Do Photons Have a Gravitational Effect?

[bcrowell]

Here is a new FAQ I've written up on this topic.

FAQ: Does light produce gravitational fields?

The short answer is yes. General relativity predicts this, and experiments confirm it, albeit in a somewhat more indirect manner than one could have hoped for.

Theory first. GR says that gravitational fields are described by curvature of spacetime, and that this curvature is caused by the stress-energy tensor. The stress-energy tensor is a 4x4 matrix whose 16 entries measure the density of mass-energy, the pressure, the flux of mass-energy, and the shear stress. In any frame of reference, an electromagnetic field has a nonvanishing mass-energy density and pressure, so it is predicted to act as a source of gravitational fields.

There are some common sources of confusion about this. (1) Light has a vanishing rest mass, so it might seem that it would not create gravitational fields. But the stress-energy tensor has a component that measures mass-energy density, not mass density. (2) One can come up with all kinds of goofy results by taking E=mc^2 and saying that a light wave with energy E should make the same gravitational field as a lump of mass E/c^2. Although this kind of approach sometimes suffices to produce order-of-magnitude estimates, it will not give correct results in general, because the source of gravitational fields in GR is not a scalar mass-energy density, it's the whole stress-energy tensor.

Experimentally, there are a couple of different ways that I know of in which this has been tested. An order of magnitude estimate based on E=mc^2 tells us that the gravitational fields made by an electromagnetic field is going to be extremely weak unless the EM field is extremely intense.

One place to look for extremely intense EM fields is inside atomic nuclei. Nuclei get a small but nonnegligible fraction of their rest mass from the static electric fields of the protons. According to GR, the pressure and energy density of these E fields should act as a source of gravitational fields. If it didn't, then nuclei with different atomic numbers and atomic masses would not all create gravitational fields in proportion to their rest masses, and this would cause violations of Newton's third law by gravitational forces. Experiments involving Cavendish balances[Kreuzer 1968] and lunar laser ranging[Bartlett 1986] find no such violations, establishing that static electric fields do act as sources of gravitational fields, and that the strength of these fields is as predicted by GR, to extremely high precision. The interpretation of these experiments as a test of GR is discussed in section 3.7.3 of [Will 2006]; in terms of the PPN formalism, if E fields did not act as gravitational sources as predicted by GR, we would have nonzero values of the PPN zeta parameters, which measure nonconservation of momentum.

Another place to look for extremely intense EM fields is in the early universe. Simple scaling arguments show that as the universe expands, nonrelativistic matter becomes a more and more important source of gravitational fields compared to highly relativistic sources such as the cosmic microwave background. Early enough in time, light should therefore have been the dominant source of gravity. Calculations of nuclear reactions in the early, radiation-dominated universe predict certain abundances of hydrogen, helium, and deuterium. In particular, the relative abundance of helium and deuterium is a sensitive test of the relationships among a, a', and a'', where a is the scale-factor of the universe. The observed abundances confirm these relationships to a precision of about 5 percent.[Steigman 2007]

Kreuzer, Phys. Rev. 169 (1968) 1007

Bartlett and van Buren, Phys. Rev. Lett. 57 (1986) 21

Will, "The Confrontation between General Relativity and Experiment," http://relativity.livingreviews.org/Articles/lrr-2006-3/ , 2006

Steigman, Ann. Rev. Nucl. Part. Sci. 57 (2007) 463

 

[atyy]

@bcrowell, do you think it would be very cheating to use this as a "proof": if we assume G=T, with T being the electromagnetic stress tensor, then we get Maxwell's equations and the Lorentz force law automatically by the covariant conservation of T implied by G (along the lines of section 20.6 in MTW)?

 

[bcrowell]

@bcrowell, do you think it would be very cheating to use this as a "proof": if we assume G=T, with T being the electromagnetic stress tensor, then we get Maxwell's equations and the Lorentz force law automatically by the covariant conservation of T implied by G (along the lines of section 20.6 in MTW)?

Well, I might say it in a somewhat different way. If you believe in G\propto T, then you get local conservation of energy-momentum. Therefore by conservation of momentum, if light is acted on by gravitational fields, it must also create gravitational fields. The argument doesn't depend on the specific properties of electromagnetic waves at all. You can substitute any other field in place of the word "light," and the answer is the same.

