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We know that Planck's constant is 6.626x10-34Js. Does the energy of the same numerical value 6.626x10-34J have any special meaning. Is it perhaps the lowest possible energy or are energies less than that energy theoretically possible.
No, no and yes. Energy is frame dependent. Only energy differences have physical meaning.We know that Planck's constant is 6.626x10-34Js. Does the energy of the same numerical value 6.626x10-34J have any special meaning. Is it perhaps the lowest possible energy or are energies less than that energy theoretically possible.
No, no and yes. Energy is frame dependent. Only energy differences have physical meaning.
Yes, as is easily seen on the example of the energy of photons, which is ##E=\hbar \omega=h \nu##. Since ##\nu## can be as close to 0 as you like, there's no "smallest possible energy" in QT.
but the energy is quantized.
The energy of a specific mode is quantized. The energy of the free em. field is not. The spectrum of the Hamiltonian is ##\mathbb{R}_{\geq 0}##.From this I could conclude the following:
The energy of one quantum E = hν can be of any value, because the frequency can also be of any value (> 0) but the energy is quantized. This means that it comes in small energy packets, ie in quanta of energy hν + hν + hν ...
Is this conclusion correct?
Energy is quantized only in some systems, e.g. atoms. Energy of free photon or electron is not quantized.
hen exchanges virtual photons, whose energies are quantized.
Any piece of measurement apparatus has only a finite number of possible measurement readings. Take measurements of time, for example. Any measurement counts a number of cycles, but can only record an answer to a whole number of cycles. There is no piece of apparatus that could record energies on a truly continuous spectrum.Thanks, that will definitely be helpful.
I would still like to ask, do we always detect quantized energy, while we are not able to detect continuous energy?
A continuous observable of course can only be measured with a finite resolution/accuracy. This does not imply that the measurement device measures only discrete numbers.
Of course, you can only measure something by letting the measured system interact with a measurement device. I don't know what you mean by saying that this interaction is a quantized process.
No, the energy transfer in a scattering event can take any value, not only discrete ones.
Systems such as atoms and molecules have discrete allowed energy levels. They do not have a continuous energy spectrum: this is the basis of spectroscopy. In such systems, we can talk about quantized transitions from one allowed energy level to another. In this case the theory can be confirmed by experiment.Is the conclusion that a quantized energy transition can be proved by experiment, while a continuous energy transition cannot be measured and proven by experiment, correct? By measuring with more and more precise measuring devices, we will come to a limitation due to the uncertainty principle. In other words, our conclusion that there is a continuous transition of energy arose only from theoretical considerations, which are practically impossible to prove.
This is not correct.Systems such as atoms and molecules have discrete allowed energy levels. They do not have a continuous energy spectrum
There is no experimental evidence for a quantized energy transition, but also vice versa, there is no experimental evidence for a continuous energy transition (unless we assume that the accuracy and resolution of our measurements are sufficient for proof)?
Obviously it all depends on the accuracy and resolution of the measurements we have achieved to date and the question of whether they are sufficient to give solid evidence. If such a quantized energy transition exists in free particles, the question is at what energy level is it visible?
Perhaps far lower than what we are able to measure.
In the end, science can only carry out a finite number of experiments with a finite number of energy values. You can always postulate that there is a quantisation below the smallest difference between any two energy values measured.
What you need is an effective theory that predicts quantisation at a certain granularity. Without that you have nothing.
It's the same with spacetime quantization. Of course it might be quantized, but unless you produce a workable theory of spacetime quantization you have nothing.