# DeBroglie's duality equation L = h / p

1. I've read somewhere that to derive deBroglie's duality equation L = h / p, where L is wavelength in nm, h is Planck's constant and p is momentum, it's possible mathematically to equate Planck's E=hf with Einstein's E=mc^2, but how to explain it in theory? I mean the m in E=mc^2 is rest-mass, meaning not moving, so how is it associated with f which is about oscillation? Is it moving or not moving?

2. Any idea where to get the exact derivation of E=mc^2? Thanks.

3. Let's say I have a time machine which allows me to go back in time by 15mins. At 8am I enter the machine, so I 'went back' to 745am. Do I see another 'me' about to enter the machine at 8am? In addition, if the second 'me' enters the machine, it will go back another 15mins, meaning it will have 3 of me? I have a problem visualising this problem. Thanks.

4. If an object can travel faster than speed of light, it will travel through time. Is there a difference if the object travels at 2c or 3c, where c is speed of light?