Einstein's E=mc^2: How Did He Reach His Equation?

[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!

 

[robphy]

http://www.fourmilab.ch/etexts/einstein/E_mc2/www/
is a starting point.

 

[pmb_phy]

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!

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

 

[WARGREYMONKKTL]

thanks very much! actually when i first look at the first website 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 !

 

[pmb_phy]

why they say that the equation will not work for nano matter ...

I never heard that.

.. or massive matter can you explain to me why?
whanks !

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

 

[WARGREYMONKKTL]

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

 

[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.

 

[pmb_phy]

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

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

 

[WARGREYMONKKTL]

can you give more information about psi. what is the phrase that decribe it

 

[pmb_phy]

can you give more information about psi. what is the phrase that decribe it

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

 

[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!

 

[WARGREYMONKKTL]

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

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

 

[AlphaNumeric]

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

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.

why there is x,y,z,t is that for space-time?

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 $$|\psi (t) \rangle$$

what is p in phrase -(pc)^2

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

 

[WARGREYMONKKTL]

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

 

[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).

 

[pmb_phy]

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

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

 

[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 receives 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.

 

[WARGREYMONKKTL]

hi

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

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.
i want to ask you a question about phylosophy of physics.
everybody have his own opinion, right?
what do you think about physics?
i am a Christian and i read the bible.
it say that all the matter in the universe just exist as it was.
"let there be light, and there was light." such as the universal gravity is itself like that, the magnetism too. i red the book name "the god equation" that tell about the modern physics, tell about string theory. i can not understand it at all because i do not have enough knowledge to comprehend it. but i think god crated this universe and there must be a universal rule for everything. i am a student but i want to pay whole my live to find that.
you have a good and achieving day sir.
nice to talk with you!
vincent