The question of multiple dimensions in quantum mechanics:

[exchemist]

Exactly, and then only if they are closely related in terms of frequency and wave-length, recall how difficult it was to jam signals in the second World War. Also, since waves do not recoil but only interfere, how does this whole question of photon emission arise? No recoil? What about the conservation of energy and momentum? Further, the rate of photon emission has proven to be at least in the hundred terahertz range, as definitively proved by the new optical atomic clocks. How do two waves, the incoming electromagnetic wave, and the electron wave-function 'interfere with each other to produce this kind of photon emission? A large part of quantum mechanics has to be taken on blind faith, and a deep belief in the absolute veracity of the mathematical systems used. How can one use imaginary numbers and get a real result? Its like saying 'pigs can fly'. The truth is pigs cannot fly, the trot around on their little trotters. Just that the circumstance exists where I can state: " Pigs can fly." Does not mean that they actually do fly!

I realise you are not responding to me, but since you ask and there may be other readers who wonder about this, photon emission arises by means of something called the "transition dipole moment": https://en.wikipedia.org/wiki/Transition_dipole_moment, to which I have drawn your attention before.

Both linear and angular momentum are conserved during the emission or absorption of a photon by an electron, as well as energy of course. The conservation of angular momentum is one of the features that determines the "selection rules" in spectroscopy. A photon has 1 unit of angular momentum, so the total angular momentum of the electron that absorbs or emits must change by one unit. This is why s ->p transitions are allowed but s -> s transitions are forbidden, as observed in the line spectra of atoms.

As James R says, a free electron cannot absorb or emit a photon, in part because a free electron has no way to change its angular momentum. It is a spin 1/2 particle and this cannot change. When it is in a bound state in an atom, it can have varying amounts of orbital angular momentum as well, so this difficulty does not arise. Furthermore, if it is in the presence of a magnetic field, e.g. from other electrons, or even the atomic nucleus, it can change the orientation of its spin relative to the field, say +1/2 to -1/2 relative to the field, i.e. changing its angular momentum by one unit, so this gives a further range of possibilities for absorption or emission. Cs and Rb atomic clocks make use of such transitions, which involve emission and absorption of photons in the microwave region of the EM spectrum.

As for your remarks about frequency, again as James R says, the frequency of emitted and absorbed photons depends entirely on the energy difference between the intial and final states of the electron. In the hydrogen atom (the simplest atomic quantum system) there are many different sets of spectral lines, depending on which atomic orbital is a the lower one involved, named Lyman, Balmer, Paschen, Brackett, Pfund etc. after the scientists that originally characterised them. https://en.wikipedia.org/wiki/Hydrogen_spectral_series. While the lines in the Lyman series are in the UV, those in the Brackett and Pfund series are in the far infra red, i.e. at far lower frequency. So the main Lyman lines have wavelengths of the order of 100nm, i.e. 3,000THz, whereas those of the Pfund series are of the order of 5,000nm i.e. 60THz.

As I say, though, atomic clocks however utilise transitions, not between orbital of different principal quantum number like those I have mentioned for hydrogen, but between level of hyperfine splitting in far heavier atoms. I explained how these arise in post 47 of this thread: https://www.sciforums.com/threads/what-if-newton-was-not-wrong.166576/page-3#post-3739164. in which I was correcting the misconceptions of somebody called Dilip James. Whoever he may be.

 

[quant]

String theory works in 10 or 11 dimensions from memory, our regular dimensions each orthogonal to the other. String has 6 or so compactified (Calabi - Yau)

A lot of misconceptions going on with Quant.

Misconceptions going on with me? You are talking in everyday terms about 10 or 11 dimensions are you aware of the implications of what you are saying? Do you understand that something orthogonal to something else is not another dimension (?) it is just at right angles to it. People have been trying to describe extra dimensions for the past hundred years ever since Brane (membrane) and string theory was introduced. If you could describe to me a single extra dimension, I won't have a problem with what you are saying. Take your time.

 

[quant]

Now that the insults slurs and snide remarks ( I do not know about the asides) have stopped or are much reduced, ( apart from the occasional derogatory remark) I find that this is a very, very interesting discussion. We are getting to the heart of the problem, this is where it all started, this is where wave-particle duality was adopted. This is the point at which the Schrodinger wave equation and wave-function were introduced. It is a dissection taking place at the very heart of quantum mechanics. Two critical points have been raised by the proponents of quantum mechanics in defense of the quantum mechanics theory of emission and absorption of photons and neither of those arguments holds up to scrutiny. The first point relates to recoil. In Christopher Foot’s Atomic Physics (2nd edition), the recoil process during photon emission is explained in terms of momentum conservation. The photon carries momentum, which results in a recoil of the entire atom (mainly the nucleus). While the electron’s wave function changes due to the energy transition, the recoil does not directly affect the wave function itself, except in subtle ways, the energy of the wave-function itself may change. The motion of the nucleus is crucial for understanding the recoil, but due to the large mass of the nucleus, its recoil velocity is typically very small compared to the momentum of the electron. If P_atom = P_gamma, The momentum change of the atom (which includes both the nucleus and the electron) leads to a recoil velocity v_atom, which is given by:

v_atom = p_gamma/M_atom : If the atom under consideration is the Hydrogen atom (m = 1.62 x 10^-27 kg) and the photon is a 500 THz photon.

