Why is the Speed of Light Squared in E=mc^2?

[free_mind]

e=mc^2 is equivalent to e=m.89875517873681764 m/s
The speed of light is a constant. How this is possible in reality?

Is not possible to have a body traveling at this speed, because simply doesn't exists (or at least we don't discover it yet).

I already read several answers to this kind of question. But the answers are around the intrinsic mathematical need to square c in the formula e=mc^2. I am looking for a logical reason for this problem, because beyond mathematical reasoning there are the reality; many times the mathematic coincides with reality, but in this problem, is what it happens?

I look for help to eliminate my difficulty in understanding this. Thank you.

 

[Doc Al]

e=mc^2 is equivalent to e=m.89875517873681764 m/s

The units of speed squared would be $m^2/s^2$.

The speed of light is a constant. How this is possible in reality?

You may find this thread helpful: https://www.physicsforums.com/showthread.php?t=80640

 

[Pengwuino]

I already read several answers to this kind of question. But the answers are around the intrinsic mathematical need to square c in the formula e=mc^2. I am looking for a logical reason for this problem, because beyond mathematical reasoning there are the reality; many times the mathematic coincides with reality, but in this problem, is what it happens?

Because simply squaring a certain value that has a reality based principle does not mean the actual principle gets squared. Just because we state that E=mc^2 does not mean the speed of light is at all changed, its value is simply squared to make use of the equation.

 

[selfAdjoint]

Because simply squaring a certain value that has a reality based principle does not mean the actual principle gets squared. Just because we state that E=mc^2 does not mean the speed of light is at all changed, its value is simply squared to make use of the equation.

At all relative speeds v less than c, you have the dilation factor $$\beta = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$. This factor can be proved from Einstein's two postulates, and from the factor you can prove that the energy of a body in its rest frame is $$e = mc^2$$. Incidentally the units of a speed squared are not length over time but length squared over time squared. This gives the product $$mc^2$$ the correct units for an energy.

The squaring of a velocity in computing an energy comes from integrating it: $$\int v dt = \frac{v^2}{2}$$. This is not just a relativity thing, it applies in Newtonian kinetic energy too.

 

[HallsofIvy]

Didn't we just do this?

https://www.physicsforums.com/showthread.php?t=80640&page=1

 

[pervect]

Let's try and make this very very simple.

The square of a velocity is not a velocity, just as the square of a foot is not a foot. (The squre of a foot is a square foot, a unit of area, not a linear dimension).

 

[free_mind]

I red the content of the URL https://www.physicsforums.com/showth...?t=80640&page=1 before

insert my question in this forum.

Focus your attention in this:
c2=89875517873681764 m2/s2

Forget the mathematic abstraction and please tell me:

1. This have pratical application?
2. Is possible to produce this conditions in order to do a pratical experience?

 

[EL]

2. Is possible to produce this conditions in order to do a pratical experience?

Yes, the squared speed of light in vacuum is always equal to c^2.


Swampeast Mike = Free_mind. Right?

 

[russ_watters]

Focus your attention in this:
c2=89875517873681764 m2/s2

Forget the mathematic abstraction and please tell me:

1. This have pratical application?
2. Is possible to produce this conditions in order to do a pratical experience?

1. Clearly, yes - in the equation for energy you posted in the first post!
2. What "conditions"? If you mean conditions where the equation has meaning, certainly yes.

m2/s2

Do you understand what those units mean for your question? We're not talking about a speed anymore.

 

[DrChinese]

Forget the mathematic abstraction and please tell me:

1. This have pratical application?
2. Is possible to produce this conditions in order to do a pratical experience?

Welcome to PhysicsForums, free_mind!

1. That there is practical application is clear, as E=mc^2 is used in physics daily. Such practical application is a hallmark of a good theory.

 

[free_mind]

1. Clearly, yes - in the equation for energy you posted in the first post!
2. What "conditions"? If you mean conditions where the equation has meaning, certainly yes. Do you understand what those units mean for your question? We're not talking about a speed anymore.

If we are not talking about the speed anymore, what we are talking about?

In the SI units I didn't find meaning for m2/s2! It is J/kg?

In what kind of experiences you get this number: 89875517873681764 m2/s2? Note that I am thinking about a total formula application and not in a parcial application.

 

[HallsofIvy]

"In the SI units I didn't find meaning for m2/s2! It is J/kg?"

There appears to be a great deal you don't find meaning for! No one has said that "speed squared" has any particular physical significance. You can if you like think of it as J/kg. The crucial point is that (1/2)mv² and mc² have units of energy- that has physical significance.

