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Why is the speed of light... Rate Topic: -----

#1 20 January 2012 - 12:40 PM Nebster173 


Lepton
300,000Km/s ?

Why isn't it some other number?
0

#2 20 January 2012 - 12:43 PM Ophiolite 


Moderately Super
All the other numbers were taken.
Data ---> Information ---> Knowledge ---> Wisdom

Per Ardua ad Astra - Through difficulties, to the cinema.
0

#3 20 January 2012 - 01:02 PM Tres Juicy 


Molecule

View PostNebster173, on 20 January 2012 - 12:40 PM, said:

300,000Km/s ?

Why isn't it some other number?



It is what it is mate
A fencing instructor named Fisk
In duels was terribly brisk
So much that in action
The Fitzgerald contraction
Reduced his foil to a disk

Like all good science, I pose more questions than I answer

Spoiler
0

#4 20 January 2012 - 01:05 PM ajb 


Icon
Physics Expert
We are free to use other systems of units. It is rather a historical accident as opposed to design that the speed of light is exactly 299,792,458 meters per second.

The question you really want to ask is why is the speed of light the same in any inertial frame of reference? That is independent of the motion of the source.

This post has been edited by ajb: 20 January 2012 - 01:05 PM

"In physics you don't have to go around making trouble for yourself - nature does it for you" Frank Wilczek.

My homepage.
0

#5 20 January 2012 - 01:06 PM Tres Juicy 


Molecule

View Postajb, on 20 January 2012 - 01:05 PM, said:

We are free to use other systems of units. It is rather a historical accident as opposed to design that the speed of light is exactly 299,792,458 meters per second.

The question you really want to ask is why is the speed of light the same in any inertial frame of reference? That is independent of the motion of the source.


This is a much better question which deserves its own thread really
A fencing instructor named Fisk
In duels was terribly brisk
So much that in action
The Fitzgerald contraction
Reduced his foil to a disk

Like all good science, I pose more questions than I answer

Spoiler
0

#6 20 January 2012 - 05:40 PM michel123456 


Molecule

View Postajb, on 20 January 2012 - 01:05 PM, said:

(...) exactly 299,792,458 meters per second.(...)


That is not what I expect from the meaning of the word "exactly".

I thought the OP question was: why this number and not another? Why not 537,163,921 m/s or 56,842,489,667,535,578,975,422 m/s?
Michel
0

#7 20 January 2012 - 06:47 PM Appolinaria 


Molecule

View Postajb, on 20 January 2012 - 01:05 PM, said:

It is rather a historical accident as opposed to design that the speed of light is exactly 299,792,458 meters per second.
0

#8 20 January 2012 - 07:03 PM ydoaPs 


just lost the game
.

This post has been edited by ydoaPs: 20 January 2012 - 07:03 PM

"Our integrity sells for so little, but it is all we really have. It is the very last inch of us. But within that inch we are free."-Valerie(V for Vendetta)

‎"Scientism" is the pejorative those who believe in magic give to Empiricism so they can pretend making stuff up is on equal footing with Science.

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#9 20 January 2012 - 07:34 PM michel123456 


Molecule

View PostydoaPs, on 20 January 2012 - 07:03 PM, said:

.


Edited for punctuation?
Michel
2

#10 20 January 2012 - 07:44 PM ydoaPs 


just lost the game

View PostNebster173, on 20 January 2012 - 12:40 PM, said:

300,000Km/s ?

Why isn't it some other number?

We start with what we call Maxwell equations. These are the equations that describe how electric fields and magnetic fields interact. Having no charges to worry about with light, we can set the charge density equal to zero which makes the equations:
\bigtriangledown\cdot{E}=0
\bigtriangledown\times{E}=-\frac{\partial{B}}{\partial{t}}
\bigtriangledown\cdot{B}=0
\bigtriangledown\times{B}={\mu_0}{\epsilon_0}\frac{\partial{E}}{\partial{t}}

Now, let's take the curl of the curl equations and see what happens.

