[Johann Mahne]

If space time in a vacuum is directly linked to the speed of light c. (big IF).
Then using only length : ΔL/ΔT=c. The ratio of distance (length) to time is a constant.
In water the refractive index is 1.3, so light is 30% faster.
So then ΔL2/ΔT2=c x 1.3; which gives us a different ratio for space time.

When a diver runs his clock his time does not change relative to time on the surface.
The distances appear greater, but this is an optical illusion only.

  So why does space time not change under water? Or is refraction really a change in space time?

[Kryptid]

Light appears to travel more slowly in water, but it's not quite that simple. Water, as with all conventional matter, is mostly empty space. When light passes through water, it is still passing through an area that is mostly vacuum. It's speed through those regions is unaffected. I'm not an expert on this, but I believe that light gets stopped/absorbed by electrons in certain energy states in the molecules before it can continue on its journey through the water.

Imagine if you were driving at 70 miles per hour down the interstate for an hour, then stopped for an hour's break, then went back and drove for another hour at 70 mph. It took you 3 hours to cover 140 miles. That's an average speed of around 46.7 miles per hour. However, you did not actually travel at the speed on your journey.

Likewise, I can imagine that photons of light energy make a lot of "pit stops" when they travel through matter which gives the illusion that the light beam is being slowed down.

Other members, please do correct me on this if I'm wrong; I want to be sure.

[burning]

It's important to remember that all precise statements concerning relativity refer to the speed of light in a vacuum.  The fact that the speed of light travels slower in water (not faster, as you state above) does not have any implications on the conclusions of relativity.  In fact, two important aspects of relativity are violated when we consider the speed of light in water (or indeed in any material substance):

1. The speed of light in a vacuum is invariant to all observers.  The speed of light in water will depend on the relative motion of the observer to the water (Fizeau experiment.)

2. Nothing can travel faster than the speed of light in a vacuum.  Objects can travel through water faster than the speed of light in water (e.g. the cause of Čerenkov radiation).

(minor edits for typographical errors)

[yor_on]

'c' is not about the way something interact with matter, to me it's just a constant describing lights speed in a vacuum, and a beat. And as long as nothing can can be proven to overtake 'c' it's doing fine. There is also a discussion of phase or group velocity that, at times can be defined as moving faster than 'c', but as long as you can't use that for transmitting information it should be okay to my eyes.

You can by turning your head at a dark night allow your eyesight to move faster than 'c' too, relative the distant stars in the sky, That doesn't contradict 'c', neither does sweeping a laser beam over the moons surface faster than 'c'. 'c' is about a invariant beat, keeping the same 'rhythm' in all frames as described locally, accelerated or not.

[Johann Mahne]

Sorry folks,
 
  You are all right. The speed of light is LESS in water than in free space.
I'll edit my question as below:
This actually does destroy my question, but anyway..

If space time in a vacuum is directly linked to the speed of light c. (big IF).
Then using only length : ΔL/ΔT=c. The ratio of distance (length) to time is a constant.
In water the refractive index is 1.3, so light is 30% slower.
So then ΔL2/ΔT2=c/1.3; which gives us a different ratio for space time.

When a diver runs his clock his time does not change relative to time on the surface.
The distances appear greater, but this is an optical illusion only.

  So why does space time not change under water? Or is refraction really a change in space time?

[yor_on]

You are mixing two definitions there, one is 'c' the other is how 'c' or in this case light interacts with matter. The question could be seen as,'what the he* is matter' from where I read it And I wonder too.

As long as we have a definition of 'c' being a state of the radiations 'speed' in a 'empty space', then that light, as soon as it meet 'space', must propagate at 'c' inside or outside matter. The rest will be interactions. And maybe you as easily could ask 'What the he* is 'space?' Because that one is on my mind constantly, as the 'time dilations' and 'Lorenz contractions' we describe always follows as a function of lights invariance over a 'space' in 'time', relative 'motion/mass'.
==

Sorry, one more, what is 'time'?
Eh, and 'motion'?

[Johann Mahne]

Hi yor_on,
 The definition for a space time interval is:

s² = Δr² - c²Δt²

where r is the differences of the "cordinates" c is the speed of light and t the difference in time. Now if the speed of light is slower in water, then according to this definition we have a different space time in water. That is if one took this literally.

[yor_on]

Okay tell me, what is the speed of light in iron? If going from your definition? The speed of light is defined in a vacuum, not in water. The equivalence to a 'medium' for light to propagate in would be an 'aether' as I think of it.

As for the rest of it?

"In a Euclidean space, the separation between two points is measured by the distance between the two points. A distance is purely spatial, and is always positive. In spacetime, the separation between two events is measured by the interval between the two events, which takes into account not only the spatial separation between the events, but also their temporal separation. The interval between two events is defined as:

   (spacetime interval),

where c is the speed of light, and Δr and Δt denote differences of the space and time coordinates, respectively, between the events."

How do you think of this? In the form of light interacting with water or as if the light doesn't annihilate meeting atoms, to then getting 'resurrected'. You should be able to define any density by measuring the speed of light, or radiation, in different mediums, but then we have the fact that different wavelengths /energies(photons) interacts differently too, so maybe that one should be relative.

[yor_on]

You know, refraction is a really tricky subject. I've seen some trying to explain it in form of 'soldiers marching', to then changing their pace and so get another direction, but that didn't feel as that good a explanation.

It seems as if the 'photon' when it interacts with the atom in any transparent medium (water/glass) comes into what is called a 'dressed state', not really allowed as the atom momentarily has too much 'energy' so the atom almost immediately re-emits the photon, but there is a interval that slows it down each time.

When it comes to why and how it angles in the water that seems to be explained through the image appearing determined by its minimum optical path length, which then is relative the location of the observer. As for space as a 'medium', it's classically a 'nothing', and any rays 'bending' is defined by lights geodesics, that then becomes the easiest paths for all radiation, and there you have 'gravity' acting on light as defined in GR. I'm not sure you can define it as a 'medium', maybe gravity though can be seen that way? Or even if Snell's law is used for a vacuum?

Maybe?

And a 'space time interval' is the relativistic analogue to the idea of two points on a paper always having a invariant distance between them, no matter what coordinate system you measure that distance by, or what angle of your measuring device you use. So when you ask about about 'refraction', wondering if it's the same phenomena as when 'c' distort a 'room time geometry' I think I will say no. They are not the same.

[yor_on]

It is actually a deeper, trickier, better question than I first understood Johan, not that I've seen you ask bad ones As I looked at it again, I found that I've missed something, and that it might be this you were aiming at?

A photon, or a wave?

It's quite interesting, it also seems to be a function of ones definitions, and so possibly the way you set up your experiment inside our arrow of time, as I think of it that is. I've seen a lot of people using frequencies and wavelengths when it comes to 'photons', and so it would be nice to see this explained as the result of a 'wave' solely.