I don't think space is expanding.

[Ziggurat]

Originally Posted by Mike Helland

You were talking about a doppler shift due to the Earth's motion.

It moves at about 100,000 km/hr around the sun, or 0.0009c.

The motion of the Earth is already taken into consideration of redshifts, as well as even the rotation of Earth.

My demo shows that regardless of the photon speed, the frequency of arrival rate doesn't change

But we aren't measuring the frequency of arrival rate. We're measuring the frequency of individual photons. This is such a fundamental thing that I don't think you comprehend how big an error you're making.

And that frequency gets Dopler shifted due to relative motion of the detector. So if the earth is moving towards a source, that blue shifts it, and if the earth is moving away, that red shifts it. And we can (and do) measure that difference as it changes over the course of a year. But the amount it shifts is also dependent on the velocity of the signal. And so we can detect if the signal is coming in at different velocities, because that would lead to different Doppler shifts. That's why you can hear the Doppler shift as a car passes you, even though your eyes aren't sensitive enough to see the difference in color: sound moves slower than light, so the Doppler shift is larger.

And do we see a difference in annual Doppler shift from the earth's orbit? No, we do not. We see that annual Doppler shift, but it's the same for all sources.

[Mike Helland]

Ffirst of all, I think you're probably right. I appreciate the time you've spent talking to me about this.

I also think you've proposed a pretty good experiment here. I'm as up for disproving this hypothesis as you are, so if you propose a test and it seems to a good test, that's a good thing.

You might think the Hubble has scanned the whole sky and pointed out our obvious mistakes in our models, but getting the Hubble to do your observations is fiercely competitive, and if you're not looking for something in particular there's no reason it will be magically spotted in all the data that comes back.

So, if you're right, we should be able to disprove the hypothesis with the following data:

Measurements from space of red-shift of a high z galaxy on the horizon while Earth is moving at its maximum toward and away velocities.

The hypothesis would predict a higher ratio of velocity / Earth's velocity than photons traveling at c.

If that difference is not observed, the hypothesis would be wrong.

Agreed?

Originally Posted by Ziggurat

And do we see a difference in annual Doppler shift from the earth's orbit? No, we do not. We see that annual Doppler shift, but it's the same for all sources.

https://physics.stackexchange.com/qu...t-measurements

It says:

It does have an effect, but whether or not you have to worry about it depends on how sensitive your measurements are. The rotational period of the Earth is about 24hours. Depending on your latitude, that could contribute to your velocity as little as 0ms−1 (at the poles) or as much as 464ms−1. Worse, the effect that this has on your observation will depend on the angle between the direction to the source when the observation is made and East along the ground. So, it's a little complicated.

That said, 464ms−1 corresponds to a Doppler shift between ±1.55×10−6, so only the most sensitive measurements will be affected, and mainly if the source is near the East/West horizons.

A much more important Doppler shift to account for in most cases is the one from the orbital revolution of the Earth about the Sun. That has a speed of about 29.8kms−1 and depends on the angle between Earth's motion and the source (worked out from the source's position in Ecliptic coordinates and solar elongation). That effect is up to ±9.9×10−5, so even then the measurement will have to be pretty precise for it to matter.

[Mike Helland]

Food for thought.

20 years ago if I was debating a Christian I would say something like:

"You think God created the Earth in 7 days, but we can see from observation that the universe has been expanding for 10 plus billions of years and galaxies evolve and planets are made over billions of years."

Now I would have to say:

"The Earth in 7 days? That's nothing. The universe inflated in a nanosecond due to dark energy.

That's an odd leap to make.

[Reformed Offlian]

Originally Posted by Mike Helland

Ffirst of all, I think you're probably right. I appreciate the time you've spent talking to me about this.

I also think you've proposed a pretty good experiment here. I'm as up for disproving this hypothesis as you are, so if you propose a test and it seems to a good test, that's a good thing.

I can think of an even simpler experiment: run light from distant galaxies through a refracting medium, like a prism. Or the earth's atmosphere. If the photons are entering the medium at different speeds, they will get refracted differently. If not, then not. Snell's law.

Since earthbound observations do this every day, I suggest that we already know what the results will be, and that they show that your hypothesis is wrong.

[Mike Helland]

Originally Posted by Reformed Offlian

I can think of an even simpler experiment: run light from distant galaxies through a refracting medium, like a prism. Or the earth's atmosphere. If the photons are entering the medium at different speeds, they will get refracted differently. If not, then not. Snell's law.

