Thread: The expanding universe proves why c in E = mc² is squared.

First, I'd like to ask the question, why is c (the speed of light) squared in "e = mc²"?

I couldn't find it anywhere online, so I tried to prove it to myself, and I ended coming up with this theory.

So my theory is based on the following information (this is the domain):

1. Space is unlimited
2. The universe is limited, but expanding
3. The universe is inside space

From these statements, we can say the universe is expanding by the speed of light, because light is being emmited through space, and light is the fastest thing we have in our universe. Since we now know the universe is expanding at the speed of light, and since we are inside the universe, then we are expanding at the speed of light. Since everything is expanding by the speed of light, it would seem as though nothing is expanding to someone inside the universe, because everything is relative.

Here's a fun sorta way to show this. Take a sponge, cut it in half on the thin side, don't cut it all the way so that it is two pieces, but rather cut it in a way that you can see the center of the sponge. Now take a permanent marker and mark the sponge in the center. Take a bowl of water, and place the sponge in the water. As the sponge expands the dot in the middle expands as well. The dot is representing an object in the universe, the sponge is representing the universe, and the water is representing space.

We now know that everything is expanding at the speed of light from an outside of universe view. But then we are moving, so it is more than the speed of light... it is the speed of light, plus the distance one is moving when compared to the universe (if you walk one foot, it's not one foot... it's one foot plus the distance the earth has spinned, plus the distance the earth has revolved.. and so on...). Based on this, we can say that the speed of light relatively is going at the speed of light squared from an outside the universe perspective. Since everything is moving at the speed of light, then the speed of light itself must be moving at the speed of light times the speed of light.

This explains why c in e = mc² is squared. For mass to become energy it must be going at the speed of light squared from an outside of universe view. I think the energy we talk about is not from a relative perspective (inside the universe perspective), but rather it is from an outside the universe perspective. So mass going at the the speed of light squared becomes energy.

Now, at what point can we go at exactly the speed of light From an outside the universe point of view? We can go at the speed of light from an outside of universe point of view when we are at 0 degrees kelvin. At 0 degrees kelvin nothing is moving relative, but the universe is still expanding. We are freezing time by going at 0 degrees kelvin.

When we go lower than absolute zero, we are reversing time (in theory). Now the universe would be expanding while the mass would be shrinking in comparison to everything else from an outside the universe point of view.

I am not sure what would happen if we are going faster than the speed of light squared...

Please criticize, but please don't flame.

Btw I know that Einstein based E = mc² off some other equations, mainly being the equation of force. But maybe the force equation is also from an outside of the universe point of view.

i always thought it was because the equation refers to the Velocity of light.

as i was told in science we always write velocity in M/S^2

hence light would travel at 2.997925 X10^8 m/s^2

besides the expansion of the universe is accelerating, so i'm told.

mass is energy and energy is mass, for an object of mass M to accelerate to the speed of light requires the input of an infinite amount of energy. hence the mass of the object goes to infinity making it impossible for objects of material mass to accelerate to the speed of light.

m/s² is acceleration and the speed of light squared's unit is m²/s² or it is velocity, which is (m/s), squared.

I thought what if the universe's expansion is accelerating, and I wouldn't be able to understand why. From our view the fastest thing in the universe is light. So the universe should be expanding at the speed of light.

"mass is energy and energy is mass, for an object of mass M to accelerate to the speed of light requires the input of an infinite amount of energy. hence the mass of the object goes to infinity making it impossible for objects of material mass to accelerate to the speed of light."

Ahhh you have proven my point! Relatively speaking, the speed of light is impossible to reach. Speaking from the outside of universe point of view looking at the universe, the speed of light from this perspective is really the speed of light squared. So relatively it is impossible for a mass to go to the speed of light. Relatively the fastest thing around is the speed of light.

Speaking from an outside the universe point of view, the speed of light is replaced by the speed of light squared. It's really confusing. I could explain it better verbally.

Pretty much I am saying that relatively the fastest thing is the speed of light. From an outside of universe point of view the fastest thing in the universe is the speed of light squared. So, what we have thought to be relative energy is really the energy from an outside of universe point of view.

Good criticism though. :wink:

Where is mitchellmckain when you need him?

Originally Posted by Nima Rahnemoon

1. Space is unlimited
2. The universe is limited, but expanding
3. The universe is inside space

the speed of light remains the same for all observers at all frames of reference, spacetime can/is, whichever you prefer, a system of reference.

according to your theory an observer outside the 'Universe', as you describe is still within the frames of reference and would see light as going at the speed of light.

one other thing that has me thinking, how can an observer outside the universe actually see the universe if the light has not yet caught up to them?

if the universe expands at the speed of light and the observer is even 1 light year away from the current boundry of the universe how will they see it since the photons have not yet reached their eyes?
and when the photons do reach there eyes it means the observer will now be apart of the universe and measure light going at the constant speed it does when travelling through a vacuum.

and upon further investigation my previous post needs some revising. thank you Wikipedia. http://en.wikipedia.org/wiki/E%3Dmc%5E2

It's ironic how you say this:

"the speed of light remains the same for all observers at all frames of reference, spacetime can/is, whichever you prefer, a system of reference. "

The reason I made this theory was because c in "e = mc²" was not making sense to me.

