This is the basis of the analysis. One cannot say much about the whole.
It is a standard operation procedure in the classical physics. L = L_1 + L_2 + L_int.. One uses addition, since the classical systems support addition. Some quantities are even extensive. That means the interaction term is considered negligible.
It is impossible in relativity since a presence of the second part breaks the invariance. One cannot break a relativistic system into two relativistic parts. If you have E^2 - p^2 = m^2, then there is no rule how to make the same with two parts with the same property. It is not linear. Moreover, all interactions are supposed to be local. Thus,, if in classical physics Earth and Sun can interact via a spooky action at distance in relativity both Earth and Sun interact with the fields and never with each other.
Quantum mechanics (nonrelativistic) actually considers a phase space, that is the configuration space plus a wavevector. 2 electrons exist in the 6 dimensional space, albeit weird. That 6 dimensional space is connected to the real space by the electromagnetic field. This is amazingly different approach.
Hi,
It's not that classical systems "support addition" and other not!
there are in fact classical systems where the interation is not at all small.
Well, As all systems are quantum mechanical let's speak about Hamiltonians and Hilbert spaces, then given a system S that we choose to decompose to two systems A and B in interaction we can always write : H{AUB)=H(A)+H(B)+ Hint(AB)
But what we call A and what we call B has an independant meaning outside of the system AUB only if
Norm(Hint) is much small compared to Norm(H(A)) and to Norm(H(B)) (Given a suitable definition of the norm of an operator) that is if the coupling is weak, otherwise this is just a convenient decomposition of the system S and in this case we cannot speak of a system A or a system B because they don't have pure quantum states or any relevent approximation to a pure state, we can only use density matrices to describe A and B.
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4th Apr, 2018
Raul Simon
L A M B
Just out of the top of my head: you might read Eddington, A.S.: "The philosophy of physical science", Ann Arbor, U. of Michigan Press, 1978, chapters VIII to X.
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4th Apr, 2018
Igor Goliney
Kiev Institute for Nuclear Research
@Faical Barzi I agree with what you said. But..
Let us consider a hydrogen atom, Some smart pants broke it into and electron and a nucleous despite the strong interraction between them
@ Raul I will look up that book, though it seems quite old.
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4th Apr, 2018
Faical Barzi
Cadi Ayyad University
@Igor Goliney
You see, the interaction is weak in a H atom: 13.6eV (binding energy) is very small compared to 0.5Mev(electron) and 1GeV(proton)
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5th Apr, 2018
Igor Goliney
Kiev Institute for Nuclear Research
Oh, no. those mc^2 come from relativity and are not relevant. In non-relativistic quantum mechanics the energy of interaction in the ground state if half the kinetic energy. The interaction is strong. But that is not the issue. Hydrogen atom has nothing in common with the composing parts. It interacts with light, for example, like neither the electron nor the nucleus can.
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Deleted profile
Dear Igor Goliney,
Your question is at the basis of scientific knowledge. First of all because we have different names for different phenomena (phenomenological physics). But at the same time we say that all the alterations in the universe represent energy. In fact the latter suggests that there is no division in the universe.
When we propose that there is no division in the universe we have the problem that a really homogeneous universe cannot exist because there is variance everywhere around.
The unit of alteration (energy) is Planck’s constant. We know the existence of Planck’s constant because we can measure/deduce it. We call Planck’s constant “the quantum” but everyone can analyse that energy isn’t restricted to a constant amount of energy. In mathematics we argue that we can draw an infinite number of lines between 2 adjacent lines on the millimetre scale (number theory).
The latter means that all the alterations in our universe are fluently and not discontinued although we – a quasi stable construction of energy – cannot detect the fluent alterations (Heisenberg’s uncertainty principle).
About 2500 years ago it was the ancient Greek philosopher Parmenides who argued that phenomenological reality is created by an underlying reality and that there is no emptiness in the universe. And Aristotle argued that this underlying reality must be “the unmoved mover”; the cause behind every alteration in the universe.
So our modern concept of “spacetime” is the continuum of the basic quantum fields, everywhere existent in the universe. Phenomena emerge from this underlying basic field-structure (QFT).
In QM we can describe the spatial distribution and concentration of a quantum of energy as a wave packet. What implies that the quantum of energy isn’t restricted to “one spot” in space, although the “Planck units” suggest the opposite (extrapolations of Planck’s constant to other units).
In other words: “Is it possible to divide something in parts?” No, it isn’t possible. However, when we simplify reality we can calculate a lot as long as we realise ourselves that the results are approximations and represent reality only partly.
With kind regards, Sydney
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7th Apr, 2018
Igor Goliney
Kiev Institute for Nuclear Research
@ Sydney
Sure, humans have a remarkable ability for analysis, which means breaking thing into parts. And then composing the world of these parts. It is an exciting ability.
However, many things you write are painful for a physicist. First of all you treat energy as some kind of substance like juice. It not so. The energy is an integral of motion for the physical systems under condition of the uniformity of time. The uniformity of time means that an experiment set today would give the same result as the experiment set yesterday or tomorrow, or any time. Such conditions exist only approximately. Gererally, time is not uniform, especially on the scale of the Universe. So, the energy generally does not conserve.
Plank constant is by no means a unit of energy. It even has different dimension. It is a unit of action. Actually, it is a constant of proportionality between the energy and the frequency. E = \hbar \omega means that the energy is in fact frequency. Of what? Of the oscillations of the wave function.
Heisenberg principle is a misnomer. It is not a principle. It follows automatically from the postulates of quantum mechanics. It is a general property of any wave. If you say wave function and operator, you get Heisenberg uncertainty.
Finally, is it possible to divide something in parts? We do that.
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Sorry, Igor, I have misinterpreted your question. I thought you wanted to know the opinions of others about one of the most foundational questions in physics. So indeed, I didn’t reflect phenomenological physics
With kind regards, Sydney
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7th Apr, 2018
Arturo Tozzi
University of North Texas
https://www.researchgate.net/publication/324277863_TOWARDS_A_POINT-FREE_PHYSICS_WHY_EUCLIDEAN_GEOMETRY_IS_SCIENTIFICALLY_UNTENABLE
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