What's the source of EM radiation

[bhobba]

A simplified concrete example may help illustrate the difference between measurements, ensembles, and blind math...

Yea - all true.

Thanks
Bill

 

[Jano L.]

The continuous wavefunction is obtained as an integral over discontinuous solutions. We often do this when solving PDEs, e.g. the use of Green's Functions

In what respect are the solutions discontinuous? Is the calculation you mention different from solving wave equation for the EM field, or the heat conduction equation? The solutions of the latter are continuous, except for some singular points.

But in any individual (ideal) measurement only ψi or ψf is observed (assuming the apparatus is for measuring energy states). That's basic QM when you've got discrete eigenstates.

Since energy and position do not necessarily commute in general, measurements by an ideal position-measuring apparatus might in principle suggest different conclusions but I have no idea how such an apparatus could be constructed in practice that would not itself interfere with the transition and associated radiation.

Yes, what state we will get would depend on how we would interact with the system. And some forms of interaction may force the system wave function into one of the Hamiltonian eigenfunctions. But we do not have reasonable theory of how such interaction works. That's partially the reason for so many versions of the theory. And it is also the reason we can't just say that the system jumps instantaneously when measured.

I suggest to circumvent this problem by avoiding talking about measurements, and instead talking about what happens to the system itself, or to its wave function. Besides, the results of measurements depend on the measuring device and thus can't provide us with invariant description of the state of the studied object.

If we do so, it is true that the wave function or density matrix are not practically measurable, but they serve well to describe the state independently of any measurement or interaction. Such invariant description consists of partial differential equations and thus does not require any jumps.

 

[Naveen3456]

Naveen:


Another 'funny' [perhaps] aspect of photons id that they don't change speed in a vacuum...they are at 'c' or they don't exist...photons don't accelerate like matter particles. That's why we model them as appearing and disappearing [emission, absorption] 'instantaneously'...there is no elapsed time interval when matter particles annihilate, photons accelerate up to light speed and then appear...its instantaneous.

Nobody knows exactly WHY things are that way any more than we know why we are carbon based life, why photons carry the electromagnetic force, unit charge has the value we observe, ...nor why we even observe four different forces [EM, strong,weak, gravity] or why there even IS an EM force...that's just the way THIS universe is built...

So, how do we explain the universe which is but an amalgamation of tiny particles? What are Einstein's views on this concept (problem) of spontaneity? Can you give me some link?

Are there any explanations or some attempts to explain these conflicting concepts?

 

[Naty1]

So, how do we explain the universe which is but an amalgamation of tiny particles? What are Einstein's views on this concept (problem) of spontaneity? Can you give me some link?

Are there any explanations or some attempts to explain these conflicting concepts?

Hundreds, likely thousands of attempts' and perspectives,,,,,,Here are a few I keep in my notes:Some scientists think everything is made of waves [ala the Schrödinger Equation for example] other scientists think only particles are 'real'. Einstein was a bit confused by quantum theory...he did NOT like it even though his work provided foundational theory.An explanation I like about particles comes from Wikipedia:

...There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields

A particle [say, matter] is a quanta of a quantum field...a concentration of energy, momentum, etc. Big bang fluctuations in the inflationary vacuum become quanta [particles] at super horizon scales. It seems that expansion of geometry itself, especially inflation, can produce matter.

For one version of this, check out the 'Unruh effect'...Rovelli: Unfinished revolution
Introductive chapter of a book on Quantum Gravity, edited by Daniele Oriti,
to appear with Cambridge University Press
Carlo Rovelli
Centre de Physique Th´eorique de Luminy_, case 907, F-13288 Marseille, EU
February 3, 2008

. The present knowledge of the elementary dynamical laws of physics is given by the
application of QM to fields, namely quantum field theory (QFT), by the particle–physics Standard Model (SM), and by GR. This set of fundamental theories has obtained an empirical success nearly unique in the history of science: so far there isn’t any clear evidence of observed phenomena that clearly escape or contradict this set of theories —or a minor modification of the same, such as a neutrino mass or a cosmological constant.1 But, the theories in this set are based on badly selfcontradictory assumptions. In GR the gravitational field is assumed to be a classical deterministic dynamical field, identified with the (pseudo) Riemannian metric of spacetime: but with QM we have understood that all dynamical fields have quantum properties. The other way around, conventional QFT relies heavily on global Poincar´e invariance and on the existence of a non–dynamical background spacetime metric: but with GR we have understood that there is no such non–dynamical background
spacetime metric in nature.

The following quote is from Roger Penrose celebrating Stephen Hawking’s 60th birthday in 1993 at Cambridge England...this description offered me a new insight into quantum/classical relationships:

...The way we do quantum mechanics is to adopt a strange procedure which always seems to work...the superposition of alternative probabilities involving w, z, complex numbers...an essential ingredient of the Schrödinger equation. When you magnify to the classical level you take the squared modulii (of w, z) and these do give you the alternative probabilities of the two alternatives to happen...it is a completely different process from the quantum (realm) where the complex numbers w and z remain as constants "just sitting there"...in fact the key to keeping them sitting there is quantum linearity...

and he goes on to relate this linearity and superposition to the 'double slit experiment'.

 

[strangerep]

[...] what state we will get would depend on how we would interact with the system. And some forms of interaction may force the system wave function into one of the Hamiltonian eigenfunctions. But we do not have reasonable theory of how such interaction works.

Actually, I think we do have a reasonable theory of such interactions -- but each experimental setup must be modeled in great detail, without some mega catch-all opiate like "collapse". (Are you familiar with Ballentine ch9? He describes the measurement interaction in terms of correlations, at least as far as one can go with only a general framework.)

I suggest to circumvent this problem by avoiding talking about measurements, and instead talking about what happens to the system itself, or to its wave function. Besides, the results of measurements depend on the measuring device and thus can't provide us with invariant description of the state of the studied object.

That's essentially one of the points in Ballentine ch9, iiuc.
Mermin's interpretation of QM emphasizing correlations rather than correlata is also relevant in this context.