The question of multiple dimensions in quantum mechanics:

[James R]

Yes it's interesting to think about what it can actually mean to speak of the "size" of a photon. It's obviously true that EM waves diffract round objects and the degree to which they can is a function of wavelength. And, in the extreme case of a single photon (e.g. in the double slit experiment), even one individual photon can diffract in this way.

To analyse the diffractive properties of photons, one is forced to use a wave model. Photons, of course, exhibit both wave-like and particle-like properties, depending on the kind of observation that is being made and depending on the particular kind of interaction they are involved in. The same can be said for literally any particle, of course.

But surely, according to the Uncertainty Principle, a single photon that is truly monochromatic can have no particular position in space: it can be detected with equal, infinitesimally low probability, anywhere along its direction of travel.

That is true for a monochromatic wave, but a monochromatic wave cannot behave like a particle. If we want to model a photon as a particle that has a localised position in space then we must model it not as a monochromatic wave but as a wave packet consisting of a bunch of different frequencies. The spread of frequencies used to construct the wave packet is then related to how "wide" the wavepacket is in space - which is how the Heisenberg uncertainty principle comes about.

So its "size", in that sense, is sort of infinite. Whereas a photon whose probability of being detected has a limited spatial extent must be non-monochromatic, being composed of a Fourier sum of different wavelengths that interfere constructively only in a limited region of space (i.e. wave packet) and thereby must have an uncertainty in its momentum (and energy).

Yes. This is the same as what I just wrote, above.

 

[exchemist]

To analyse the diffractive properties of photons, one is forced to use a wave model. Photons, of course, exhibit both wave-like and particle-like properties, depending on the kind of observation that is being made and depending on the particular kind of interaction they are involved in. The same can be said for literally any particle, of course.

That is true for a monochromatic wave, but a monochromatic wave cannot behave like a particle. If we want to model a photon as a particle that has a localised position in space then we must model it not as a monochromatic wave but as a wave packet consisting of a bunch of different frequencies. The spread of frequencies used to construct the wave packet is then related to how "wide" the wavepacket is in space - which is how the Heisenberg uncertainty principle comes about.


Yes. This is the same as what I just wrote, above.

OK thanks for confirming.

 

[quant]

quant is talking about something different to the wavelength. He is talking as if photons are particles of a certain diameter. If they are, then that's largely irrelevant to how they interact.

The resolving power stuff is all about diffraction of waves. Photons have an associated wavelength, of course, so they exhibit wave-like properties as well as particle-like properties.

quant is confusing the "size" (diameter) of a particle with the wavelength of a wave.

I am particularly concerned about how one wave can 'reflect' off another wave without experiencing recoil. In fact leaving aside the recoil, how can two waves recoil off each other, in nature such things do not take place. Of course with quantum mechanics and its bland acceptance of multiple dimensions, although certain elements here will swear blindly that such Multiple dimensions do not form a part of quantum mechanics, anything is possible. This especially so since the claim that "at the level of the very, very small things are different, has become a watch word for anything that cannot be explained." . In actual fact multiple dimensions are core to quantum mechanics. . The discussions at the 5th Solvay Conference held in 1927 highlighted the role of measurement in determining the properties of quantum systems, suggesting that the act of observation plays a crucial role in the collapse of the wave function, transitioning from a superposition of states to a definite outcome. This superposition of states correspond to multiple dimensions. Further although there a consensus on regarding the wave function as a real entity was not reached. The idea from this time gained credibility. (I think it is not credible that a wave function can represent reality. But that is what the Copenhagen interpretation says ) Similarly there is much talk of multi-dimensional Hilbert space, in actual fact the reality is different, most leading contemporary physicists believe in the Many Worlds Interpretation ( I had posted a list in a previous post) which is another way of saying that multiple dimensions are real.

Again if you remember, the main reason quantum mechanics ignored the possibility of photons as being carriers of electric charge, a free electron does not have the massive nucleus on which to recoil. So the arguments put forward at this thread are mere straw men.

 

[Pinball1970]

Yes it's interesting to think about what it can actually mean to speak of the "size" of a photon. It's obviously true that EM waves diffract round objects and the degree to which they can is a function of wavelength. And, in the extreme case of a single photon (e.g. in the double slit experiment), even one individual photon can diffract in this way.