Using e = hf to find energy of the photon gives : 3.31 x 10^-19 J

The momentum of the photon is given by e/c = 1.10 x 10^-27 kg/m/s

So the velocity of the atom is given by p_gamma/ m_atom = 1.10 x 10^-27/1.67 x 10^-27 = 0.662 m/s.

Although this recoil might seem huge for an atom that is 10^-10 m in diameter, in the context of the time intervals involved it is quite tiny. Such is the present thinking. HOWEVER, in light of new evidence that the electron emits photons (in this case) at the rate of 500 x 10^12 per second. (n.b. Look up the new optical atomic clocks). For instance if the given 500 THz photon has an energy in electron volts of 6.87 x 10^-19 ev, If this energy is multiplied by 500 x 10^12 = 1.034 x 10^ 15eV ( 1.6 x 10^-4 J) . Enough to completely destroy the atom, especially if, as observation shows, such irradiation can continue for extended periods. Take events in the solar system involving conditions of continuous irradiation.

Conclusion, the present theory must be wrong, not only wrong but irrevocably wrong!

Going on to photon size: Here is what D J Griffiths has to say in his ‘Introduction to Electrodynamics: "The photon is often described as a point particle with no intrinsic size. Its energy and momentum are related to its frequency and wavelength, but these properties do not imply the photon has a well defined spatial extent in the traditional sense. Instead, the photon’s behaviour is governed by its wave-function, and the wave-length determines the spatial extent of the electromagnetic wave associated with the photon. “

I guess no-one did the calculations to show that the size difference was so great 178 million times for the electron, which (He who should not be named) has disparaged so much or 36,000 times approximately the size of the atom, in either case an impossible situation!

(n.b. The equation editor doesn’t seem to be working for me, the end result only adds to the confusion. The simpler notation used may ameliorate the problem.)

 

[DaveC426913]

Going on to photon size: Here is what D J Griffiths has to say in his ‘Introduction to Electrodynamics: "The photon is often described as a point particle with no intrinsic size. Its energy and momentum are related to its frequency and wavelength, but these properties do not imply the photon has a well defined spatial extent in the traditional sense. Instead, the photon’s behaviour is governed by its wave-function, and the wave-length determines the spatial extent of the electromagnetic wave associated with the photon. “

I guess no-one did the calculations to show that the size difference was so great 178 million times for the electron, which (He who should not be named) has disparaged so much or 36,000 times approximately the size of the atom, in either case an impossible situation!

You've been told this is not how it works. You have done yourself a favour by quoting Griffiths that that's not how it works. And yet you still assert, ignorantly, that that's how it works. You are lost to reason; stuck in an echo chamber with an occupant of one. You're hopeless.

 

[quant]

The standard (Copenhagen) interpretation of quantum mechanics says that photons can be described as probability waves (roughly speaking). So, light propagates from A to B as a wave. When something measures the light, the wavefunction "collapses" and a photon will be observed (e.g. absorbed by a detector of some kind) at a particular point in space. The probability that the photon will be observed at different points is determined by the wavefunction at each point.

That is a wonderful explanation, one that, if true, or rather, accurate, it would be accepted by everyone and there would be nothing to worry about, would there? The problem is it is not accurate, light according to quantum mechanics does not travel as a wave it travels as a wave-function. In the context of the Copenhagen interpretation, the wave function is seen as a mathematical description of the system's potentialities, or possible states, prior to measurement. According to this view, light (or any quantum system) can be thought of as existing in a superposition of states as it propagates from Point A to Point B. This means that, while the photon is traveling and interacting with the environment, it doesn't have a definite, classical trajectory or precise properties until it is measured. Does light exist or is it real when in such a state?

 

[quant]

You've been told this is not how it works. You have done yourself a favour by quoting Griffiths that that's not how it works. And yet you still assert, ignorantly, that that's how it works. You are lost to reason; stuck in an echo chamber with an occupant of one. You're hopeless.

You seem to swallow the content without making any attempt to digest it. Furthermore, since you persistently have only negative or obfuscative comments, why don't you do yourself a favour and ignore me? I will make one last attempt; do you see what Griffiths is saying, he is saying the photon may be thought of as a point particle but its area of influence is represented by its wave-length, which as I had stated before is too huge when compared to the atom's size, to fit the observed properties and outcomes. You may not agree with this statement, that is no excuse to be rude or insulting.

 

[exchemist]

Misconceptions going on with me? You are talking in everyday terms about 10 or 11 dimensions are you aware of the implications of what you are saying? Do you understand that something orthogonal to something else is not another dimension (?) it is just at right angles to it. People have been trying to describe extra dimensions for the past hundred years ever since Brane (membrane) and string theory was introduced. If you could describe to me a single extra dimension, I won't have a problem with what you are saying. Take your time.

James R has already done this for you in post 73. Suggest you re-read it, more carefully. Take your time.

