Why is speed of light 299 792 458 m / s

[Phil Irvine]

I am not a physicist, so apologies if this is something that has been discussed before and is well understood. I, sort of, understand why it has been theorized that light (or mass) has a maximum speed that can't be exceeded. Also that experiments have shown it to be 299,792, 458 m/s in a vacuum. But I haven't seen whether there is a good theoretical reason that the maximum speed should be at that level. Why, for example, shouldn't the speed of light be 250,000,000 m/s or 350,000,000 m/s? Put another way, what is special about that speed?

 

[jtbell]

We have an entry about this in the Frequently Asked Relativity Questions section at the top of this forum. Try reading that, and if you have further questions, by all means ask!

 

[HallsofIvy]

I don't know that anyone can give a reason why it is "this" number rather than "that" number. One way of answering that, in a sense, answers the question you ask but not the question you intend, is that the numerical valule depends upon your system of units. In fact, in 1983, the meter was specifically defined as the distance light travels in 1/299 792 458 sec. which is why the speed of light has no decimal part (earlier definitions of "meter", such as that based on the wavelength of Krypton light, or before that, the length of a given bar of metal in Paris, gave slightly different values for the speed of light that had decimal parts.

In Cosmology, it is not unusual to use "one light second" as the unit of length. In that system, the speed of light is "1".

 

[phinds]

I am not a physicist, so apologies if this is something that has been discussed before and is well understood. I, sort of, understand why it has been theorized that light (or mass) has a maximum speed that can't be exceeded. Also that experiments have shown it to be 299,792, 458 m/s in a vacuum. But I haven't seen whether there is a good theoretical reason that the maximum speed should be at that level. Why, for example, shouldn't the speed of light be 250,000,000 m/s or 350,000,000 m/s? Put another way, what is special about that speed?

One of the things you'll discover if you poke around about this topic is that the "speed of light" is NOT so much the speed of LIGHT, it is the fundamental speed limit of the universe, and is a speed that is the necessary speed of all massless particles including, but not limited to, light photons.

 

[bcrowell]

I don't know that anyone can give a reason why it is "this" number rather than "that" number.

Well, the reason it's that particular number in the SI is that it's based on the properties of our planet. The meter was originally defined in terms of the circumference of the earth, and the second in terms of the mean solar day. The value of c expressed in the SI is basically a description of the inverse of the rotational speed of a point on the equator (along with some other conversion factors).

There is a good discussion of this kind of thing in Duff, 2002, "Comment on time-variation of fundamental constants," http://arxiv.org/abs/hep-th/0208093 .

 

[bobc2]

I am not a physicist, so apologies if this is something that has been discussed before and is well understood. I, sort of, understand why it has been theorized that light (or mass) has a maximum speed that can't be exceeded. Also that experiments have shown it to be 299,792, 458 m/s in a vacuum. But I haven't seen whether there is a good theoretical reason that the maximum speed should be at that level. Why, for example, shouldn't the speed of light be 250,000,000 m/s or 350,000,000 m/s? Put another way, what is special about that speed?

Phil, the above posts are all very good. There is also another complimentary way of looking at this. I've shown a sequence of graphs representing the coordinate systems for observers moving at ever higher speeds with respect to some reference rest system. The pictures include just one of our normal 3-D coordinates, X1, along with the 4th dimension, X4.

These coodinate systems are the way they are in order that nature can provide a universe in which the laws of physics are the same for all observers, regardless at what constant velocity they move relative to some arbitrarily chosen rest system. It is a special set of coordinates to be sure. Notice that angle between the the X4 and X1 coordinates are always bisected by a 45 degree world line in the reference system.

The X4 coordinate rotates clockwise to some angle, consistent with representing the velocity with respect to the rest system. But, the unusual aspect of these systems is that the X1 coordinate is always rotated counterclockwise by the same angle. The other fascinating detail in special relativity (by some interpretations) is that all observers are moving along their own X4 axes at the speed of of light.

But, specifically to your question is the observation that a photon of light moves at a velocity corresponding exactly to the 45 degree world line (the one that bisects the angle between X4 and X1 for all observers)--and as an observer moves faster and faster (as in the sequence of coordinates) the X4 axis and X1 axis keep rotating closer and closer to each other. In the limit they would become colinear--a result that has no physical comprehension in terms of a world that could be experienced by an observer who would then be moving at the speed of light.

The box in the lower right corner shows why the ratio of displacement along the 4th dimension to displacement along the X1 dimension, X4/X1, for a photon moving at speed c is the same for any of the special relativity coordinate systems. The fundamental observation is really that the ratio of the spatial distances is equal to 1.0 for all observers. The speed c comes out as a result of our arbitrarily chosen system of units for time and spatial distance. That, along with the aspect of all observers moving along their X4 dimensions at speed c. Thus, X4 = ct in any of the coordinate systems. Then, the speed of a photon,
X1/X4 = X1/(ct) = 1. Thus, c = X1/t for a photon (in any of the coordinate systems).

That's what makes c so special. It's that 45 degree world line in the spacetime diagrams. And it represents that limiting case of the X4 and X1 axes rotating toward each other--nature has built into the physics a way of avoiding the rotation of X4 and X1 to the point of becoming colinear.

 

[harrylin]

I am not a physicist, so apologies if this is something that has been discussed before and is well understood. I, sort of, understand why it has been theorized that light (or mass) has a maximum speed that can't be exceeded. Also that experiments have shown it to be 299,792, 458 m/s in a vacuum. But I haven't seen whether there is a good theoretical reason that the maximum speed should be at that level. Why, for example, shouldn't the speed of light be 250,000,000 m/s or 350,000,000 m/s? Put another way, what is special about that speed?

In classical and relativistic physics, it's a property of the vacuum.

"Maxwell's equations [..] predict that the speed c with which electromagnetic waves (such as light) propagate through the vacuum is related to the electric constant ε0 and the magnetic constant μ0 by the equation c = 1/√ε0μ0.
- http://en.wikipedia.org/wiki/Speed_of_light#Propagation_of_light

Does that help?

Harald