But surely, according to the Uncertainty Principle, a single photon that is truly monochromatic can have no particular position in space: it can be detected with equal, infinitesimally low probability, anywhere along its direction of travel. So its "size", in that sense, is sort of infinite. Whereas a photon whose probability of being detected has a limited spatial extent must be non-monochromatic, being composed of a Fourier sum of different wavelengths that interfere constructively only in a limited region of space (i.e. wave packet) and thereby must have an uncertainty in its momentum (and energy).

That at least is what I was thinking. Is that wrong?

I'm not a physicist, reading exchanges with those guys this is what I have picked up.

The photon is a photon (a quanta interacting with matter)when it is picked up in a detector ( the wave function has collapsed to a single point in space.) Before that is has no path and no definite point in space.

There were several level descriptions of photons on another site and references to size and I came across this.
Vanhees gave it a thumbs up, a physicist on the site, a personal recommendation.

 

[DaveC426913]

Of course with quantum mechanics and its bland acceptance of multiple dimensions, although certain elements here will swear blindly that such Multiple dimensions do not form a part of quantum mechanics, anything is possible.

What do multiple dimenssons have to do with quantum mechanics? What books are you reading?

This especially so since the claim that "at the level of the very, very small things are different, has become a watch word for anything that cannot be explained."

It is not a claim; it is an observation. The only reason QM exists is because we obeserved behaviour that can't be predicted by our classsic models.

QM is a mathematical description of what we observe; it is not a theory about how or why things behave the way they do. That's the realm of interpretations.

. In actual fact multiple dimensions are core to quantum mechanics. . The discussions at the 5th Solvay Conference held in 1927 highlighted the role of measurement in determining the properties of quantum systems, suggesting that the act of observation plays a crucial role in the collapse of the wave function, transitioning from a superposition of states to a definite outcome.

That was almost 100 years ago. We have long since debunked the notion of observation causing collapse.

Keep up.

This superposition of states correspond to multiple dimensions.

According to whom? (anyone from this century?)

 

[exchemist]

I'm not a physicist, reading exchanges with those guys this is what I have picked up.

The photon is a photon (a quanta interacting with matter)when it is picked up in a detector ( the wave function has collapsed to a single point in space.) Before that is has no path and no definite point in space.

There were several level descriptions of photons on another site and references to size and I came across this.
Vanhees gave it a thumbs up, a physicist on the site, a personal recommendation.

OK, but I'm not watching a 20 minute video about this.

 

[exchemist]

What do multiple dimenssons have to do with quantum mechanics? What books are you reading?


It is not a claim; it is an observation. The only reason QM exists is because we obeserved behaviour that can't be predicted by our classsic models.

QM is a mathematical description of what we observe; it is not a theory about how or why things behave the way they do. That's the realm of interpretations.


That was almost 100 years ago. We have long since debunked the notion of observation causing collapse.

Keep up.


According to whom? (anyone from this century?)

Yes, it seems pretty hopeless. This guy has managed to get so much so wrong, and to have so little apparent understanding in spite of evidently having read a fair bit (one does not come across the classical electron radius without looking fairly hard), that one wonders what is going on. I can only think it's deliberate misrepresentation of the physics in order to justify some house of cards of his own, yet to be disclosed. He seems reluctant to do that, though.

 

[Pinball1970]

OK, but I'm not watching a 20 minute video about this.

I know you are not keen on videos but this one is a little different I think.
He goes through some theory then an experiment he set up with a laser and a beam splitter and resulting interference.

 

[quant]

That was almost 100 years ago. We have long since debunked the notion of observation causing collapse.

You are incapable of even checking references with specific citations of the number of contemporary scientists in the leading edge of physics who believe in the the mant world interpretation of quantum mechanics. If you can't understand the significance
of that. What can you understand? Stop making derogatory remarks just because you can get away with it.

 

[DaveC426913]

You are incapable of even checking references with specific citations of the number of contemporary scientists in the leading edge of physics who believe in the the mant world interpretation of quantum mechanics.

Did you see what passage I was referring to? I quoted it. You are not talking about the MWI here; you are talking about observers causing collapse.
I will quote it again:

The discussions at the 5th Solvay Conference held in 1927 highlighted the role of measurement in determining the properties of quantum systems, suggesting that the act of observation plays a crucial role in the collapse of the wave function, transitioning from a superposition of states to a definite outcome.