IMO the theoretical side of all this is much more straightforward than the experimental side. The experimental side is complicated and requires a lot more effort for interpretation. E.g., Kreuzer didn't interpret his results as a test of GR; Will did that years later.

 

[threadmark]

A photon has zero mass, zero charge, and zero gravity. Let me explain why.
A photon being single she likes to walk on the beach alone. A Photon vector is not affected if two photons cross paths. Because a photon is a boson, it likes to be left alone. So much that it can occupy the same point in space if a physical possibility that two photons could be confine in a symmetric vector. Meaning if a photon could be seen in faze with another photon, it would not affect the two photons. Photons do not have a charge so the electric field in light must be caused by time varying magnetic fields which photons produce. But the electric properties of light are caused in my opinion by the W and Z bosons. However I cannot produce a formula you would understand, I think it’s correct but not relevant to prove a photon can not produce gravity. The magnetic field produced by a photon is a property of the wave function and of course we all know gravity is the affect on space (TIME) being time is a key factor hear. A Photon has a rest mass of zero if E=mc2. it can be seen as a particle in this state being at rest, so the idea that it can produce a gravitation affect in this state is humorous at best. The particle at rest does not produce a magnetic field, thus does not have time varying magnetic fields to produce electric fields. And if you check your GR because I am sure we didn’t read the same notes, I’m sure there is a notation that energy is required to produce gravity. Photons at rest do not have energy because they have no momentum. To further my disappointment in myself for actually trying to help this filtered opinion based discussion, photons as a wave is not a body that can be compressed and mass density is apart of many calculations working with the production of gravity.
Sorry if this doesn’t make sense to you. But its like I am trying to prove the moons not made of cheese.

TM

 

[bcrowell]

A photon being single she likes to walk on the beach alone.

This is not a scientific argument.

A Photon has a rest mass of zero if E=mc2. it can be seen as a particle in this state being at rest

There is no rest frame in which a light wave is a rest.

To further my disappointment in myself for actually trying to help this filtered opinion based discussion,

In #31, I provided four references to peer-reviewed scientific papers. Have you read any of them?

 

[PAllen]

I'll add one more reference which discusses the 'weight' of a box of light in gravity (along with discussing experimental verification of the weight of kinetic energy):

http://arxiv.org/abs/gr-qc/9909014

Note, the box of light here is two (I believe unconstrained) mirrors reflecting light between them, so the pressure issues of spherical box of light are removed.

[EDIT] This reference is not relevant to the current dispute here, which concerns light as a source of gravity. The given reference discusses the effect of gravity on light.

 

[threadmark]

This is not a scientific argument.


There is no rest frame in which a light wave is a rest.


In #31, I provided four references to peer-reviewed scientific papers. Have you read any of them?

A photon is not light, being E=mc2 photons travel at the speed of light but they travel at the same speed In a magnetic field produced from a fridge magnet. The fridge magnet does not produce light and E=mc2 is a notion In describing a speed of a particle with a zero rest mass not a light wave.

 

[Dale]

threadmark, there is no quantum theory of gravity, so it is premature to make any statements about photons as bosons and how that relates to gravitation. What is certain, however, is that for any massless field such as classical light GR does predict that it will produce gravitation. Additionally, GR also predicts that static EM fields gravitate. As bcrowell pointed out there is experimental support for both of these assertions.

Unless you can cite some mainstream sources clearly supporting your position you should probably take a step back and re-evaluate and possibly learn some more before continuing.

 

[threadmark]

Balderdash, you are miss interpreting the affect on space time as required to explain how em fields maintain momentum.

 

[Dale]

I can't parse that sentence. Could you try again?

 

[Passionflower]

threadmark, there is no quantum theory of gravity, so it is premature to make any statements about photons as bosons and how that relates to gravitation. What is certain, however, is that for any massless field such as classical light GR does predict that it will produce gravitation.

But a single photon does not make a field right?

For instance a collection of photons can have rest mass but not a single photon.

One cannot have the cake and eat it too, if one person is calling someone wrong when he claims that there is no proof that a single photon creates spacetime curvature, then it is a cop out to speak about EM fields and claim photons do not apply because the theory does not apply. How can one possibly call someone wrong if he makes a statement about a single photon if the theory you are using in the argument does not even recognize single photons. I suppose only lesser minds as I am can see a fallacy in this.

Let's use some logic here:

A claims that X is false
B says that according to GR Y is true and GR does not deal with X
Therefore X is true

Sure, I must be just too stupid to understand this 'logic'.

