What is the refractive index of the Universe?

[confusedhome]

TL;DR Summary

Due to the ever changing directions of light through the Universe it must be treated as though it has an Index of Refraction.

I have not seen anything published siting a value, so being the curious type I was wondering if any has and what is the value? Also it would be nice to know at what Energy it is referenced to
Thanks all,
Bob

 

[phinds]

Summary: Due to the ever changing directions of light through the Universe it must be treated as though it has an Index of Refraction.

Uh ... I think you misunderstand the way light works in the universe. Light "changes direction" only in that it follows geodesics and near massive bodies those geodesics, which, while straight lines in the geometry of the universe, are "curved" if you insist on describing them using Euclidean geometry. That has nothing to do with an index of refraction.

 

[PeterDonis]

Due to the ever changing directions of light through the Universe it must be treated as though it has an Index of Refraction.

No, it does not have to be treated that way. Mathematically you could treat it that way, by pretending that the bending of light due to gravity is actually due to a hypothetical "medium", but only if you allowed the index of refraction to vary continuously based on position. I believe Andrei Sakharov, back in the 1960s, tried this approach, but it didn't catch on, probably because it just makes the math more complicated than it needs to be.

 

[kimbyd]

Also, in electromagnetism the index of refraction is a direct consequence of the relationship between the electric permittivity and magnetic permeability of the medium. The first term defines how electric fields behave in the medium, while the second defines how magnetic fields behave.

So when you're asking about the index of refraction, you're really asking about how electric and magnetic fields themselves act within the medium. Since the stuff that light is traveling through is near-perfect vacuum, the index of refraction is almost identically equal to one. There is a slight deviation from unity because the intergalactic medium isn't actually a perfect vacuum, but it's close enough for most purposes.

The curvature of space-time doesn't change the above description at all, because it doesn't change how electric and magnetic fields behave (in terms of the permittivity/permeability).

 

[PeterDonis]

Since the stuff that light is traveling through is near-perfect vacuum, the index of refraction is almost identically equal to one.

That's true if we take "index of refraction" to have only its usual meaning in electromagnetism.

But, as I mentioned, it is possible mathematically to treat the bending of light by gravity as if it were due to an index of refraction of a medium--i.e., to treat spacetime curvature, mathematically, in a similar way to the usual treatment of the index of refraction in electromagnetism. As I understand it, this approach is not much used because it makes the math more complicated and doesn't enable you to solve any problems you can't solve using more conventional methods in GR.

 

[Vanadium 50]

If you have an index of refraction that is homogeneous and isotropic, how do you get a change in direction?

 

[PeterDonis]

If you have an index of refraction that is homogeneous and isotropic

It is when averaged over the universe, but it isn't if you look at individual gravitating systems, like a galaxy or a star system or an individual gravitating mass like a star or a planet (or a black hole).

 

[Vanadium 50]

Fine, but now you're not talking cosmology.

 

[confusedhome]

Hi Folks, Thanks for joining the discussion.
I am only looking at it from the view that if matter affects light (Photons) then any matter will affect the Photon regardless of its size or distance from the mass, and therefore the Universe as a whole should also be looked at as having a Index of Refraction.
Granted, it can be seen as though the mass of a Black Hole would basically have the same effect as an Atom in a lens or spectrometer, only on a smaller scale.
It also seems that it would not matter is Space were curved or not it is the overall effect that matters.
Bob

 

[PeterDonis]

if matter affects light (Photons) then any matter will affect the Photon regardless of its size or distance from the mass, and therefore the Universe as a whole should also be looked at as having a Index of Refraction

No, this is not valid reasoning, because if we are going to model the photon as moving through a medium (with vacuum spacetime being the medium), then the photon's motion is affected by the index of refraction of the medium at the point where the photon is moving. The fact that the index of refraction at that point will be a function of the distribution of matter everywhere (more precisely, everywhere in the past light cone of that point) doesn't change this. And the index of refraction at different points will be different because of the variation in matter distribution--the universe is not exactly the same everywhere.

