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The Speed of Light - c Goto Page: 1 2 [>] [»|]

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ZigguratII

PostPosted: Tue May 16, 2006 2:44 pm


So, as I was reading a book on relativity it mentioned that light from the sun to earth has a curviture of 1.2 seconds. Not a lot, but it's there. So I began to think of how the speed of light in a vacuum was measured, and assured to be what we call c. If it was a measurement from time to travel from point a to point b, when taken in respect to the theory of relativity does that not mean that what is defined as c is not actually the speed of light, and that the speed of light is instead c+k, where k is the speed required to cover the curviture between point a and b in the time required?

Did I miss something here? How was c defined? It doesn't seem like it's something one could test well.
PostPosted: Tue May 16, 2006 4:48 pm


Alright, and here's where I use the Feynman explanation:

The speed of light with respect to a given reference frame is constant and defined to be 299 792 458 meters per second. Note: defined. As in, the meter is defined to be 1/299792458 the distance that light travels in one second (the second is defined by atomic emissions; I don't know that one).

This is light in a vacuum of "uncurved" space. The way I learned relativity (from my dad) is like; take a piece of graph paper. Each grid is a square meter. Now put a solid object in it, and let it dip down. Depending on how heavy the object is, the more your "space" curves. The object may only be say, 5 grids in diameter, but now, to travel from one side to the other, it might take 9 or 10 grids.

This is how the "curvature" is defined. It's not special relativity; it's GTR, and you'll have to ask VorpalNeko to describe that. What I can say is what Feynman said: "Light always takes the shortest (least amount of time) path between any two points."

What this means is that; the speed of light in a vacuum is constant. What's changed is the space that light is travelling in; the "space" itself is longer. In equation terms, it's not that
distance=x=v*t=(c+k)*t
If this were the case, the time taken would be shorter. We could have
distance=x+delta x=(c+k)*t
But this is also not the case; the time taken is not the same. Rather,
distance=(x+delta x)=c*t
So the time taken is longer. c is still constant (in a vacuum); the only thing that's changed is the "distance" travelled.

Again, ask VorpalNeko for a better description of GTR. I am so unworthy! sweatdrop

Swordmaster Dragon


VorpalNeko
Captain

PostPosted: Tue May 16, 2006 9:58 pm


[ Message temporarily off-line ]
PostPosted: Wed May 17, 2006 2:13 pm


I apologize, it was 1.7 seconds and it was referencing light passing by the sun(but not from the sun.) However the point I was trying to get to was not the number but rather the concepts it leads to, as well as the difficulty of truly measuring the speed of light.

And I see. What I am getting out of this so far is that matter causes space/time to be warped(or the converse, that space/time being warped causes matter, but as saying that matter is produced by gravity and not the opposite is not as sensible.) and as such perspectives of actions from different locations can very greatly.(Mostly in relative differences of gravity/velocity)

ZigguratII


VorpalNeko
Captain

PostPosted: Wed May 17, 2006 2:39 pm


ZigguratII
I apologize, it was 1.7 seconds and it was referencing light passing by the sun(but not from the sun.)

Oh! A measurement of 1.7 seconds of arc is just about riight for the Sun's gravitational lensing effect.

ZigguratII
And I see. What I am getting out of this so far is that matter causes space/time to be warped(or the converse, that space/time being warped causes matter, but as saying that matter is produced by gravity and not the opposite is not as sensible.)

Indeed. In fact, the most important part of GTR is the Einstein field equation, which explicitly identifies a portion of the curvature (called Ricci curvature) with the stress-energy-momentum tensor. This structure keeps track of energy density/flux (which includes mass) and momentum density/flux (i.e., pressure and viscosity). All of these contribute to Ricci curvature, and it can be said that they are spacetime curvature.

ZigguratII
... and as such perspectives of actions from different locations can very greatly.(Mostly in relative differences of gravity/velocity)

Right. An object crossing an event horizon of a large enough black hole will observe nothing special happening--locally, event horizons are just like everyplace else. Globally, there is something interesting going on--the crossing will never be observed.

Incidently, there is something like event horizons already present in special relativity. It's a pretty neat effect.
PostPosted: Wed May 17, 2006 7:07 pm


But that does bring up the problem of, what if one were to pass nearby a blackhole and overcome its gravity to reach the 'other side' which never saw the person/craft finish passing by the blackhole, but to the person passing by they are going at a normal rate. Would the object ever pass by it for those on the 'other side' of the blackhole, it would just take a long time? And for the person passing by the blackhole, a long time would pass without much effect?

Edit: Though I suppose this may be taking the generality that time is not relative and is instead something consistent, and that is something the theory addresses.

ZigguratII


VorpalNeko
Captain

PostPosted: Wed May 17, 2006 8:00 pm


Are you referring orbits that just come within some very small ε of the event horizon? Such a trajectory would take an arbitrarily large amount of time relative to an observer at infinity, but the orbiting object itself would have some only a finite elapsed proper time. It should not be possible to just 'skim' the surface of the horizon (which would take an infinite amount of coordinate time) without actually falling into the black hole (I'll try to confirm this later).
PostPosted: Thu May 18, 2006 8:11 pm


VorpalNeko
Are you referring orbits that just come within some very small ε of the event horizon? Such a trajectory would take an arbitrarily large amount of time relative to an observer at infinity, but the orbiting object itself would have some only a finite elapsed proper time. It should not be possible to just 'skim' the surface of the horizon (which would take an infinite amount of coordinate time) without actually falling into the black hole (I'll try to confirm this later).