 

[PAllen]

Balderdash, you are miss interpreting the affect on space time as required to explain how em fields maintain momentum.

Maybe we can say the if photons were at rest they wouldn't produce gravity. This is equivalent to saying if the moon was made of cheese we would all live forever.

 

[atyy]

Well, I might say it in a somewhat different way. If you believe in G\propto T, then you get local conservation of energy-momentum. Therefore by conservation of momentum, if light is acted on by gravitational fields, it must also create gravitational fields. The argument doesn't depend on the specific properties of electromagnetic waves at all. You can substitute any other field in place of the word "light," and the answer is the same.

IMO the theoretical side of all this is much more straightforward than the experimental side. The experimental side is complicated and requires a lot more effort for interpretation. E.g., Kreuzer didn't interpret his results as a test of GR; Will did that years later.

Is this essentially the same argument in the footnote on p7 of the reference that PAllen gives?

I'll add one more reference which discusses the 'weight' of a box of light in gravity (along with discussing experimental verification of the weight of kinetic energy):

http://arxiv.org/abs/gr-qc/9909014

Note, the box of light here is two (I believe unconstrained) mirrors reflecting light between them, so the pressure issues of spherical box of light are removed.

[EDIT] This reference is not relevant to the current dispute here, which concerns light as a source of gravity. The given reference discusses the effect of gravity on light.

Regarding the edit: Although he does say "test particle" which suggests it is not relevant, the equation he gives in footnote 7 does have a coupling between the energy of the test particle and metric, so it is not clear that it is not relevant.

It does seem very hard to nail down, I have to say. He says at the end "For an electromagnetically bound system, for instance, a term in equation (4) of the form #(2T + U)/c2 is inherently unobservable. ... If the coefficients # have any universal significance, we can now combine the limits coming from the energy content of nuclei with those coming from atomic electrons to obtain information about # alone. It seems safe to assume that there should be no perverse cancellation between the gravitational couplings of, say, electron kinetic energy in beryllium and nuclear binding energy in platinum." (All the # are different symbols that just wouldn't copy correctly)

 

[PAllen]

But a single photon does not make a field right?

For instance a collection of photons can have rest mass but not a single photon.

I would dispute this. A collection of photons can have kinetic energy not rest mass.

 

[Dale]

But a single photon does not make a field right?

Right. Which is why I am careful to make sure to make statements only about classical fields and not try to make inferences about photons. I think it is a bad idea to claim to know how a quantum theory of gravity would function.

How can one possibly call someone wrong if he makes a statement about a single photon if the theory you are using in the argument does not even recognize single photons. I suppose only lesser minds as I am can see a fallacy in this.

I didn't say he was wrong. I said he was premature, and I chose that word deliberately. He is asserting that a photon does not gravitate. As of today, there is no mainstream theory which would either support or contradict him, therefore it is too early to make such an assertion. Hence the word "premature".

The rest of my post was simply explaining the GR stance on gravitation of classical EM fields.

Let's use some logic here:

A claims that X is false
B says that according to GR Y is true and GR does not deal with X
Therefore X is true

Sure, I must be just too stupid to understand this 'logic'.

Please don't put words in my mouth like this. I certainly never made this claim. If you would read what I actually wrote you would see that it actually went:
A claims that X is false
B says there is no mainstream theory about X
B mentions that according to GR Y is true and has experimental support
Therefore B recommends further study

 

[Passionflower]

Right. Which is why I am careful to make sure to make statements only about classical fields and not try to make inferences about photons. I think it is a bad idea to claim to know how a quantum theory of gravity would function.

I didn't say he was wrong. I said he was premature, and I chose that word deliberately. He is asserting that a photon does not gravitate. As of today, there is no mainstream theory which would either support or contradict him, therefore it is too early to make such an assertion. Hence the word "premature".

The rest of my post was simply explaining the GR stance on gravitation of classical EM fields.

Please don't put words in my mouth like this. I certainly never made this claim. If you would read what I actually wrote you would see that it actually went:
A claims that X is false
B says there is no mainstream theory about X
B mentions that according to GR Y is true and has experimental support
Therefore B recommends further study

Actually B is not referring to you Dalespam. As far as I can see, only one person in this topic claims that there is experimental proof.

