E=mc^2

[learnin to learn]

Besides Einstein has anyone actually been able to use e=mc^2 ????

I tryed using it but somewhere I messed up.

does E= potential energy???????

[Erasmus00]

Besides Einstein has anyone actually been able to use e=mc^2 ????

I tryed using it but somewhere I messed up.

does E= potential energy???????

 

The equivalence of mass and energy is used all the time, by physicists in many different fields. In this case the energy E= mc^2, it is standard to think of E as the energy the particle has just because it has mass, and the m in the formula is the rest mass of the particle.

-Will

[CraigD]

Besides Einstein has anyone actually been able to use e=mc^2 ????

I tryed using it but somewhere I messed up.

does E= potential energy???????

 

You can use

E = M*c^2

and

Mcurrent = Mrest/(1-(V/c)^2)^.5

to replace

Ekinetic = .5*M*V^2

with

Ekinetic = Ecurrent–Erest = ((Mrest/(1-(V/c)^2)^.5)–Mrest)*c^2

 

 

The calculate values will closely agree with E=.5*M^V^2 for values of V that are small compared to c. For values of V that are a sizable fraction of c, the disagreement becomes large, which is why these velocities are called “relativistic”.

 

Try it – it’s fun! :)

[arkain101]

The E in E=mc... Does it mean energy as anyform? As in electromagnetic energy, heat.. the ability to apply it how you choose to? Well I suppose that is what energy is, but my teachers confused me by making it see that the E in E=mcsquared.. meant radio wave energy. meaning you can turn a 100% of a particle into millions of light waves.

but really it applies to all things correct?

[CraigD]

The E in E=mc... Does it mean energy as anyform? As in electromagnetic energy, heat.. the ability to apply it how you choose to? Well I suppose that is what energy is, but my teachers confused me by making it see that the E in E=mcsquared.. meant radio wave energy. meaning you can turn a 100% of a particle into millions of light waves.

but really it applies to all things correct?

Correct. It describes both energy from rest mass, and energy due from the relativistic increase of mass from velocity.

[Aki]

And if you want to find the energy of a wave, you can use:

 

E= h*f,

where h is the Planck's constand and f is the frequency

[CraigD]

And if you want to find the energy of a wave, you can use: E= h*f

And, what’s totally mind-blowing, is that the wave energy equation of Quantum Physics is equivalent to the Mass energy equation of Relativity – they give the same results!

[Bo]

how do you mean that?

(in particular: what is the 'wave energy equation of QM?' the schrodinger equation? or the Klein-Gordon equation?) (in the latter case you should look up the derivation of the KG equation :eek:)

 

Bo

[IrishEyes]

Sorry to be a thread-buster...

Bo, could you please check your PMs?

Thanks.

Please continue on with your discussion now... :eek:

Irish

[learnin to learn]

does m= mass in grams?? or does it matter?

[CraigD]

how do you mean that?

(in particular: what is the 'wave energy equation of QM?' the schrodinger equation? or the Klein-Gordon equation?) (in the latter case you should look up the derivation of the KG equation :))

I mean De_Broglie’s equation a form of E=h*f, which supplies a frequency for particles with mass traveling at any velocity < c:

f = Mcurrent*V/h

 

I’m hinting that there’s a clear connection between the De Broglie wave equation and the quantum mechanical wavefunction of a particle, of which Schrodinger’s equation and the KG equation are forms. Since, unlike De Broglie’s and KG’s equations, Schrodinger’s isn’t relativistic, I’d say it’s not useful here.

 

At the moment, though, my formalism isn’t up to the challenge of proving this connection, or, sadly, even following the derivation of KG. :eek:

[CraigD]

does m= mass in grams?? or does it matter?

If you want energy in Joules, use Kilograms for mass, and Meters/Second for velocity (the SI, otherwise known as the MKS system).

 

If you don’t care about getting energy in standard units, you can use any units you want, as long as you use them consistently. It’s particularly convenient to use the speed of light as a unit of velocity, since it saves having to divide by it so often (eg: (1-(v/c)^2)^.5 becomes (1-v^2)^.5), as long as you don’t mind everyday velocities being pretty tiny and hard-to-round numbers (eg: 1 m/s = ~ 0.000000003337 c)

[steelengineer]

Another use for the equation is also in calculating the binding energy of matter in nuclear physics. the sum of the dispersered mass gives an energy that is lower than the mass when combined, the difference of the energy is what is released as nuclear energy, such as upon the explosion of nuclear bombs.

this was the use which made Einstein guilty about ever coming up with the equation. he said he would rather have been a "clockmaker" !

[cwes99_03]

One might note that E=mc^2 is used in a middle school science class to teach why when one measures the difference between the mass of a hydrogen atom and the mass of a helium atom is not equivalent to a proton and a neutron (besides the weighting of isotopes as to their commonness in the universe.) This implies that there is mass-energy in the nuclear forces that hold the proton/neutron nucleus together.

[Bo]

I mean De_Broglie’s equation a form of E=h*f, which supplies a frequency for particles with mass traveling at any velocity < c:

f = Mcurrent*V/h

I'm sorry but i still don't understand :confused:

Debroglie's equation is lambda=h/p. To what should this exactly be equivalent? (you shouldn't be confused about the second equality on the wiki page; they just substitute the relativistic expression for p; so there is no 'hidden link' to relativity there; it is just substitution)

At the moment, though, my formalism isn’t up to the challenge of proving this connection, or, sadly, even following the derivation of KG. :confused:

Deriving the Kg equation is relatively simple:

1)You take the schrodinger equation: H|psi>=E|psi> (with H the hamiltonian of a free particle)

2) you demand that E^2=p^2+m^2 (one could call this an axiom for consistency with relativity) (notice that c=1)

3) after some algebra you get the KG equation

 

Bo

[learnin to learn]

what other equations did einstien discover?

[Edge]

One question: is there a chance that any mass could travel faster than light?

 

I mean, sure Einstein's theory says that not, but is it definite?