Discussions Regarding Quantum Theory , by David Bohm

[gunslingor]

Discussions Regarding "Quantum Theory", by David Bohm

Hi,

I am an Electrical and computer engineer. I recently decided to start studying physics in my spare time in the futile attempt to understand the universe, or at least parts and interpretations of it. I decided to start with quantum physics, a book called "Quantum Theory" by David Bohm. It has been good so far. I can even understand a great deal of the math.

If there are any professors out there, I could use some direction. As an electrical engineer I have had classes in calculus, differential equation, physics I/II, and such to that effect. I could use a road map to understanding; all the way to M-Theory. Any help is appreciated.

I am creating this thread to continously ask questions related to this book, as I read, which will end up being general quantum theory questions.

 

[gunslingor]

Question about quantization of energies

The book is stating that energy transfers between particles (such as radio waves impacting an electron orbiting a proton) are always in descrete values E=hv, where h=Plank's Constant and v=frequency of the incident radiation.

But, I don't see how E=hv is a discrete value. Frequency, v, is not quantized and is a continuous distribution of values. So the only way I see Energy as a quantum value is to say that frequency is also a quantum value. The book never mentions that a radio wave can only take on discrete frequency values. In fact, the book implies that even if you use a resonant cavity to perfectly define the frequency, the frequency is never perfectly defined and always takes on a range of continuous values. So, if v is continuous so must be E=hv. It appears to me that quantum theory accounts for the truely continuous nature of energy transfers (resulting from the continuous nature of the frequency spectrum) simply by approximating a continuous frequency to a quantum frequency and adding a probablily factor N such that E=Nhv.

So, it seems to me that the quantum theory is really an approximation of the classical theory as opposed to the well accepted view that the classical theory is a limit of the quantum theory.

Opinions/Corrections?

 

[muscaria]

Hi gunslingor,

But the book doesn't really give an introduction to the variables used and just seems to assume the user knows what "J", "k", "a", "del", etc is.

Are you talking about the definition of the electromagnetic potentials on p7?

 

[gunslingor]

hi gunslingor,
Are you talking about the definition of the electromagnetic potentials on p7?

Not really. That is the development of maxwells equations. Specifically, look at page 18, the first paragraph under plank's hypothesis:

"In searching for a modification of the above treatment that would reduce the contribution of high frequencies to the energy, Planck was led to make an assumption equivalent to the following: The energy of an oscillator of natural frequency v is resitricted to integral multiples of a basic unit E=nhv, where n is any integer from 0 to infinity. With this assumption, Planck obtained an exact fit, within experimental error, to the observed distribution of radiation"

My question is this. Instead of assuming quantized values of energy obsorbtion in order to make the math fit the observation, couldn't he have simply made the assumption that, since energy contributions are less at higher and lower frequencies, couldn't that be a result of the fact that, when an incident radiation is emitted from our instruments, it is actually made up of a range of frequencies with a bell curve type distribution with our intended frequency at the center.

So, it appears to me that quantum theory is just another approximation (or method of solvings, approach or unique but equivalent system of equations) as is the classic theory, however, the classic theory may have left out my previously stated assumption. As a result, the results were in error because they had assummed a perfectly defined frequency.

 

[JesseM]

But, I don't see how E=hv is a discrete value. Frequency, v, is not quantized and is a continuous distribution of values. So the only way I see Energy as a quantum value is to say that frequency is also a quantum value. The book never mentions that a radio wave can only take on discrete frequency values. In fact, the book implies that even if you use a resonant cavity to perfectly define the frequency, the frequency is never perfectly defined and always takes on a range of continuous values. So, if v is continuous so must be E=hv. It appears to me that quantum theory accounts for the truely continuous nature of energy transfers (resulting from the continuous nature of the frequency spectrum) simply by approximating a continuous frequency to a quantum frequency and adding a probablily factor N such that E=Nhv.

My understanding is that the reason substances emit photons with quantized energy values is not that the laws of physics forbid photons from having arbitrary energies, but because photons are typically emitted by a substance when an electron in the potential well created by the atomic nucleus jumps from a higher energy state to a lower one, emitting a photon which allows energy to be conserved in this process. It's possible to show that a particle in a potential well will have only a discrete range of energy eigenstates, see here and here (Looking at Bohm's book on a google book search, it looks like he discusses bound states and their discrete energies starting on p. 247 of the book). Other processes which release photons, like scattering events which are dealt with in quantum electrodynamics, can probably create photons at arbitrary energies, though I'm not really sure about the details.

 

[gunslingor]

My understanding is that the reason substances emit photons with quantized energy values is not that the laws of physics forbid photons from having arbitrary energies, but because photons are typically emitted by a substance when an electron in the potential well created by the atomic nucleus jumps from a higher energy state to a lower one, emitting a photon which allows energy to be conserved in this process.

