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Comment by cyberax | Hacker News Reader

> Is there anything stopping you from putting 2+ satellites out "closer" but in the path of the lensed light

The Sun. Literally.

Satellites have to be that far for the Einstein ring to be bigger than the apparent size of the solar disk.

Edit: to make it a bit more clear, the gravitational lens does not quite behave like a normal lens. Instead, you see the light from _behind_ the object. So if you're too close to the lensing object so that the Einstein ring is not larger than it, you'll just see a part of the object to be a bit more bright.

Also, the gravitational lens does not actually _focus_ the image, it distorts it into a band around the lensing object.

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But if the light is "warping" around the object then would you be able to grab the light from either side by intercepting it there? If you are at the X AU required for lending, but you sit at X/2 AU with some slight offset, you would be in the path of the light that would be traveling to X AU eventually.

I understand if what I'm trying to describe is impossible, I just don't fully understand why. (Is it out of focus? Is the sun too big/bright?)

I'm no expert here. You mention "either side" as if the light came from both the left and the right. But I think the light would be coming along a circle all around the sun depending on exact position.

So the trick here is that if you are at the focus point, you get all that light in a small area "for free". But if you try to catch the light on the way, you now need to catch eveywhere in a whole massive circle, which is basically impossible, so you only catch a minuscule amount of the light. And then have to deal with interferometry.

> But if the light is "warping" around the object then would you be able to grab the light from either side by intercepting it there?

Certainly. But it won't be any more focused at that location. There's no real advantage compared to just building a regular phased antenna array.

>to make it a bit more clear, the gravitational lens does not quite behave like a normal lens. Instead, you see the light from _behind_ the object.

Or to put it another way: A gravity lens bends space so that the light from behind an object curves around it while travelling straight.

"Normal" lenses bend light more strongly farther out towards the edges. Gravitational lensing is shaped differently.

The point is you aren't bending the light, no the light is travelling straight.

You are bending the dimension, the light travels straight through a bent dimension thus coming out curved.

I think that's mindblowing.

No, light doesn't travel in straight lines.

Stronger gravity around massive objects causes slow down of the part of a light wave closer to object, compared to outer part.

This difference in speed, caused by _interaction_ between the photon and gravitational field of the body, results in the bending of the light's trajectory.

Bending of spacetime is just a simplification of this process to model that easier.

from what I understand, slowing down would be true for a non-massless particle, but speed of light in vacuum is still the same around massive objects. What changes is the frequency of the light in this particular direction, and that "turns" it, probably because of self-diffraction?

Parts of photon cannot have different frequencies than whole photon. Both inner and outer parts of photon will make exact same number of fluctuations for the same period of time, but inner part will travel slightly smaller distance.

It's the same effect as in reflections, except that speed difference between air and solid objects is much much bigger, which results in sharp turning radius.

The speed of light is constant as measured from any observer. This has been verified experimentally to a very high precision and motivated the development of special and general relativity.

Otoh there is no requirement for a wave front to have the same frequency as when it started. A gradient in the gravitational field can cause a gradient in the gravitational redshift and thus "parts of photon" can very well have slightly different frequencies. If you recombine the paths and have the photon to interfere with itself, the interference pattern will capture the shape of such a wave function as affected by the distortion in the gravitational field.

IIRC this is the "standard" way of thinking about what's going on although marrying quantum mechanics and general relativity is still a work in progress.

If you buy into another theory that involves a variable speed of light, I'd love to hear more about what exact theory are you talking about since it seems to me that the burden of proof is on who makes the most extraordinary claims.

LIGO/Virgo/KAGRA found that speed of light in vacuum is affected by gravitational waves. This is verified experimentally to very high precision (1.2E-20m). If merge of neutron stars 200 megaparsec away can affect propagation of light here, on Earth, then why it cannot affect it near to the star?

ok I think we're talking past each other. let's take a step back.

Let's imagine two points in space A and B, that are let's say 10 light minutes distant from each other. A signal going straight from A to B will thus take 10 minutes.

