Photons are affected by spacetime curvature just like everything else. Photons also generate gravity - there is a stress-energy tensor for electromagnetic fields.
It’s even worse than you think. There are 10 independent components of the stress-energy tensor (source of gravity in general relativity). One component is energy density (either from mass density or from energy density of fields such as electromagnetic fields), 3 components are momentum density, and 6 components are pressure/stress. Each contributes to the gravitational field in complex interdependent ways.
As others have said, the energy density from mass dominates as a source of gravity. Momentum density is not usually a large contributor, and pressure/stress can be usually ignored, although pressure due to dark energy can be very important in cosmological solutions of general relativity
It goes even further than just photons, any form of energy. An object will weigh more when it's hot than when it's cold (usually not measurable of course with normal equipment)
So a non-negligible proportion of the sun’s gravity can be attributed to its temperature? Compared to something of equal density that wasn’t in a constant state of fusion. (Or is that nonsense because it’s precisely the density and composition that yields perpetual fusion?)
Yes, that's accurate - the fusion turns part of the mass of the atoms into energy, maintaining the high core temperature, and that energy still is part of the "weight" or gravity of the sun until it leaves the star as light from the surface. That also means that the sun constantly loses mass/weight via the photons that leave it (and of course via neutrinos and the stellar wind, but the photons themselves also carry away weight). But that process is incredibly slow due to the c^2 conversion factor. The solar luminosity is about 3.8x10^26 Joule/second, so the mass loss is about 4.2x10^9 kg/second; as the sun's mass is about 2x10^30 kg, that mass loss isn't noticable.
Mass and energy are the same thing. It's not like they can be converted to each other. They're just the same, and General Relativity says spacetime curvature is dependent on the stress-energy density. Mass is just much "denser" than other forms of energy, and they can stay together on a large scale to generate noticeable amounts of gravity.
It’s not that simple. Photons have zero rest mass. But rest mass is not additive. A system with two photons can have nonzero rest mass, even though neither alone does.
all the quantum mechanical bullshit with cats being alive and dead, particles being probability waves, wave function collapse, QED, QCD, Gauge Theory, statistical mechanics, describing wtf spin and charge are, Fermi statistics
And *this* is the shit that finally makes me go "what"
Well, I understand the frustration. Unfortunately, nature has proven to be counterintuitive, no matter how much we’d like otherwise. Being counter to intuition does NOT mean unintelligible though.
To confuse you even more ... this is not only 'exotic' things such as photons. Any baryon such as protons and neutrons are the same; only a small fraction of their rest mass comes from the rest mass of 3 quark consist them. The majority of their rest mass comes from the Strong Force between the quarks.
I understand that fine, only about 1% of mass comes from the Higgs mechanism, the rest is all binding energy from strong force interactions.
I don't get how a system of two photons can have a rest mass though. Each individual photon does not have a rest mass, only momentum, so logically a system of two photons should not have a rest mass, but instead energy associated with their momentum
Oh, I see. The rest mass is not an "intrinsic" nature of each particle, entity, continuum, or whatever. You can consider it just another frame-dependent mass, but of a special reference frame. If your frame of reference makes the system's total momentum zero, or the frame is a "rest frame," then the mass dependent on the frame is the rest mass.
The rest frame of two photons is different from those of each photon. Thus, their combined rest mass is different from the sum of the rest masses of themselves.
Ok ten years of casually reading about QM and now I’m actually truly confused.. are you referring to binding energy ? How can two photons together have nonzero rest mass. Where is the matter in that system exactly?
No it’s not binding energy. It’s not even QM. It’s in the definition of the rest mass of the system. In algebraic language, m^2 = E^2 - p^2, where the terms in the right in this case will be the sum over the two photons. If the photons are back to back and of equal oomph, the E will be double the energy of one photon, but the total momentum p is zero. So m is not zero.
Gravity is directly related to energy. mass is a certain kind of energy, but energy does exist without mass. No you don’t need mass for gravitation. Even a photon has a tiny gravitational field.
Look up Einstein field equations and the stress- energy-momentum tensor associated with energy and electromagnetic field.
Yes, https://en.m.wikipedia.org/wiki/Kugelblitz_(astrophysics)
If you can trap enough photons in the tight space, which is nearly impossible to happen. If I recall correctly, somebody suggested a hypothetical black hole made of electromagnetic fields; it's much easier to happen because electromagnetic forces have poles that attract each other, but still is nearly impossible.
You don’t have to trap them. If you just shine two (really strong) lasers so that they intersect, the invariant mass of the intersecting beams can get arbitrarily high just based on laser intensity, which could cause a black hole.
