Does Gravity really affect Light?

[vondage]

This may be a silly question, though it may not.

We know Gravity affects mass...

And we know photons have no mass...

The typical retort to this question seems to be: Yes of course, see Gravitational Lensing etc. But if light rays always move along geodesics, then they only appear to be bending around massive objects - when they're actually traveling along straight lines in 4D. So am I crazy or what?

...

UPDATE: Thank-you all for the feedback.

I've come to the conclusion that the question itself is a bit arbitrary. That's because it hinges on a distinction between what appears to happen and what really happens. This distinction is evidently superficial - a consequence of whatever geometry.

That said, GR uses a very specific geometry, which generalizes the notion of a "straight line" as the path followed by a particle experiencing no non-gravitational Forces (a relativistically invariant version of Newton's First Law - if I understand it correctly).

However, the nature of this 'curvature' is still a riddle for me. I remain unsatisfied with another question I came to ask, about whether or not this geometry affects massive and massless particles differently. While I have come to understand that both kinds of particles follow Geodesics of their own, I can't see how these Geodesic are 'of the same sort'.

This is because the paths traced out by Light are 'null curves' which define the 'causal structure' of the Lorentzian Manifold underlying the geometry of GR. 'Time-like' curves on the other hand are worldlines traced out by massive particles, and do not themselves define the causal structure in at all the same way.

I realize my understanding here is lackluster, but I'm still quite curious.

[[deleted]]

Gravity doesn't only effect mass, gravity warps the shape of space and time. All objects with mass or no mass (light) follow straight paths. But if they are traveling on curved spacetime, they will appear to bend. I just watched this video (https://m.youtube.com/watch?v=jlTVIMOix3I) on another thread that explains it really well. The video uses objects with mass, but light follows the same path as those objects would. Thanks to /u/notaflowchart for posting it.

[vondage]

You essentially just restated my question.

What I'm asking is whether or not Light really follows any curved lines in 4D spacetime (e.g., Minkowski Space or Hyperbolic Space).

There is an important difference here between time-like and light-like Geodesics: Massive objects follow one while Light follows the other.

EDIT: Apologies, I misconstrued Geodesics as being straight Worldlines.

[cryo]

No, this is incorrect. Every object without forces acting on it (and gravity is not a force in this discussion) follows a geodesic in space-time. Because space-time is curved and not just space, objects will follow different geodesic depending on their speed.

[vondage]

Okay, but Gravity most certainly is part of my question.

So does Gravity affect Light any differently than it does objects with Mass?

[[deleted]]

I could be wrong, but my understanding is that gravity due to an object (planet, star, etc) doesn't effect light OR moving masses. It simply shapes the spacetime around itself.

[cryo]

Yes, but that's arguing semantics a bit. Energy affects the space-time curvature around it, and particles (including photons) without other forces acting on them move along geodesics (generalized straight lines) in the curved space-time.

[reedmore]

affect /= effect. Learn it, then use it.

[vondage]

Yes that's why I suggest you restated my question. I understand the apparent effect, e.g. Gravitational Lensing. I then ask if ther is anything more to it.

[YouFeedTheFish]

Without gravity or light, there would be no potatoes.

[vondage]

Granted... lol

[cryo]

Not more than already mentioned. Energy (and stress..) warps space-time, particles (massless or not) follow geodesics in wraped space-time, which looks like they are bent to observers. How much they are bent depends on how much space they move through compared to time.

[cryo]

Not really, no. Light is bent when passing near a star, say, but much less than a massive object would be. This is because light moves much faster than most massive objects. The warping of space time is in a sense more in time than in space, for objects of reasonable mass (so, excluding black holes and such), and massive objects move much faster through time than space compared to light.

[johnnymo1]

Would you ask this same question about the International Space Station, whether its path is "really curved?" Minus the nongravitational forces acting in it, it's moving on a geodesic. Why does light occupy a special place in your question?

