# Square speed of light!

#### free_mind

russ_watters said:
You mean an experience to which c^2 is relevant? Certainly.

That doesn't come from e=mc^2. All e=mc^2 tells you is how much energy is released by converting a given mass to energy (the energy equivalency of mass).

free_mind, even setting aside your initial error in thinking c^2 was still a velocity, now it seems like you're looking for a physical significance to a fragment of an equation. C^2 has no more or less significance on its own than D^2 has in the Newtonian gravity equation.
The connection between atomic bombs and e=mc^2 is subtle. A nuclear explosion is not caused by the transformation of matter and energy. I already knew this connection, but the problem is that I don't know any pratical experience in which the "full" formula has been proved.

c^2 couldn't be interpreted as if it was a simple mathematic factor that result from a development of other equations. Einstein didn't choose the speed of light for "c" by chance.

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#### free_mind

Swampeast Mike said:
ABSOLUTELY NOT! I have never and will never engage in such deception.

I'm most sincerely trying to understand this concept (both speed of light and speed of light squared) when "time and space are relative".

Gravity, light, heat (IR), etc. all appear by our perspective to move at the speed of light. Such can only move at this speed because it has no mass—it's in the form of "energy bundles" that have characteristics of both mass and energy.

Agreed and understood with the provision that I don't believe that the "rest frame" conforms to our concepts of time and space.

So, we have a body that can be "viewed" as bundle of energy equal to its mass times velocity of an individual "packet" in that bundle squared.

Now, we add another body and photons move between them. ALWAYS between—NEVER just from one to another. PLUS—they ALWAYS move between—even if the bodies are identical there are still photons moving between them. Those photons would [seem] to be the embodiment of E = M(C^2) as they exist only as energy.

If I think small, this transference is happening between all atoms (and likely components of atoms) as if they are bodies separated by space. If I think big—really big—the entire universe could be considered one giant bundle of energy in a constant state of reorganization.

As long as I view those bodies (no matter their mass) as energies in their "rest frame", everything makes sense. BUT, these bodies DO have mass and individually they conform to our concepts of space and time. The photons moving between them would [seem] to have to come from the matter of both being converted into energy—or at least energy from that "rest state" where mass, space and time no longer conform to our perceptions.

THIS is the stage where I have a problem understanding the "speed of light squared" as an individual concept. Speed of light is immutable and unchanged regardless of the velocity of any object. No matter how fast I move towards the sun, energy from my body arrives on the sun before me and energy from the sun arrrives on my body as if I were not moving.

Simultaneously the universe appears to act as both the coalescence of energy bundles into individual objects that appear in space and time and as energy itself where space, time and distance cease to have meaning.

As I was told many times (and agree), "the square of the speed of light is not a velocity".

From what I understand, the result of squaring the speed of light is pure energy where time and space cease to have meaning–YET it only occurs between objects where space and time DO have meaning. How can this be?

I can think of one way. That e=m(c^2) is only part of the equation. That "c" cannot be squared unless it is simultaneously equal to one (c^0) as related to bodies separated by our concept of "space".

This would not change any universal understanding but it would [appear] to explain them all: the fundamental attraction of matter (gravity); the nature of energy transfer between objects (radiation); the ability of some forms of matter to express non-directional attraction to other certain forms via the movement of electrons (electro-magnetism); a universe that expands while simultaneously being attracted together into super-massive black holes until distance looses all meaning and for an instant all matter ceases to exist being replaced by the speed of light squared (big bang); the inability of man to find himself separate from the universe (spiritualism).

Again, this is written with the utmost sincerity and in the spirit of attempting to understand relativity. My [seeming] simple quest to understand how my proportionally controlled cast iron radiators interact with both the boiler and the house has led me to this point.
Could you explain what did you mean with "deception".

Seams to me that you have a clear explanation to my question; do you give the pleasure to know it?

#### pervect

Staff Emeritus
Swampeast Mike said:
Why (when c has been assigned the value of 1) would c^2 be the same as c any more than c^2 is the same as c???
c^2 is not the same as c. This is regardless of the numerical value of 'c'. This is similar to saying that 1 square foot is not the same as 1 foot, in spite of the fact that the number '1' appears in both measurements.