 

[Dale]

I would dispute this. A collection of photons can have kinetic energy not rest mass.

No, Passionflower is correct. Consider an electron and a positron, together they have a four-momentum of about (1,0,0,0) MeV/c and therefore a mass of about 1 MeV/c². By conservation of four-momentum, after anhilation the resulting collection of photons also has a four-momentum of about (1,0,0,0) MeV/c and therefore a mass of about 1 MeV/c².

 

[PAllen]

While GR certainly says nothing about photons, it would say something about a light wave packet. While it is only an intuition, I would guess most physicists would think that if a light wave packet produces gravity, then a single photon produces gravity.

 

[Dale]

While GR certainly says nothing about photons, it would say something about a light wave packet. While it is only an intuition, I would guess most physicists would think that if a light wave packet produces gravity, then a single photon produces gravity.

According to GR a light wave packet produces gravity. This is called a pp-wave spacetime.

However, although I understand how attractive it is, I would caution such physicists about making that intuitive jump. A photon is not merely a small classical wave packet. It may not even be localized nor have any definite energy. Since a photon may not have a definite energy or locationit quickly becomes difficult to figure out how much curvature it should produce and where it should produce it.

 

[Passionflower]

Searching for a key word is not the same as reading something and making an effort to understand it. There is no reason for the word "photon" to appear there, because the article is about classical physics, not quantum mechanical physics.

Yes no kidding, but it is you who made the claim about photons remember? I quote you here:

I thought this forum was to discus actual real science, not hypothetical nonsense. There is no evidence to suggest that photons create gravity.

Step 1: Read this review article: http://relativity.livingreviews.org/Articles/lrr-2006-3/
Step 2: Lose the attitude.

Then I wrote:

Perhaps you could be a little more specific. Where in this article is there a reference to experimental evidence that photons create gravity (leaving for the moment in the middle what 'creating gravity' is actually supposed to mean)?

Your answers:

Section 3.7.3. But you're going to need to understand the whole PPN discussion in the article before you'll understand why that's what 3.7.3 means.

Searching for a key word is not the same as reading something and making an effort to understand it. There is no reason for the word "photon" to appear there, because the article is about classical physics, not quantum mechanical physics.

When I told you the article is not about photons you replied in your usual denigrating way referring to people's lack of understanding.

 

[PAllen]

No, Passionflower is correct. Consider an electron and a positron, together they have a four-momentum of about (1,0,0,0) MeV/c and therefore a mass of about 1 MeV/c². By conservation of four-momentum, after anhilation the resulting collection of photons also has a four-momentum of about (1,0,0,0) MeV/c and therefore a mass of about 1 MeV/c².

Interesting. That must lead to an interesting formula for adding/combining 4-momenta (I guess not surprising; you can't 'add' 4-velocities either). Is there a simple formula for adding two 4 momenta explaining how each may have 0 in the first component (using your convention; I've sometimes seen this as the last component), but combined they have something there?

Thinking further, it makes perfect sense - the analog of momentum cancels, so conservation must make the first component signficant.

 

[atyy]

I guess what is not clear to me is - could Nordstrom gravity account for all the data given in support of light causing spacetime curvature. The data is primarily EP data (which is implemented in Newton as inertial mass = gravitational mass), and Nordstrom gravity does have some form of EP, but light does not cause spacetime curvature in Nordstrom gravity (because Nordstrom gravity couples to the trace of the stress-energy tensor, and the EM field is traceless). Is the precise EP of Nordstrom gravity (but Will says Nordstrom has strong EP!?) different from the EP of GR?

 

[Dale]

Interesting. That must lead to an interesting formula for adding/combining 4-momenta (I guess not surprising; you can't 'add' 4-velocities either). Is there a simple formula for adding two 4 momenta explaining how each may have 0 in the first component (using your convention; I've sometimes seen this as the last component), but combined they have something there?

Thinking further, it makes perfect sense - the analog of momentum cancels, so conservation must make the first component signficant.

Sorry for the confusion, I should have been more explicit with the convention. So this is the convention with time as the first component (ct,x,y,z), for the four-momentum that results in (E/c,px,py,pz). So an electron and a positron each have a four-momentum of (.5,0,0,0) MeV/c so the total system is:
(.5,0,0,0)+(.5,0,0,0)=(1,0,0,0) MeV/c

When they anhilate they will generally produce two photons, for convenience let's say that one goes in the +x direction. Then for momentum to be conserved the other must go in the -x direction and they must be equal in energy.
(.5,.5,0,0)+(.5,-.5,0,0)=(1,0,0,0) MeV/c

Note that the mass of each individual photon (m²c²=E²/c²-p²) is 0, even though the mass of the system of photons is 1 MeV/c².

