# Do Photons Have Mass?

1. Oct 14, 2006

### duu57f

Many people have been arguing for a long time that it doesn't. Of course, they couldn't actually give solid proof for this. They based their theory on the fact that if photons had mass at rest than many laws and theories we know today would be wrong. But the question still remains, if photons have no mass at rest, then why is light sucked into black holes. I mean, if light has no mass at rest, then the concept of gravity doesn't apply to it. Also, where does all the energy and momentum come from. I know about the concept of relative mass, but still, even with this, the energy has to come from a source and in my opinion that source has to be an initial mass.

2. Oct 14, 2006

### Parlyne

It is not known absolutely for sure that photons do not have mass. However, there is an experimental upper limit on what that mass could be; and it's pretty darn small.

Additionally, if photons had mass, there should be a third possible polarization for light, and electrostatic potentials should fall off as $$\frac{1}{r} e^{-\frac{m_\gamma c r}{\hbar}}$$.

To understand the statement that even light can't escape from a black hole, you have to understand a little bit about how general relativity describes gravity.

General relativity says that the presence of mass (or energy or momentum or pressure, etc.) actually bends the fabric of space and time. When the path of a particle is affected by gravity it happens, not because the particle is feeling a force, but because the particle is travelling along what is effectively a straight line path on a curved surface. When you think about it this way, it seems natural that even light should be affected.

A black hole is simply the case where space and time are so bent that every single straight line path that exists leads to one single place. (Of course, to be exact, we should say that every path that exists inside the event horizon leads to one single place. Outside the event horizon, there are paths that don't lead into the black hole.)

3. Oct 14, 2006

### FunkyDwarf

this isnt entirely true as gravity does exert a force. in the example you used youre correct, but if that applied everywhere then two masses at rest relative to each other would feel no gravitational force as there is no inital motion, which im pretty sure isnt true (correct me if im wrong anyone)

photons are said to have no mass, or specifically no rest mass, for two reasons. well really theyre the same one but anyway. firstly because an inertial observer can never catch up with a photon and view it at rest. secondly because mass addition requires something traveling at the speed of light to have infinite mass (as a product of its initial mass) which requires an infite amount of energy to accelerate to c. thus nothing with mass can get to speed c, but because the mass addition is a product value something with zero rest mass can.

4. Oct 15, 2006

### ZapperZ

Staff Emeritus
If that is such a glaring evidence for light having a mass, then would something as obvious as that be missed by the whole physics community. I mean, let's get real here. How dumb do you think physicists are to miss such a thing?

This issue has been discussed to death in several threads in both the Quantum physics forum, and the SR/GR forum. Please do your search there and figure out how gravity is a spacetime curvature, and why light follows the "geodesic" of that spacetime curvature. It has NOTHING to do with light having a mass.

Zz.

5. Oct 15, 2006

### pmb_phy

The arguement is not about the physics of whether photons have mass. Its a debate about the definition of "mass" which will give either a yes or no according to the definition.

There is a possibility that a photon has a finite rest mass. The best of current measurements of the photon's proper mass does not have the precision to detect any photon proper mass.

The concept of mass that you speak of here is not proper mass but inertial mass and passive gravitational mass. And yes. The photon has both

Best wishes

Pete

6. Oct 15, 2006

### MeJennifer

It seems you are mistaken in thinking that gravity only works between objects that have mass, that is not the case.

Suppose we have an object with mass. It will curve spacetime and as a consequence all inertial paths are curved in its neighborhood. So any other object nearby, regardless whether it has mass or not, will be subject to these conditions of spacetime.

Consider flat spacetime. Each particle that is inertial for a given time interval shows a straight line segment, and each particle that is not inertial for a given time segment shows a curved line segment.

Now an object that has mass influences the curvature of spacetime.

Then it follows that near an object of mass anything else that showed a straight line segment before does not longer show a straight line segment and the curved line segments are also different. And by the way not only the spatial dimensions of spacetime are subject to curvature, the time dimension is subject to curvature as well. At low relativistic speeds the time curvature is actually stronger than the spatial curvature.

Now with regards to black holes sucking in light, it depends on the direction of the light, most light paths will simply approach and then leave the vicinity of the black hole. But some light paths will encounter such curvature that it will be directed to go to the center of the black hole.