Since earthbound observations do this every day, I suggest that we already know what the results will be, and that they show that your hypothesis is wrong.

In the model in my experiment there is only distance and energy in the model of the photon.

The interaction between photons and electrons in this case is absorption and emission that is purely energy and distance dependent.

I'm not sure this tests that model, since once the slow ancient photon hit the medium, they are absorbed by the first atoms at the reduced energy level and emitted at the same energy with a D = 0 and therefore v = c.

I would expect the photons to interact with the medium the same whether they were initially redshifted by the expansion of space, simply emitted at a lower energy, or by the hypothesis being tested.

I hope you don't take this as being contrarian. I'm just trying to make sure the model is properly being tested.

[Reformed Offlian]

Originally Posted by Mike Helland

In the model in my experiment there is only distance and energy in the model of the photon.

The interaction between photons and electrons in this case is absorption and emission that is purely energy and distance dependent.

I'm not sure this tests that model, since once the slow ancient photon hit the medium, they are absorbed by the first atoms at the reduced energy level and emitted at the same energy with a D = 0 and therefore v = c.

I would expect the photons to interact with the medium the same whether they were initially redshifted by the expansion of space, simply emitted at a lower energy, or by the hypothesis being tested.

I hope you don't take this as being contrarian. I'm just trying to make sure the model is properly being tested.

Interaction with the medium isn't a bug; it's a feature. If the angle of incidence, angle of refraction, and speed of light through the medium are known, the speed with which the light entered the medium can be calculated. Again, Snell's law. We're taking sin(theta)2/sin(theta)1 = v2/v1 and solving for v1 based on our measurements of the other three values.

[Mike Helland]

Originally Posted by Reformed Offlian

Interaction with the medium isn't a bug; it's a feature. If the angle of incidence, angle of refraction, and speed of light through the medium are known, the speed with which the light entered the medium can be calculated. Again, Snell's law.

Understood.

That's based on a constant speed of light in a vacuum, c = fw.

In my model, that doesn't hold up any more. Nor does anything based on the law that an object in motion remains in motion.

That said, I suppose that suggest that Snell's Law could be adjusted to includes Hubble's constant.

Baically, Maxwell's equations would need to reflect c - H * D, and from what I just read on wikipedia (I'm a loser, I know), Snell's Law can be derived from Maxwell'as equations, so from a modified Maxwell you'd get the modified Snell, based on the modified Hubble, c - H * D.

The more I talk about this with other people, the more the idea seems to just become "Hubble's constant may be part of inertia itself, at least the photon".

[Ziggurat]

Originally Posted by Mike Helland

Understood.

That's based on a constant speed of light in a vacuum, c = fw.

No, it isn't. Snell's Law works on the interface between any two regions with different velocities, regardless of what those velocities are.

In fact, this is a perfect experiment because if you're right, then light from a distant enough source would actually deflect in the opposite direction as it speeds up rather than slowing down as it enters the prism glass.

[Mike Helland]

Originally Posted by Ziggurat

No, it isn't. Snell's Law works on the interface between any two regions with different velocities, regardless of what those velocities are.

In fact, this is a perfect experiment because if you're right, then light from a distant enough source would actually deflect in the opposite direction as it speeds up rather than slowing down as it enters the prism glass.

Snells law is about one medium from another, or from c in a vacuum to a medium, or vice versa.

It doesn't say anything about a photon traveling at less than c in a vacuum.

That just places Snell's Law, like the rest of Newtonian physics, in a limited domain of applicability.

Outside that domain, where cosmological redshift lives, we'd need to include Hubble's constant.

[Reformed Offlian]

Originally Posted by Mike Helland

Understood.

In my model, that doesn't hold up any more. Nor does anything based on the law that an object in motion remains in motion.

Snell's law is an empirical law that "holds up" because it matches observations; it isn't necessarily predicated on any particular theory. Any proposed revision/replacement would have to match the same observations.

Having a new model doesn't mean you get to pretend Snell's law isn't a thing; it means you need a new explanation for why it is a thing.

[theprestige]

Does anyone have a bingo card? I think we just got the "if only we had photos I would be convinced... no, not those photos" dodge.

