# Problem about equality of energy formulas

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1. Feb 9, 2016

### georg gill

Above they use the equality that the massless energy hv is equal to einsteins energy. Both have the same velocity. How can not this mean that einsteins formula has more energy then the other. I have added a proof of einsteins formula just in case it can be used:

In the proof above I don't know why the speed stops at c. But at least c is the same speed as in E=hf.

2. Feb 10, 2016

### Staff: Mentor

Can you give a source for all these equations? What exactly are you trying to figure out?

3. Feb 10, 2016

### bcrowell

Staff Emeritus
4. Feb 10, 2016

### BvU

Dear Georg,

You are using some unfamiliar (well ... ) terms: what do you mean with massless energy and what do you mean with einstein's energy ?
And do the various clippings actually not belong together at all ? Where do they come from ?

5. Feb 10, 2016

### georg gill

Well the one with the green background are my own derivation but it should be correct. The next white box is from a blog. And the third I will add the link to here:

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/E=mcsquared/proof2.html

By massless energy I was thinking about E=hf. By einsteins energy I was thinking about $E=mc^2$. It is proved that EM-waves in vacuum have velocity=c which is the same as the velocity in $E=mc^2$.

6. Feb 10, 2016

### BvU

So the 'they' in post #1 is in fact 'I' ?

And where is there an energy that is more than some other energy ?

7. Feb 10, 2016

### georg gill

Yes the green part would be me. It is pretty classic physics reasoning I think. The problem for me is that if E=hf is transfered to an object with mass. The speed of the object must be dependent on how big it is. Let us say that $mass_1=0.0001 g$ and $mass_2=1000000000 kg$. If both had the same velocity then we could create infinite energy by infinitely increasing the mass if the speed always was c?

8. Feb 10, 2016

### georg gill

9. Feb 10, 2016

### Mister T

When you say "how big it is" presumably you refer to the mass, not the volume. But yes, that's correct.

Are you perhaps thinking that if an object of mass $m$ has energy $mc^2$ it means the object is moving with speed $c$? That's not a correct interpretation.

10. Feb 10, 2016

### georg gill

Can you explain a bit more?

11. Feb 10, 2016

### Mister T

Suppose we have a particle of mass $m$ and total energy $E$. They are related by $E=\gamma mc^2$ where $\gamma$ is defined as $(1-\frac{v^2}{c^2})^{-\frac{1}{2}}$ and $v$ is the particle's speed. So if you're looking for the relationship between speed $v$ and energy $E$ this is it. Note that when $v$ is zero $E$ equals $mc^2$, the so-called rest energy.

(Note that you may be used to referring to $\gamma m$ as the mass, in which case you'd refer to $m$ as the rest mass. That's an old convention that most of us don't use. We refer to $m$ as the mass.)

12. Feb 10, 2016

### Staff: Mentor

Derivation of what? It just looks like a bunch of equalities to me, with no argument for why they should be true. I still don't understand what you are trying to figure out.

13. Feb 11, 2016

### BvU

You can't. Objects with mass can not have speed c and you can't increase the mass. Unless you mean the relaticvistic mass and then you have to put in exactly the energy difference as per the formula. Seems to me you are applying classic physics reasoning to things that need to be looked at with simple relativistic considerations. And I still don't see an energy that is more than some other energy when it should have been the same.

Where are you in your curriculum ?
Can you work out and post an example, so we can lay a finger on the spot where things go wrong ?

14. Feb 11, 2016

### georg gill

Thanks for all the feedback. I am not in curriculum I tried to solve the schrÃ¸dinger equation :) But I am taking classes

15. Feb 11, 2016

### BvU

Don't see what is the link between what you posted and the schroedinger equation ?

16. Feb 11, 2016

### georg gill

17. Feb 11, 2016

### BvU

Yes. Now Peter and I still have no idea what your problem is and how we can help you. Could you help us with that ?

18. Feb 11, 2016

### Staff: Mentor

This thread is closed as the question being asked is unclear, and from the link in post #16 it doesn't even appear that it's a question about relativity, it's a question about quantum mechanics and wave-particle duality.