# Spontaneous Velocity.

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1. Sep 13, 2015

### TheDarkness

Hypothetically, a particle p of mass M is sitting at velocity v. Assuming M = 0, and the vi of p is 0 m/s, 0 seconds passes and vf 100 m/s is reached. Since time t is 0, acceleration cannot exist, as no t has passed between the vi and vf states. And, knowing that a = (vf - vi)/ Δt, a = (100 - 0)/0-0, a = 100/0. Because of the divisional zero, would not a be both equal to ∞ m/s^2 and -∞ m/s^2?

2. Sep 13, 2015

### Staff: Mentor

Hi TheDarkness, welcome to PF

The only speed that a massless particle can travel at is c.

3. Sep 13, 2015

### TheDarkness

So a massless particle cannot be stationary?

4. Sep 13, 2015

### Staff: Mentor

Correct, it can only move at c never more and never less.

5. Sep 13, 2015

### TheDarkness

Yes, but when an electron jumps to a lower shell, and emits a photon, would not the acceleration of the photon from the point of creation be infinite?

6. Sep 13, 2015

### Staff: Mentor

Any real photon is on-shell, meaning that it travels at c at all times. If it traveled at less than c then it would be off shell and could not conserve both energy and momentum.

7. Sep 13, 2015

### TheDarkness

I see. Thank you.

8. Sep 13, 2015

### TheDarkness

What of virtual particles?

9. Sep 13, 2015

### Staff: Mentor

Virtual particles are off shell, by definition, so all bets are off. Virtual photons can have mass, travel at speeds other than c, and so forth.