Mike, your hypothesis makes predictions that we can test right now, today. Predictions for which we already have a plethora of test data. Those tests falsify your predictions. Proposing some other test that hasn't been carried out yet won't change the results of the tests that have been carried out. Your predictions have already been falsified.

[Ziggurat]

Originally Posted by Mike Helland

Snells law is about one medium from another, or from c in a vacuum to a medium, or vice versa.

It doesn't say anything about a photon traveling at less than c in a vacuum.

No, Mike, you're wrong. It's about light traveling at one velocity in one region and another velocity in another region. It doesn't matter what the two velocities are, or what the two regions are. That's why it works on transitions between media where it's not c on either side (for example, between water and glass, or glass and diamond). Only the velocity on each side matters, and that velocity can be anything.

[Mike Helland]

Originally Posted by Reformed Offlian

Snell's law is an empirical law that "holds up" because it matches observations. Any proposed revision/replacement would have to match the same observations. Simply rejecting current theoretical derivations doesn't make it go away.

Having a new model doesn't mean you get to pretend Snell's law isn't a thing; it means you need a new explanation for why it is a thing.

Ok, change v_1 to V_1 + H * D.

Where H * D = 0, nothing changes.

Where there is cosmological red-shift of a photon, entering a medium resets its v to c.

[Reformed Offlian]

Originally Posted by Mike Helland

Snells law is about one medium from another, or from c in a vacuum to a medium, or vice versa.

It doesn't say anything about a photon traveling at less than c in a vacuum.

Snell's law isn't limited in the way you propose. It predates Maxwellian electrodynamics and can be applied to any pair of "before and after" speeds for light. That Maxwellian ED provides a derivation for it doesn't mean the law itself is predicated on that derivation. There can be and have been non-Maxwellian derivations for it.

Again, having a new model doesn't mean you get to pretend Snell's law isn't a thing; it means you need a new explanation for why it is a thing

[Mike Helland]

Originally Posted by theprestige

Does anyone have a bingo card? I think we just got the "if only we had photos I would be convinced... no, not those photos" dodge.

One of the tests proposed seems to be pretty good.

The other doesn't actually test the hypothesis, it tests a different hypothesis because it treats cosmologically redshifted photons as traveling through a medium, which is explicitly not what the hypothesis says.

I appreciate the enthusiasm though.

[Reformed Offlian]

Originally Posted by Mike Helland

Ok, change v_1 to V_1 + H * D.

Where H * D = 0, nothing changes.

Where there is cosmological red-shift of a photon, entering a medium resets its v to c.

Great, now derive Snell's law from that, or the approximation of it within what you claim is the domain of applicability.

[Mike Helland]

Originally Posted by Reformed Offlian

It predates Maxwellian electrodynamics and can be applied to any pair of "before and after" speeds for light.

Even light moving at less than c in a vacuum?

[Mike Helland]

Originally Posted by Reformed Offlian

Great, now derive Snell's law from that, or the approximation of it within what you claim is the domain of applicability.

sin theta_2 / sin theta_1 = v_2 / (v_1 + H * D)

Or just reset D to 0 when you move media and that works too.

[theprestige]

Originally Posted by Mike Helland

Even light moving at less than c in a vacuum?

Yes.

What makes you think that moving at less than c in a vacuum would exempt light from Snell's law?

[Reformed Offlian]

A further question for Mike: let's think of two situations:

In one, light is travelling through a medium at .8c and transitions into a different medium through which it travels at .7c.

In the second, light is (somehow) traveling through a vacuum at .8c and transitions to the same refracting medium.

According to you, the light would behave differently in those two cases. Why? What makes them different?

[Reformed Offlian]

Originally Posted by Mike Helland

sin theta_2 / sin theta_1 = v_2 / (v_1 + H * D)

Or just reset D to 0 when you move media and that works too.

That's not a derivation, that's just your proposed revision of the formula. How do you *derive* it? Specifically, why are we adding H*D to v_1? What's the theoretical rationale for that? Apart from the obvious: "Mike needs it to get his idea out of this specific problem?"

[Mike Helland]

Originally Posted by theprestige

Yes.

What makes you think that moving at less than c in a vacuum would exempt light from Snell's law?

Because if we were to assume that we can calculate the density of a medium based on how fast light travels through it, we would get the wrong answer.

Doesn't it assume a 1 to 1 ratio for velocity of light of medium density?

As in two different densities shouldn't predict the same velocity?