 

[Pinball1970]

Misconceptions going on with me? You are talking in everyday terms about 10 or 11 dimensions are you aware of the implications of what you are saying?

I did not say it, the String theoreticians did. Just Google string theory ten dimensions.
A lot of your misconceptions are very basic stuff.
In order to tackle QT you need a solid grounding in linear algebra for a start. If you had done some of the basics there you would not be assuming QM needs extra dimensions.
Superposition is nothing to do with extra dimensions either.

I suggest you read some of the detailed responses to your questions.
Then I suggest you follow up with a decent text book. Also, Leonard Susskind has done some free lectures on YouTube via Stanford University.

 

[Pinball1970]

That is a wonderful explanation, one that, if true, or rather, accurate, it would be accepted by everyone and there would be nothing to worry about, would there?

In terms of the science no, there is nothing to worry about. The interpretation of QM is not the same as QT, it does not QT the predictions or results.
Many Physicists do not give it much thought from experience.

 

[exchemist]

You seem to swallow the content without making any attempt to digest it. Furthermore, since you persistently have only negative or obfuscative comments, why don't you do yourself a favour and ignore me? I will make one last attempt; do you see what Griffiths is saying, he is saying the photon may be thought of as a point particle but its area of influence is represented by its wave-length, which as I had stated before is too huge when compared to the atom's size, to fit the observed properties and outcomes. You may not agree with this statement, that is no excuse to be rude or insulting.

Except for the fact that it has already been explained to you - by the very source you are quoting, in fact - that the electron does not behave as a point particle (still less as some mythical entity with a "classical" electron radius) in its interactions with atoms.

This is an observed fact, not some unsubstantiated theoretical idea. When a person starts arguing with observed facts in a science discussion, they deservedly lose respect.

 

[quant]

I did not say it, the String theoreticians did. Just Google string theory ten dimensions.
A lot of your misconceptions are very basic stuff.
In order to tackle QT you need a solid grounding in linear algebra for a start. If you had done some of the basics there you would not be assuming QM needs extra dimensions.
Superposition is nothing to do with extra dimensions either.

I suggest you read some of the detailed responses to your questions.
Then I suggest you follow up with a decent text book. Also, Leonard Susskind has done some free lectures on YouTube via Stanford University.

Pinball 1970, I would like to ask you a question and I would like you to take a deep breath and to think long and deeply about what I am going to say. Why do you screech as stridently as a virgin who thinks her virginity is being violated or a religious fanatic who is foaming at the mouth because his holy of holies is being invaded, whenever any criticism, even the slightest criticism or shortcoming is pointed out about quantum mechanics? It is really quite amazing! Grow up. Quantum mechanics is far from being the perfect, idealistic system you seem to think it is. It is riddled with inconsistencies, it is illogical and poorly constructed, it is far from being the best solution that is available, it is far from being the most perfect theory devised by man. It frequently overlooks insurmountable inconsistencies and provides esoteric and exotic excuses to make things work. Schrodinger’s equation should have never have been adopted , if logic had held sway, neither should wave-particle duality, have had a place.

The phase velocity v_p of a wave is the speed at which the phase of the wave propagates. For a relativistic wave (such as those associated with a particle), the phase velocity is related to the relationship between energy, momentum, and the wave's frequency and wavelength.

In relativistic physics, the total energy E and momentum p of a particle are related by the energy-momentum relation:

E^2=p^2c^2+m^2c^4

where:

• E is the total energy of the particle,
• p is the relativistic momentum,
• m is the rest mass of the particle,
• c is the speed of light.

Now, consider a wave that describes a particle with a wave-like behavior or a matter wave. For such a matter wave, the angular frequency omega and wave number k are related to the energy and momentum of the particle via:
omega = E and k = p/hbar
where hbar is the reduced Planck's constant.
The phase velocity v_p is given by:
V_p = k/omega
Substituting the expressions for omega and k:
v_p = E/p
using the relativistic energy-momentum relation, and substituting E= sqrt p^2c^2+m^2c^4 and
p = hbar x k
simplifying: v_p = sqrtp^2C^2+m^2c^4/p
= v_p = c^2/v
Therefore, the speed of the matter wave v_p is always greater than the speed of c.

Similarly the multiple dimensions required by the Schrodinger wave-function are not orthogonal to our Universe. They are weird dimensions into which we can’t enter and cannot describe.

 

[DaveC426913]

he is saying the photon may be thought of as a point particle but its area of influence is represented by its wave-length, which as I had stated before is too huge when compared to the atom's size, to fit the observed properties and outcomes.

Why, exactly, do you think it's "too huge"? Too huge to do what? You have never explained why this is a problem for you.


Visible light with a wavelength of 600nm has a frequency of 4THz. Traveling at c, it takes all of 2 femtoseconds for its entire length to interact with a particle. Interactions do not happen instantaneously; if they did you would have an energy transfer rate of infinity (or more accurately 1/infinity)

Would you argue ocean waves that span 100 metres from crest to crest are somehow "too huge" to interact with a child's toy boat? You you expect the boat will be unaffected by the passage - or impact - of ocean waves?



So again: what exactly is your difficulty?