You really need to read a bit about "dimensional analysis". Seriously. Assuming you're serious about wanting to understand physics, that is. You could try the

wikipedia article

for starters.

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#### free_mind

Doc Al said:
Think of $c^2$ as a conversion factor. It's always there; you don't have to "get to it". It tells you the equivalent energy that an object has due to its rest mass.

Again, $E = m c^2$ does not require anything to reach the speed of light. ($c^2$ is a constant serving as a conversion factor, not some kind of "barrier".) While the equation applies to all sorts of interactions where rest mass is exchanged for other forms of energy, a "practical experience" where the released energy is significant is found in nuclear reactors. A fission reactor breaks down larger radioactive molecules (for example, U-235) into smaller fragments. If you add up the masses of those smaller fragments, their total mass is less than the original uranium. That "loss" of rest mass ($\Delta m$) relates to the amount of energy released in the nuclear reaction according to the Einstein formula: $E = (\Delta m) c^2$.
There are chemical reactions where there are tiny mass differences as well. An example: When hydrogen and oxygen explosively combine to make water, the sum of the rest masses of the initial hydrogen and oxygen atoms is just a little bit less than the sum of the rest masses of the resulting water molecules.

I know that E = m c^2does not require anything to reach the speed of light. Was an example. Einstein didn't say the particular situations where the formula will make sense. In your example, the complete formula application has not been proved.

89875517873681764 m^2/s^2 is not only a number (a factor). This has a physic pratical sense. which one?

#### free_mind

Doc Al said:
Think of $c^2$ as a conversion factor. It's always there; you don't have to "get to it". It tells you the equivalent energy that an object has due to its rest mass.

Again, $E = m c^2$ does not require anything to reach the speed of light. ($c^2$ is a constant serving as a conversion factor, not some kind of "barrier".) While the equation applies to all sorts of interactions where rest mass is exchanged for other forms of energy, a "practical experience" where the released energy is significant is found in nuclear reactors. A fission reactor breaks down larger radioactive molecules (for example, U-235) into smaller fragments. If you add up the masses of those smaller fragments, their total mass is less than the original uranium. That "loss" of rest mass ($\Delta m$) relates to the amount of energy released in the nuclear reaction according to the Einstein formula: $E = (\Delta m) c^2$.
There are chemical reactions where there are tiny mass differences as well. An example: When hydrogen and oxygen explosively combine to make water, the sum of the rest masses of the initial hydrogen and oxygen atoms is just a little bit less than the sum of the rest masses of the resulting water molecules.

I know that E = m c^2does not require anything to reach the speed of light. Was an example. Einstein didn't say the particular situations where the formula will make sense. In your example, the complete formula application has not been proved.

89875517873681764 m^2/s^2 is not only a number (a factor). This has a physic pratical sense. What it is?

__________________________________________
Why is it that nobody understands me, yet everybody likes me?
(Albert Einstein, 1944)

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#### Entropy

A nuclear explosion is not caused by the transformation of matter and energy.
Yes it is.

I already knew this connection, but the problem is that I don't know any pratical experience in which the "full" formula has been proved.
Millions of experiments have proven this. Just about every experiment ever to involve particle accelerators involves Einstien's equations.

#### Swampeast Mike

free_mind said:
Could you explain what did you mean with "deception".

Seams to me that you have a clear explanation to my question; do you give the pleasure to know it?
In this context "deception" would mean pretending to be a different coalescence of mass in the universe.

Your question is universal as is my attempted explanation of a universe where time and space are relative. It is not however, and I repeat NOT, based upon faith.