[Mike Helland]

Originally Posted by Reformed Offlian

That's not a derivation, that's just your proposed revision of the formula. How do you *derive* it?

I'd have to get back to you on that one.

In any case, you're treating cosmologically red-shifted photons as traveling through a medium, and that's not how my model treats them.

[Reformed Offlian]

Originally Posted by Mike Helland

Even light moving at less than c in a vacuum?

Yes. v_1 is v_1. Nothing about what medium, if any, the wave is travelling through.

[Reformed Offlian]

Originally Posted by Mike Helland

I'd have to get back to you on that one.

In any case, you're treating cosmologically red-shifted photons as traveling through a medium, and that's not how my model treats them.

No, I'm simply treating them as traveling with a given velocity, which is all that Snell's law references. The idea that there's something magically different about their passing through a medium is your gratuitous addition.

[Reformed Offlian]

Originally Posted by Mike Helland

Because if we were to assume that we can calculate the density of a medium based on how fast light travels through it, we would get the wrong answer.

Doesn't it assume a 1 to 1 ratio for velocity of light of medium density?

Nope.

For example, hydrogen gas at a given temperature and pressure is less dense than helium gas, but has a higher refractive index.

For a *given* material, there tends to be a strong relationship between density and RI, but even then I don't think it's always linear.

[WhatRoughBeast]

Originally Posted by Mike Helland

Ok, change v_1 to V_1 + H * D.

Where H * D = 0, nothing changes.

Where there is cosmological red-shift of a photon, entering a medium resets its v to c.

Sorry to jump in late, but you should realize that, at a minimum, your theory invalidates Maxwell's equations, and does so at a very fundamental level.

Consider that, if we think of light as an electromagnetic wave, it consists of both electric and magnetic fields which oscillate 90 degrees out of phase. This can only happen in a consistent fashion when the velocity of propagation (c in a vacuum) is equal to 1 over the square root of the product of free space permeability and permittivity.

If your theory is correct, space is filled with EM radiation travelling at a wide variety of speeds. Every star with a different redshift produces light which has a different value for c, and over quite a broad range, too. This in turn implies that there is no such thing as a unique value for permittivity and permeability. However, such unique values have been measured repeatedly in the laboratory, and to far greater precision than stellar radiation would allow (Oh, those pesky high-z objects!).

So, unless you are able to extend your theory to explain how space can have a broad range of values for permeability and permittivity, I'm afraid that you're going to have give up on it for a while.

On another note, you need to be aware that everything is a medium. Even intergalactic space is not a pure vacuum, so "entering a medium resets its v to c" is pretty meaning-free. You would need to establish a threshold of density at which a vacuum ceases being a vacuum - and justify it. Numerically.

Good luck.

[Reformed Offlian]

Originally Posted by WhatRoughBeast

Sorry to jump in late, but you should realize that, at a minimum, your theory invalidates Maxwell's equations, and does so at a very fundamental level.

Consider that, if we think of light as an electromagnetic wave, it consists of both electric and magnetic fields which oscillate 90 degrees out of phase. This can only happen in a consistent fashion when the velocity of propagation (c in a vacuum) is equal to 1 over the square root of the product of free space permeability and permittivity.

If your theory is correct, space is filled with EM radiation travelling at a wide variety of speeds. Every star with a different redshift produces light which has a different value for c, and over quite a broad range, too. This in turn implies that there is no such thing as a unique value for permittivity and permeability. However, such unique values have been measured repeatedly in the laboratory, and to far greater precision than stellar radiation would allow (Oh, those pesky high-z objects!).

So, unless you are able to extend your theory to explain how space can have a broad range of values for permeability and permittivity, I'm afraid that you're going to have give up on it for a while.

You're responding to a guy who doesn't believe in conservation of momentum; I don't think round-filing Maxwell's equations is going to give him pause.

Quote:

On another note, you need to be aware that everything is a medium. Even intergalactic space is not a pure vacuum, so "entering a medium resets its v to c" is pretty meaning-free. You would need to establish a threshold of density at which a vacuum ceases being a vacuum - and justify it. Numerically.
Good luck.

He ignored my earlier question about how extinction figures in his "model"; I'm not sure he knows what that is.

[Ziggurat]

Originally Posted by Mike Helland

I'd have to get back to you on that one.

In any case, you're treating cosmologically red-shifted photons as traveling through a medium, and that's not how my model treats them.

