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Understanding Special Relativity

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DentArthurDent
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10 Apr 2015, 9:08 pm

Hi all, I have been getting my head around Special Relativity and General Relativity. One basic concept has me a little confused. Einstein was looking for something that was invariant to all observers and this he discovered is the speed C. However C is only constant in a vacuum, so how can it be invariant to all observers?

Clearly I am missing something fundamentally important.


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Humanaut
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10 Apr 2015, 9:23 pm

DentArthurDent wrote:
C is only constant in a vacuum, so how can it be invariant to all observers?

Are you referring to observers not residing in a vacuum?



Fnord
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10 Apr 2015, 9:41 pm

C is indeed invariant to all observers, no matter what the medium.

If a light beam looks like it goes through a block of Lucite at 0.9c to the man standing next to it on the ground, the beam will still look like it's going at 0.9c if the man and the block are also traveling through space at 0.9c.



eric76
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10 Apr 2015, 11:12 pm

Fnord wrote:
C is indeed invariant to all observers, no matter what the medium.

If a light beam looks like it goes through a block of Lucite at 0.9c to the man standing next to it on the ground, the beam will still look like it's going at 0.9c if the man and the block are also traveling through space at 0.9c.


How about if the man is traveling through a block of lucite at 0.9 c?

Seriously, if the man and the block are traveling through space at 0.9 c, then they would be in an inertial reference frame. To make it more related to special relativity, consider an observer traveling at 0.9 c relative to the block of lucite.



eric76
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10 Apr 2015, 11:15 pm

DentArthurDent wrote:
Hi all, I have been getting my head around Special Relativity and General Relativity. One basic concept has me a little confused. Einstein was looking for something that was invariant to all observers and this he discovered is the speed C. However C is only constant in a vacuum, so how can it be invariant to all observers?

Clearly I am missing something fundamentally important.


It's the speed of light in a vacuum that matters.



eric76
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10 Apr 2015, 11:20 pm

By the way, it is quite possible and does happen (I've personally observed it) to exceed the speed of light in a medium not a vacuum.

Check out Cherenkov Radiation.



Humanaut
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11 Apr 2015, 1:47 am

Was Einstein insane?



eric76
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11 Apr 2015, 1:48 am

Humanaut wrote:
Was Einstein insane?
Huh?

What do you mean?



eric76
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11 Apr 2015, 1:54 am

DentArthurDent wrote:
Hi all, I have been getting my head around Special Relativity and General Relativity. One basic concept has me a little confused. Einstein was looking for something that was invariant to all observers and this he discovered is the speed C. However C is only constant in a vacuum, so how can it be invariant to all observers?

Clearly I am missing something fundamentally important.


By the way, on another note, he wasn't looking for something that was invariant and discovered it to be the speed of light. Instead, he was trying to understand why the speed of light was not different in perpendicular directions as was demonstrated by the Michelson-Morley experiment.



Humanaut
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11 Apr 2015, 2:21 am

eric76 wrote:
Humanaut wrote:
Was Einstein insane?
Huh?

What do you mean?

Just look at his hair.



eric76
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11 Apr 2015, 2:45 am

Humanaut wrote:
eric76 wrote:
Humanaut wrote:
Was Einstein insane?
Huh?

What do you mean?

Just look at his hair.


I'm in trouble, then.

Whenever someone asks me why I keep my hair like it is, I tell them it is so that I can dress up as Dr Einstein for Halloween.



Fnord
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11 Apr 2015, 8:43 am

eric76 wrote:
By the way, it is quite possible and does happen (I've personally observed it) to exceed the speed of light in a medium not a vacuum. Check out Cherenkov Radiation.
Cherenkov radiation is not produced by photons, but occurs (for example) when electrons traveling faster than 0.75c and less than 1.00c strike water, such as in the cooling vessel of some nuclear reactors.
Quote:
Cherenkov radiation, also known as Vavilov-Cherenkov radiation, is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity of light in that medium.

[...]