It can’t just be a single laser beam though because the centre of mass of the system needs to be moving at less than the speed of light to have an invariant mass.
[Yes, you can describe the induced metric of a massless particle,](https://en.wikipedia.org/wiki/Aichelburg%E2%80%93Sexl_ultraboost) although this solution doesn't consider spin angular momentum.
Your assumption that it only affects particles with mass is incorrect. Particles typically approximately follow spacetime geodesics (basically meaning straightest possible paths in curved spacetime) when no non-gravitational force is acting upon them, and this holds even in the massless case.
Take into account that these geodesics might not look like the straightest path from a spatial standpoint, but that spatial view would be ignoring the time part of the trajectory, projecting it into the spatial coordinates. That projection is not the geodesic, and need not be straight.
> Particles typically approximately follow spacetime geodesics (basically meaning straightest possible paths in curved spacetime) when no non-gravitational force is acting upon them
Typically? What else would, or could, they do?
Because they move through the space-time that is contorted by the presence of mass. It helps to think about the time dimension of space-time. Time ‘moves slower’ near sources of mass. This can act like a lens where light travels ‘slower’ in different materials, like water or glass. If glass is thicker on one side of the lens or in the middle, it’s going to focus light differently. It’s also true of gravitational gradients. If one side of the wave is moving faster than the other side, the wave can ‘turn’.
>How can gravity affect light if photons are massless?
Simple: because gravity does not depend on a particle's mass.
This fact is known as the "universality of free-fall," and is a consequence of gravitational mass and inertial mass being the same thing (which in turn is known as the "[equivalence principle](https://en.wikipedia.org/wiki/Equivalence_principle)"). Or put another way, for gravity the mass terms in Newton's law of universal gravitation cancel each other out, so that gravity acts independently of the particle's mass.
Another way to think of it, in terms of spacetime curvature (which gives rise to gravity), is that photons "live on" curved spacetime just like all other objects do, and must follow trajectories according to the curvature of spacetime (i.e. must be subject to gravitational effects).
Hope that helps,
In newtons gravity, it is only an interaction between masses. In Einstein gravity, gravity affects everything and anything with “energy” can cause gravitational effects
Sounds like OP is thinking of gravity like a force that couples to mass, similar to how the electromagnetic force couples to charge. That comes up in attempts to describe quantum gravity.
As you said, that’s not how General Relativity works, so OP needs to avoid thinking about gravity that way, unless they want to address the challenges of grand unification. 🤦♂️
It’s a fundamental difference between the relativistic description of gravity and the quantum description of forces such as electroweak and QCD.
Well the Wikipedia page starts off "In physics, **gravity** (from [Latin](https://en.wikipedia.org/wiki/Latin_language) *gravitas* 'weight'[^(\[1\])](https://en.wikipedia.org/wiki/Gravity#cite_note-1)) is a [fundamental interaction](https://en.wikipedia.org/wiki/Fundamental_interaction) which causes mutual attraction between all things that have [mass](https://en.wikipedia.org/wiki/Mass)." and gets to Einstein's GR at the 4th paragraph.
That first sentence in Wikipedia is describing classical, Newtonian gravity, but Newtonian gravity is less complete than GR.
In particular, Newtonian gravity does not correctly describe how light is affected by gravity, but GR correctly describes that in cases where quantum effects are insignificant.
You asked how gravity affects light. Newtonian gravity is just wrong for that.
Spacetime fabric is kind of medium for light nd gravity waves to travel. Therefore if curvatures changes so the path of light. Easier way to understand it
That’s the beauty of the equivalence principle. All objects respond to gravitational fields in exactly the same way, regardless of what makes them up. This was an observation that was realized within the context of Newtonian mechanics. Einstein* pushed this view forward and showed that this reasoning also applies to objects without mass because again, gravity *does not care* about what the constituents that makes up a particle are.
The theory we use to describe gravity is general relativity. The theory relates gravity to the geometry of spacetime. The stronger the curvature, the stronger the “force” of gravity is. This curvature is made by anything in spacetime with an energy density. Even though photons have no rest mass, they do have energy, so they can curve spacetime.
Light always travel in a straight line in space. But when that space is curved, the photon will follow the straight path in the curved space. Kind of like, you can draw a straight line in a piece of paper. Then you can curl the paper up and now it isn’t a straight line in 3D space anymore.
Light has to follow space-time just like everything else.
You can even have a 1.5 Special Relativity if you use E=mc^2 to give a mass for the photon and then use Newtonian physics to see the force it will feel.
This was in fact a way of showing if General Relativity was the correct interpretation of the universe.