In short, you are thinking of index of refraction as a property of the medium as a whole, but it isn't; it's a property that
can vary from point to point within the medium.

It also seems that it would not matter is Space were curved or not it is the overall effect that matters

First, it's the curvature of spacetime that matters, not space.

Second, as above, there is no "overall effect"; there is an effect at each point, and it can vary from point to point.

 

[confusedhome]

If a quantity cannot be measured by current technology, does that mean that it doesn't exist? No.
The Universe is in existence and therefor does have an overall effect.
Nothing in the Universe is homogenous, everything varies from point to point in space and time.
Bob

 

[PeterDonis]

The Universe is in existence and therefor does have an overall effect.

This is not valid logic.

Nothing in the Universe is homogenous, everything varies from point to point in space and time.

Yes. How does this support your claims? (Hint: it doesn't.)

 

[kimbyd]

If a quantity cannot be measured by current technology, does that mean that it doesn't exist? No.
The Universe is in existence and therefor does have an overall effect.
Nothing in the Universe is homogenous, everything varies from point to point in space and time.
Bob

The universe is, however, on average homogeneous and isotropic. Local structures such as galaxies and galaxy clusters have minimal impact on this broader picture.

Perhaps more to the point, space-time curvature doesn't look anything like an index of refraction, because if you pass a light ray through something with an index of refraction, the light ray will change direction at the boundary, but it will then move in a straight line once it enters the new material (just at a different speed).

Space-time curvature, on the other hand, causes light rays moving parallel to one another to start converging or diverging over time. If it were an index of refraction effect, this would be because the light rays are entering a new region with different properties. Plus the light rays would also change speed. Neither of these two effects makes any sense, because light rays moving in the opposite direction will see the same convergence/divergence, and the light rays don't change speed at all.

 

[PeterDonis]

space-time curvature doesn't look anything like an index of refraction

It does (if you write the math appropriately--but, as I've said previously, doing the math this way makes it harder, not easier) for a medium in which the index of refraction varies continuously, instead of changing discontinuously at boundaries.

Plus the light rays would also change speed

Light rays do change coordinate speed if you choose appropriate coordinates (doing that is part of what needs to be done to make the math for spacetime curvature look like the math for refraction in a medium whose index changes continuously).

 

[kimbyd]

That's true if we take "index of refraction" to have only its usual meaning in electromagnetism.

But, as I mentioned, it is possible mathematically to treat the bending of light by gravity as if it were due to an index of refraction of a medium--i.e., to treat spacetime curvature, mathematically, in a similar way to the usual treatment of the index of refraction in electromagnetism. As I understand it, this approach is not much used because it makes the math more complicated and doesn't enable you to solve any problems you can't solve using more conventional methods in GR.

I will admit that you could create something that kinda sort of looks like an index of refraction, but then you'd just be talking about space-time curvature using different terminology. I doubt it's useful, since this "index of refraction" would be a fundamentally different kind of thing.

This idea works okay for compact objects, because the amount of space-time curvature varies with distance from the object. The scalar curvature $R$ does actually act as a sort of "index of refraction" in that case, as a light ray traveling from background flat space-time into a region with curvature and out again gets deflected just like it would if it passed through a spherical lens with the appropriate index of refraction (with the only difference that the speed of light would vary with the spherical lens, but not with the gravitational lens).

This way of thinking about it works for that very specific circumstance, but cannot capture cosmological curvature at all. The problem is a fundamental one: cosmological curvature is the same at every point in space and time. With constant curvature, parallel light rays will either converge or diverge depending upon the curvature, but the properties of the space-time they are traveling through has never changed. It's simply impossible to capture that with an index-of-refraction-like idea, because light rays always travel in straight lines through an object with unchanging index of refraction (assuming flat space). You can't vary the pseudo-index-of-refraction from place to place because then light rays traveling in different directions would have different behavior. But if you don't vary it, you don't get any deflection.

 

[kimbyd]

Light rays do change coordinate speed if you choose appropriate coordinates (doing that is part of what needs to be done to make the math for spacetime curvature look like the math for refraction in a medium whose index changes continuously).