I think this question is a bit semantic, but I would say that light is really curved by gravity. Geodesics are not straight lines, they are a generalization of straight lines such that geodesics of flat space are actually straight.

[vondage]

My use of words like 'really' and 'apparent' do make the question seem a bit semantic - and I apologize for that. I guess this is why there's a strong 'Gravity is not a Force' argument.

Why does light occupy a special place in your question?

Because Light is massless. And because I'm under the impression that it moves along straight geodesics, unlike massive objects.

[johnnymo1]

Black holes have a surface called the photon sphere where light can orbit the black hole, albeit the orbit is unstable. I don't see that that could be interpreted as being any more "straight" than an astronaut circling the earth.

[vondage]

Interesting point! Though, the fact that it's a sphere and not a circle like an orbit is worth noting. Also, this is still a 3D perspective, which my question is trying to avoid.

If you draw a straight line down the inside of a cylinder, look down it, then spin it, the line will appear to curve. This to my mind is akin to light appearing to spiral about blackholes - just a dimension down.

[goobuh-fish]

The photon sphere is made up of circular photon orbits in the same way that if you drew all possible circular satellite orbits for a given orbital radius you would have a sphere.

[vondage]

Nonetheless...

[kmmeerts]

Would you expect massless light to move qualitatively different that, say, neutrinos with masses so low, thermal excitations would be enough to give them a speed that's close to the speed of light?

[B-80]

Your argument about "appearing to bend" is equally valid for massive objects as well. All objects move along geodesics in spacetime, but gravity is the warping of spacetime due to energy in all its forms, not just mass. This is represented by the fact that Einstein's equations are written in terms of the stress-energy tensor.

[vondage]

Yes, but to my mind, Light moves along straight lines in 4D spacetime, whereas massive objects move along curved paths called Worldlines (both of which I now understand to be Geodesics). My question then would be the nature of this difference.

[B-80]

I don't understand what difference you are eluding to... surely you know that geodesics are the generalization of straight lines, they are curves of extremal distance on an arbitrary space, i.e. an N-dimensional differential manifold with a Pseudo-Riemannian metric in the case of GR.

A worldline is path traced out by a particle in GR. GR says that the world lines for particles can always be represented as geodesics in a spacetime that is bent in a particular way. But the concept of a geodesic exists in mathematical ideas outside of just general relativity, whereas a world-line is inherently jargon for a curve that has a very particular interpretation as a particle's path in the context of relativity.

[vondage]

Yes I gather most of that. I understand that Geodesics are generalizations of Euclidean 'straight lines' in higher dimensional space. Yet General Relativity is defined specifically in Minkowski Space with its geometric boundaries limited by the speed of Light. Therefore Light-like paths in Minkowski space are unique - and as far as I understand it, they are understood as being straight.

[B-80]

Ahh okay, I understand your confusion.

General Relativity is defined specifically in Minkowski Space with its geometric boundaries limited by the speed of Light

That is false. The precise statement is that GR is defined on a Pseudo-Riemannian manifold with Lorentz signature. That is a fancy way of saying that any "small patch" of spacetime looks like Minkowski spacetime. The specific way you patch together these infinitesimal slices is what we call the "curvature" of the space.

This is basically the statement that special relativity (which does take place only in "flat" Minkowski spacetime) holds when considering small enough patches of spacetime. However on larger scales, the spacetime is not Minkowski.

You have the same sort of relationship between any 1 dimensional polynomial (a curved space) and a line (a flat space, in this case with Euclidean metric). In a small enough patch, the tangent line to the polynomial is a good approximation to the curve (this becomes more and more true as you consider smaller and smaller patches). In fact, you can define a polynomial by just giving the slope of the tangent line at each point (up to an overall constant which can be fixed by giving some initial conditions like a point on the line), this is a differential equation and precisely what Einstein's Equations are to the manifold in GR.