#### russ_watters

Mentor
free_mind said:
The connection between atomic bombs and e=mc^2 is subtle. A nuclear explosion is not caused by the transformation of matter and energy. I already knew this connection, but the problem is that I don't know any pratical experience in which the "full" formula has been proved.
Clearly, you do not understand. See Doc Al's post #15(among others): Nuclear reactions are based on e=mc^2.
c^2 couldn't be interpreted as if it was a simple mathematic factor that result from a development of other equations. Einstein didn't choose the speed of light for "c" by chance.
He didn't choose it at all - he derived it.
There are chemical reactions where there are tiny mass differences as well. An example: When hydrogen and oxygen explosively combine to make water, the sum of the rest masses of the initial hydrogen and oxygen atoms is just a little bit less than the sum of the rest masses of the resulting water molecules.
Really? How much, exactly?

#### Doc Al

Mentor
free_mind said:
There are chemical reactions where there are tiny mass differences as well. An example: When hydrogen and oxygen explosively combine to make water, the sum of the rest masses of the initial hydrogen and oxygen atoms is just a little bit less than the sum of the rest masses of the resulting water molecules.
Yes! Even in chemical reactions $E = m c^2$ applies. Of course the amount of rest mass "converted" to energy is much less in chemical reactions than in nuclear reactions.

I know that E = m c^2does not require anything to reach the speed of light. Was an example. Einstein didn't say the particular situations where the formula will make sense. In your example, the complete formula application has not been proved.
What are you talking about? $E = m c^2$ is a result derived from Special Relativity, which has been exhaustively tested. Nuclear reactions, controlled or otherwise, have directly confirmed $E = m c^2$.

89875517873681764 m^2/s^2 is not only a number (a factor). This has a physic pratical sense. What it is?
Again, what are you talking about? We've given several examples. You've even supplied one. (What do you mean by a "practical" sense?)

#### free_mind

russ_watters said:
Clearly, you do not understand. See Doc Al's post #15(among others): Nuclear reactions are based on e=mc^2. He didn't choose it at all - he derived it. Really? How much, exactly?
Another example of this:

Chemical reactions involving spontaneous oxydation, in other words we are talking about burning.

#### free_mind

Entropy said:
Yes it is.
NO, it isn't. Because to Einstein, realtivistic mass and energy are simply two different names for one and the same physical quantity. Read Einstein carefully and you will verify that this is as Iam saying.

Entropy said:
Millions of experiments have proven this. Just about every experiment ever to involve particle accelerators involves Einstien's equations.
Humm. The formula has been partially proven. But I am talking from the begining about a total proof.

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#### free_mind

Swampeast Mike said:
In this context "deception" would mean pretending to be a different coalescence of mass in the universe.

Your question is universal as is my attempted explanation of a universe where time and space are relative. It is not however, and I repeat NOT, based upon faith.
If you call "Faith" to the will of discover the truth freely without blarney anybody, YES is faith what determines my study, faith of getting the truth. The faith that you are talking about, you only could deduce it from my words with a great faith.

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#### russ_watters

Mentor
free_mind said:
Humm. The formula has been partially proven. But I am talking from the begining about a total proof.
There isn't total proof in science. But the equivalence of matter and energy is as close to completly proven as anything in science ever gets.

#### free_mind

russ_watters said:
There isn't total proof in science. But the equivalence of matter and energy is as close to completly proven as anything in science ever gets.
Don't interpret my words literally, they are not a mathematic formula :) . In science nor in nothing you have 100% . But show me an example where the E=mc^2 formula has been completely (not parcially and not because has been important to get conclusions in other observations, etc) proved.

#### Pengwuino

Gold Member
free_mind said:
Don't interpret my words literally, they are not a mathematic formula :) . In science nor in nothing you have 100% . But show me an example where the E=mc^2 formula has been completely (not parcially and not because has been important to get conclusions in other observations, etc) proved.
Didn't someone already point that out to you a few times already? Big flash of light.... mushroom cloud....

#### free_mind

Doc Al said:
Yes! Even in chemical reactions $E = m c^2$ applies. Of course the amount of rest mass "converted" to energy is much less in chemical reactions than in nuclear reactions.

What are you talking about? $E = m c^2$ is a result derived from Special Relativity, which has been exhaustively tested. Nuclear reactions, controlled or otherwise, have directly confirmed $E = m c^2$.

Again, what are you talking about? We've given several examples. You've even supplied one. (What do you mean by a "practical" sense?)
Until now I saw examples of parcial pratical application of the formula E=mc^2 .