Sure, but the total travel time won't be impacted by this coordinate change. Such coordinate-specific quantities are meaningless, but measurable quantities like round-trip or relative travel time are not. Gravitational lenses tend to only impact travel time by affecting the total distance light rays traverse.

 

[PeterDonis]

I will admit that you could create something that kinda sort of looks like an index of refraction, but then you'd just be talking about space-time curvature using different terminology. I doubt it's useful

As I mentioned in previous posts, it indeed has not been found to be useful. But it was (AFAIK) tried.

the total travel time won't be impacted by this coordinate change

Agreed; coordinate changes can't change invariants.

 

[PeterDonis]

The problem is a fundamental one: cosmological curvature is the same at every point in space and time

But we don't observe light ray trajectories due to "cosmological curvature". We observe light ray trajectories that covered a particular path through the universe, with particular gravitating masses (or lack thereof) in that path.

With constant curvature, parallel light rays will either converge or diverge depending upon the curvature, but the properties of the space-time they are traveling through has never changed.

The curvature is not constant, because the spacetime of the universe is not stationary; along any worldline (timelike or null), the curvature invariants vary with affine parameter. So it is not the case that "the properties of the spacetime never change" along the worldline of a light ray (or of a timelike observer). They do.

 

[kimbyd]

But we don't observe light ray trajectories due to "cosmological curvature". We observe light ray trajectories that covered a particular path through the universe, with particular gravitating masses (or lack thereof) in that path.

Sure we do, though it's a bit tricky. This curvature determines the angular size of objects relative to their physical size and distance. Measuring the amount of curvature means having some way of estimating the "true" physical size of objects, or, more commonly, the relative physical sizes of different objects/structures at different distances.

The curvature is not constant, because the spacetime of the universe is not stationary; along any worldline (timelike or null), the curvature invariants vary with affine parameter. So it is not the case that "the properties of the spacetime never change" along the worldline of a light ray (or of a timelike observer). They do.

Space-time curvature is nearly constant in space (at large distances, at least), though not in time. When I said "never change" I was playing a little bit fast-and-loose with the terminology, but I meant that they don't change in space.

Also, it can be worth considering space-times for which the curvature doesn't actually change in space or time, such as a universe dominated by a positive-valued cosmological constant. In such a universe, there is a genuinely constant space-time curvature, and parallel light rays tend to deflect over time.

 

[confusedhome]

'Gravitational Lensing' occurs because photons are refracted by gravity. Although it may be more intense from point to point, much like raindrops or clouds in Earths atmosphere the atmosphere has an overall Index of refraction.
The reason we can detect 'Lensing' is because we are not at the focal point, if we were we would only see the source not the lens itself.
So, what is the Index of Refraction of the Universe?
Bob

 

[PeterDonis]

Space-time curvature is nearly constant in space (at large distances, at least), though not in time

Yes, but that's irrelevant to what happens to a light ray over the course of its travels, because the light ray's worldline is not a spacelike curve in a surface of constant comoving time; it's a null curve. And along that null curve, spacetime curvature changes (but see the caveat below).

it can be worth considering space-times for which the curvature doesn't actually change in space or time, such as a universe dominated by a positive-valued cosmological constant

Yes, this is a fair point. It's rather counterintuitive that de Sitter spacetime actually does have a timelike Killing vector field (strictly speaking, it's timelike only inside the cosmological horizon), even though it is also "expanding" in the usual sense of an expanding universe.

 

[PeterDonis]

'Gravitational Lensing' occurs because photons are refracted by gravity. Although it may be more intense from point to point, much like raindrops or clouds in Earths atmosphere the atmosphere has an overall Index of refraction.
The reason we can detect 'Lensing' is because we are not at the focal point, if we were we would only see the source not the lens itself.
So, what is the Index of Refraction of the Universe?
Bob

You are evidently not even reading the replies given to you in this thread, so there is no point in continuing the discussion.

Thread closed.