\bigtriangledown\times\bigtriangledown\times{E}=-\frac{\partial}{\partial{t}}\bigtriangledown\times{B}=-{\mu_0}{\epsilon_0}\frac{\partial^2{E}}{\partial{t^2}}
\bigtriangledown\times\bigtriangledown\times{B}={\mu_0}{\epsilon_0}\frac{\partial}{\partial{t}}\bigtriangledown\times{E}=-{\mu_0}{\epsilon_0}\frac{\partial^2{B}}{\partial{t^2}}

Since \bigtriangledown\times(\bigtriangledown\times{V})=\bigtriangledown(\bigtriangledown\cdot{V})-\bigtriangledown^2{V} for any vector field V, we can write:
\frac{\partial^2{E}}{\partial{t^2}}-\frac{1}{{\mu_0}{\epsilon_0}}\cdot\bigtriangledown^2{E}=0
\frac{\partial^2{B}}{\partial{t^2}}-\frac{1}{{\mu_0}{\epsilon_0}}\cdot\bigtriangledown^2{B}=0
which are the electromagnetic wave equations. The speed term is \frac{1}{\sqrt{{\mu_0}{\epsilon_0}}} where \mu_0 is the permeability of free space and \epsilon_0 is the permattivity of free space. Plug in the numbers and that's how we get c.

View Postmichel123456, on 20 January 2012 - 07:34 PM, said:

Edited for punctuation?

I accidentally hit "Add Reply" instead of "Preview Post".
"Our integrity sells for so little, but it is all we really have. It is the very last inch of us. But within that inch we are free."-Valerie(V for Vendetta)

‎"Scientism" is the pejorative those who believe in magic give to Empiricism so they can pretend making stuff up is on equal footing with Science.

Don't forget to follow me on facebook.
If you like my post, please show me by clicking the green plus ------->
1

#11 20 January 2012 - 07:54 PM mississippichem 


Icon
fluorescent protein
Ah. I love the good ole curl of the curl identity. All the dels brighten my day.

It has a nice ring to it.

"the curl of the curl is the gradient of the divergence less the laplacian"

Nice derivation ydoaps. Well said.

This post has been edited by mississippichem: 20 January 2012 - 08:02 PM

You've come a long way. Remember back when we defined what a velocity meant? Now we are talking about an antisymmetric tensor of second rank in four dimensions.

-Feynman Lectures on Physics II
1

#12 20 January 2012 - 08:00 PM michel123456 


Molecule

View PostydoaPs, on 20 January 2012 - 07:44 PM, said:

We start with what we call Maxwell equations. These are the equations that describe how electric fields and magnetic fields interact. Having no charges to worry about with light, we can set the charge density equal to zero which makes the equations:
\bigtriangledown\cdot{E}=0
\bigtriangledown\times{E}=-\frac{\partial{B}}{\partial{t}}
\bigtriangledown\cdot{B}=0
\bigtriangledown\times{B}={\mu_0}{\epsilon_0}\frac{\partial{E}}{\partial{t}}

Now, let's take the curl of the curl equations and see what happens.

\bigtriangledown\times\bigtriangledown\times{E}=-\frac{\partial}{\partial{t}}\bigtriangledown\times{B}=-{\mu_0}{\epsilon_0}\frac{\partial^2{E}}{\partial{t^2}}
\bigtriangledown\times\bigtriangledown\times{B}={\mu_0}{\epsilon_0}\frac{\partial}{\partial{t}}\bigtriangledown\times{E}=-{\mu_0}{\epsilon_0}\frac{\partial^2{B}}{\partial{t^2}}

Since \bigtriangledown\times(\bigtriangledown\times{V})=\bigtriangledown(\bigtriangledown\cdot{V})-\bigtriangledown^2{V} for any vector field V, we can write:
\frac{\partial^2{E}}{\partial{t^2}}-\frac{1}{{\mu_0}{\epsilon_0}}\cdot\bigtriangledown^2{E}=0
\frac{\partial^2{B}}{\partial{t^2}}-\frac{1}{{\mu_0}{\epsilon_0}}\cdot\bigtriangledown^2{B}=0
which are the electromagnetic wave equations. The speed term is \frac{1}{\sqrt{{\mu_0}{\epsilon_0}}} where \mu_0 is the permeability of free space and \epsilon_0 is the permattivity of free space. Plug in the numbers and that's how we get c.

Since Posted Image, it is circular reasoning.
Michel
0

#13 20 January 2012 - 08:06 PM ydoaPs 


just lost the game

View Postmichel123456, on 20 January 2012 - 08:00 PM, said:

Since Posted Image, it is circular reasoning.