Agreed. So the real question is this: Can an electron really instantaniously jump to another energy state (move closer or farther from the nucleous) or is it a gradual decent/ascent? If it is really instantaneous then, for some period of time, the particle disapears and then reappers at a lower elevation to the nucleous, which doesn't really make sense. Conservation of energy would be broken by this treatment since since matter is destroyed and then created, all be it equal matter/energy since photons are released; but for that short "instantanious time", the laws are broken. I can think of no way a quantum jump like that can occur, unless, however, time is also quantized.

 

[JesseM]

Agreed. So the real question is this: Can an electron really instantaniously jump to another energy state (move closer or farther from the nucleous) or is it a gradual decent/ascent?

This question presupposes that the electron really has some definite position when the wavefunction is not in a position eigenstate, which would imply a hidden-variables theory. Are you familiar with Bell's theorem which shows QM is incompatible with local hidden-variables theories? You can still have a nonlocal hidden variables theory like Bohm's own interpretation of QM, but it will have to involve FTL influences between particles, and it's not experimentally testable.

 

[gunslingor]

This question presupposes that the electron really has some definite position when the wavefunction is not in a position eigenstate, which would imply a hidden-variables theory. Are you familiar with Bell's theorem which shows QM is incompatible with local hidden-variables theories? You can still have a nonlocal hidden variables theory like Bohm's own interpretation of QM, but it will have to involve FTL influences between particles, and it's not experimentally testable.

It makes sense to me that QM is incompatible with expected hidden-variables. But QM does imply that an electron has some difinite position since it has a definite particle interpretation, at least in QM. It just moves way to fast for us to see it. I suspect, that If we are tiny enough to be on the surface of a nucleaus, time would move slow. This is just my intuition. I suspect physical magnitude is a defining property/dimension in the universe. I think I have a long way to go, lol.

 

[JesseM]

It makes sense to me that QM is incompatible with expected hidden-variables. But QM does imply that an electron has some difinite position since it has a definite particle interpretation, at least in QM.

What do you mean by "definite particle interpretation"? Certainly if you measure the position you collapse the quantum state onto a position eigenstate where the particle has a definite position, but in between measurements, or when you measure a variable that doesn't commute with position like momentum, the quantum state may not be a position eigenstate, and the usual non-hidden-variables interpretation of QM says the electron has no definite position when its wavefunction is not a position eigenstate.

 

[DeepThought42]

You must get into the wave packet section of the book which will give you more insight into how an electron moves from one state to the other as well as what a photon really is.

Also if E=hv than v = E/h. So yes, v comes in discrete values. As the book puts it, anything in between can not interact with matter.

Edit: I should clarify the last comment... v = E/h is rather vague proof.

The idea is: If the electron does not emit any photons until it reaches the next quantum state then it can't oscillate between states in a way that can be observed or interact with matter. So v comes in discrete amounts as well.

This is not to say the electron can not oscillate between states at all and just jumps from one state to the next. Chances are.. what goes on between states is involved in the formation of the photon and is just another oscillatory function... and so wave theory is born.

 

[DeepSeeded]

If E = hv and v = 0 then E would = 0. Thats not right? E = q for a standing electron.

Are you saying no photons exist in an electromagnetic force (non-wave)?

 

[Minich]

Bohmian Quantum Mechanics is not generally accepted by physisists.
Copenhagen interpretation of quantum mechanics is more or less accepted.
So i should advice another textbook (there are a greate number of them).

 

[JesseM]

Bohmian Quantum Mechanics is not generally accepted by physisists.
Copenhagen interpretation of quantum mechanics is more or less accepted.
So i should advice another textbook (there are a greate number of them).

From what I remember (and from looking at the table of contents) Bohm's textbook is just standard QM, he doesn't push his own interpretation there.

 

[Demystifier]

From what I remember (and from looking at the table of contents) Bohm's textbook is just standard QM, he doesn't push his own interpretation there.

Exactly!
In fact, Bohm has written this book before he discovered his controversial interpretation of QM.
It is also interesting to mention what Einstein said on the Bohm's book: "The first book on QM that I understand."

 

[gunslingor]

Hey,

Thanks All. That does help a little. As I read further, I may post more questions here.

Thanks again.

 

[Minich]

Exactly!
In fact, Bohm has written this book before he discovered his controversial interpretation of QM.
It is also interesting to mention what Einstein said on the Bohm's book: "The first book on QM that I understand."

If did Einstein said so ))
So it (Bohmian QM) is not Copenhagen QM,
Einstein hadn't accepted Copenhagen interpretation. )

My first QM textbook in 1971 was "Fundamentals of quantum mechanics" by V. Fock (director of my QM department in Saint-Petersburg State University) published in USSR in 1930 (in russian).
I feel it is the best textbook in QM for beginners (so are notes of Fermi lectures, parallel in russian/english languages, Notes on quantum mechanics, a course Given by Enrico Fermi at the University of Chicago).
As i know Fock's textbook is now available in english.

 

[Demystifier]

If did Einstein said so ))
So it (Bohmian QM) is not Copenhagen QM,
Einstein hadn't accepted Copenhagen interpretation. )

The Bohm's book was not yet what we call today "Bohmian QM". Still, since Einstein liked it, I would say that it was standard QM but not the Copenhagen version of standard QM.