# Energy of an electron at rest?

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1. Jun 11, 2015

### K.Callaghan

An electron rest mass in kilograms is calculated from the definition of the Rydberg constant R∞:

where α is the fine structure constant and h is simply Plancks constant. Now, assuming the electron has an associated rest energy, Any idea on how this is calculated? I'm assuming using relativistic means...but of what nature? Any thoughts? Formulas? Ideas?...

2. Jun 11, 2015

### Topolfractal

Use E = mc^2 with m being the rest mass of the electron

3. Jun 11, 2015

### K.Callaghan

Thank you for responding! Yes of course, of which I assume would be the easy answer. My concern is more of where this relationship has mechanical meaning... Which is to say what other formulas explain this relationship...this energy = mass light squared? Is there an equivalent? Can anyone explain in lamen terms why a particle at rest has energy other than to say it has "quantum behaviour"?

4. Jun 11, 2015

### Topolfractal

Please can you explain more on what you mean by quantum behavior. Also there is another formula E^2=m^2 c^4 + p^ 2 c^2 which when p=0 reduces to e= mc^2. The proof of e= mc ^2 is,...... ( A good proof is on the you tube channel minute physics).

5. Jun 11, 2015

### K.Callaghan

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Sure. I'm not doubting whether the proof is sound, yet rather searching for another explanation for this relationship other than mass displays energy in states of "quanta", or as a wave function... As we know an electron exhibits both paticle and wave like characteristics... Such is what we would call quantum like behaviour. However such behaviour is usually calculated using multiple systems of momenta rather than a single particle at rest which essential to my understanding still has an associated energy, frequency, and wavelength...

6. Jun 11, 2015

### ChrisVer

so you want a proof of $R_\infty = \dfrac{m_ec \alpha^2}{2h}$?

7. Jun 11, 2015

### Topolfractal

No I don't want a proof of that , but thank you for offering. Now it sounds like you are trying to prove a relativistic formula quantum mechanically. The proof though in that video has nothing to do with quantization and proves it using the relativistic Doppler effect. He equates the doppler shifted perspective and the stationary perspective from energy conservation.

8. Jun 11, 2015

### Topolfractal

My last message is to Callaghan sorry I should have quoted, and the first sentence to Chris ver

9. Jun 11, 2015

### K.Callaghan

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Exactly. Although more specifically, when considering a rest particle with an associated E irrespective of multiple systems of momenta and of course it's relationship with C^2... And I appoloize as I am not familiar with the video you speak of ? From minute physics did you say?

10. Jun 11, 2015

### Topolfractal

Yes minute physics ,and please can you teach me how to quote people.

11. Jun 11, 2015

### K.Callaghan

I'll will definitly check it out ! As far as quoting someone Its my understanding that when you hit reply the previous post is quoted automatically.

12. Jun 11, 2015

### K.Callaghan

Although I am online via mobile thus the reply layout may be different if your on your computer.

13. Jun 11, 2015

### Topolfractal

I'm on my iPad, please though can you teach me how to quote. It could very well still work. No for me it isn't quoted.

14. Jun 11, 2015

### K.Callaghan

Instead of replying directly in the "have something to add?" Column. Tap on the last response and hit reply. It's my understanding that the quotes are highlighted automatically. Hope this helps.

15. Jun 11, 2015

### Topolfractal

Shsjsjsjsj

16. Jun 11, 2015

### Topolfractal

Thank you

17. Jun 11, 2015

### Topolfractal

Now minute physics yay or nay ( help or not )

18. Jun 11, 2015

### K.Callaghan

19. Jun 11, 2015

### Topolfractal

Your quantum thinking has inspired me to wonder if e= mc^2 can be derived from quantum mechanics.
Now the non - relativistic Hamiltonian would correspondingly equal zero from being stationary but considering a relativistic free Hamiltonian instead that takes in moving particles. The formula E^ 2 = m^2c^4+ p^2 c^2 can be quantized to produce such a Hamiltonian and reduces to e= mc^2 on p= 0. This isn't a proof of course but is the foundational insight to the Dirac equation.

20. Jun 11, 2015

### Topolfractal

Now actually because traditional quantum mechanics is based from classical mechanics which doesn't contain e= mc^ 2 there is no such notion in traditional quantum mechanics and therefore it can't be derived or proven using that theory.