Energy Uncertainty Less For High-Energy Particles?

[LarryS]

Energy (frequency) and Time are related via the Fourier Transform of the Wave Function. A quantum state has to hang around for a while in order to have a precise energy value. In other words, it takes time to define one whole cycle of a frequency. But it takes less time to define one whole cycle of a frequency for higher frequencies than for lower frequencies.

My question: Suppose that we have two sources of (hypothetical) particles, one source is known to be of higher energy than the other source. Assume also that our hypothetical particles both decay in the same amount of time. Would the particles from the high energy source have more precise (smaller relative standard deviation) energy than the particles from the lower energy source? Does it take less time to precisely define energy for higher energy particles than for lower energy particles?

Thanks in advance.

 

[SpectraCat]

Energy (frequency) and Time are related via the Fourier Transform of the Wave Function. A quantum state has to hang around for a while in order to have a precise energy value. In other words, it takes time to define one whole cycle of a frequency. But it takes less time to define one whole cycle of a frequency for higher frequencies than for lower frequencies.

My question: Suppose that we have two sources of (hypothetical) particles, one source is known to be of higher energy than the other source. Assume also that our hypothetical particles both decay in the same amount of time. Would the particles from the high energy source have more precise (smaller relative standard deviation) energy than the particles from the lower energy source? Does it take less time to precisely define energy for higher energy particles than for lower energy particles?

Thanks in advance.

I would suggest that you read http://en.wikipedia.org/wiki/Uncertainty_principle#Energy-time_uncertainty_principle", and then rephrase your question, if you have not already figured out a satisfactory answer for yourself.

 

[LarryS]

I would suggest that you read http://en.wikipedia.org/wiki/Uncertainty_principle#Energy-time_uncertainty_principle", and then rephrase your question, if you have not already figured out a satisfactory answer for yourself.

Here is a quote from the wikipedia article that you referenced (the bold italics are mine):

"Nevertheless, Einstein and Bohr understood the heuristic meaning of the principle. A state that only exists for a short time cannot have a definite energy. To have a definite energy, the frequency of the state must accurately be defined, and this requires the state to hang around for many cycles, the reciprocal of the required accuracy."

It is not how long a state is unperturbed but how many cycles (of frequency) that it stays unperturbed that is important in order for the energy to be sharp.

So, your referenced article does answer my question.