michel123456

Wikipedia is not enough. It is not mentioned that spacetime is not full. It looks like Euclidian space with the addition of the time dimension. But Euclidian space is full. I mean the coordinates are free, there is no constraint. When one introduces time, the constraint appears, as you explained in your post. Which means that the 4 coordinates are not free. You posted the formula. So, again, what is the Spacetime like? If it is not full? What kind of geometrical object?

Do you mean something like my infamous pencil universe? (beware Martin - where is he?- didn't like it)

Wonderful! You should publish. So, the 4D spacetime is not full, isn't it? Like a circle is a part of a plane, the equation that you posted (s2 = x2 + y2 + z2 -c2t2) describes what kind of geometric figure? --------------- Sorry but I feel the thread is splitting in 2 very interesting parts.

Ah. So the vacuum plays a role in the invariance.

My question is: If the different observers in other frames, moving with respect to the material, will they measure the same velocity of c inside the material?

Great explanation! One of the clearest ever. Only, only the bold part should be stated otherwise because it leads to confusion: if they coincide in space and not in time that mean that they do not meet together. (their world lines cross but they do not meet*) You surely meant something else: that they do indeed meet but that their measure of time is different. If you didn't mean that then you have a problem and that would make me very glad (no offense intended). *don't ask me how that can be possible

Question: does the velocity of light remain an invariant when it goes through a material? Explaining the question: It is known that C is an invariant when C is speed of light in vacuum. It is also known that C has other values when it goes through materials (water, glass): is it still a constant regardless of the velocity of the observer / material or is it "linked" to the material?

Evidence of lack of evidence perhaps? Like dark matter, dark energy.

Dismissive

A friend of mine is dying. The song goes like this Ah, the title: Supplication to be buried on the beach of Sete (Sete is the town on the Mediterranean where George Brassens was born.)

Redbone? Their only song I can recall is..

It should be that way.

When Rock takes a 300 years old piece (happy birthday Ian)

What do you mean?

To me it is even worse: it is because the people who explain it do not understand it. It was a time when almost nobody could understand GR. Now anybody is entitled to understand.

But in the ruler's frame, you are quacking like a duck. What i say is that the ruler cannot be a rabbit, a duck, a dog, a cat, etc. at the same time just because it is been observed by many. Look: even without Relativity, it is known that distance & time are obstacles. We don't know that enough about the Moon, we must go there. We don't know enough about Mars and Jupiter, we must go there. We don't even know enough about our mother Earth, we have to dig and go there inside. If you get a new pencil as a present, you will open the box, take the pencil at hand, feel it in your hand, take a piece of paper and write a little, even you will open it to see the mechanism inside (I do that). Don't tell me that an observer thousand kilometers away traveling at half the SOL knows better the pencil than you do. If he tells you that it is blue while you admire your red pencil, who is right? You will tell me that as physics are concerned, they are both right: the pencil is blue and the pencil is red. To me it is not right. The one who has the pencil at hand knows better, because 1 he is closer 2 he is "in real time" 3 he is in the same frame. That is my point, yes. Because if the ruler IS shorter, and you put this shorter dimension into your equations, then you will find it would appear even shorter-shorter. In fact, what you put into your equations is the ruler real dimension (in its own frame) and then get the contracted result as observed by you, or by another. It is all about observation. Now, if this observation has a real effect upon you, that is not a mystery that comes fom Relativity, the entire physics world is like this. I mean, if I throw a stone at you, and you are observing the stone coming right to your face, you may expect to hurt. Some other observer outside of the stone's path will not hurt. Another observer thousand of kilometers away will not hurt. You and only you will hurt, because it is your reality, not anyone else's reality. And the stone's velocity will be the velocity as measured by you. And the physical effects will be those corrwesponding to this velocity, not the velocity as observed by anyone else. If you observe a mirror sideways at an angle, you will see the reflection of something (say, a red light). Some other observer next to you will see in the same mirror the reflection of something different at the same time, (say a blue light). So your face will become slightly red (because of the red light rays), and the observer-next-to-you's face will become blueish. If there is a mystery in this it is not caused by Relativity.

Can get no sleep?

Correct

Yes. Because there is something that you observe. All the observers from all the frames converge, focus to a point where there is "something". And this "something", the starting point, the physical object of observation does not physically change. The ruler never "physically" contracts. However, the ruler may appear as contracted by some observer B. In this case, the situation should be symmetric and the guy who has the ruler at hand should observe observer B contracted.

They are all explainable. They are not all understandable.

From the beach bar

Is that the case?

+1 for good memory and sense of humor. However my point about mathematics (that nobody agreed with) is exactly the contrary.

Which shows that if physics progress enough to explain the problem of time, the metaphysical issue may vanish. IOW that the metaphysical arises only because there is no affordable explanation from the physicists.

For an observer on Earth looking at a clock orbiting the Earth. So. An observer on Earth is roughly 12700 km away from the gravity source (the center of the Earth). An orbit 1 1/2 away is 6350km above. From what you say, a clock orbiting at this distance runs at the same time as his own. A lower orbit would result with the clock running slower than his. It means when my clock says 5 minutes, the orbiting clock says 4 (exaggerated for the sake of simplicity). Do I understand correctly?