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### Ask the Experts: What is the significance of E = mc2? And what does it mean?

Posted April 23, 2007 4:13 PM
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From Scientific American:

Ronald C. Lasky, director of the Cook Engineering Design Center at Dartmouth College, explains the significance behind this hallowed equation: It is the most famous equation in the world. Many can recite it—and attribute it to Albert Einstein—but few know its significance. It tells us that mass and energy are related, and, in those rare instances where mass is converted totally into energy, how much energy that will be. The elegance with which it ties together three disparate parts of nature—energy, the speed of light and mass—is profound.

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#1

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/24/2007 1:36 AM

Interesting bit of history and mathematics.

The reason for the c2 in the equation is simply due to the way the units of mass and energy were chosen originally. In reality, they are the same thing and with smartly chosen units, the equation is simply E = m.

On the other hand, E = mc2 looks so good!

J

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#2

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/24/2007 9:13 AM

Excellent Jorrie!

I have often wondered, had it been the other way around (E=m/c2), would they have built the bomb or just decided that (at first glance) it just wasn't enough bang for the buck.

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#3

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/24/2007 9:52 AM

E=MC2???

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#4

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/25/2007 2:48 AM

Once, while playing around with the math of physics, I had some really complex equation containing a bunch of historical constants and coefficients. As I started canceling like factors, the equation suddenly resolved to three factors: E, m and c2. I looked at it and saw that within the factor's units, that's what it would all have to come down to. Funny.

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### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/25/2007 4:08 AM

Hi Vermin, yep, I guess all equations for energy eventually boil down to those parameters! A Joule is a Joule is a....

-J

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#6

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/25/2007 6:48 PM

What would be the units of E = m?

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#7

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/26/2007 5:18 AM

Hi Harbinger, you asked: "What would be the units of E = m?"

The simplest answer is: Joules, of course. The c2 simply converts mass (kg) to Joules.

Relativists do not like the Joules, because they prefer geometric units, where energy, distance and time are all expressed in the same units. Now time and distance in Joules do not sit so well, so they use distance in meters or cm as the base unit.

To convert time to meters, one simply multiply by c. To convert mass to meters, one multiply by a factor G/c2, where G is Newton's gravitational constant, and all are geometrized. If you have energy in Joules, divide by c2 to get meters.

This may look like unnecessarily complicating things, but believe me, it makes relativity much easier to comprehend!

So, what is your mass in meters?

-J

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#11

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/26/2007 11:34 PM

What would that be in fortnights and furlongs???

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#14

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/27/2007 3:34 PM

I would say that the true profundity of the equation lies in its expansion
rather than simplification.

Written E = M / (Distance)/ Time[in a specific ratio]), it related mass, energy,
time, and space, all into one formulation.

Now thats profound.

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#15

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/27/2007 3:48 PM

Hi Pragmatist, you wrote: "Written E = M / (Distance)/ Time[in a specific ratio]), it related mass, energy, time, and space, all into one formulation."

I do not follow your thoughts here. Do you mean E = M/(x/t) or Mt/x? Neither makes sense to me. Please elaborate.

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#8

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/26/2007 12:10 PM

Lest not forget the missing time factor!!!!

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#9

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/26/2007 8:15 PM

If x = ab then, a = x/b and b = x/a, right?

He says:

Pphoton = Pbox = E / c = Mvbox

Then vbox = E / cM (1)

If E/c = Mv then, M = E/c/v and v = E/c/M, not E/cM.

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#10

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/26/2007 11:27 PM

You wrote: "If E/c = Mv then, M = E/c/v and v = E/c/M, not E/cM."

But E/c/M = E/cM is normally taken as the same!

It's a standard shorthand way of writing the right-hand side, but I prefer to write: E/(cM) to avoid such confusion.

-J

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#12

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/26/2007 11:48 PM

Actually, I'm looking at it as (E/c) = Mv

and (E/c)/M

Ok, I think I see whats going on here.

If I divide 100 by 4 (=25) and then divide 25 by 3, I get 8.3333...

which is the same as dividing 100 by 12 (4*3) = 8.3333...

What a trip!

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#13

### Re: Ask the Experts: What is the significance of E = mc2? And what does it mean?

04/27/2007 12:02 AM

Hi Harbinger you wrote:

"How then does (E/c)/M equate to E/(cM)?"

The simplest is to just put it into a spreadsheet or a scientific calculator and see that the answers are the same! It will save a lot of arithmetic arguing.

-J

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