 

[free_mind]

"In the SI units I didn't find meaning for m2/s2! It is J/kg?"

There appears to be a great deal you don't find meaning for! No one has said that "speed squared" has any particular physical significance. You can if you like think of it as J/kg. The crucial point is that (1/2)mv² and mc² have units of energy- that has physical significance.

Can you decribe an experience in which will be possible to get c2?

If a body reaches the speed of light will not become equal to all of it's energy, because we have an "obstacle" the c2. I would like to have a pratical "image" (a pratical experience) of this.

 

[russ_watters]

Can you decribe an experience in which will be possible to get c2?

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

If a body reaches the speed of light will not become equal to all of it's energy, because we have an "obstacle" the c2.

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.

 

[Doc Al]

Can you decribe an experience in which will be possible to get c2?

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.

If a body reaches the speed of light will not become equal to all of it's energy, because we have an "obstacle" the c2. I would like to have a pratical "image" (a pratical experience) of this.

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: $E = (\Delta m) c^2$.

 

[Swampeast Mike]

Swampeast Mike = Free_mind. Right?

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.

you can prove that the energy of a body in its rest frame is e=m(c^2)

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.

 

[HallsofIvy]

"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"."

I'll try one more time! "c" is a number. Any number can be squared! The fact that the speed of any object with nonzero mass must be less than the speed of light doesn't say numbers can't be greater than c²!

In any case, exactly what c is depends upon your units of measurement which are completely arbitrary. It is quite common for scientists writing about relativity to take the "light second" as their unit of distance so that "c" is 1 (light second per second).

 

[EL]

ABSOLUTELY NOT! I have never and will never engage in such deception.

Then I'm sorry.

What if we use natural units where c=1?
Or maybe introduce EL-units where c=0.00004815376501846?
Then there is no problem with squaring it, or?

 

[Swampeast Mike]

I'll try one more time! "c" is a number. Any number can be squared! The fact that the speed of any object with nonzero mass must be less than the speed of light doesn't say numbers can't be greater than c2!

You are correct and I do understand.

Please let me pose these situations:

Say we have one linear foot and square it. We get one square foot.

Take that same linear foot to the zeroth power. Do we still have one linear foot or do we have a one point in space? Perhaps a "one" that masquerades as a "zero"? Could that perhaps be why zero seems to masquerade as a real number?

What about the square root of one lineal foot? While I can take the square root of the NUMBER one, the square root of one lineal foot is "undefined".

Now we have the speed as light expressed as one. We square it and we get one unit of a velocity squared.

Take that same speed of light as expressed by one and take it to the zeroth power. Do we have one unit of velocity or one unit of something else?

Can you see how I'm getting into trouble with zero sometimes appearing to equal one and one sometimes appearing to equal zero depending on the perspect of time and space?

 

[selfAdjoint]

The zero power of any number is 1. To say the same thing in other words, the logarithm of 1 in any base is zero. This shouldn't confuse you.

 

[Entropy]

Take that same speed of light as expressed by one and take it to the zeroth power. Do we have one unit of velocity or one unit of something else?

You would get 1 and it would be unitless.

 

[Swampeast Mike]

What if we use natural units where c=1?

If you look back at the replies to this and the previous similar that WAS started by me, I think you'll see a problem.

When I say that I have a problem squaring the speed of light, am told that it's no problem because you're squaring a concept, not a number; e.g. one lineal foot squared equals one squared foot.

When I agree (in fact that was part of what I was saying in my replies even if they are extremely abstract) and then in this thread do my best to show how why I find the speed of light squared as an absolute (not relative to space and time) concept I'm essentially told, that it's no problem because I'm dealing with numbers!

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?

 

[Entropy]

Why would c^2 be the same as c^0 any more than c^2 is the same as c?

They aren't the same! What are you taking about?

 

[Swampeast Mike]

Entropy: Please see edit. I was typing fast. Not sure if the change will help, but it's what I meant.

 

[Swampeast Mike]

You would get 1 and it would be unitless.

Please let me embellish: You would get 1 and it would be unitless as relative to space and time.

Speed of light squared [seems] a concept based only on the perspective of physical entities where space and time are fixed.

Combine the two and you find rational duality. :rofl:

Please continue to destroy this view.

 

[free_mind]

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.

 

[free_mind]

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]

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.

 

[free_mind]

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 physics pratical sense. which one?

 

[free_mind]

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 physics pratical sense. What it is?

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

 

[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]

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]

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]

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 physics 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]

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.