So my question is this, if the speed of light is always the same by all observersers, then why is 'c' in "e = mc²" squared?

I have to think about how a person from outside the universe could see the universe. Because I see what you are saying.

This theory only works in theory, it can never actually be proven, or even be done. It doesn't work in theory too well either.

If someone can explain to me why 'c' in "e = mc²" squared i'll throw away this entire theory. I know that "e=mc²" is based on other equation, but why does it make sense

did you read link i posted above?
i know it still doesn't explain why we have c² but it puts the equation into perspective.

equation defines a relationship between energy and mass

The equation resulted from Albert Einstein's inquiry into the dependence of mass on its energy content.

According to the equation, the total amount of energy obtainable from an object is equivalent to the mass of the object multiplied by the square of the speed of light.

With the right units, the square of the speed of light is unnecessary (Energy = Mass).

and so on...there's much more info there esspecialy some stuff on the electromagnetic and gravitational forces.

so maybe the c is squared because it just leads to some right answers.

I see what you mean about how you can't see light from outside the universe.

So I began to think maybe energy has something to do with surface area. Again, if the universe is expanding at c, then everything is expanding at c. So, the surface area that everything is expanding at is c². So E might be referring to the rate at which the surface area of everything expands times the mass. So the amount times the surface area gives us energy?

I don't know. I'd like to hear what some of you think about "why c is squared in e = mc²". I looked at the wikipedia page, but it still doesn't answer that question, I know you are aware of that, but I agree it is a useful links... Thanks. I couldn't find any website answer that question.

What is this unit (g(m²))/(s²)? ( I know it is the equivalent of one Joule, but what is it representing)

Could anyone explain each part of that unit? Why does this unit make sense to represent a unit of energy?

What is s² representing?

How does E = mc² lead to the right answers?

What is g(m)²?

That's a lot to ask in one post. Sorry for asking soo many questions.

"when you have a problem...Just hit it with a shovel", lol, let's hit these questions with shovels.

Edit: I can answer one of these questions, s² is just a change in time as seen in the accelration unit m/s²

i don't think the equation has much to do with the expansion of the universe, but really just describes the energy content of mass or the mass of a defined amount of energy.

why is the c^2, just because. there is probably some complex math to it but i wouldn't know anything about that.

but i agree i reacon if we beat c with a shovel it'll crack and tell us the answer.

There was a documentary on e=mc² recently. E=mc2

2 is for squared

There is only one 'number' represented in Einstein's great equation and it designates that the speed of light, c, must be squared. A number which is squared is simply one that is multiplied by itself. Squaring 4 equals 16, for example.

In E=mc2, the speed of light is multiplied by itself, 670 million (miles an hour) by 670 million, giving the preposterously large number of 448,900,000,000,000,000. But why square the speed of light at all? The answer lies with the discovery made by a brilliant French aristocrat, Emilie du Chatelet.

At the age of 23, du Chatelet discovered a talent for advanced mathematics which she relished. So much so that she began to formulate ideas of her own; ideas that challenged the great physicists, including Sir Isaac Newton.

Newton stated that the energy (or force) of a moving object could simply be expressed as its mass multiplied by its velocity. But while corresponding with a German scientist called Gottfried Leibniz, du Chatelet learned that Leibniz considered the energy of a moving object is better described if its velocity is squared. But how to test this? Du Chatelet tried an experiment that would prove her point – dropping lead balls into clay.

Newton's formula says that doubling the velocity of a ball would double its energy and so one would expect it to travel twice as far into the clay. But if the velocity is squared, as Leibniz and du Chatelet believed, the force should be four times greater, and the ball should travel four times the distance into the clay.

Du Chatelet conducted her lead ball experiment and sure enough, doubling the velocity of the ball (by dropping it from twice the height) resulted in the ball travelling four times further into the clay. This simple but brilliant experiment proved that when calculating the energy of moving objects, the velocity at which they travel must be squared. The energy of an object is a function of its velocity squared – it is for this reason that the speed of light in Einstein's equation must be squared.

This was a factor that profoundly changed the meaning of Einstein's equation – since c is already a large number, once squared it is vast. Thus, a vast amount of energy (E) can be associated with a very small amount of mass (m) because mass is always multiplied by the speed of light (c) squared – a vast number. Under these laws, even a tiny amount of mass will equate to a huge amount of energy.

thank you for settling that for us.

