Uncertainty of when a photon is absorbed

[free_electron]

Does the uncertainty principle provide an estimate of the uncertainty of when a photon is absorbed in a transition corresponding to an energy difference of delta_E=E_final-E_initial? This uncertainty being roughly delta_t= Planck's constant divided by delta_E?

So for example, if delta_E = 5 eV, delta_t = 4.14 fs/5 = 0.83 fs. (1fs = 1 femtosecond = 1e-15 seconds).

 

[marlon]

Does the uncertainty principle provide an estimate of the uncertainty of when a photon is absorbed in a transition corresponding to an energy difference of delta_E=E_final-E_initial? This uncertainty being roughly delta_t= Planck's constant divided by delta_E?

So for example, if delta_E = 5 eV, delta_t = 4.14 fs/5 = 0.83 fs. (1fs = 1 femtosecond = 1e-15 seconds).

You are interpreting the HUP incorrectly. The HUP follows the statistical nature of QM. The "delta's" in the HUP equation arise because the same experiment is repeated a certain number of times. In each experiment both position and momentum are measured. One will observe that there is a spread in those values which respects a certain relationship called the HUP.

marlon

 

[free_electron]

You are interpreting the HUP incorrectly. The HUP follows the statistical nature of QM. The "delta's" in the HUP equation arise because the same experiment is repeated a certain number of times. In each experiment both position and momentum are measured. One will observe that there is a spread in those values which respects a certain relationship called the HUP.

marlon

Yes the experiment is done a number of times, the uncertainty product relates to time and energy as well. For example, the energy state decay is not instantaneous but has a characteristic lifetime delta_t which can be correlated to the energy transition uncertainty (~delta_E) from the uncertainty principle.

 

[lightarrow]

Yes the experiment is done a number of times, the uncertainty product relates to time and energy as well. For example, the energy state decay is not instantaneous but has a characteristic lifetime delta_t which can be correlated to the energy transition uncertainty (~delta_E) from the uncertainty principle.

They say it doesn't exist actually an uncertainty relation between time and energy.

 

[marlon]

Yes the experiment is done a number of times, the uncertainty product relates to time and energy as well.

Ofcourse it does.

The time energy uncertainty means that when you measure the energy of a system and you want an accuracy of dE (after several measurements on that same system), you will need a measurement time of dt (ie the period in which you measure the system).

The characteristic lifetime and its connection to the difference in energy levels before and after decay have nothing to do with this uncertainty because no measurement needs to be performed here. This is where you are wrong. If you study one decay proces, you will be able to calculate this lifetime and this energy difference, but you are not able to apply the HUP because you need to repeat that same measurement

Do you see the difference ? The lifetime is determined by the decay process, the HUP for energy and time is determined by the measurement and has nothin to do with the decay-mechanism itself.

marlon

 

[free_electron]

Ofcourse it does.

The time energy uncertainty means that when you measure the energy of a system and you want an accuracy of dE (after several measurements on that same system), you will need a measurement time of dt (ie the period in which you measure the system).

The characteristic lifetime and its connection to the difference in energy levels before and after decay have nothing to do with this uncertainty because no measurement needs to be performed here. This is where you are wrong. If you study one decay proces, you will be able to calculate this lifetime and this energy difference, but you are not able to apply the HUP because you need to repeat that same measurement

Do you see the difference ? The lifetime is determined by the decay process, the HUP for energy and time is determined by the measurement and has nothin to do with the decay-mechanism itself.

marlon

I think we should include that the lifetime IS the measured quantity in the relevant experiments. No energy transition takes zero time; there is always a lifetime. The textbook example has always been quoted, for a stationary state, lifetime (delta_t) is infinite, so the energy is a fixed value (delta_E=0), and vice versa.

 

[free_electron]

Just to make one more thing clear, the lifetime does not indicate a fixed time after which a state decays, it is a measure of the distribution of such decay times (like a standard deviation).

 

[DaTario]

Mr. Sergio Dutra , in his book "cavity quantum electrodynamics" seems to have put the HUP in new terms, at least for me. Let me bring some part of this text to you:

"This uncertainty relation has a status different from that of the position-momentum uncertainty relation as, unlike that relation, it is not derived from a commutator relation (see the recomended reading at the end of the chapter), and it has been often misinterpreted. It does not mean that the energy cannot be known exactly at a given time, nor that the energy cannot be measured with arbitrary accuracy within a fixed time interval. What it does mean is that the measurement makes the state after the measurement differ from that before the measurement. This difference causes an energy uncertainty in both the states before and after the measurement on the order of at least \hbar/ \Delta t, where \Delta t is the time the measurement lasts."

Best wishes,

DaTario

 

[marlon]

Just to make one more thing clear, the lifetime does not indicate a fixed time after which a state decays, it is a measure of the distribution of such decay times (like a standard deviation).

Exactly, a quantity you can only achieve after repeating the same measurement over and over again. The delta t in the HUP does not represent a decay interval but the variation in observed/measured decay intervals ! That is my entire point.

marlon

 

[marlon]

I think we should include that the lifetime IS the measured quantity in the relevant experiments.

Yes but my point is that a decay interval or decay time is not the same as the delta t in the time-energy HUP !

marlon

 

[free_electron]

Exactly, a quantity you can only achieve after repeating the same measurement over and over again. The delta t in the HUP does not represent a decay interval but the variation in observed/measured decay intervals ! That is my entire point.

marlon

Agreed.

Thanks,
f