There are all sorts of oddities to your model that I don't think you've thought through.

For example, what does a photon traveling at 0.5c look like to an observer traveling at 0.5c? It's stationary in their frame, but it was also emitted by a source that was less than 1 D away.

Or how can a photon even know how far away it comes from? That information is supposedly coded in its current velocity (in which reference frame?), but if photons can have different velocities, why are they only ever emitted with one velocity? That also breaks time reversal symmetry, since a process which allows photons to be absorbed at < c should also be able to emit them at < c.

I don't think it's even possible to make this theory even self-consistent, let alone consistent with experiment.

[Mike Helland]

Originally Posted by WhatRoughBeast

Sorry to jump in late, but you should realize that, at a minimum, your theory invalidates Maxwell's equations, and does so at a very fundamental level.

True, and Newton's first law of motion.

Everyone tends to think I'm some relativity crank.

I'm just following the hypothesis. Newton's first law may not be true to infinity.

Do you have evidence its true to infinity?

We have evidence of red-shifting.

Quote:

Every star with a different redshift produces light which has a different value for c, and over quite a broad range, too.

Stars? If they're affected by the Hubble flow.

In my model stars and galaxies still have peculiar motion that leads to velocity shifts.

Cosmological redshifts are posited to be their own phenomenon.

Quote:

So, unless you are able to extend your theory to explain how space can have a broad range of values for permeability and permittivity, I'm afraid that you're going to have give up on it for a while.

Instead of an objects light cone defined by c, it's defined by c - H * D.

Hubble's constant is built into the light cone.

Quote:

On another note, you need to be aware that everything is a medium. Even intergalactic space is not a pure vacuum, so "entering a medium resets its v to c" is pretty meaning-free. You would need to establish a threshold of density at which a vacuum ceases being a vacuum - and justify it. Numerically.
.

True, we can tell from Lyman lines when far away light hit clouds of hydrogen for examples.

[Mike Helland]

Originally Posted by Ziggurat

For example, what does a photon traveling at 0.5c look like to an observer traveling at 0.5c? It's stationary in their frame, but it was also emitted by a source that was less than 1 D away.

What does a 1c photon look like to an observer at rest?

I've never seen a photon. Have you?

My model only gives the values to photons its observed. Not in flight.

Quote:

Or how can a photon even know how far away it comes from?

It's stored in the d variable of the model.

Quote:

That information is supposedly coded in its current velocity (in which reference frame?),

Actually, velocity is a function of distance, v = c - H * D, not the other way around.

Quote:

but if photons can have different velocities, why are they only ever emitted with one velocity? That also breaks time reversal symmetry, since a process which allows photons to be absorbed at < c should also be able to emit them at < c.

I've never seen time go backwards either.

[Mike Helland]

Originally Posted by Reformed Offlian

No, I'm simply treating them as traveling with a given velocity, which is all that Snell's law references. The idea that there's something magically different about their passing through a medium is your gratuitous addition.

The difference between a vacuum and a medium matters. (Rimshot!)

In QM, a photon always travels at c, even in a medium, it's just spends time in between absorption and emission not traveling.

[Ziggurat]

Originally Posted by Mike Helland

What does a 1c photon look like to an observer at rest?

Like a photon traveling at 1c.

If a photon is stationary... what is it?

Quote:

I've never seen a photon. Have you?

That's literally not true. Photons are the only thing you ever see.

Quote:

My model only gives the values to photons its observed. Not in flight.

Not to be rude, but if your model can't handle photons in flight, your model is garbage.

Quote:

It's stored in the d variable of the model.

A model is not reality. Information in reality has to be stored in actual properties of things. What property of the photon contains the information about how far it's traveled? Its current velocity? That doesn't actually work, because unless its current velocity is equal to c, then its velocity isn't invariant. And that introduces internal contradictions into your theory.

Quote:

Actually, velocity is a function of distance, v = c - H * D, not the other way around.

Doesn't work. Neither D nor v will be invariant. They will both depend on reference frame. And they will both depend on reference frame differently, in a manner that makes consistency impossible.

Quote:

I've never seen time go backwards either.

It's not necessary to. It suffices to simply note that individual interactions are reversible.

[Mike Helland]

Originally Posted by Ziggurat

Like a photon traveling at 1c.

I see my laptop.

I see a piano.

I see a space heater.

