How can Einstein?

1. Feb 25, 2006

WARGREYMONKKTL

hi!
i have a question. can you help me answer it?
i have studied physics about the equation E=mc^2. i know that everybody who studying physics know it. can some body show me how he got there? what maths mean that he used to reach that? i wonder if it is really complex?
thanks!

2. Feb 26, 2006

robphy

3. Feb 27, 2006

pmb_phy

Hi!

In addition to Rob's link you can take a look at my own derivation of the relation. See -
http://www.geocities.com/physics_world/sr/mass_energy_equiv.htm
http://www.geocities.com/physics_world/sr/einsteins_box.htm

Pete

4. Feb 27, 2006

WARGREYMONKKTL

thanks very much! actually when i first look at the first web site i don't really know what it is talking about. but the second one is helping me work out very good. i have one more question why they say that the equation will not work for nano matter or massive matter can you explain to me why?
whanks !

5. Feb 27, 2006

pmb_phy

I never heard that.
If you're speaking about large objects then it holds for isolated objects and isolated systems. If the object is interacting with its surroundings then the relation E = mc2 will not hold since there may be stress on the object and the mass of an extended object is a function of stress and that relation is invalid. There is a derivation to show this. I thought I placed it online but I can't find it. I'll upload it someday. Meanwhile you can see an example in a paper I wrote. See

http://www.geocities.com/physics_world/mass_paper.pdf

See the part where it talks about a rod under stress. Enjoy!

Pete

6. Feb 27, 2006

WARGREYMONKKTL

can you show me how to go to the wave function psi from the einstein equation e=mc2?
thanks you very much!

7. Feb 28, 2006

AlphaNumeric

The wave function $$|\psi \rangle$$ or $$\psi (x)$$ is a quantum mechanical idea. E=mc^2 is a special relativistic one. You can indeed combine the two of them to make quantum field theory, but you cannot use E=mc^2 to derive a quantum picture of something, since that isn't what relativity is about.

It's like being given a large canvas and paint and then being asked to produce a carved statue, they are not the same form of art.

8. Feb 28, 2006

pmb_phy

e=mc2 can be used to obtain the relationship

E^2 - (pc)^2 = (mc^2)^2

Now substute the operators for E = > E_op = H (Hamiltonian) and p => p_op to get

H^2 - (c*p_o)^2 = (mc^2)^2

Now multipiply through by the ket corresponding to psi => |psi> to obtain

H^2|psi> - (c*p_o)^2 |psi> = (mc^2)^2 |psi>

This is called the Klein-Gordon Equation.

Pete

9. Feb 28, 2006

WARGREYMONKKTL

10. Mar 1, 2006

pmb_phy

I thought you knew what psi was since you asked

"can you show me how to go to the wave function psi from the einstein equation e=mc2?"

|psi> is the state ket corresponding to the wave function psi(x,y,z,t). I.e.

psi(x,y,z,t) = <x,y,z,t|psi>

Pete

11. Mar 1, 2006

WARGREYMONKKTL

thanks for that. actually i don't really know about the wave function so can you help me know more clear about it. such as what is its use in physics, why there is x,y,z,t is that for space-time?
my math skill is not enough to comprehend it.
thanks!

12. Mar 1, 2006

WARGREYMONKKTL

what is p in phrase -(pc)^2
how can you substitute it in that equation please give more advice.

13. Mar 1, 2006

AlphaNumeric

It's the state symbol given to a particle or field. You might be better off reading some of the quantum physics forum.

Quantum mechanics is normally introduced via differential equations and potentials. $$|\psi\rangle$$ is a form of notation usually used later, once someone is comfortable with the basic notions of quantum physics. It's hard to explain the details of the $$|\psi \rangle$$ notation if you're not familiar with the basics of Hilbert spaces.
Yes. Generally implicit within $$|\psi \rangle$$ are the variables x,y,z,t along with anything else needed to describe the particle or field like spins, momentum, charge, etc. If you're specifically wanting to talk about a certain variable, like time, you might write it as $$|\psi (t) \rangle$$
p is the standard notation for momentum.

If you're unfamiliar with any of the notation in this thread, you'd probably find it easier (and a lot less frustrating) if you start at the basic ideas of QM and work your way up. Having decent knowledge of differential equations is a good place to start I think

14. Mar 1, 2006

WARGREYMONKKTL

thanks you for helping with that.
i want to ask that are you a college student or a high school student?

15. Mar 1, 2006

AlphaNumeric

I'm in the UK, so I don't know exactly what ages 'high school' or 'college' apply to, but I'm a 4th year applied maths student in university (I'm 22).

16. Mar 1, 2006

pmb_phy

If you were asking that question to me then I'am a 45 year old physicist. I got a BA in physics and mathematics and did part of a masters degree in physics. - Pete

Last edited: Mar 1, 2006
17. Mar 1, 2006

WARGREYMONKKTL

hi
i am in the united state.
i am a high school student. like you you probably a student in university.
what will you do after you graduate?
sorry to talk too much.
i want to ask you about a thinking that i can not understand it.
we know that math is a most powerful tool of physics right?
but how can we apply math in really simple physics problems and really complex phyiscs problem?
such as the problem about a pond that have a faucet that let the water in and a faucet that let the water out. some body say it is really easy to solve that kind of problem. but some people say it must have applied calculus to get the result?
you are an applied math student can you give me some advice or suggestion about that.
by the way if i have a solar panel and i put it is to the space. is it possible that the light is recieves will propell is(give it the momentum?) if so how can we calculate that propulsion?
thanks !
nice to talk with you!
vincent is my real name.

18. Mar 1, 2006

WARGREYMONKKTL

hi

it is my pleasure to talk to a physicist!
the internet is so wonderful!
i am only 18 year old and i am a student in high school.