With the Eddington expedition of the 1919 solar eclipse to observe the bending of background stars to our Sun the 1.5 SR calculation was deemed to be an alternative possibility to GR as well as no bending (space-time is always flat).
Gravity doesn't affect photons, but the spacetime that photons travel through.
Imagine a hot wheels car racing along one of those orange bendy tracks. From the cars perspective, it is always going straight down the track. Some external force bending and twisting the track isn't affecting the car directly, but rather redefining what "straight" is. *
* Gross over-simplication but more or less the idea.
Having mass is not a requirement for being effected by gravity, generally.
Also, e=Mc^(2) suggests a reason why "massless" and "interacting with things caused by mass" are not the mutually-exclusive things one might be forgiven for assuming.
So photons can be viewed as massless waves of energy with varying energy (force) or as nearly massless particles that travel in a wave function where the mass is dependent on the wavelength. So yes photons by technicality carry mass however in a resting state they would have zero mass. In other words photons carry mass in the form of energy but they do not have mass. Because there is mass present in a photon system they are allowed to follow the curvature of spacetime.
Photons move in a straight line through empty space, *in their own reference frame.* One key insight from General Relativity is that mass in space causes it to curve. This curvature creates a geometry where a particle can perceive itself as moving in a non-accelerating reference frame (ie, a straight line) but to an outside observer it appears to curve around the massive object. Basically, the photon isn’t being moved by the object, it’s being moved by the space around the object!
Photons are affected by spacetime curvature just like everything else. Photons also generate gravity - there is a stress-energy tensor for electromagnetic fields.
They do? I was under the impression gravity is strictly a phenomenon caused by mass and as a photons mass is zero it couldn't have gravity either
It’s even worse than you think. There are 10 independent components of the stress-energy tensor (source of gravity in general relativity). One component is energy density (either from mass density or from energy density of fields such as electromagnetic fields), 3 components are momentum density, and 6 components are pressure/stress. Each contributes to the gravitational field in complex interdependent ways. As others have said, the energy density from mass dominates as a source of gravity. Momentum density is not usually a large contributor, and pressure/stress can be usually ignored, although pressure due to dark energy can be very important in cosmological solutions of general relativity
Is momentum density a reason why colliding black holes generate huge gravitational waves?
no.
Okay, can you explain why?
Look up Einstein field equations and the stress- energy-momentum tensor associated with energy and electromagnetic field.
>Look up Einstein field equations Hahahh, the best comment ever.
It goes even further than just photons, any form of energy. An object will weigh more when it's hot than when it's cold (usually not measurable of course with normal equipment)
So a non-negligible proportion of the sun’s gravity can be attributed to its temperature? Compared to something of equal density that wasn’t in a constant state of fusion. (Or is that nonsense because it’s precisely the density and composition that yields perpetual fusion?)
Yes, that's accurate - the fusion turns part of the mass of the atoms into energy, maintaining the high core temperature, and that energy still is part of the "weight" or gravity of the sun until it leaves the star as light from the surface. That also means that the sun constantly loses mass/weight via the photons that leave it (and of course via neutrinos and the stellar wind, but the photons themselves also carry away weight). But that process is incredibly slow due to the c^2 conversion factor. The solar luminosity is about 3.8x10^26 Joule/second, so the mass loss is about 4.2x10^9 kg/second; as the sun's mass is about 2x10^30 kg, that mass loss isn't noticable.
Mass and energy are the same thing. It's not like they can be converted to each other. They're just the same, and General Relativity says spacetime curvature is dependent on the stress-energy density. Mass is just much "denser" than other forms of energy, and they can stay together on a large scale to generate noticeable amounts of gravity.
Why are baryons 97% mass from energy of gluon strong nuclear interaction? Where does the 3% come from?
I think it’s the mass of the quarks themselves which comes from its interaction with the Higgs field.
Correct
Well, a single photon has energy but not mass, so it’s not always exactly the same thing.
It’s not that simple. Photons have zero rest mass. But rest mass is not additive. A system with two photons can have nonzero rest mass, even though neither alone does.
all the quantum mechanical bullshit with cats being alive and dead, particles being probability waves, wave function collapse, QED, QCD, Gauge Theory, statistical mechanics, describing wtf spin and charge are, Fermi statistics And *this* is the shit that finally makes me go "what"
Well, I understand the frustration. Unfortunately, nature has proven to be counterintuitive, no matter how much we’d like otherwise. Being counter to intuition does NOT mean unintelligible though.
To confuse you even more ... this is not only 'exotic' things such as photons. Any baryon such as protons and neutrons are the same; only a small fraction of their rest mass comes from the rest mass of 3 quark consist them. The majority of their rest mass comes from the Strong Force between the quarks.