Don't see any photons.

Quote:

That's literally not true. Photons are the only thing you ever see.

I've never seen one. I think they literally let us see other things might be more accurate.

Quote:

Information in reality has to be stored in actual properties of things.

Where is c stored? Where is an electron's mass stored?

Quote:

It's not necessary to. It suffices to simply note that individual interactions are reversible.

That's great.

But we observe time always going forward. So... I think that's what the model should do.

[Reformed Offlian]

Originally Posted by Mike Helland

The difference between a vacuum and a medium matters. (Rimshot!)

This is a claim to be demonstrated. I await your demonstration.

Quote:

In QM, a photon always travels at c, even in a medium, it's just spends time in between absorption and emission not traveling.

Which means we can add QM to the list of physics that has to be wrong before your model can be right.

ETA: Oh, and speaking of absorption and emission: what role does extinction play in your model?

[Mike Helland]

Originally Posted by Reformed Offlian

Which means we can add QM to the list of physics that has to be wrong before your model can be right.

Yes, at scales where redshift is observed.

Anything based on Newton's first law of motion holding true to infinity would be wrong at cosmological scales if the hypothesis is right.

To fix the model we give the photon a velocity of c - H * D.

I'm saying the speed of light is based on c and H.

It could be, it's the speed of galaxies that is based on H. It could be, the big bang is right.

It could be, there's actually no such thing as dark energy and/or the expansion of space.

[Ziggurat]

Originally Posted by Mike Helland

I see my laptop.

I see a piano.

I see a space heater.

Don't see any photons.

No. You see photons coming from them, which creates an image which your brain interprets as being them. But it's the photons you actually see. That's why you can't see them in the dark. Those objects are still there, it's the photons which are gone.

Quote:

Where is c stored?

c doesn't have to be stored. It's a property of spacetime itself, it's not unique to photons.

Quote:

Where is an electron's mass stored?

An electron's mass is not a variable quantity. Variable quantities need some way of being stored.

Quote:

That's great.

But we observe time always going forward. So... I think that's what the model should do.

If you watch a video, how can you tell whether it's playing forward or backward? A video of the earth orbiting the sun would look the same either way.

There are some processes where you can tell, namely processes which increase entropy on a macroscopic level. But your photon conversion idea isn't one of them. That's a zero entropy change process. It must be reversible.

[Mike Helland]

I don't think the hypothesis would have a different effect on extinction than the expansion of space.

Both in the expanding model and the decelerating model the photon's duration or travel increases (either extra space to cross or not going as fast).

[Mike Helland]

Originally Posted by Ziggurat

You see photons coming from them

What do they look like?

Quote:

c doesn't have to be stored. It's a property of spacetime itself, it's not unique to photons.

Presumably you have a position in space and a velocity (perhaps you're at rest, v = 0).

Where is that stored?

In your knee caps?

Quote:

Variable quantities need some way of being stored.

Where is your mass stored?

Quote:

There are some processes where you can tell, namely processes which increase entropy on a macroscopic level. But your photon conversion idea isn't one of them. That's a zero entropy change process. It must be reversible.

You're saying that if photons lose energy by traveling in space, they should also gain energy by traveling backwards?

We observe redshift. We don't observe systemic blue shifts.

[Reformed Offlian]

Originally Posted by Mike Helland

Yes, at scales where redshift is observed.

Anything based on Newton's first law of motion holding true to infinity would be wrong at cosmological scales if the hypothesis is right.

It's not really about scale though, is it? We're not talking about how the light behaves on a scale of billions of lightyears, we're talking about how it behaves right here, in the atmosphere and in our telescopes, depending on what object it comes from. Right here on earth, these things don't work, if we're looking at certain galaxies. Right here on earth, our apparatus doesn't work the way we think it does, if it's pointed at certain galaxies. That's not a question of scale, that's special pleading for an arbitrary set of objects.

ETA: To be more specific, let's consider Snell's law as it applies to the experiment I had suggested. None of the relevant values (angle of refraction, angle of incident, speed of light in a vacuum or in a medium) are outside the *scales* over which Snell's law is known to apply. Not even if you think light coming from the most distant galaxies are only travelling at, say, .01c. Heck, Snell's law works for sound waves. So saying that Snell's law doesn't work at "cosmological scales" doesn't mean anything, unless we're talking about a refracting medium billions of lightyears across or something.