The speed limit squared?, It's the amount of energy in mass

Why is it that the speed limit in the
universe squared is the amount of energy
in mass?

Mass is bound or concentrated energy.
Why the square of the speed of light
and not some other quantity?

God gave more meaning to the speed of
light than meets the eye.

Hello Nick.

All of the observations you make concerning the speed of light squared may apply to the speed of sound squared. In other words, the energy/mass/momentum values for ANY DISTURBANCE SOLITON propagating 'in the NATURAL MEDIUM' for that soliton can be mathematically related to the propagation cross-sectional (frontal area) crossing per unit 'time' for the full passing of the whole body of that soliton disturbance through the energy-'measuring/absorbing' structure.

The only difference between the two in reality is that the 'natural' medium for light propagation does NOT allow LIGHTWAVE SOURCES to propagate faster than the wave disturbances they produce; whereas we can observe with supersonic airplanes that the 'natural' medium for sound propagation DOES allow SOUNDWAVE SOURCES to propagate faster than the wave disturbances they produce (in that 'natural' medium).

This suggests:-

1) The 'natural' medium for LIGHT represents an IRREDUCIBLE MINIMUM requirement 'medium' for any and all phenomena to propagate; and is therefore a more fundamental medium than...

2) The 'natural' medium for SOUND; and that...

3) Whereas the TRANS-SONIC propagation regime can be got through and beyond, the TRANS-LUMINAL propagation regime CAN NOT; thus leading to the situation where...

4) CERENKOV RADIATION (counterpart to 'sonic boom') compression waves in 'vacuum' DO NOT have a spread of energy' content because they arise ONLY when the source is IN the © regime, there being NO acceleration into HYPER-LUMINAL regimes possible, and there is therefore NO change in LIGHT-CONE angles unless there is a change in the 'medium' through which the lightsource is traveling; whereas SONIC-BOOM compression waves CAN have a 'spread' of 'energy' content which increases because their source (in air for instance) can be accelerated well into HYPER-SONIC regimes, which also results in a NARROWING SOUND-CONE; which means that in hypers-sonic regimes the energy content of the soundwave disturbance is related to increasingly GREATER POWERS than 'the SQUARE'.


The upshot being that there is nothing 'special' about © 'squared', because in any situation where the SOURCE CAN EXCEED the speed of propagation of the wave disturbances it produces, it will involve something OTHER than 'squaring' to arrive at a value for 'energy' content. The only thing that can be said about the 'luminal' scenario is that the 'fundamental' Universal 'vacuum' medium constrains the energy content of LIGHT/MATTER waves to a 'squared' function.

There are probably more cogent treatments/comments to be offered by others; I hope that in the meantime the above gives you something to be going on with.

Smiling and sun-drenched regards from: RealityCheck.

Good afternoon RealityCheck,

I go to school and do not have time for all the sites dealing with physics, but this is one subject I am very interested in, could you give me some resources that I might read to help me along.

Bye,
Sara

Hi Guest_Sara,

I assume that what you are referring to is "propagation" of light and the inverse square law. Reality_Check has asked me to "pick up the threads" on your original request.

I could refer you to standard treatments of this concept. Here is an encyclopedia reference...
Inverse Square Law

"Missed it by that much" as Maxwell Smart would say. I will say more about this later...
There is also the concepts of Special Relativity that Reality_Check has also alluded to...
Special Relativity
In the end it is a very open ended subject and I could refer you to hundreds of texts. What I will now try to do is to "zoom in" on what I think is the core issue here and regardless of your level of knowledge try and put this across...

The propagation of energy, especially electromagnetic energy, is usually described by the propagation of "plane waves". Most texts will deal with this concept such as when you see such illustrations as those above. Here is the catch... these plane waves cannot be used to transfer energy... to do that the waves need to be curved like the surface of a soap bubble or the inner tube of a tire. Only curved surfaces transfer energy. This is a crucial concept for the propagation of energy. The energy can only "propagate" if the ratio of curvature is EXACTLY the inverse square relationship. No other ratio will actually transfer that energy from point to point. The is so for gravity, electromagnetism such as light and sound. The "index" of 2 is "most" important and 1.99999 just will not do. Neither will 2.00001 do either. Two is the number, probably the most important number in the creation of the Universe or any Universe EVER.

This is because between any two enclosed spherical surface "shells" the energy that enters it must also exit it for propagation to continue. If this does not happen energy will be "lost" between the shells and "pretty quickly" there will be nothing left to propagate. In that condition the field is thus "inductive". For propagation Light absolutely requires this to happen for energy to be transferred.
Hence E = MC
...Where C is the speed of light and relates to the radius of a sphere of propagation or the surface area of that sphere. To see it's derivation you need to look at Special Relativity. As you know the surface area of a sphere is ...

Notice pi is also very important and also occurs in the derivation of any energy related systems. This includes the speed of light itself...
Wikipedia: the speed of light
Notice © is in terms that involve all that propagation information and so on... light can only propagate successfully in "flat spacetime" or "spacetime" that conserves this curvature property overall.

See that the speed of light itself is related to....

the permittivity of free space...
and

the permeability of free space...
therefore the speed of light is actually...

... paradoxically a simple geometric ratio.
If you have some other need please be a little more specific... Physics is an awfully big subject... as big as the Universe.

Cheers

Hi All,

Critical Addendum:

Consider a photon that does not curve spacetime on its own (massless). Any space it traverses will be possible since overall the inverse square law applies (spacetime is conservatively curved - affinely connected). Consider a "particle" such as that electron that is created from a topological photon... now it "gravitates" and curves spacetime around it (it is a source of gravity) . This affects the ability of the particle to "propagate" as before, and over a certain range, the energy cannot leave the "source" (trapped in its vicinity) since the inverse square law no longer applies to the energy... The area (A) of the surface of an "excribed" sphere is NOT equal to...

In that region of space the extra curvature of spacetime will eventually trap the energy from spreading and "return" it to its source (evanescent field).

Not exactly as simple as this ... tunneling effects and so on. But I am sure you can see the point. Particles do not "spread". Deeply philosophical isn't it! But dead easy and convincing.

Cheers