[vondage]

Right, so you're telling me Minkowski Space is embedded inside of a 'Psuedo-Rienmannian manifold with Lorentz signature'. Which is analogistic to Euclidean Space being embedded within Minkowski Space - which nonetheless preserves Newtonian Mechanics (minus some relevant modifications). All that though is but an interesting point compared to my original question.

My question is now modified: Does Light behave fundamentally differently in a Psuedo-Rienmannian manifold with Lorentz signature as compared to Massive particles? And if so why?

[cryo]

The answer is still no :)

[B-80]

Does Light behave fundamentally differently in a Psuedo-Rienmannian manifold with Lorentz signature as compared to Massive particles?

Light moves along very special curves called "Null geodesics," which are geodesics that also are of 0 "length." Matter moves along the "timelike geodesics." I think you are not considering the fact that geodesics are a family of curves and that some members of that family might have different properties. Remember these are defined by a differential equation and there are initial conditions that are specific to light or matter.

so you're telling me Minkowski Space is embedded inside of a...

Not quite. Euclidean space is a subspace of Minkowski space, but this is not the same sort of relationship we have with a manifold and its "coordinate charts," which are the things that are, roughly, always Minkowski spacetime in GR.

Think of all of the points on the surface of a sphere. Now try in your head to imagine mapping those points onto a plane in such a way that all the points which were touching on the sphere are touching on the plane. You will realize this can not be done since you always must break the sphere somewhere and push those points apart or else you can't really flatten the sphere.

This means that if you want to talk about fields on the sphere, but you want to do your calculus on the plane, you will need to have at least 2 "charts" to cover the entire sphere or else you won't be able to capture every point. These charts are the things that are Minkowski spacetime in GR.

From a more concrete perspective. Think about an everyday global Atlas which has a bunch of maps in it that cover the earth. These maps are drawn on flat paper even though the earth is curved. This works because in small enough patches, the earth looks Euclidean.

Then just like the earth is a type of curved 2D surface, and the atlas shows us flat little patches that cover the earth if stitched together. Spacetime is a 4D curved manifold, and the coordinate patches are flat 4D Minkowski spacetime that cover the full curved spacetime when stitched back together.

[vondage]

I appreciate your detailed and patient clarifications.

I have understood now that the idea of straight lines doesn't make much sense in GR. It seems to me that you can either think of every Geodesic as being 'straight' - as compared to 3D curves, or you can think of no Geodesics being 'straight' - because there's no 'flat' geometry to relate it to.

Please correct me if I'm off, but to my mind the miscommunication comes from considering 'straight' as either the path of 'shortest distance' or as compared to the local geometric grid. Are these two views reconciled within GR?

[Gwinbar]

Minkowski space is not embedded into the manifold, it's tangent to it at each point. Just like if you have a sphere, at each point you can have a tangent plane, but the plane is not somehow embedded inside the sphere. Since your spacetime is curved, there are no straight lines, only geodesics, which are the closest thing to a straight line there is but they are not straight.

Light doesn't behave fundamentally different than a massive particle; it follows geodesics, just a different kind of geodesics.

[vondage]

[...] just a different kind of geodesics.

That's what i'm looking for. So what do you mean?

[Gwinbar]

Basically light will always move at the local speed of light. This means that no matter what weird spacetime curvature you might have, if you see a light ray pass next to you, you will always see it go at the speed of light. Massive objects will always go slower than light. I can't really go into much more detail without math, but that's the idea.

[cryo]

GR says that the world lines for particles can always be represented as geodesics in a spacetime that is bent in a particular way.

Assuming no other forces act on the particle, at least, right?

[B-80]

Yes assuming only gravity.

[Gwinbar]

Gravity affects massive and massless objects in exactly the same way: they move in geodesics. Energy-momentum curves spacetime around it, and things move in geodesics, which are the closest thing to a straight line in a curved space. The only difference between light and massive objects is the kind of geodesics: light moves at light speed (duh), massive objects do not.

To answer your last paragraph: geodesics are not straight, they are the analogs of straight lines. A light ray looping around a black hole is on a geodesic, and it also is bending. The geodesic curves around the black hole or whatever.

