Speed of Light Limit: Factors & Vacuum Conditions

[hagar]

Under Ideal conditions (a vacuum and no gravity) what is the limiting factor or factors for the speed of light ?

Thank you,
Pat Hagar

 

[e.bar.goum]

The speed of light in a vacuum is defined as 299 792 458 m/s.

 

[hagar]

Yes, I have read that. I would like to know what makes that the constant speed of light and not say faster. I realize that gravity and other things can modify the speed of light but I do not understand why it is set at 299 792 458 m/s under ideal conditions.

Thank you for your response,
Pat Hagar

 

[e.bar.goum]

Yes, I have read that. I would like to know what makes that the constant speed of light and not say faster. I realize that gravity and other things can modify the speed of light but I do not understand why it is set at 299 792 458 m/s under ideal conditions.

Thank you for your response,
Pat Hagar

The speed of light being 299 792 458 m/s is a definition. c is the speed at which massless particles travel. You can just as well define the speed of light to be c = 1 (this is often done in natural units). The number tells you more about the size of the stick you use to measure distance, and the rate at which you measure time. I could define it to be 455555566778900 potatoes per aardvark, and all this tells us is how big my "potato" and "aardvark" units are.

 

[Drakkith]

Yes, I have read that. I would like to know what makes that the constant speed of light and not say faster. I realize that gravity and other things can modify the speed of light but I do not understand why it is set at 299 792 458 m/s under ideal conditions.

Thank you for your response,
Pat Hagar

There is no underlying reason that we can give. It's a postulate of special relativity (and general relativity when talking about 'local' effects). In other words, its a fundamental fact of nature that has no explanation at the moment.

 

[PeroK]

Under Ideal conditions (a vacuum and no gravity) what is the limiting factor or factors for the speed of light ?

Thank you,
Pat Hagar

The limiting factors are the "permittivity" and "permeability" of free space. Essentially, even a vacuum only allows electro-magnetic radiation to propagate at a finite speed. Why these factors are what they are has no immediate explanation (as mentioned above).

https://en.wikipedia.org/wiki/Vacuum_permittivity

https://en.wikipedia.org/wiki/Vacuum_permeability

https://en.wikipedia.org/wiki/Speed_of_light#Propagation_of_light

 

[hagar]

"The speed of light being 299 792 458 m/s is a definition. c is the speed at which massless particles travel. You can just as well define the speed of light to be c = 1 (this is often done in natural units). The number tells you more about the size of the stick you use to measure distance, and the rate at which you measure time. I could define it to be 455555566778900 potatoes per aardvark, and all this tells us is how big my "potato" and "aardvark" units are."

Are you saying that it is basically an arbitrary number chosen to represent the speed of light in an equation and it could just as easily have been any other number. If this is the case then I did not phrase my inquiry correctly.

Still, the question remains and I do not know how to present it in a better form. I believe my problem is based in semantics but at this point I am not sure how to express it.

Thank you,
Pat Hagar

 

[hagar]

There is no underlying reason that we can give. It's a postulate of special relativity (and general relativity when talking about 'local' effects). In other words, its a fundamental fact of nature that has no explanation at the moment.

Thank you. This helped a great deal. That I understand.

 

[hagar]

The limiting factors are the "permittivity" and "permeability" of free space. Essentially, even a vacuum only allows electro-magnetic radiation to propagate at a finite speed. Why these factors are what they are has no immediate explanation (as mentioned above).

https://en.wikipedia.org/wiki/Vacuum_permittivity

https://en.wikipedia.org/wiki/Vacuum_permeability

https://en.wikipedia.org/wiki/Speed_of_light#Propagation_of_light

Thank you. The links will be most helpful. I have already read [QUOT " https://en.wikipedia.org/wiki/Speed_or_light#Propagation_of_light " ] but I have not yet seen the others.
This sums up what I was asking.

Respectfully,
Pat Hagar

 

[hagar]

Also I still need to work out exactly how the software works for quotes etc.

 

[Drakkith]

Also I still need to work out exactly how the software works for quotes etc.