Last edited: Oct 15, 2006
7. Oct 16, 2006

### pmb_phy

Why not? The development of GR was based on the hypothesis that all objects have mass (whether inertial or proper mass). If this is not true then there would be no justification of the Equivalence Principle and hence particles without any kind of mass would not follow a geodesic. To see that this is the case I would suggest that one follows the development of GR from the beginning and leave out the postulate that all objects must have passive gravitational mass. That isn't an easy task by far. But it would be highly instructive. In fact I intend to do that myself soon.
Its quite possible that an object with an extremely high energy density and an extremely hi tension would have a zero active gravitational mass. This would yield a zero spacetime curvature outside the body. Geodesics would then be straight. However the topology of the spacetime could be changed such that these straight geodesics would intersect. Such an object is postulated to exist and the topology would be that of a cone. E.g. a straight cosmic string is just such an example.

Pete

8. Oct 16, 2006

### pervect

Staff Emeritus
I've said this once or twice or ten times before, but in GR, gravity is not based on "mass", but on the stress-energy tensor. In fact, mass is only defined in GR under special circumstances, such as asymptotically flat space-times, or stationary space-times.

9. Oct 18, 2006

### gonegahgah

Mass is usually used as a comparative measure. Further, the more mass a space object has the more 'gravitational influence' that space object presents.

In this respect for any other object, be it light or a space ship, their mass is not relevant as we all know things fall at the same speed. So whether light has almost no mass and a spaceship has greater mass, all things fall at the same rate.

What does affect the apparent rate of fall over ground distance covered is velocity. If the space ship is travelling faster sideways then it will fall to the ground at a greater distance. Give it enough distance and it will miss the Earth all together and continue falling (also called orbiting).

The same with respect would go for light if it has mass. Light travels extremely fast so it should be bent from its path much less than the rocket which is travelling much slower. It is not because light weighs less but simply because it is going faster. Hence why we need stars and galaxies to gain noticeable bending of light as they need to exert greater gravitational influence to overcome the light's speed in sufficient time.

But the key difference for light, if it has mass, is frequency. Frequency represents the oscillation of light through a point of space as it passes through. We have already established that it does not matter how much mass the light has so if higher frequencies were say heavier than lower frequencies then this would make no difference to the path of either frequency as their mass is inconsequential.

However I mentioned frequency because frequency represents how quickly the crests and troughs of the light pass through a point of space. The faster the light rises and falls (the higher its frequency) through its oscillations should effect the path of the light around a gravitational body.

Higher frequency light which is oscillation faster should bend less around a gravitational body than should lower frequency light which is oscillating slower. This effect would be similar to the effect found when passing light through triangular prisms.

However according to science light is achromatic. This means that the different frequencies are not supposed to bend different degrees around large graviational bodies.

10. Oct 18, 2006

### pervect

Staff Emeritus
This is basically misguided and somewhat reminiscent of argumentative arguments that heavier objects must fall faster than lighter objects.

Just as light and heavy objects fall at the same rate, different frequencies of light are not chromatically aberrated. They both essentially follow geodesics.

Like the case of light and heavy objects falling, this argument iignores the back reaction effects.

The clearest argument is this. If you drop a light and heavy argument, the Earth "may move" (note that it won't move as a point mass!). However, the light and heavy object will both arrive at the same point at the same time. It's just that the Earth will move, and stretch by a totally insignificant amount.

Similarly, if you send a high frequency and a low frequency light beam around a black hole, the black hole "may move" by a totally insignifcant amount. But there will be no relative deflection of the high frequency vs the low frequency beam if they are sent at the same time.

Last edited: Oct 18, 2006
11. Oct 18, 2006

### student85

so sound waves are affected by a curvature in space?

12. Oct 19, 2006

### Zelos

everything is

13. Oct 19, 2006

### gonegahgah

God pervect

Do you actually read anything I write?

Nothing I wrote in my post that you quoted disagreed with what you rehashed. I'm sorry that I don't use meaningless scientific words.

I really don't know where you get the idea that I argued that heavier objects fall faster than smaller objects.

I did deliberately ignore the "back reaction effects" as I didn't think this necessary to help the original poster. I apologise that you felt its absence. These "back reaction effects" are that while one body A falls towards another body B; body B will also fall towards body A; and this affects the combined closure speed. If you have two massive spheres of lesser density then they will fall together at a slower speed than two massive spheres of greater density. Simply because both denser spheres will experience greater acceleration towards each other than will the less dense spheres towards each other.