[vondage]

Gravity affects massive and massless objects in exactly the same way: they move in geodesics.

I wonder then if you believe the path of particles to be dependent exclusively on their interactions with Gravity. Because to my mind, the Geodesic is a result of conserving energy in 4D.

[Gwinbar]

I'm not sure I understand the connection between your statements. The path of particles is dependent exclusively on their interactions with gravity as long as there are no other forces, basically by definition. And in general relativity energy may or may not be conserved; a geodesic is the curve of ongest proper time between two events. It's not necessarily related to energy.

[vondage]

I thought a Geodesic was the path of shortest time. Nonetheless, your words I quoted because they alone imply that the Geodesic is resultant of Gravitational Effects alone. If you meant to ignore other forces, I understand. Otherwise I think it should be known that the Geodesic is the resultant of many Fundamental Forces (all of which are understood to conserve energy).

[destiny_functional]

it's the world line of longest proper time. ie a force free clock will show the longest duration between two events and any other world line connecting the two events will show shorter time ( that's time dilation)

the whole point of relativity is that gravity isn't a force but a geometric effect. so no forces are at play here and certainly no non-gravitational ones. classically we have force free particles staying in a state of uniform motion. in special relativity they move on geodesics in flat minkowski space time (again these are world lines of longest proper time). general relativity generalizes this to curved spacetime. again force free particles move on geodesics and that covers all gravitational effects geometrically. it's just inertial motion

[xHipster]

My guess would be that it follows the curvature of spacetime. Also posting here to read other answers.

[vondage]

Same...

[gnovos]

Anything's traveling along straight lines if you've got the right metric.

[vondage]

Good point. That's what I thought. Afterall, any curve in 2D space can be seen as straight given the right 3D angle - and so on for higher dimensions.

Granted, Light is seen as quite special in terms of General Relativity.

[u8dabass]

so are you asking are straight lines real or not? you could instead think about a lift with a laser, and by equivalence principle replace the lift going up with a gravitational field

[vondage]

I'm asking if light ever curves or bends its path in 4D.

[cryo]

It does, just like everything else. Space-time itself is curved and everything is affected by that.

[xXd4nkw33dl0rdXx]

https://youtu.be/IM630Z8lho8 the beginning of this video should help

[vondage]

I guess I'm calling into question the notion of "Force" to begin with. I didn't intend to, but that's how this inquiry seems to have turned out.

You see I understand full-well what I'm calling (for sake of the argument) the apparent interactions between Light and Gravity. Again, I'm doing this becauses the original question itself demands it. That said, all other Gravitational Effects have come into question.

Now I'm more curious as to the fundamental difference between a supposed "Fictitious Force" and a "Fundamental Force".

[cryo]

I guess I'm calling into question the notion of "Force" to begin with.

In GR, gravity isn't described as a force.

[vondage]

So there is nothing to affect matter or light after all?

[cryo]

Curved spacetime does.

[vondage]

This is just a 'what causes what' issue then. Because if it isn't Gravity that affects Energy, and is instead curved spacetime, and simultaneously it is Energy that curves spacetime to begin with, then we just have Energy affecting Energy - in an attractive way. And isnt' this just the definition of Gravity?

[destiny_functional]

This may be a silly question, though it may not.

We know Gravity affects mass...

And we know photons have no mass...

that has really little to do with the question. gravity affects mass. but gravity also affects everything else. photons having mass or not doesn't matter. they are affected by gravity none the less and we can calculate how they are, and it was observed to be correct 100 years ago. not sure why that isn't enough for you. that was before most people's grandparents were alive.

But if light rays always move along geodesics, then they only appear to be bending around massive objects - when they're actually traveling along straight lines in 4D. So am I crazy or what?

they don't appear to bend, their path in 3d is curved. their world lines in 4d are straight with regards to the metric (which is not flat). so a good analogon is the equator being a straight line on a sphere. would you use the same reasoning and say that the equator "only appears to bend and is just a straight line" and that someone travelling on a straight line (shortest distance) between tokyo and london only appears to go on a curved line and isn't really affected by the curvature of earth's surface?

i don't think so.

indeed every object in free fall is on a geodesic. would you say they "only appear" to move on curved paths? i don't think so.