If point A sits in a strong gravitational field (e.g. it's orbiting a very heavy star), the signal will still take 10 light minutes to reach point B. (please tell me if you disagree with this assumption).

Now, let's place another heavy star at the midpoint between points A and B.

How long will it take for a photon emitted by A to reach B? Well, it won't reach it because it will hit the start that's in between.

But another photon whose direction wasn't directly in the path from A to B will follow a longer path, be deflected around the star and reach point B.

It will take longer than 10 minutes to reach point B because it will move along a longer path.

Do you agree this is what would happen?

> How long will it take for a photon emitted by A to reach B? Well, it won't reach it because it will hit the start that's in between.

Now imagine that it's not a star, but a black hole with a small radius to make arguments easier. You shoot a photon slightly off the axis, and it gets deflected.

You can try to treat a photon as a moving object, and integrate the forces acting on it. Taking Lorentz transformations into account, of course.

But the thing is, your calculations will be off, and the experimental results won't match your predictions. You will need to take into account that the lightspeed near massive objects is _slower_ for distant observers.

Another example, suppose that you have a star surrounded by a massive cloud of fog. Somebody shoots a laser beam from one side of the fog bank to another, while you are far away from the star. The fog is there just to allow you to see the beam as it moves, it does not by itself slow the light.

But you will actually see the light moving _slower_ than lightspeed!

Or equivalently, you can take a clock that ticks every second. And if you lower that clock to the surface of a planet, you will see the clock ticking slower. And this is a very real effect, we have to correct for it in the GPS satellites.

Yes the clock will indeed tick slower deep in the gravity well and that's the reason why from the point of view of the observer outside the gravity well the photon will be red shifted!

The speed of light is the same in both frames of reference. What you think is going affect the speed is actually the slowing of the proper time which effectively causes the photon to redshift.

> The speed of light is the same in both frames of reference. What you think is going affect the speed is actually the slowing of the proper time which effectively causes the photon to redshift.

No. You can drop a ruler onto the surface of Earth and measure from the Moon the time it takes the light to travel from one end of the ruler to the other. It will be slower than the lightspeed from your point of view. This is a real effect, we've measured it.

However, it will be lightspeed from the point of view of an Earth observer.

Ok but that's exactly what it means when we say that clocks are ticking slower in a gravity well (after all you can implement a clock by bouncing light).

And this effect falls out directly from the warping of space-time described by general relativity

am I understanding correctly that you claim that the warping of space-time is just a mathematical trick and that the phenomena are better explained by just postulating they light slows down in a gravity well?

> am I understanding correctly that you claim that the warping of space-time is just a mathematical trick and that the phenomena are better explained by just postulating they light slows down in a gravity well?

Light slows down in gravity wells because the space-time is "denser" near massive objects. This is not a mathematical trick, this is actually a real effect.

It's also the reason for gravitational lensing, as the shortest path through a gravity well is not a straight line. Light can avoid the slowdown near the massive object, if it instead "goes around" it. The curved path is longer, but faster lightspeed along it compensates for the additional length.

> The speed of light is constant as measured from any observer.

That is not true. The "speed of light" in vacuum is not constant for all observers in the _general_ relativity. It is constant only _locally_, Lorentz invariance is a local symmetry in GR. Special relativity thus simply becomes an edge case of GR, where the Lorentz invariance is also a global symmetry.

That's how we get lensing, regions of space near a massive object are more "viscous" and the light moves slower through them.

> Stronger gravity around massive objects causes slow down of the part of a light wave closer to object, compared to outer part.

That only matters in areas with _really_ high fields, this effect is negligible for areas far away from a singularity of a black hole.

Instead, it's really the space that curves. The light does not slow down, it always moves at the speed of light. In the general relativity there is no "gravity field", gravity is a fictitious force.

Edit: also, gravitational lensing applies to massive point-like particles as well. For slow-moving particles and weak fields, it's negligible compared to regular Newtonian orbits, but if a particle moves at a speed that is close to lightspeed, it'll be lensed just like the light.