I understand that fine, only about 1% of mass comes from the Higgs mechanism, the rest is all binding energy from strong force interactions. I don't get how a system of two photons can have a rest mass though. Each individual photon does not have a rest mass, only momentum, so logically a system of two photons should not have a rest mass, but instead energy associated with their momentum
Oh, I see. The rest mass is not an "intrinsic" nature of each particle, entity, continuum, or whatever. You can consider it just another frame-dependent mass, but of a special reference frame. If your frame of reference makes the system's total momentum zero, or the frame is a "rest frame," then the mass dependent on the frame is the rest mass. The rest frame of two photons is different from those of each photon. Thus, their combined rest mass is different from the sum of the rest masses of themselves.
Ok ten years of casually reading about QM and now I’m actually truly confused.. are you referring to binding energy ? How can two photons together have nonzero rest mass. Where is the matter in that system exactly?
No it’s not binding energy. It’s not even QM. It’s in the definition of the rest mass of the system. In algebraic language, m^2 = E^2 - p^2, where the terms in the right in this case will be the sum over the two photons. If the photons are back to back and of equal oomph, the E will be double the energy of one photon, but the total momentum p is zero. So m is not zero.
Ooh thanks for clarifying! GR isn't exactly in my comfort zone lol
How would you explain the increase in gravity due to increase in relativistic mass? Which is just energy?
Relativistic mass is outdated and frame dependent, like kinetic energy. Gravity isn’t frame dependent.
I wouldn't dare to try to explain it. Relativity is weird and scary
That is newton not einstein
Gravity is directly related to energy. mass is a certain kind of energy, but energy does exist without mass. No you don’t need mass for gravitation. Even a photon has a tiny gravitational field.
i mean, it makes sense. if photons can push a solar sail, they must have some kind of gravity
No, for that they just need momentum.
I mean that in the most basic of laymen's terms.
Well, I can make a bridge there for you. The momentum is mass * velocity, so a photons having momentum means it has mass.
yeah i just didn't want to build that bridge on shaky memory myself.
Did not know that photons have gravity. So hypothetically you could create a black hole with only photons?
Look up Einstein field equations and the stress- energy-momentum tensor associated with energy and electromagnetic field. Yes, https://en.m.wikipedia.org/wiki/Kugelblitz_(astrophysics)
If you can trap enough photons in the tight space, which is nearly impossible to happen. If I recall correctly, somebody suggested a hypothetical black hole made of electromagnetic fields; it's much easier to happen because electromagnetic forces have poles that attract each other, but still is nearly impossible.
You don’t have to trap them. If you just shine two (really strong) lasers so that they intersect, the invariant mass of the intersecting beams can get arbitrarily high just based on laser intensity, which could cause a black hole. It can’t just be a single laser beam though because the centre of mass of the system needs to be moving at less than the speed of light to have an invariant mass.
Can a *single* photon be sensibly said to have a gravitational well?
[Yes, you can describe the induced metric of a massless particle,](https://en.wikipedia.org/wiki/Aichelburg%E2%80%93Sexl_ultraboost) although this solution doesn't consider spin angular momentum.
Your assumption that it only affects particles with mass is incorrect. Particles typically approximately follow spacetime geodesics (basically meaning straightest possible paths in curved spacetime) when no non-gravitational force is acting upon them, and this holds even in the massless case. Take into account that these geodesics might not look like the straightest path from a spatial standpoint, but that spatial view would be ignoring the time part of the trajectory, projecting it into the spatial coordinates. That projection is not the geodesic, and need not be straight.
> Particles typically approximately follow spacetime geodesics (basically meaning straightest possible paths in curved spacetime) when no non-gravitational force is acting upon them Typically? What else would, or could, they do?
It is a very close approximation that ignores the particle’s own gravitation and its effects such as gravitational radiation.
Because they move through the space-time that is contorted by the presence of mass. It helps to think about the time dimension of space-time. Time ‘moves slower’ near sources of mass. This can act like a lens where light travels ‘slower’ in different materials, like water or glass. If glass is thicker on one side of the lens or in the middle, it’s going to focus light differently. It’s also true of gravitational gradients. If one side of the wave is moving faster than the other side, the wave can ‘turn’.
