# Square speed of light!

1. Aug 14, 2005

### 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.

2. Aug 14, 2005

### Staff: Mentor

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

3. Aug 14, 2005

### Pengwuino

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.

4. Aug 14, 2005

Staff Emeritus

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.

5. Aug 14, 2005

### HallsofIvy

Staff Emeritus
6. Aug 14, 2005

### pervect

Staff Emeritus
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).

7. Aug 15, 2005

### 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.

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?

8. Aug 15, 2005

### EL

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

Swampeast Mike = Free_mind. Right?

Last edited: Aug 15, 2005
9. Aug 15, 2005

### Staff: Mentor

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.

10. Aug 15, 2005

### DrChinese

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.

11. Aug 15, 2005

### free_mind

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.

Last edited: Aug 15, 2005
12. Aug 15, 2005

### HallsofIvy

Staff Emeritus
"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.

13. Aug 15, 2005

### free_mind

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.

14. Aug 15, 2005

### Staff: Mentor

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.

Last edited: Aug 15, 2005
15. Aug 15, 2005

### Staff: Mentor

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

16. Aug 15, 2005

### Swampeast Mike

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.

17. Aug 15, 2005

### HallsofIvy

Staff Emeritus
"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).

18. Aug 15, 2005

### EL

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?

Last edited: Aug 15, 2005
19. Aug 15, 2005

### Swampeast Mike

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?

20. Aug 15, 2005