Do Photons have Exact Energies ?

[Widdekind]

If a photon is a wave packet, of finite spatial spread, then the Heisenberg Uncertainty Principle (HUP) imposes some spread in momentum, as well. But, for photons, energy is proportional to momentum, so there should be some corresponding spread in energy... and, hence, by the Energy-Time version of the HUP, another corresponding spread in the lifetime of photons. What's wrong ??

[swansont]

There's a lifetime associated with the creation of the photon, which corresponds to a finite linewidth.

[IM Egdall]

There's a lifetime associated with the creation of the photon, which corresponds to a finite linewidth.

 

And energy is proportional to frequency (E = hV). So then a photon's frequency also has a spread. Is this true?

[swansont]

And energy is proportional to frequency (E = hV). So then a photon's frequency also has a spread. Is this true?

 

To determine the frequency of a photon, you have to measure it, and the time taken to measure it will set the uncertainty in the frequency or energy. To measure it to an arbitrarily small precision, you need a measurement that takes an infinite amount of time.

[Widdekind]

To determine the frequency of a photon, you have to measure it, and the time taken to measure it will set the uncertainty in the frequency or energy. To measure it to an arbitrarily small precision, you need a measurement that takes an infinite amount of time.

 

(thanks for the responses)

 

If a photon has an infinite lifetime ([math]\Delta t = \infty[/math]), then how can it have a non-zero spread in energy ([math]\Delta E \neq 0[/math]), and still obey the HUP ?

[granpa]

think of its fourier transform

[swansont]

(thanks for the responses)

 

If a photon has an infinite lifetime ([math]\Delta t = \infty[/math]), then how can it have a non-zero spread in energy ([math]\Delta E \neq 0[/math]), and still obey the HUP ?

 

 

A photon doesn't have a lifetime. The time is the interaction time, whether that is the lifetime of the decay that produced the photon, or the interaction that measures the photon. The only way to get an energy width of zero is to get a perfect sine wave, and that takes an infinite amount of time to generate or detect. Otherwise you have harmonics, and get a wave packet — more localized, but less well-defined in terms of energy or momentum.

[Widdekind]

A photon doesn't have a lifetime. The time is the interaction time, whether that is the lifetime of the decay that produced the photon, or the interaction that measures the photon. The only way to get an energy width of zero is to get a perfect sine wave, and that takes an infinite amount of time to generate or detect. Otherwise you have harmonics, and get a wave packet — more localized, but less well-defined in terms of energy or momentum.

 

Thanks, that's an important point. Ultimately, it seems to me, that Einstein's explanation, of the photo-electric effect, in precise technicality, only proves that photons are absorbed in "lumps" (on wave function 'collapse'), not that they necessarily propagate through space as such localized "lumps" (cf. electrons' w.f.'s spread out, through double-slit apparati, before "collapsing" into a single micro-detector (phosphor grain), on the irregular array of the same, comprising the macro-detector (detector screen)).

[IM Egdall]

I agree. As I understand it, Enstein's 1905 interpretation of the photo-electric effect just said that photons are absorbed as discrete particles (later called photons) whose energy is proportional to frequency per Planck's E = hv. It really says nothing about how light is propagated through space. (The idea of a wave function and its collapse wouldn't come, I think, until the 1920's.)

[Widdekind]

Wave functions spread, between measurements (from source to screen, say); and then the wave function 'collapses' upon measurement (into a single screen detector element, or 'micro-detector', like a phosphor or silver salt grain). Roughly related, this seems sort-of like a "dance like a butterfly, sting like a bee" behavior.