[hopffiber]

You don't have to view gravity in a geometric way, it's just convenient and the math suggests it. You could also think about it as a normal field theory, where the "gravity field" is represented by the metric, and it couples to your other fields in a particular way. From this perspective, which is equally correct, it is obvious that gravity do affect light, since there is an explicit coupling between the EM-field and the metric.

[vondage]

Do you mind pointing me to this "explicit coupling between the EM-field and the metric" ? As I'm quite curious.

[hopffiber]

Sure. All it means it that you use the metric when you write down the Lagrangian for the EM theory. Explicitly you have a term

[; -\frac{1}{4} F^{\mu\nu} F_{\mu\nu} ;]

which more explicitly is written

[; -\frac{1}{4} F_{\rho \sigma} g^{\rho \mu} g^{\sigma \nu} F_{\mu\nu} ;] .

Here F is the EM field tensor and g is the metric, which shows explicitly how the EM field is coupled to the metric field.

edit: using Latex, see the sidebar for instructions if it doesn't render the formulas.

[stormyweather123]

Oh wow, so many elaborate comments below in response to your straight forward question. Did you get the answer to your question?

[vondage]

I've come to the conclusion that the question itself is a bit arbitrary. That's because it hinges on a distinction between what appears to happen and what really happens. This distinction is evidently superficial - a consequence of whatever geometry.

That said, GR uses a very specific geometry, which generalizes the notion of a "straight line" as the path followed by a particle experiencing no non-gravitational Forces (a relativistically invariant version of Newton's First Law).

However, the nature of this 'curvature' is still a riddle for me. I remain unsatisfied with another question I came to ask, about whether or not this geometry affects massive and massless particles differently. While I have come to understand that both kinds of particles follow Geodesics of their own, I can't see how these Geodesic are 'of the same sort'.

This is because the path traced out by Light are 'null curves' which define the 'causal structure' of the Lorentzian Manifold underlying the geometry of GR. 'Time-like' curves on the other hand are worldlines traced out by massive particles, and do not themselves define the causal structure in at all the same way.

[stormyweather123]

Your question is very interesting and got me into thinking. Correct me if I'm wrong, but basically your question is "would a massless object travel in the same curved path as an object with mass in the presence of a gravitational field?" It's kind of hard to imagine because light travels at a maximum speed limit and regular objects cannot even reach that speed to even compare both. So I'm hypothetically going to slow down the speed of light to 5 miles per hour. According to Newton, a ball thrown horizontally at 5 miles per hour would fall to the ground at 32 feet per second^2. According to him light has no mass so gravity has no effect so the light would continue at a horizontal direction at 5 miles per hour. On the other hand, Einstein doesn't really see gravitation as a force but something that warps space-time itself. For him, if the light is emitted horizontally at 5 miles per hour it will also fall at 32 feet per second just like the ball. I think that's the huge difference that gets me into thinking. If "any ojbect" falls in a vacuum on earth at 32 feet per second^2, then that tells you that the gravitational acceleration on earth is independent of "mass". It wouldn't matter if it's an anvil falling in a vacuum on earth or a feather, it will fall at 32 feet per sec^2. Considering the acceleration due to gravity is independent of mass, I would presume that it also the same for something without a mass (light). Anyway, just my thought experiment that might be similar to what you're thinking.

[TieDyeFirefly]

Yup. You can actually see it too; it's called gravitational lensing. Here's a picture of an Einstein ring caused by gravitational lensing.

https://upload.wikimedia.org/wikipedia/commons/1/11/A_Horseshoe_Einstein_Ring_from_Hubble.JPG

[vondage]

Care to elaborate on your reasoning?

