In E=mc^2, why is the speed of light squared?

Where V is less than what?

 

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There should be another "less than" symbol and a 'c' following the "0 'less than' v 'less than' " and "v 'less than' " in my posts to represent "much less than c" The board must assume that the second 'less than' symbol is the start of a HTML tag, and thus fails to show it and the following text.

 

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A non-relativistic proof of e=mc^2

[this proof is found in Max Born, “Einstein's Theory of Relativity,” pp 218-222, 1962]

"Einstein’s equation e=mc2, which states the proportionality of energy and inertial mass, is perhaps the most important result of the theory of relativity. We shall give another simple proof of it, due to Einstein himself, a proof which does not make use of the mathematical formalism of the theory of relativity. ( ) It is based on the fact that radiation exerts a pressure. From Maxwell’s field equations, supplemented by a theorem first deduced by Poynting (1884), it follows that a light wave which falls on an absorbing body exerts a pressure on it. It is found that the momentum transferred to an absorbing surface by a short flash of light is equal to e/c, where e is the energy of the light flash. This fact, which we will prove in the following section, was confirmed experimentally by Lebedew (1890) and again later with greater accuracy by Nichols and Hull (1901) and others. Exactly the same pressure is experienced by a body which first emits light, just as a gun experiences a recoil when a shot is fired."

[ .... followed by the mathematical formalisms and diagrams and then...]

Suitable calculations should now show that

E = MC^2

[...]


The vagueness of “proofs” based on unwarranted “assumptions”, using as experimental tools items such as light and heat and mass and energy whose ultimate nature was a total mystery, could have led only to the type of flagrant errors that now exist in the world of the theoretical mathematical physicists who constantly and uncritically permit and use such tactics.

Though entropy and the second law of thermodynamics make it hard to accept this “proof” as valid, we are glad to discover that even this last stronghold of the Theory of Relativity, i.e., e = mc2, is independent of that four-dimensional Moebus-inversion of logic and could have been assumed from classical physics."


from The Orb by du Gabriel -- www.anpheon.org

 

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....

Also, c is not actually constant!
Changes in different mediums

 

Re: ....

Yes, c is always constant. c refers to the speed of light in a vacuum alone, and is not used to denote the speed of light in other mediums.

 

....

So true, sorry bout that - a bit too hasty!

 

Hi, I'd like to clear up a few issues regarding Einstein's famous equation, E = mc².

Section 1: Where did E = mc² come from?
Let's see... Energy is some silly abstract idea which helps physicists keep a tally to help them solve their problems. You may recall that they have defined energy to by the product of force and distance:
E = ∫F(x) · dx
Ok, we all know that force (another abstract idea) is given by the product of the mass of an object and the acceleration its experiencing. Since the acceleration is given by the derivative of the velocity (with respect to time), we can write
F = ma = m(dv/dt).
We can plug in the second equation into the first (by substitution), and rearrange a little, to arrive at a third equation:
E = ∫m(dv/dt)·dx = ∫m(dx/dt)·dv = ∫mv·dv
Now, if we were to integrate right here, we would arrive at the classical mechanical formula for kinetic energy, E = ½mv².
However, this would not take relativity into account. We must use another relationship of special relativity
m = m0/√(1-v²/c²).
Ok, where the heck did this come from, and what does it mean. Ok, we all know that, according to speical relativity, as you travel faster and faster, time slows down. However, two other things occur at the same time (the reason why this is not well known is a mystery). The travelling vehicle shinks lengthwise (the length contraction effect), and the travelling vehicle gets more massive (not bigger, it just starts to weigh more)! Its the later effect that's being described by the equation above. In words the equation says, "the new mass of the object is equal to the rest mass of the object divided by the sqaure root of stuff."
Ok, enough of that, we simply plug this ugly equation into our equation that we have been working on, and arrive at
E = ∫m0v/√(1-v²/c²)·dv.
Ok, to finish things up, we integrate the right side of the equation (with the limits being 0 ―>v) Integration by trigonometric substitution will work best here (or a TI-89, or Mathematica will do nicely).
E = c²m√(1-v²/c²)
Since m√(1-v²/c²) = m0, we arrive at Einstein's famous equation,
E=mc².
(Note, the 0 on m has been dropped for aesthetic purposes)

 

Is there any link here with E=mc^2 and c^2 = mu 0*epsilon 0? (Permeability and permitivity of vacuum)

 

Listen Einstein considered that the speen of light in vaccum is constant but i don't think so i'm doing some researches adn experiments in college about it and when i get to anything new i'll inform u about it

 

Einstein wanted to express his theorys so that the layman could understand.

E=mc^2 is the relation of energy, Mass, and Light. All mass is energy in it's stored state. Mass must be multiplyed by the speed of light squared to quantify the amount of energy the mass contains.

 

Why don't you think so?

 

haha well u can put E=MC^2 as E=PC where P = momentum n c is speed of light as usual

Then P can also = MV there4 E=MVC whereas V is the velocity of a photon which travels at the speed of light coz its light energy so there 4 u can subsitute V as C and making E=MCC then E=MC^2

 

It is squared because that's how much potential energy there is within matter. You know... like an anhilliation between particles and antiparticles? Essentially you can turn energy into matter but that's quite impossible.

 

Maxwell defined c as the mathematical result of a specific relationship between the permeability and the permittivity of whatever medium electromagnetic waves are travelling through.

He did this about a half century before Einstein felt like it would be neat to postulate c to be constant.

Does anybody know what an index of refraction is?

 

An index of refraction is the speed of electromagnetic radiation travelling through a given object w/ respect to a vacuum. This is unrelated to the constant c because of what happens at the microstate as the radiation travels through the object.

As the radiation passes through the object theres a slight disturbance that occurs within the object's electrons, and then this oscillation gives off a radiation of the same frequency as the original source, but this radiation has been delayed. So essentially its a stop-go-stop-go situation, and c remains the same.

 

No it's not. You can expend energy to make elementary particles.

 

How can this be accomplished?

 

"Essentially you can turn energy into matter but that's quite impossible."

Somebody's participle is dangling out in the open, or, something like that.

..."but THAT'S quit impossible.".... To what is "THAT'S" referring?

Pair annihilation and pair production are symmetrical reactions which are very well proven in both theory and practice and which perfectly illustrate conversation of mass into energy and energy into mass.

Which THAT is posted as claimed to be impossible?

 

Doesnt that show theres something wrong with the whole theory ?

 

Huricane Angel is obviously perplexed by the problem analgous to deciding which came first, the chicken or the egg?

First, Maxwell rigorously devised a wave equation that explained the velocity of his newly theorized electromagnetic waves as being exactly related to the permeability and permittivity IN WHICH THE WAVES ARE TRAVELLING. His work was exactly mathematically and logically consistent with all experimental observations performed up to that time in the fields of electricity and magnetism.

Second, or, next, or something like that, Einstein invented out of thin air the POSTULATE that all observers may observe the identical speed for c.

Does anyone here know the difference between a rigorously derived mathetmatical equation and a POSTULATE?

The meaning of the word POSTULATE might be found in some dictionaries.