In E=mc2, the speed of light is multiplied by itself, 670 million (miles an hour) by 670 million, giving the preposterously large number of 448,900,000,000,000,000. But why square the speed of light at all? The answer lies with the discovery made by a brilliant French aristocrat, Emilie du Chatelet.

At the age of 23, du Chatelet discovered a talent for advanced mathematics which she relished. So much so that she began to formulate ideas of her own; ideas that challenged the great physicists, including Sir Isaac Newton.

What? Einsteinian theory is based on something deduced bya woman!!?? That can't be right.........!

:P

It's also bizarre to discover that Isaac Newton didn't know that the Kinetic Energy of a moving object was ½mv²....

"The energy of an object is a function of its velocity squared – it is for this reason that the speed of light in Einstein's equation must be squared. "

Thanks, but I don't understand it.

She did not prove why c is squared in e=mc². What she proved is simple physics.

Tell me if you shoot a bullet into the air, what is the path of the bullet?

It's a parabola... the equation would be y=x² or a form of that equation. All she did was she doubled the height, and she saw the x become squared. Here is an example

y=x²... y = 1 ... x= 1
1 = 1 check
Now... y=4 ... x=2
4 = 4 check

When she doubled "x" the "y" is being squared... 2² is four so in this case the "y" is increasing by four times. As seen in these coordinates (1,1) versus (2,4).

Might be confusing, but I don't see how that proves the speed of light should be squared. I see that it proves that the velocity increases/ decreases quadratically.

By the way, I changed my theory, I'll post up the revised theory tomorrow or on Friday. Thanks for the criticism it really helped.

Originally Posted by Nima Rahnemoon

She did not prove why c is squared in e=mc². What she proved is simple physics.

perhaps it is squared because it is simple physics.

velocity is kinetic energy isn't it. so the energy increases/decreases quadraticly.

speaking of quadratics time for school i was going to add more but i think i'm confused. :?

BTW how do you get the squared in a post, all i can do is type ^2.

"BTW how do you get the squared in a post, all i can do is type ^2."

It's alt + 0178, the problem is if you hold alt +7 on a browser it goes to the homepage.

One way to do it is to copy mine, a second way is to go to your homepage and type "alt+0178", and then copy it.

Now about this whole e = mc² ordeal... the difference between y=x² and y=c² is that c is a constant ... y=c² is linear, while in y=x² the graph is a parabola (it changes x values as well as y values).

"velocity is kinetic energy isn't it. so the energy increases/decreases quadraticly." -Wallaby

"I see that it proves that the velocity increases/ decreases quadratically. " -Nima

I agree, this is true in air (It is probably different in a vacuum). I messed up though. Velocity decreases quadratically, pauses (this is the maximum), and then increases quadratically. (The energy is being stored on the way up, and released on the way down, like electrons :P )

C is a constant because it is measured in a vacuum. In air the value of C is slower due to air resistance. She did not do this experiment in a vacuum. Therefore, you can't relate C to the velocity of the ball.

Anyhow, I was just trying to say that she 'discovered' something else.

You are right. It probably is simple physics and we're overlooking it... or maybe I'm just overlooking it.

Originally Posted by wallaby

BTW how do you get the squared in a post, all i can do is type ^2

On Windows there is an application called "Character Map" in Accessories\System Tools. Check that for the ASCII codes which can be entered by holding ALT whilst entering the code on the numeric pad e.g ALT + 0153 = ™. I don't know the code for ² so I just copied & pasted :wink:

As for the topic at hand I've tried a few times and given up on articulating my thoughts...

Please try one more time, I think I am misunderstanding... sorry I'm slow with understanding things like this.

Notice how it took me 4 days to even try to understand what you were saying. You're language was clear, it just didn't click in my head. So please re-explain. I really want to know why c is squared even if my theory is wrong.

i guess the best thing we can do is look at a few examples.

i know that there is a book in our school library on the equation with one chapter dealing with each of the variables the history of and its relation to the equation. i'll have to borrow it again on friday.

Ultimately, Nima, c is squared because if you don't square c you get the wrong answers! Newton, for example, knew that the faster an object was moving the more energy it would have, but he assumed that it was a direct relationship. It is the result of the ball-dropping into mud experiment that showed that the velocity had to be squared to give an accurate value for the energy.

Einstein derived E=mc² from that (½mv² and many other equations, but the proof of the pudding is in the experimental results, which have shown it to be correct. (By "experimental results" I mean all sorts of different things like the gravitational lensing effect of distant galaxies, to the yield of an atomic bomb).

Originally Posted by wallaby

BTW how do you get the squared in a post, all i can do is type ^2

I do the following: E=mc², and then click off the "Disable HTML in this post" immediately beneath the edit window.

c²

thanks silas