Highlight the text you want to quote and an option to quote or reply will pop up. Click reply to immediately copy the text into the reply box below. Clicking +quote will add the text to a quote que, which can be added to the reply box by clicking insert quotes. (Or use the +quote and reply buttons at the bottom of any post)

 

[Hadzi]

This is a way to calculate the speed of light using the permittivity and permeability of vacuum:

 

[e.bar.goum]

Thank you. The links will be most helpful. I have already read [QUOT " https://en.wikipedia.org/wiki/Speed_or_light#Propagation_of_light " ] but I have not yet seen the others.
This sums up what I was asking.

Respectfully,
Pat Hagar

This is a way to calculate the speed of light using the permittivity and permeability of vacuum:

Except, $\mu_0$ and $\epsilon_0$ are defined in terms of the speed of light. It's circular to use this definition to understand the speed of light.

By definition
$\epsilon_0 = \frac{1}{\mu_0 c^2 }$
$\mu_0 = \frac{1}{\epsilon_0 c^2 }$

 

[HallsofIvy]

Except, $\mu_0$ and $\epsilon_0$ are defined in terms of the speed of light. It's circular to use this definition to understand the speed of light.

By definition
$\epsilon_0 = \frac{1}{\mu_0 c^2 }$
$\mu_0 = \frac{1}{\epsilon_0 c^2 }$

No. Those are formulas that can be used to find the permittivity and permeability of vacuum but are NOT definitions.
see
https://en.wikipedia.org/wiki/Vacuum_permittivity and
https://en.wikipedia.org/wiki/Vacuum_permeability

 

[Hadzi]

@e.bar.goum True that. I don't know, but it's still fascinating to me that the speed of light is almost a perfectly "shaped" number, leaning towards 3x10⁸ m/s. Talking about the meter as the unit of measurement, it was defined before the speed of light was calculated (even approximately), right?

 

[Drakkith]

@e.bar.goum True that. I don't know, but it's still fascinating to me that the speed of light is almost a perfectly "shaped" number, leaning towards 3x10⁸ m/s. Talking about the meter as the unit of measurement, it was defined before the speed of light was calculated (even approximately), right?

The length of the meter was recently redefined in 1983: https://en.wikipedia.org/wiki/Metre#Distance_travelled_by_light_in_a_specified_time

The metre is the length of the path traveled by light in vacuum during a time interval of 1/299792458 of a second.

There's nothing 'shaped' about it (or perhaps you could say it is perfectly shaped because we made it that way). Prior to 1983 there had been several different definitions of the meter. Redefining the meter to be based on the speed of light actually simplifies things and let's us calculate distances more accurately since it is much easier to measure small amounts of time than small distances.

 

[e.bar.goum]

There's nothing too remarkable about 299 792 458 m/s really, as a number. No more remarkable than 594 742 458. The meter was first defined in 1793 as one ten-millionth of the distance from the equator to the North Pole, and has been redefined a few times since then.

 

[e.bar.goum]

No. Those are formulas that can be used to find the permittivity and permeability of vacuum but are NOT definitions.
see
https://en.wikipedia.org/wiki/Vacuum_permittivity and
https://en.wikipedia.org/wiki/Vacuum_permeability

$\epsilon_0$ is an exact value in NIST. It is derived from $c$ and $\mu_0$, using the definition upthread.

See:
http://physics.nist.gov/cuu/Constants/RevModPhys_80_000633acc.pdf

 

[Hadzi]

Okay, thanks for clearing that up.

 

[hagar]

Highlight the text you want to quote and an option to quote or reply will pop up. Click reply to immediately copy the text into the reply box below. Clicking +quote will add the text to a quote que, which can be added to the reply box by clicking insert quotes. (Or use the +quote and reply buttons at the bottom of any post)

Thank you, this worked quite well and will make things much easier. Occasionally one needs to be a bit more intelligent than the average monkey but I am afraid I do not always meet that requirement rigorously. Please excuse me while I go for another banana. :-)

 

[hagar]

Also, thanks to all for the additional information but most of the math on this forum is Greek to me as I have not used more than basic math in over fifty years.