Think before you speak please before telling me that I'm presenting flat earth principles.

Last edited: Oct 19, 2006
14. Jun 17, 2008

### stone1

One related question, which may be less ambiguous, would be "What happens to the mass/gravitational field of a black hole when it sucks up more photons?"

From my casual readings, I have to agree with Pete that the issue is more about what the question really means rather than what the answer is. A photon is a quantum object and terms like "stationary" mass (and "constant" momentum for that matter) are not well-defined. My understanding is that an answer like "The stationary mass of a photon is equal to X" is wrong even if you make X = 0.

15. Jun 17, 2008

### pmb_phy

The mass of the black hole increases. Nobody who understands GR has any doubt about that regardless of whether they believe that photons have mass or not (i.e. regardless of how they define the term "mass").

Pete

16. Jun 17, 2008

### W.RonG

Does a photon have mass? in a word, No.
Light is not a substance; light is electromagnetic energy.
a "photon" is a unit of measure of that energy. a photon is no more a particle of light than a phon is a particle of sound.
rg

17. Jun 17, 2008

### pmb_phy

Whether light has mass or not will depend on how it is defined. Without stating a definition then its impossible to say whether light has mass or not.
Light is, by definition, an electromagnetic wave. It has energy. It cannot be said to be energy. Also, perhaps there are people who wish to think of light as not being a substance. When this is the case then such people will seek out a definition of the term "substance" such that light is not a substance. As of now the term "substance" is an undefined term in physics. It is only used loosely. Einstein himself referred to electromagnetic fields as being "matter" and as such I'd hazard to guess that he'd also refer to light as a "substance." Einstein referred to light as matter in his 1916 review article on the foundations of general relativity.
I disagree. By definition a photon is a quantum of light. A photon is not energy. It merely has energy. Your analogy regarding phonons and photons is flawed because you are thinking of it in a way which is inconsistent with how it is defined in physics.

Best wishes

Pete

18. Jul 19, 2008

### JoeBachofen

Way back in 10/14/06, FunkyDwarf said:

“photons are said to have no mass, or specifically no rest mass, for two reasons.
...firstly because an inertial observer can never catch up with a photon and view it at rest.
secondly because mass addition requires something traveling at the speed of light to have infinite mass
(as a product of its initial mass) which requires an infite amount of energy to accelerate to c. thus
nothing with mass can get to speed c, but because the mass addition is a product value something
with zero rest mass can.”

The first point is incorrect. If you could “catch up” to a photon you would still measure its velocity as c, the speed of light, because c is an invariant. You would, however, measure its frequency as 0 due to red shift.

The second point is correct but misses the point. The point is that anything that travels at the speed of light can ONLY travel at the speed of light. It can never be “at rest” because it IS light and the speed of light in a vacuum is invariant. Therefore, the “rest mass” of a photon is NOT zero; the photon has no rest mass because it can NOT be “at rest”.

I know this is an old thread and my response is to a 2 year old post but the thread, in total, has helped me think through some basic issues in a concise way.

The discussion about photons being E&M waves versus being or having energy has nothing to do with “rest mass” and is more metaphysics (or semantics) than physics. Interesting and correct, but not on point.

The point is: photons are light, light travels at an invariant speed, c, in a vacuum and cannot be at rest; therefore photons cannot have “rest mass” which does NOT mean the “rest mass” of a photon is zero.

Incidentally, it is not a "theory" that the speed of light in vacuum is invariant; it is an axiom.
It is the foundation on which both Special and General Relativity are built.

19. Jun 14, 2010

### Steven.D.N

hmmm

Last edited: Jun 14, 2010
20. Jun 14, 2010

### Steven.D.N

according to einstien E= mc^2
photons deffinatly have energy
this is soemthign noone can deny
so lets say the photon has a standard unit of 1 where energy is concerened
so
1 = mc^2 when dealign with a photon
therefore its mass when in motion is m = 1/c^2
if a photon stops moving under this model it has 0 energy and 0 mass
and cannot exist
it can only exist if it is in motion

at least logically anyway, but then again nothing works the same in the quantum world anyway , but it still leaves the question why doesnt it have infinate mass when it is in motion , using it as a standard for 1 unit of energy would certainly show it has a mass.

Last edited: Jun 14, 2010