You forgot about conservation of momentum. Photon cannot change it's direction without interaction with something to exchange momentum.

"Bending of spacetime" is just computational trick to increase precision of the model.

Bending of trajectory because of change of speed of light is negligible, yes. It's only visible on light-year long distances.

Photon is very wide. Dual slit experiment show that single single photon interacts with two slits up to millimetre apart. Even small difference in speed/frequency at such large distance will accumulate to noticeable change of course at light year long distances.

I can calculate bending radius, if you wish.

> Photon cannot change it's direction without interaction with something to exchange momentum.

Doesn't the entire photon simply exchange momentum with the star, without needing to invoke any higher-order effects? Just as the star exerts a gravitational pull on the entire photon, the entire photon exerts a (very miniscule) gravitational pull on the star.

Photon is massless, so it cannot use the same physical process as non-massless particles. For example, when photon will aim at a object, it will not «fall» and increase it speed, like a regular particle.

> You forgot about conservation of momentum. Photon cannot change it's direction without interaction with something to exchange momentum.

No. I'm not forgetting anything. Photons _do_ _not_ change direction. They always move in straight lines (from their "point of view"). It's just that if you step a bit away, these straight lines are not actually "straight" globally.

A classic example is a 2D ant crawling on a surface of a sphere. From the ant's point of view, it moves in a straight line, but a 3D observer will see that a straight line is actually a 3D circle.

Conservation laws are not violated. A photon (or another particle) will cause its own slight bending of the space-time, that in turn will slightly bend the star's trajectory.

It does sound like an interaction between gravitational fields, but the models give different numeric predictions.

> "Bending of spacetime" is just computational trick to increase precision of the model.

It really is not.

> Photon is very wide.

Facepalm. Sorry dude, but you have no idea what you're talking about. Lensing and time dilation also happen for point-like particles like electrons.

> Conservation laws are not violated. A photon (or another particle) will cause its own slight bending of the space-time, that in turn will slightly bend the star's trajectory.

It's not possible, because EM field doesn't affect all particles.

> Lensing and time dilation also happen for point-like particles like electrons.

If we stick 2E15 electrons together in a long line, then it will start to rotate too due to differences in gravitational field at inner and outer segments of the line. Something like that must happen to an 1mm wide photon too. I'm not talking about orbit of those electrons around object, but about rotation alone.

> It's not possible, because EM field doesn't affect all particles.

It's not the EM field, but gravity.

> If we stick 2E15 electrons together in a long line, then it will start to rotate too due to differences in gravitational field at inner and outer segments of the line.

Just look at an individual electron. Why would it curve? It's sufficiently point-like for the gravitational field gradient to be negligible.

The speed of light in vacuum is constant and is not impacted by gravity, AFAIK. Really the light is travelling in a straight line in space but gravity bends space and time.

LIGO/Virgo/KAGRA found that speed of light in vacuum is affected by gravitational waves. This is verified experimentally to very high precision (1.2E-20m).

Light doesn't travel in a straight line because, to change trajectory of photon, photon must interact with something to exchange momentum. You are talking about mathematical model[1].

[1]: https://en.wikipedia.org/wiki/Curved_spacetime

Aren't gravitational waves the same effect I described?

c is an universal constant and it seems that you're saying that it is not!

> Aren't gravitational waves the same effect I described?

I cannot read your mind.

> c is an universal constant and it seems that you're saying that it is not!

Yep, c is universal constant for many physical models.

In physical world, c is constant as long, as properties of physical vacuum (permitivity and permeability) are constant, which in turn depends on α (Fine-structure constant[1]), which, in turn, variates at higher energies[2].

[1]: https://en.wikipedia.org/wiki/Fine-structure_constant

[2]: https://arxiv.org/abs/hep-ph/0201198

Obviously, you are correct. Gravity bends space, it doesn't bend vectors in space.

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