Why Does E=mc2? (And Why Should We Care?) Brian Cox Brian Cox (Author)

Curly Judge

Have been wading my way through this book recently and have come up very disappointed.
This is at least the fourth book on relativity I have read and I'm still as far on as ever.
It's not that I don't accept Einstein's genius, I really do!
If he is to be proved wrong in the future it will only be to the same extent that he proved Newton wrong.
I fully accept that the speed of light is the speed limit of the Universe [unfortunatly] and that an object's mass approaches infinity as it is accelerated to the speed of light while it's length decreases towards zero.
All this I can get my head around. Not because I fully understand it but mainly because I respect the veracity of people who tell me that this is so.
Much as in the way I accept that Mozart's music is wonderful. My ear is not educated enough to be able to discern it for myself so I bow to the opinion of my betters.
One question I would like answered:
Is the speed of light a universal constant in it's own right and has it's almost complete association with light -in the public's mind - detracted from it's importance in the wider scheme of things.
In other words, "Why does E=mc2"?
Brian Cox hasn't answered it in this book, at least not for me.
Professor Fink will probably give me a D minus for this.

krd

It can be derived from several different equations.

It's only recently I saw an explanation that made sense to me. And that was looking at different equations on several different websites, where I could see how the substitutions could be made. And then it just pops out as E=mc2. I didn't write it down - I should have because it's not firmly lodged in my head - I would have to sit down and plot the whole thing out and memorise it.

I had seen several different derivations but they didn't click with me.

The full equation is E2 = m2c4 + p2c2 . If you consider the particle at rest, you can throw away the momentum p2c2.....And you get E2 = m2c4, which then gives you E = mc2. For a photon that has no mass, you can throw away the m2c4 and you get E = pc, which is an important equation too.

You can see things like E = hf, E = pc, so hf = pc, h = pc/f. The thing is, if you keep playing with the formulas interesting things emerge.

The E=mc2 is just one little formula, it's by playing with them all that you see stuff. It's virtually meaningless by itself.

Energy is very difficult concept. It seems obvious but it isn't.

I'd like to do my own derivation for E=mc2, something that uses several different connected equations - where I will be able to see all the important relationships on one page. So, I can know it inside out without any ambiguities or contradictions.

If you set c = 1, the equations change

E = pc, becomes E = p, E = mc2 becomes E = m, h = pc/f becomes E = p/f

E2 = m2c4 + p2c2, becomes, E = m + p.

Squashie

I wouldn't waste your time with popular science books if you're really interested in the topic. Information is always vague in them. So much time spent glamorizing the topic, there's not enough space for proper facts. In the time it's taken to read those 4 books you could have taught yourself a little maths and gotten a proper fully comprehensive undergraduate textbook on the subject.

Morbert

In relativity, energy and momentum are unified as energy-momentum in the same way space and time are unified as spacetime. The "space-time relation" is

s^2 = t^2 - d^2

where t is time and d is spatial distance. This is effectively the 4D spacetime equivalent of pythagoras's theorem h^2 = x^2 + y^2. The energy-momentum relation, similarly, is

s^2 = E^2 - p^2

where E is energy and p is momentum. S, in this case, is mass! I.e. We can rewrite it as

m^2 = E^2 - p^2

In other words, mass turns out to be a measure of the difference between energy and momentum of a system. If a system is massless (m = 0), this means its energy equals its momentum (E.g. A photon). If a system is at rest, it has no momentum (p = 0) and so its energy is equal to its mass (E = m). This is where E = m comes from.

What is important in relativity is not energy and mass, but rather energy and momentum. These are the more fundamental quantities.

*Note, c is not important. It is a number that reflects arbitrary units. I have used natural units above, so that c = 1, and can be ignored.

doctoremma

Read it, didn't like it. Too many motorbikes going up hills and down valleys for my tastes.

Quite odd to say that - I'd probably be lynched for uttering such profanity at work (Manchester Uni)

Justin1982

I recommend getting your hands on a book called (Sears and Zemanskys) "University Physics" by Young and Freedman, go to chapter 39 called "Relativity" and you will be treated to the simplest mathematical introduction to Special Relativity that you'll find anywhere. Just 25 pages of simple leaving cert level maths, really nice diagrams and a few words to explain it all.
(Note: I had the Tenth edition from 2000. It may have evolved since then but I hope not)

Most of the other books on beginner relativity that I read were a pile of bollocks as far as I could see when compared to University Physics.

Essentially you can explain special relativity using a variety of ways mathematically. The simplest method is the way Einstein discovered it using his thought experiments and this method is adopted by University Physics. The worst introduction I've seen is by D'Inverno in "Introducing Einsteins Relativity".

Once you've mastered Special Relativity then you probably want to move on to General Relativity. I used D'Inverno for this (yes his introduction to general relativity is much better than his introduction to special relativity).
I'm not sure its the best introduction but it would be decent enough although not for the faint hearted.

IamtheWalrus

Currently reading this book. To be honest, I didn't pick it up to find out why e=mc2. I wanted to gain knowledge from the things Cox uses to explain it, if that makes sense. If I still don't get e=mc2, I'll still have learned a lot about physics so the effort won't be wasted.

Justin1982

In fairness if the book is as boring and waffly as his tv series then I wouldnt waste my time.
Its a shame, there is a wealth of really interesting physics out there and the BBC give that lad a mad amount of resources and air time to waffle on with bad explanations.
For anyone interested I cant recommend "Big Bang" by Simon Singh highly enough. Really good job on explaining the history of Cosmology.

krd

Justin1982 wrote: »

In fairness if the book is as boring and waffly as his tv series then I wouldnt waste my time.

To be fair, I don't know. I have his The Quantum Universe, and it's a lot more in depth than you'd find in typical popular science books - and you're expected to use pen and paper.

Its a shame, there is a wealth of really interesting physics out there and the BBC give that lad a mad amount of resources and air time to waffle on with bad explanations.

Because he's sexy, he waves his hands a lot, and smiles.

For anyone interested I cant recommend "Big Bang" by Simon Singh highly enough. Really good job on explaining the history of Cosmology.

I haven't read it, but there's full length video on Youtube of him doing the talk tour for the book.

A lot of pop science books are actually very easy going - you breeze through them in a day or two. After a while you notice, I won't call it plagiarism, but there's an element of cogging each others books.

Lapin

Squashie wrote: »

So much time spent glamorizing the topic, there's not enough space for proper facts.

I see what you did there.