply #9 on: 29/03/2011 19:28:55 »
The basis for talking about "envelope" (I did put it in quotes) is the wave function for the photon, the normalised square of which I understand to provide a spatial probability distribution. What is your take on that?

When it comes to massive collisions, what is it that you mean "between matter and the fields". The fields interact on their corresponding localised "focii" (not the right term). For example, gravity acts on mass, EM on charge etc, etc.
Therefore the query is if, say, two hydrogen atoms collide (at a certain relative speed), it is electromagnetic repulsion that causes the transfer of momentum. This, I understand is also true of macroscopic matter, the table, the floor. So, how does the mass (the bearer of momentum) get impacted by what is in the first instance an electromagnetic exchange of momentum.
I think the answer must be that charge is "bound to" the mass. What is the nature of this binding?
A wavefunction if assumed "real" can have both mass and charge. I realise this is a founding assumption for a lot of physics, but these wonderings are asking what does this binding really tell us about the nature of mass or the wave function.
Can anyone remind me if a wave function is a particle description that includes its mass/charge/spin and color etc. Is mass really any different from charge (i.e. can charge be considered to warp space time on its own scales? Can a particle have charge or color without mass?)

#### yor_on

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##### If photons have no mass, how do they have momentum?
« Reply #10 on: 29/03/2011 20:16:29 »
JML me man, dangerous grounds this :) Are you expecting photons to have a mass? What about 'virtual' photons then? As I see it, according to Heisenberg uncertainty principle a virtual photon can have any 'energy' it like. If you now introduce 'invariant mass' as a parameter, then you have introduced the possibility for virtual photons to have a infinite mass too. I'm rather sure you also will have to change a lot of other mathematics and definitions if photons would be found to be of a mass, even though not all.

To define 'charge' as 'mass' you better know what 'charge' really is? I know I don't now what 'charge' really, really, is :). Otherwise it becomes difficult. And charge is renormalizable, gravity isn't, at least not in the standard model, the one schools seems to have stopped teach the physicists :) nowadays.

Charge and invariant mass are very different, well, as I see it.

#### Astrogazer

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##### If photons have no mass, how do they have momentum?
« Reply #11 on: 31/03/2011 23:15:03 »
For a few decades I have been lead to believe that gravity attracts objects - just as Newton told us.  But having watched Prof. Brian Cox's Universe series he said a couple of things that I am still pondering and may be for me beging to make sense of all this.  He said that, (at least I think that he said?!?!) that all objects are 'falling' in a straight line with respect to space-time.  He also said in a recent sky at night program that as exemplified by the Apollo astronauts on the moon that with out air resistance a feather falls at the same rate as a hammer.  And then he said something that is so obvious, and so profound.  He said if they also had a perfectly aligned horizontal laser, and also (a mind experiment here) the surface of the moon was about 5 light seconds long, dead flat and the same g long its length, the laser light and the feather and the hammer would all hit the lunar ground at the same time!  Obvious when its pointed out to me but not so obvious that it occurred to me without me being told.

So I wonder if its right to conclude that is not that light has mass, (or doesn't), or momentum, or whatever that attracts it to a star and therefore bends the light around it, its the warp in space-time that is the cause - so you probably even an object with no mass will still follow a warp in space-time and therefore be bent around a strong gravity well such as a star.

I'm not expressing myself too well as I'm still trying to cope with space-time warps rather than gravitational attraction.

On a related subject I want to question if gravity waves are detectable even though they exist - is there an existing thread can anyone tell me to join?  Its just that if the fabric of space-time wobbles as a result of passing gravity waves, then why should gravity detectors e.g. lasers, not suffer the same wobble thus our 'gravity ruler' is lengthening and shortening and time is wobbling too thus when one is divided by the other we get the same answer thus we couldn't ever detect gravity waves.

#### yor_on

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##### If photons have no mass, how do they have momentum?
« Reply #12 on: 01/04/2011 00:07:05 »
"The wave moves from behind the computer screen towards the reader. The coordinated dance of stretching and shrinking - stretching in one direction, while distances shrink in the perpendicular direction - is a general property of gravitational waves, as is the fact that all distortion takes place in a plane perpendicular to the direction in which the wave travels."

Brian Cox's description of the 'laser light and the feather and the hammer all would hit the lunar ground at the same time' can't be exactly correct though? Maybe if you/he meant the 'center of a black hole'? And just take a look, there's a lot of discussions going on about gravity here for the moment :)

#### Pmb

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##### If photons have no mass, how do they have momentum?
« Reply #13 on: 01/04/2011 23:25:39 »
Quote
If photons have no mass, how do they have momentum?
It all hinges on how one is using the term "mass". See the article I wrote on the subject if you're *really* into this point. It's at http://arxiv.org/abs/0709.0687

#### The Naked Scientists Forum

##### If photons have no mass, how do they have momentum?
« Reply #13 on: 01/04/2011 23:25:39 »