I am, and I was posing it theoretically, as obviously we couldn't do it now. However I suppose if you passed too closely, you might need to exceed c to pass by the blackhole, which is impossible sine it would require infinite energy.

ZigguratII


Swordmaster Dragon

PostPosted: Thu May 18, 2006 10:56 pm


Hmmm...I wonder if that implies another property of c. Is c the minimal speed required to approach an event horizon tangentially and not get "sucked in"? If inside the event horizon implies larger-than-c speeds and within epsilon requires sub-c speeds...it just seems like c should be the tangential speed. Though I think that means the object (photon) would simply "orbit" the event horizon forever...that seems like a problem sweatdrop
PostPosted: Thu May 18, 2006 11:28 pm


Swordmaster Dragon
Hmmm...I wonder if that implies another property of c. Is c the minimal speed required to approach an event horizon tangentially and not get "sucked in"?

Yes. If your speed is c and your velocity vector is tangent to the event horizon, then you will not fall in. On the other hand, you will be stationary relative to any external observer, so you will not make it out either. Additionally, this assumes that you are an idealized massless point-particle--this trick is impossible for extended bodies (every massive body is extended).

Edit: This is a bit counterintuitive, but the only "tangent to the horizon" direction possible is "in the t-direction only". It is tangent in the sense of spacetime, but non-tangent in the spatial section.
Swordmaster Dragon
If inside the event horizon implies larger-than-c speeds and within epsilon requires sub-c speeds...it just seems like c should be the tangential speed. Though I think that means the object (photon) would simply "orbit" the event horizon forever...that seems like a problem

t doesn't orbit--it is stationary relative to external observers. As for light orbits, that's an interesting question. The full Schwarzschild metric is dλ² = (1-2m/r)dt² - dr²/(1-2m/r) - r²[dθ²-sin²θ dφ²]. By symmetry, it is obvious that any constant-speed orbits will be circular (dr = 0), and the coordinates can be chosen so that the orbit is in the equatorial plane (θ = π/2, dθ = 0), so in particular d²r/dλ² = d²φ/dλ² = 0. Under these conditions, the geodesic deviation for x^1 = r simplifies to [2m/r²][dt/dλ]² = 2r[dφ/dλ]². This essentially Kepler's third law Ω²r³ = m, except that reference frames are mixed. I can provide the details of the calculation if you're interested, but it's really just a lot of partial differentiation. Substituting this form of Kepler's third law back into the metric (along with dr = dθ = 0) gives dλ² = (1-3m/r)dt². Consequently, (1) there are no circular orbits below r = 3m and (2) r = 3m gives dλ = 0, i.e., a lightlike geodesic. This is the only closed orbit available for light.

VorpalNeko
Captain


Dave the lost

PostPosted: Thu May 18, 2006 11:30 pm


That's because event horizon is defined that way.

The same way a meter is 1/299,792,458th the distance light travels in one second (in a vacuum), that's not some arcane property, that's just because 'they' decided to define it like that.
PostPosted: Fri May 19, 2006 4:51 pm


Swordmaster Dragon
The speed of light with respect to a given reference frame is constant and defined to be 299 792 458 meters per second. Note: defined. As in, the meter is defined to be 1/299792458 the distance that light travels in one second (the second is defined by atomic emissions; I don't know that one).


According to Wikipedia:
Quote:
The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. This definition refers to a caesium atom at rest at a temperature of 0 K.

I've always wondered about this: If the speed of light is defined as 299792458 metres per second, and a metre is defined as being 1/299792458 the distance that light travels in one second, then where does this terminate?

The MoUsY spell-checker


ZigguratII

PostPosted: Fri May 19, 2006 5:44 pm


The MoUsY spell-checker
Swordmaster Dragon
The speed of light with respect to a given reference frame is constant and defined to be 299 792 458 meters per second. Note: defined. As in, the meter is defined to be 1/299792458 the distance that light travels in one second (the second is defined by atomic emissions; I don't know that one).


According to Wikipedia:
Quote:
The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. This definition refers to a caesium atom at rest at a temperature of 0 K.

I've always wondered about this: If the speed of light is defined as 299792458 metres per second, and a metre is defined as being 1/299792458 the distance that light travels in one second, then where does this terminate?

It's the meter that is defined by the speed of light, not the other way around. However this does bring up the questions of how the speed of light was measured and whether it's accurate or not. Though I suppose that there's a reason 'c' is used instead of 299,792,458 m/s.
PostPosted: Mon May 22, 2006 11:07 pm


Prof. Verlinde was explaining this to us after the review session. The notion of a "pure vacuum" is still relatively undefined, and certainly not generally present on earth. Perhaps there are regions of space where, due to some nature of the space, the light travels even faster - an even purer vacuum, of sorts. Still, our measurements here on earth are pretty damn accurate, if you've ever seen the experimental setup.

Swordmaster Dragon


ZigguratII

PostPosted: Wed May 31, 2006 2:35 pm


Am I right in my thoughts that the speed of light is considered maximum speed, because since a photon has not mass it takes no energy to accelerate?
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Astrophysics, Cosmology, and Relativity

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