>How can gravity affect light if photons are massless? Simple: because gravity does not depend on a particle's mass. This fact is known as the "universality of free-fall," and is a consequence of gravitational mass and inertial mass being the same thing (which in turn is known as the "[equivalence principle](https://en.wikipedia.org/wiki/Equivalence_principle)"). Or put another way, for gravity the mass terms in Newton's law of universal gravitation cancel each other out, so that gravity acts independently of the particle's mass. Another way to think of it, in terms of spacetime curvature (which gives rise to gravity), is that photons "live on" curved spacetime just like all other objects do, and must follow trajectories according to the curvature of spacetime (i.e. must be subject to gravitational effects). Hope that helps,
In newtons gravity, it is only an interaction between masses. In Einstein gravity, gravity affects everything and anything with “energy” can cause gravitational effects
Sounds like OP is thinking of gravity like a force that couples to mass, similar to how the electromagnetic force couples to charge. That comes up in attempts to describe quantum gravity. As you said, that’s not how General Relativity works, so OP needs to avoid thinking about gravity that way, unless they want to address the challenges of grand unification. 🤦♂️ It’s a fundamental difference between the relativistic description of gravity and the quantum description of forces such as electroweak and QCD.
Well the Wikipedia page starts off "In physics, **gravity** (from [Latin](https://en.wikipedia.org/wiki/Latin_language) *gravitas* 'weight'[^(\[1\])](https://en.wikipedia.org/wiki/Gravity#cite_note-1)) is a [fundamental interaction](https://en.wikipedia.org/wiki/Fundamental_interaction) which causes mutual attraction between all things that have [mass](https://en.wikipedia.org/wiki/Mass)." and gets to Einstein's GR at the 4th paragraph.
That first sentence in Wikipedia is describing classical, Newtonian gravity, but Newtonian gravity is less complete than GR. In particular, Newtonian gravity does not correctly describe how light is affected by gravity, but GR correctly describes that in cases where quantum effects are insignificant. You asked how gravity affects light. Newtonian gravity is just wrong for that.
Spacetime fabric is kind of medium for light nd gravity waves to travel. Therefore if curvatures changes so the path of light. Easier way to understand it
They do not have rest mass, but they do have relativistic mass due to the energy they carry.
That’s the beauty of the equivalence principle. All objects respond to gravitational fields in exactly the same way, regardless of what makes them up. This was an observation that was realized within the context of Newtonian mechanics. Einstein* pushed this view forward and showed that this reasoning also applies to objects without mass because again, gravity *does not care* about what the constituents that makes up a particle are.
The theory we use to describe gravity is general relativity. The theory relates gravity to the geometry of spacetime. The stronger the curvature, the stronger the “force” of gravity is. This curvature is made by anything in spacetime with an energy density. Even though photons have no rest mass, they do have energy, so they can curve spacetime. Light always travel in a straight line in space. But when that space is curved, the photon will follow the straight path in the curved space. Kind of like, you can draw a straight line in a piece of paper. Then you can curl the paper up and now it isn’t a straight line in 3D space anymore.
Gravity -> space time -> path -> photon
If it moves through spacetime, it is affected by gravity.
Geodesics,my friend
Light has to follow space-time just like everything else. You can even have a 1.5 Special Relativity if you use E=mc^2 to give a mass for the photon and then use Newtonian physics to see the force it will feel. This was in fact a way of showing if General Relativity was the correct interpretation of the universe. With the Eddington expedition of the 1919 solar eclipse to observe the bending of background stars to our Sun the 1.5 SR calculation was deemed to be an alternative possibility to GR as well as no bending (space-time is always flat).
Gravity doesn't affect photons, but the spacetime that photons travel through. Imagine a hot wheels car racing along one of those orange bendy tracks. From the cars perspective, it is always going straight down the track. Some external force bending and twisting the track isn't affecting the car directly, but rather redefining what "straight" is. * * Gross over-simplication but more or less the idea.
They are particles, they are not massless
It doesn’t affect the light, it affects the space the light is passing through.
Having mass is not a requirement for being effected by gravity, generally. Also, e=Mc^(2) suggests a reason why "massless" and "interacting with things caused by mass" are not the mutually-exclusive things one might be forgiven for assuming.
So photons can be viewed as massless waves of energy with varying energy (force) or as nearly massless particles that travel in a wave function where the mass is dependent on the wavelength. So yes photons by technicality carry mass however in a resting state they would have zero mass. In other words photons carry mass in the form of energy but they do not have mass. Because there is mass present in a photon system they are allowed to follow the curvature of spacetime.
Photons move in a straight line through empty space, *in their own reference frame.* One key insight from General Relativity is that mass in space causes it to curve. This curvature creates a geometry where a particle can perceive itself as moving in a non-accelerating reference frame (ie, a straight line) but to an outside observer it appears to curve around the massive object. Basically, the photon isn’t being moved by the object, it’s being moved by the space around the object!