#### free_mind

Pengwuino said:
Didn't someone already point that out to you a few times already? Big flash of light.... mushroom cloud....
Study the Einstein theory and you will find that Einstein's politics played a more decisive role in the story of the atomic bomb than his physics.

#### Pengwuino

Gold Member
free_mind said:
Study the Einstein theory and you will find that Einstein's politics played a more decisive role in the story of the atomic bomb than his physics.
.... Someones political feelings does not change the laws of physics. E=mc^2 was fully demonstrated by the atomic bomb. How exactly can you dispute that? What is the "part" that is explained that isnt the whole of the theory?

#### Doc Al

Mentor
free_mind said:
Study the Einstein theory and you will find that Einstein's politics played a more decisive role in the story of the atomic bomb than his physics.
Why not study Einstein's theory to find out how $E = m c^2$ is derived and what it means?

#### free_mind

Pengwuino said:
.... Someones political feelings does not change the laws of physics. E=mc^2 was fully demonstrated by the atomic bomb. How exactly can you dispute that? What is the "part" that is explained that isnt the whole of the theory?
Ok. I will try to be synthetic taking in account the place where we are.

The strength of the nuclear bond depends on the number of neutrons and protons involved. It varies in such a way that binding energy is released both in splitting up a heavy nucleus into smaller parts and in fusing light nuclei into heavier ones. This, as well as the chain reaction phenomenon, explains the immense power of nuclear bombs.

Einstein's formula it's all about different kinds of energy. Sure, there are some radioactive decay processes following nuclear fission, and, if so inclined, one can view the decay of a neutron decaying into a slightly lighter proton as a transformation of rest energy into other energy forms. But these additional processes contribute a mere 10 per cent of the total energy set free in nuclear fission. The main contribution is due to binding energy being converted to other forms of energy - a consequence not of Einstein's formula, but of the fact that nuclear forces are comparatively strong, and that certain lighter nuclei are much more strongly bound than certain more massive nuclei.

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#### free_mind

Doc Al said:
Why not study Einstein's theory to find out how $E = m c^2$ is derived and what it means?
The mathematic meaning could be far from the pratical world. Don't you know many situations in which this happens?

Mathematics couldn't be seen as an absolute concept to explain the world, notwithstanding the enormous help that gave and will give in our understanding of the world .

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#### pervect

Staff Emeritus
free_mind said:
NO, it isn't. Because to Einstein, realtivistic mass and energy are simply two different names for one and the same physical quantity. Read Einstein carefully and you will verify that this is as Iam saying.
It is true that for single point particles, relativistic mass and energy are the same. It's also true that nuclear reactions transform matter into energy. I don't see why you are advancing the first point as a counter-argument to the second - both are true.

#### free_mind

pervect said:
It is true that for single point particles, relativistic mass and energy are the same. It's also true that nuclear reactions transform matter into energy. I don't see why you are advancing the first point as a counter-argument to the second - both are true.
Einstein would say that in a system where there is energy (E), it automatically has the relativistic mass m=E/c2; whenever a system has the mass m, you need to assign it an energy E=mc2. Once the mass is known, so is the energy, and vice versa. In that context, it makes no sense to talk about the "transformation of mass into energy" - where there's one, there's the other.

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Staff Emeritus
Gold Member
Dearly Missed
free_mind said:
Einstein would say that in system where there is energy (E), it automatically has the relativistic mass m=E/c2; whenever a system has the mass m, you need to assign it an energy E=mc2. Once the mass is known, so is the energy, and vice versa. In that context, it makes no sense to talk about the "transformation of mass into energy" - where there's one, there's the other.
Some energy you can do work with. But a mass just sitting at rest (you do know the formula $$e=mc^2$$ is only true in the rest frame don't you?) can't do any work. In order to transform the frozen form of energy we call matter into the fluid kind that can do work we need some specific physical transformation to take place.

#### russ_watters

Mentor
free_mind said:
The mathematic meaning could be far from the pratical world. Don't you know many situations in which this happens?
Name one relevant to this thread.