That's been debunked for a long time now.

 

[quant]

That's been debunked for a long time now.

You really do not have a good grounding on the subject.

 

[Pinball1970]

You are incapable of even checking references with specific citations of the number of contemporary scientists in the leading edge of physics who believe in the the mant world interpretation of quantum mechanics

So what? A lot do not too, others are not that concerned since it does not affect the physics.

 

[DaveC426913]

You really do not have a good grounding on the subject.

It's not really hard to address your misunderstandings of the subject. You are
1. basing your arguments on the long debunked idea of observers being necessary to collapse the wave function, and
2. confusing quantum mechanics with several different interpretations: MWI is an interpretation - one of many. They are metaphysics - not part of the core of QM. I've not actually head of any interpretation of QM that invokes multiple dimensions (unless that's what you think MWI is), but I am always open to enlightenment.

 

[Pinball1970]

You really do not have a good grounding on the subject.

You do have a grounding?

You have made several incorrect statements.

 

[exchemist]

It's not really hard to address your misunderstandings of the subject. You are
1. basing your arguments on the long debunked idea of observers being necessary to collapse the wave function, and
2. confusing quantum mechanics with several different interpretations: MWI is an interpretation - one of many. They are metaphysics - not part of the core of QM. I've not actually head of any interpretation of QM that invokes multiple dimensions (unless that's what you think MWI is), but I am always open to enlightenment.

Both QuarkHead and I suspect he has confused the orthogonality of eigenfunctions of Schrödinger's equation, which can be represented as a (potentially unlimited) number of mutually orthogonal vectors in a mathematical space called Hilbert space, with the 3 dimensions of physical space.

Worse, it look as if he may even be thinking of "dimension" in a Star Trekky (i.e. neither physical nor mathematical) sense, to mean alternative universes existing in parallel with our own.

So huge confusion here - and this from someone who can't even get his head around complex numbers: https://www.sciforums.com/threads/the-necessary-truth-of-mathematics.166536/page-6#post-3738973 - so pretty rich to accuse others of lacking "grounding" in QM.

But he evidently needs the multiverse idea for some reason of his own: perhaps (I speculate) for some kind of "Eastern" mystical woo, cf. his earlier comments about wisdom of "Ancients"https://www.sciforums.com/threads/what-if-newton-was-not-wrong.166576/.

 

[DaveC426913]

Both @QuarkHead and I suspect he has confused the orthogonality of eigenfunctions of Schrödinger's equation, which can be represented as a (potentially unlimited) number of mutually orthogonal vectors in a mathematical space called Hilbert space, with the 3 dimensions of physical space.

Yep. And it's OK to not know stuff. That's what discussions are for.

But he seems to have no interest in updating his knowledge to the 21st century. Worse, he's gone and built an entire idea on his faulty foundations.

 

[quant]

So what? A lot do not too, others are not that concerned since it does not affect the physics.

I had asked you a specific question, how does one wave, the incoming photon or emr, reflect off another wave, the electron cloud or wave function, to emit a photon? How is this possible without recoil? How can two waves interact in this manner. How can the conservation of momentum and energy laws be suspended in this way ? Too complicated, to put into simple terms? Or is it just too implausible?

 

[quant]

It is not a claim; it is an observation. The only reason QM exists is because we obeserved behaviour that can't be predicted by our classsic models.

Look at pinballs answer at #44

The photon is a photon (a quanta interacting with matter)when it is picked up in a detector ( the wave function has collapsed to a single point in space.) Before that is has no path and no definite point in space.

I assume 'picked up by a detector's could be taken to mean "observed" it then " collapses". You are being extremely discriminatory.
Tell me this, how does light travel from point A to point B according to quantum mechanics? I just want to hear your understanding of how this happens.

 

[DaveC426913]

I had asked you a specific question

Well thats progress...

You're asking questions now, rather than advancing your ideas in a vacuum of knowledge.

What you need to do is some reading. Pick something from this century.

It is beyond the scope of this thread to teach you the fundamentals of QM.

 

[DaveC426913]

Look at pinballs answer at #44

I assume 'picked up by a detector's could be taken to mean "observed" it then " collapses". You are being extremely discriminatory.

No, you were being extremely vague.

You might want to read up on the quantum eraser experiments.