While electrodynamics holds that the speed of light in a vacuum is a universal constant (c), the speed at which light propagates in a material may be significantly less than c. For example, the speed of the propagation of light in water is only 0.75c. Matter can be accelerated beyond this speed (although still to less than c) during nuclear reactions and in particle accelerators. Cherenkov radiation results when a charged particle, most commonly an electron, travels through a dielectric (electrically polarizable) medium with a speed greater than that at which light would otherwise propagate in the same medium.
Source: "Cherenkov Radiation"



eric76
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11 Apr 2015, 9:35 am

Fnord wrote:
eric76 wrote:
By the way, it is quite possible and does happen (I've personally observed it) to exceed the speed of light in a medium not a vacuum. Check out Cherenkov Radiation.
Cherenkov radiation is not produced by photons, but occurs (for example) when electrons traveling faster than 0.75c and less than 1.00c strike water, such as in the cooling vessel of some nuclear reactors.
Quote:
Cherenkov radiation, also known as Vavilov-Cherenkov radiation, is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity of light in that medium.

[...]

While electrodynamics holds that the speed of light in a vacuum is a universal constant (c), the speed at which light propagates in a material may be significantly less than c. For example, the speed of the propagation of light in water is only 0.75c. Matter can be accelerated beyond this speed (although still to less than c) during nuclear reactions and in particle accelerators. Cherenkov radiation results when a charged particle, most commonly an electron, travels through a dielectric (electrically polarizable) medium with a speed greater than that at which light would otherwise propagate in the same medium.
Source: "Cherenkov Radiation"


Correct.

The point was that the it is possible for objects to exceed the speed of light where the speed of light is less than that in a vacuum. Naturally, light does not exceed the speed of light.



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11 Apr 2015, 10:28 am

Since we are on the subject of "Relativity" and the speed of light "c". I've got to wonder. Does the speed of light have some "absolute" reference point in the universe in which is speed limit is confined to? For example. let say I have a spaceship with headlight's on it and I am traveling at half the speed of light (0.5c). I know as the pilot of that ship that the light from my headlight is traveling at the speed of light away from my ship. What does an observer, not traveling at all and is right in front of me see? Is the light coming from the headlights of my ship traveling a 1.5c in the eyes of are observer? Will there be some kind of dopier shift? for example. let say the headlights on my ship are a infrared(800mn) color. will my observer see my headlights as a ultraviolet(400mn) color because of dopier compression?



eric76
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11 Apr 2015, 11:36 am

LupaLuna wrote:
Since we are on the subject of "Relativity" and the speed of light "c". I've got to wonder. Does the speed of light have some "absolute" reference point in the universe in which is speed limit is confined to?


No. All inertial reference frames (i.e. a reference frame in which the observer feels no acceleration at all) are equal.

Quote:
For example. let say I have a spaceship with headlight's on it and I am traveling at half the speed of light (0.5c). I know as the pilot of that ship that the light from my headlight is traveling at the speed of light away from my ship. What does an observer, not traveling at all and is right in front of me see? Is the light coming from the headlights of my ship traveling a 1.5c in the eyes of are observer?


No. it will always be c (in a vacuum).

Quote:
Will there be some kind of dopier shift? for example. let say the headlights on my ship are a infrared(800mn) color. will my observer see my headlights as a ultraviolet(400mn) color because of dopier compression?


There will be a doppler shift, but for 800 nm on the spaceship, it would be approximately 462 nm at 0.5 c. To shift it from 800 nm to 400 nm should take a velocity of .6 c.

The shift in frequency is given by √((1+β)/(1-β)) where β is positive if moving toward the observer and negative if moving away.



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11 Apr 2015, 3:28 pm

eric76 wrote:
The point was that the it is possible for objects to exceed the speed of light where the speed of light is less than that in a vacuum.

Galaxies are said to be moving at superluminal speed away from each other due to space expanding, which, as far as I can tell, would imply the existence of a luminiferous aether (nothing expanding into nothing seems a bit counterintuitive).