Welcome to NRICH.

 
E=mc2
By Aly Crowley (P1162) on Wednesday, September 01, 1999 - 12:49 pm:

What exactly does E=mc2 mean? I am wondering as we are doing a project on famous scientists at school and I chose albert Einstein.

I am a 12 year old female from Adelaide Australia who recently returned from 4.5 months studying in Bahrain (look it up in an atlas if you don't know where it is and also in your reply tell me).

Bye

By Jonathan Malcolm (P1094) on Friday, September 03, 1999 - 11:14 pm:

The full meaning of E=mc2 is Energy equals Mass times the Speed of Light squared. This means that you can find the energy an object has by finding its mass and multiplying it by the square of the Speed of Light.

I don't know if this is all correct because I am only 14.

By Michael Doré (P904) on Saturday, September 04, 1999 - 06:02 pm:

Einstein was said to have been inspired to discover special relativity (and hence E=mc2) by Maxwell’s theory of electromagnetism. This theory showed that light consists of oscillating electric and magnetic fields.

One key result of the theory of electromagnetism is that the apparent speed of light is the same no matter what your own speed is. This was confirmed by the Michelson-Morley experiment.

Imagine yourself on a motorway. You are travelling at 50 mph and you are watching another car at 60 mph. How fast does this second car appear to be going? 10mph – because every hour it has travelled 10 miles more than you. What if you are going at 40 mph? Now the car in front appears to be going at 20 mph. And if you were moving at 60 mph the car would look still. So you can see that normally the apparent speed of an object depends on your own speed.

But with light it’s different. The speed of light is always the same no matter whether you are sitting still, in a car, on a plane or in the fastest space rocket ever made. And it also means you can never go as fast as light. For if you did then you would see it staying still (like a car you are driving beside on a motorway looks still). And this can’t happen.

So what is there to stop you going as fast as light? By Newton’s laws of motion:

v = u + at
F = Ma

So to get up to the speed of light from rest:

c = at (c = speed of light, a = acceleration)

a = F/M (F = force)

t = c M/F

So the time it takes for a rocket of mass M to get up to the speed of light with a constant force of F should be c M/F. Something’s gone wrong! It is impossible to get to the speed of light yet by using classical physics the speed of light will be reached after time c M/F.

What actually happens is the mass M increases the faster you get. This is not noticeable with everyday speeds but at just over half the speed of light the mass of the rocket (and anything inside) would double! When you get close to the speed of light the rocket becomes so massive that the engines cannot quite get you to the speed of light – it would take an infinite amount of energy! This is because it is harder to push a heavy object.

So due to the mass increase the faster the rocket goes the less effective the engines are (even though they are delivering maximum power). The rocket needs a huge amount of energy even to push you to half the speed of light. (Imagine trying to push something that gets heavier and heavier the more you push it).

But where has this energy gone? You have added a huge amount of energy to the system and all that you have accomplished is you’ve made the rocket heavier (and go slightly faster). Energy is considered to have been stored in the extra mass. If you put an energy E into a system (like here) its mass increases. If you take the energy out the mass decreases again. Mass is considered to be a form of energy and if you do the calculations you find that E = mc2 where c is a constant, the speed of light.

All mass contains this energy, but it can seldom be released. One example where it can be released is when two opposite sub-atomic particles collide. (e.g. an electron and a positron) The two particles annihilate each other but their energy (due to their mass) is released as photons of light.

Hope that helps,

Michael

By Graham Lee (P1021) on Friday, September 03, 1999 - 06:57 pm:

I'll have a go at this, too.
E=mc² is the most famous, if one of the least useful product's of Einstein's General Theory of relativity. It says that if you could convert mass directly into energy, then the amount of energy you get is calculated by the amount of mass multiplied by the square of the speed of light.
This is a huge amount of energy (I theoretically could be converted into over 5400000000000000000J of energy), but it only happens in very small amounts, such as fusion reactions. As you may know, the Sun converts Hydrogen into Helium. But what you may not know is that your chemistry teachers have been lying to you. An atom of He is not exactly twice as heavy as an atom of deuterium, it is about 0.0001 protons or something lighter. This is due to the binding energy, which is obtained directly from a mass-energy conversion. The 0.0001 proton is known as the "Mass defect" and it is this which is converted into energy, given out in the reaction.
I hope this is useful,

GL.

By Graham Lee (P1021) on Monday, September 06, 1999 - 08:04 pm:

The application of E=mc² actually occurs in nuclear fusion. If you hit two deuterium atoms together (mass number slightly above 2 each) then you get one helium atom (mass number just above 4). But the mass number of He is not 2×(mass number Dt). It is slightly less, in fact about one-ten thousandth proton mass or something. Put this value (called the mass defect) into m in E=mc², and you have the energy of a fusion reaction.
Multiply this by avogadro's number to find the energy per mole, then by the number of moles in 4000000000000kg of deuterium (which is 200000000000000 I think) to get the power output of the Sun in Watts! Groovy, eh?

GL.

By Aly Crowley (P1162) on Wednesday, September 08, 1999 - 01:19 am:

Thanks heaps this has helped me heaps and especially Graham.

AR

By Aly Crowley (P1162) on Wednesday, September 08, 1999 - 02:10 am:

What is the speed of sound?
sorry for the trouble.

By Aly Crowley (P1162) on Wednesday, September 08, 1999 - 02:12 am:

Did anyone in their reply tell me where they thought Bahrain was? nnnnnnoooo

By Graham Lee (P1021) on Wednesday, September 08, 1999 - 07:13 pm:

The speed of sound is 330m/s or about 650mph at sea level in air. It is much faster (about 1550m/s I think) under water.
Bahrain is a peninsula of Saudi Arabia, it may be part of the UAE but I can't remember. Quite warm, though. Got a tan?

By Aly Crowley (P1162) on Wednesday, September 08, 1999 - 01:15 am:

Thanks GL
When I asked my chem teacher she just shuffled her shoes and said she would have to delve deeper into the theory to come to a conclusion.

Thanks again
AR

By Aly Crowley (P1162) on Saturday, September 11, 1999 - 11:24 pm:

Graham,
Actually Bahrain is a state of Saudi Arabia. The answer to your question is yes!

Aly

By Yatir Halevi on Sunday, October 14, 2001 - 05:29 pm:

Actually, E=mc2 is not a result of the general theory of relativity but of the special one.
He reached it by seeing that the summation of the energies of a moving body, when his mass-energy is included, is E=mc2

By Edvin Deadman on Sunday, April 21, 2002 - 11:32 am:

This E=mc2 lark is really weird stuff! But does anybody know anything about how exactly energy can be converted into mass? The maths works if you accept that the statement is true but if you think about it, its a really strange concept: energy and mass as we understand them in 'every day life' are so different that I find it impossible to understand how one can change into the other!

By Yatir Halevi on Sunday, April 21, 2002 - 08:51 pm:

They way I like to look at it, is that mass is just compressed energy, just like a nucleus of an atom is made up of protons and neutrons.

Yatir

By Julian Pulman on Wednesday, June 12, 2002 - 05:52 pm:

I think what Einstein was getting at was that even though *we* perceive Energy and Mass to be unique and different, their properties are identical. Matter and Energy both bend spacetime, and thus both exert impulse - they are equivalent because they produce the same effect.