IIRC, this derivation was first done before we knew light was an EM wave.
"Our integrity sells for so little, but it is all we really have. It is the very last inch of us. But within that inch we are free."-Valerie(V for Vendetta)

‎"Scientism" is the pejorative those who believe in magic give to Empiricism so they can pretend making stuff up is on equal footing with Science.

Don't forget to follow me on facebook.
If you like my post, please show me by clicking the green plus ------->
0

#14 21 January 2012 - 12:28 AM D H 


Icon
Physics Expert

View Postmichel123456, on 20 January 2012 - 08:00 PM, said:

Since Posted Image, it is circular reasoning.

That is an after the fact definition, just as defining the speed of light to be exactly 299,792,458 meters per second was an after the fact definition.

The last meeting of the General Conference on Weights and Measures (Conférence Générale des Poids et Mesures, or CGPM) proposed to take this to a new level. It proposed making each of the Planck constant h, the elementary charge e, the Boltzmann constant k, the Avogadro constant NA, and the luminous efficacy Kcd a defined constant. There's still a lot of work to be done on this. It won't happen for at least four years (the next CGPM meeting). The proposed resolution just set the framework. There are still a lot of TBDs ("To be determined") in the resolution.
1

#15 21 January 2012 - 02:01 PM michel123456 


Molecule
I think the clear answer to the OP is "no one knows".
However, one can imagine how weird world would that be a universe with Speed Of Light 1m/s for example, or even less.
IOW there must be some relation between our dimension (and all dimensions from electrons to galaxies) and the value of SOL. Some expect this relation to be geometrical, but no one really knows yet.
Michel
0

#16 22 January 2012 - 12:29 AM granpa 


Atom
the speed of light is

\frac{1}{\sqrt{{\mu_0}{\epsilon_0}}}

\mu_0 and \epsilon_0 represent the 'springiness' of space.

the wavelength of light needs to be about the size of a cell or eyes wont work.

the freqency of light is determined by teh frequency of the atoms which is determined by h (plancks constant)

wavelength of light = speed of light / frequency of light

so if the speed of light were different then the wavelenth of light would be the wrong size of our eyes.
In relativity, reality doesnt change just because you change velocity. Only your perspective on that reality changes.
If event A causes event B then it will do so for all observers.
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#17 23 January 2012 - 01:14 PM PeterJ 


Atom
Much confused about this.

Am I right to suppose that for a photon time stands still, and if it went any faster time would have to go backwards?
0

#18 23 January 2012 - 01:18 PM granpa 


Atom
time dilation doesnt apply to light.
only to things that move slower than the speed of light.
In relativity, reality doesnt change just because you change velocity. Only your perspective on that reality changes.
If event A causes event B then it will do so for all observers.
0

#19 23 January 2012 - 01:47 PM ajb 


Icon
Physics Expert

View PostPeterJ, on 23 January 2012 - 01:14 PM, said:

Am I right to suppose that for a photon time stands still,


You cannot really think like this. There is no notion of an inertial reference from of a photon. Thus one cannot talk about "from the photon's point of view".

View PostPeterJ, on 23 January 2012 - 01:14 PM, said:

and if it went any faster time would have to go backwards?



If a particle travels faster than the speed of light as measured in some inertial frame then it is always possible to find an inertial frame in which the particle is travelling backwards in time.
"In physics you don't have to go around making trouble for yourself - nature does it for you" Frank Wilczek.

My homepage.
0

#20 23 January 2012 - 01:59 PM PeterJ 


Atom

View Postajb, on 23 January 2012 - 01:47 PM, said:

You cannot really think like this. There is no notion of an inertial reference from of a photon. Thus one cannot talk about "from the photon's point of view".

Um. What does 'no notion' mean here? Do you mean the idea makes no sense? Didn't Einstein do quite well by giving the photon a pov? Not arguing, just clarifying. If I were riding on a photon then wouldn't time stand still for me?

Quote

If a particle travels faster than the speed of light as measured in some inertial frame then it is always possible to find an inertial frame in which the particle is travelling backwards in time.

Why would it not be the very same frame in which the particle is measured as travelling faster than c?
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