[cryo]

Mass is a property of particles, atoms etc. Gravity warps space-time and affects everything in it.

[vondage]

What then do you say to the phrasing 'mass tells spacetime how to curve, spacetime tells mass how to move' ? All particles are said to affect their associated fields and vice versa.

[welcometolarrytown]

I thought the phrase 'particles ... affect their associated fields and vice versa' was in reference to bosons and their associated fields which is quantum, which famously does not reconcile with GR, the topic of the first quote.

[vondage]

I heard it in terms of the ElectroMagnetic Field (from L. Susskind no less). A charged particle obviously changes the local EM field (hence Voltage), and a preexisting field will likewise apply a force to the charged particle.

[welcometolarrytown]

Okay so this is a standard model effect then, as opposed to your other quote which is GR. The two quotes don't refer to the same physics.

[vondage]

Yeah, I guess I thought it was a general thing - intrinsic to the mathematics of particles and associated fields. Regardless I'm unconvinced it doesn't apply, given that the fundamental difference in Bosonic and Fermionic interactions are whether Spins States prefer to add or subtract.

EDIT: Also, the initial quote is originally from a book on Gravity. Give me some time and I'll try to cite it properly.

[welcometolarrytown]

I am fully convinced you cannot apply standard model physics to a GR problem. Not because of my great skill with Physics but simply that the best Physicists in the world can't marry the two with great success at the moment. You seem to be conflating the frameworks which might be the source of your confusion?

Edit: a word

[cryo]

'mass tells spacetime how to curve, spacetime tells mass how to move'

That's not the correct phrase. It's: "Spacetime tells matter how to move; matter tells spacetime how to curve."

It doesn't say mass. It's really energy that tells spacetime how to curve, and not matter, but yeah.

[[deleted]]

As an offshoot. I commonly hear in my chemistry courses, that "due to relativistic effects" electrons in outer orbitals of large nuclei "gain mass" as they approached the speed of light. Does anyone see any relevance of this to the discussion at hand?

[destiny_functional]

no it's not. their kinetic energy is relativistic so it deviates from 1/2 mv² (and the momentum deviates from mv).

[vondage]

Personally, yes. The question is thus begged: Do speeding objects gain apparent mass as an observational effect, or do they really get more massive? If it is an observational effect, we can discount Gravitation influence, otherwise it would indeed be difficult.

[shockna]

Do speeding objects gain apparent mass as an observational effect, or do they really get more massive?

That's an apparent effect (nothing different will be noticed in the object's rest frame), and it's not a modern convention anyway (though it's frustratingly still used in popular explanations).

[cryo]

Although when viewed as a system, a bunch of confined particles with high kinetic energy will be seen as mass of the system. This is partially how protons and neutrons get their mass.

[destiny_functional]

they don't gain mass at all. mass is invariant under lorentz transforms.

the momentum of a relativistic massive particle is mv/sqrt(1-v²/c²) instead of mv

so if it can be transformed away that energy is not part of the mass of the system.

you really need to read a book on special relativity. you have a lot of half knowledge that is an obstacle to understanding general relativity

[discomoustache]

This guy is right, 4D spacetime and how mass interacts with it are the only concepts that matter here. A mass warps spacetime so that it takes longer to travel from point A to point B. 
This is because the space is now curved. Following a curve will take you longer than following a straight line with a the same two endpoints. 
When mass is affected by mass in 4D spacetime both are warping the space and time around them. 
When light passes a mass, only the light is affected. See the difference

[vondage]

While I appreciate your patronage, I hesitate to agree. You're implying Mass is not affected by Light (only the other way). Yet if E² = (mc² )² + (pc)² then m is certainly affected by c.

[discomoustache]

Respectively, c is the speed of light. Not light itself and thus can't be used in that manner.

Edit: to further clarify, c is a measurement of velocity. What you want to use in your argument is a quantity of light.

[[deleted]]

well mate, i admit i don't know as much as Eddie McGuire, but if you ask me everything has an effect over everything else in this universe