# Photon speed going from $0$ to $c$ initially? [duplicate]

I have read many questions which ask whether there can be photons at speed other than the speed of light and all of them are answered no!

But when the photon is created for ex during electron transition from higher to lower energy level, it cannot simply be at initial speed $c$!

Why it cannot be at $c$: It would not suffice momentum conversation. Suppose one electron releases a photon, then the photon will need to have momentum of $\frac{h}{\lambda}$ and so would the electron in opposite direction, but that would push the electron towards the nucleus which would then again take it to (though unstable) lower energy state which would result in another photon. Since this does not happen, initial momentum cannot be $\frac{h}{\lambda}$

Since initially photon cannot be at speed $c$ it must reach the speed of light, may it be in unmeasurable less time and thus go through all the speeds between $\text{0}$ and $c$

Am I right? If I am right, why are all the questions answered no, then answered no? If I am wrong, where and why am I wrong?

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## marked as duplicate by John Rennie, DavePhD, Kyle Kanos, Qmechanic♦Jun 7 '14 at 11:47

Suppose one electron releases a photon

Wrong. An electron cannot release a photon there is always an interaction with another elementary particle or with a field for a photon to be emitted. The system emits a photon.

In the quantum mechanical solution of the hydrogen atom, an electron from a higher energy level can fall to a lower energy level, and the energy and momentum of the atom is balanced by a photon leaving with velocity c, because that is the speed of on mass photons.

If I am wrong, where and why am I wrong?

You are wrong because you are treating the electron as a generator of photons, whereas photons come from interactions of the electron with another particle or a field.

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You're thinking about this too classically. Electrons do not have a definite distance from the nucleus corresponding to their energy and there is no reason to think that emission of a photon will cause the electron to change its momentum preferentially towards the nucleus. Even in a semiclassical treatment of an atom if the photon is emitted towards the nucleus, which is totally possible, then the electron will recoil and be kicked further away. Or the photon can be emitted along the direction of the electron's velocity and the electron will simply slow down. Again, this is using a semiclassical and therefore fundamentally incorrect model of the atom. One of the fundamental postulates of special relativity, which has been supported by every experiment since the late 1800s, is that light travels at $c$. The other part where you're wrong is about the energy levels of atoms, and this comes from quantum mechanics. There is a minimum energy that electrons in atoms can have, so you wouldn't actually get another photon emission like you claim.

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Quote by Richard P Feynman: "It may surprise you that there is an amplitude for a photon to go at speed faster or slower than conventional speed $c$. The amplitudes for these possibilities are very small compared to the contribution from speed $c$; in fact they cancel out when light travels over long distances."$_1$

This must be considered as a partial answer to notice the conventional speed of light.

Credits: $_1$QED, The strange theory of light and matter-Page No.89-90

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This is misquoted. These are virtual photons, not real photons. They can't be measured. – jinawee Jun 7 '14 at 9:33