Yes, it surely allows: at given moment electron in atom has no energy level, thus the atom is A) not ionized and is C) not neutral. Holds the "not ionized"="neutral". Thus, we have logical contradiction.
I think what you are asking is why the energy levels in atom are quantized and not subjected to the uncertainty of energy? Actually given a volume containing probability cloud of the position of electron in hydrogen atom in the ground state, the uncertainty of energy does apply to that volume. It means to say that given smaller and smaller time interval, there is bigger and bigger amplitude of energy perturbation in that volume. This perturbation of energy may or may not be stably transferred to the electron depending upon whether it can lead to a time evolution of electron to the next stable energy state. The intermediate unstable -- non time evolving states are described as virtual states: http://en.wikipedia.org/wiki/Virtual_state_(physics). In fact Raman Effect has been explained by the virtual energy level.
This is also means that a hydrogen atom in the ground state has a extremely small but non-zero probability of spontaneously jumping state.
Shalender Singh: "given smaller and smaller time interval". Me: but what if you consider a point in time? The instant "picture" of atom?
To Remi Cornwall: yes, the Creator takes regard on the uncertainty principle. But the philosophy of this principle is wrong, because if in a point of time particle has no definite energy, then the particle in fact has no energy. Particle without energy is nothingness. My view: the uncertainty in Heisenberg's historical paper is shown as our impotence to objectively measure the real, CERTAIN micro-world.
Dmitri> "but what if you consider a point in time? The instant "picture" of atom?" For QM that picture does not exist because instantaneous time implies a singularity. If the time interval is smaller and smaller the electron has lesser time to "time evolve" into a different state. The energy perturbation is not a single number but is a probabilistic variable and if you solve the QFT equations (which actually use dE . dT for virtual particles) then you can directly deduce the probability of spontaneous jump to a higher energy state. It is very small but not zero.
To Shalender: so the QM demands the Planck time boundary, to avoid the (probabilistic) singularity. However, there is "Integral challenges physics beyond Einstein" in Google. "... the probability of spontaneous jump to a higher energy state. It is very small but not zero." Me: thank You! It is like the quantum tunneling. But there is higher potential in excited level, even in ionized state. Therefore, to stay there for long is impossible. However the atom remains for long the ionized. Therefore, the perturbation modes must be bound from above.
Thank You, Remi, you have just described the Heisenberg's result. The C.Darwin has discovered the adaptation of animal organisms to the varying conditions in nature. However Darwin made deadly (for Normal Theology) hypothesis: the seen adaptation is evolution on micro-scale. The Heisenberg also have made the hypothesis, which is deadly for Normal Reality: if we can not objectively measure a thing, then there is no thing, nothing. It is the solipsism: surely exists only my perception as the observer.
"to get a glimpse of that objective reality before measurement?"
that is hardly possible for the Heisenberg has calculated the uncertainty inequality. However I have (not reviewed) thought in the section "Critical Remarks on Heisenberg's microscope" in file paperBell7.pdf, I quote: "if the uncertainty principle is not assumed from the beginning, then at point Q we can measure all properties of photon very exactly".
The known uncertainty \delta x \delta p 0 can have mathematical value, if one avoids the popular thinking, that particle has not the impulse and not the position within p +\- \delta p, x +\- \delta x. That thinking do means, that particle has no position and no impulse within all |p| < infinity and |x| < infinity. It is criminal solipsism: let the other rot, he is not the real. Therefore, the particle has in fact certain x and p, which exact detection is limited by Heisenberg uncertainty. If we detect infinitely precise the position, we influence the impulse of particle in uncontrolled way. But what about energy-time uncertainty? For a point in time, the particle can have any energy after the detection experiment: if to detect infinitely fast.
Dmitri> That what QM is, it limits to the planck time boundary. i do not know whether I understand you statement fully, but do you want to say that even though the an ionized hydrogen atom is at the highest energy state, it is not likely that it spontaneously goes down to a lower energy state automatically generating a electron-positron pair from the space-time. Is my understanding correct?
Dear Shalender, it is very interesting, that even in ground state the hydrogen atom can radiate the photons (low probability spontaneous transmission to excited state, then the decay of latter with releasing of photon - that is low probability violation of energy conservation LAW). Can You back it up with nice publication? Bye!
Dear Remi, that only tells, that you have not the state of brain cells the Shalender Singh has. Please read his comments again. He tells, that there is very, tiny little probability, that electron in ground state will jump to excited level (without energy from outside the atom), it is spontaneous self-excitement of atom. Is the Shalender correct? Bye!
Dear Dmitri, please read Fourier Analysis!
https://worldtracker.org/media/library/Mathematics/Advanced%20Calculus/Spiegel%20-%20Fourier%20Analysis%20(Schaum%20Outline).pdf
Sure, You're very kind, Demetris. However my worldview holds. Heisenberg has derived the great result (one can get it through Fourier Analysis): we can not objectively measure the micro-world. But it does not mean, that there is no micro-world in existence. P.S. not any kind of function is a discrete sum of Fourier functions exp(i k x).
Hi, a few things on the similar theme:
1. "Spontaneous emission from the bare ground state of an optically driven three-level atom: Perturbation theory and energy conservation" http://journals.aps.org/pra/abstract/10.1103/PhysRevA.54.1686
2. http://onlinelibrary.wiley.com/doi/10.1002/prop.19770250111/abstract
3. http://arxiv.org/pdf/1109.2426.pdf
BTW there is definitely a problem with relativistic energy and momentum conservation. This paper: https://www.researchgate.net/publication/265643349_Problem_in_the_relativistic_energy_and_momentum_conservation proves it using existing equations with no extra assumption. Only the design of experiment is novel, which is observation by a continuum of observers.
Article Problem in the relativistic energy and momentum conservation
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