 

[threadmark]

Please! In this thread there has been nothing but manipulation of Albert’s general relativity to produce a theoretical scenario where imaginary particle states can produce gravitation. Its not the photon with gravitation that is bugging me, it’s the use of Albert’s notions in producing general relativity to prove your hypothesis of bosons produce gravity is false because the theory in its entirety didn’t explain theoretical zero mass particles producing gravity and your existence to interpret the information in such a way to try and change theoretical understandings of a particle. What are you suggesting number 1? Where in Einstein’s formulas does it produce an explanation of zero mass particles producing gravity 2. And please note that a wave’s propagation can be seen as action at a distance but not gravity. How can you compress a field for density not field compression or amplification which will create distortion not density . Propagation is not gravity. Waves like light (sigh), do not produce gravity

 

[PAllen]

I guess what is not clear to me is - could Nordstrom gravity account for all the data given in support of light causing spacetime curvature. The data is primarily EP data (which is implemented in Newton as inertial mass = gravitational mass), and Nordstrom gravity does have some form of EP, but light does not cause spacetime curvature in Nordstrom gravity (because Nordstrom gravity couples to the trace of the stress-energy tensor, and the EM field is traceless). Is the precise EP of Nordstrom gravity (but Will says Nordstrom has strong EP!?) different from the EP of GR?

Nordstrom says light isn't deflected at all by gravity; it says light doesn't produce gravity. Together, these are consistent with any ep.

 

[atyy]

Nordstrom says light isn't deflected at all by gravity; it says light doesn't produce gravity. Together, these are consistent with any ep.

Yes, we can rule out Nordstrom based on non-EP data such as global light deflection. So I guess we use EP plus global light deflection? Wow, this is delicate.

 

[atyy]

Please! In this thread there has been nothing but manipulation of Albert’s general relativity to produce a theoretical scenario where imaginary particle states can produce gravitation. Its not the photon with gravitation that is bugging me, it’s the use of Albert’s notions in producing general relativity to prove your hypothesis of bosons produce gravity is false because the theory in its entirety didn’t explain theoretical zero mass particles producing gravity and your existence to interpret the information in such a way to try and change theoretical understandings of a particle. What are you suggesting number 1? Where in Einstein’s formulas does it produce an explanation of zero mass particles producing gravity 2. And please note that a wave’s propagation can be seen as action at a distance but not gravity. How can you compress a field for density not field compression or amplification which will create distortion not density . Propagation is not gravity. Waves like light (sigh), do not produce gravity

There is no controversy that GR predicts that light bends spacetime.

 

[PAllen]

According to GR a light wave packet produces gravity. This is called a pp-wave spacetime.

However, although I understand how attractive it is, I would caution such physicists about making that intuitive jump. A photon is not merely a small classical wave packet. It may not even be localized nor have any definite energy. Since a photon may not have a definite energy or locationit quickly becomes difficult to figure out how much curvature it should produce and where it should produce it.

Point granted. However, we can agree that 'rest mass being zero (while energy and momentum nonzero) is a false reason to argue that something doesn't produce gravity (as threadmark has argued). Thus, if a quantum gravity theory eventually says individual photons don't produce gravity, it will not be simply because their rest mass is zero.

 

[PAllen]

Yes, we can rule out Nordstrom based on non-EP data such as global light deflection. So I guess we use EP plus global light deflection? Wow, this is delicate.

I would say we don't rule out Nordstrom based on EP at all. It is the only theory other than GR that is indistinguishable from it in this way. For other theories of gravity, we may use EP to rule them out. For Nordstrom we simply use major conflict with experiment.

 

[Dale]

the theory in its entirety didn’t explain theoretical zero mass particles producing gravity ... Where in Einstein’s formulas does it produce an explanation of zero mass particles producing gravity 2.

The Aichelburg–Sexl ultraboost solution does exactly that for a classical localized zero mass particle. You really should read up on pp-wave spacetimes.

Waves like light (sigh), do not produce gravity

According to GR they do.

Are you claiming that GR is wrong, or do you just not understand GR?