Radio waves propagate spherically, how comes the photon moves in a straight line

[radiolistener]

Sure they can, and the conditions have been created and observed.

https://en.wikipedia.org/wiki/Two-photon_physics
https://atlas.cern/updates/briefing/atlas-observes-light-scattering-light

Not quite. Those references are about quantum processes involving the EM field and charged particles at the quantum limit. They do not show that the classical EM field itself consists of, or behaves like, a collection of little corpuscular objects.

In the quantum description these processes can be represented in terms of photons. But that is a quantum description of the interaction, not evidence that the EM field itself is made of particles.

Nor do these experiments show that the EM field can simply interact with itself in the absence of charged particles. In classical electromagnetism, the vacuum EM field does not self-interact.

These experiments demonstrate quantum features of the interaction between charged particles and the EM field, rather than showing that the EM field is itself a collection of corpuscles.

And they don't show that the classical EM field is a gas of corpuscles. They show that the quantum theory of the EM field allows processes that do not exist in classical Maxwell theory. And this is not surprising, because in QED the vacuum is not completely empty - virtual charged particles can contribute to these processes.

[studiot]

I was not talking about cavity resonators when considering the properties of a photon considered as an object in spacetime (although it partly depends upon one's definition of spacetime).

Photons have no mass and I agree the concept of lifetime is meaningless in their frame.

But photons do carry and can transfer momentum to massive objects.

This is a purely corpuscular property in spacetime.

Unlike the particles in a gas they cannot transfer momentum between each other.

Spin is a dual property which is why I said It also has a foot in the quantum camp.

Imagine floats on the surface of water. The floats can transfer momentum to each other through the water but the water does not thereby become a collection of floats. The water is what mediates the interaction between them.

Likewise, the EM field can carry energy and momentum and transfer momentum to charged matter. That does not make the EM field itself a collection of little corpuscular objects.

And the same applies to molecules in a gas. Molecules can exchange momentum through their interactions, but the EM field mediating those interactions does not thereby become a molecule or a corpuscular object.

So the ability to carry or transfer momentum does not by itself imply that something is a spacetime corpuscle. 


PS: Classical electromagnetism already describes the transport and transfer of energy and momentum by the EM field using the Poynting vector and the Maxwell stress tensor, without introducing photons at all. You don't need QED to describe this.

Sure they can, and the conditions have been created and observed.

https://en.wikipedia.org/wiki/Two-photon_physics
https://atlas.cern/updates/briefing/atlas-observes-light-scattering-light

Not quite. Those references are about quantum processes involving the EM field and charged particles at the quantum limit. They do not show that the classical EM field itself consists of, or behaves like, a collection of little corpuscular objects.

In the quantum description these processes can be represented in terms of photons. But that is a quantum description of the interaction, not evidence that the EM field itself is made of particles.

Nor do these experiments show that the EM field can simply interact with itself in the absence of charged particles. In classical electromagnetism, the vacuum EM field does not self-interact.

These experiments demonstrate quantum features of the interaction between charged particles and the EM field, rather than showing that the EM field is itself a collection of corpuscles.

And they don't show that the classical EM field is a gas of corpuscles. They show that the quantum theory of the EM field allows processes that do not exist in classical Maxwell theory. And this is not surprising, because in QED the vacuum is not completely empty - virtual charged particles can contribute to these processes.

What EM field ?


I did not say that classical electrodynamics is unable to account for photon linear momentum transfer I said that quantum effects arise because of the photons spin.
Linear momentum transfer is the reason why a particle explanation (model) is adequate.

I did say quantum effects arise on account of the photon's spin.

Photons have a spin quantum number of \(s = 1\), meaning their intrinsic spin angular momentum along a chosen axis is quantized to values of \(+\hbar \) or \(-\hbar \) (where \(\hbar \) is the reduced Planck constant), while the longitudinal component along the direction of motion is forbidden because light waves are transverse.Key Properties of Photon Spin QuantizationSpin Value (\(s = 1\)): Photons are vector bosons with a spin quantum number \(s=1\).Allowed Projections (\(m = \pm 1\)): When measured along the axis of propagation (the \(z\)-axis), the spin component \(m\hbar\) can only be \(+\hbar \) or \(-\hbar \).Missing \(m = 0\) State: Unlike massive spin-1 particles, a photon's zero-component (\(m=0\)) state is physically absent because electromagnetic waves lack longitudinal oscillations in a vacuum.Relation to Polarization:\(+\hbar \) corresponds to right-handed circular polarization.\(-\hbar \) corresponds to left-handed circular polarization.Superposition: Linear polarization (such as horizontal or vertical) exists as a quantum superposition of both the \(+\hbar \) and \(-\hbar \) spin states.You can explore more foundational details on the RP Photonics Encyclopedia or read the technical framing via Quantum Field Theory for Spin Operator of the Photon.If you'd like, let me know:Are you looking for the mathematical derivation using quantum electrodynamics (QED)?Or do you want to explore how photon spin relates to orbital angular momentum (OAM)?APS JournalsQuantum field theory for spin operator of the photon31 May 2022 — Abstract. All elementary particles in nature can be classified as fermions with half-integer spin and bosons with integer spin. Wi...WikipediaSpin (physics) - WikipediaThe spin–statistics theorem splits particles into two groups: bosons and fermions, where bosons obey Bose–Einstein statistics, and...WikipediaQuantization of the electromagnetic field - WikipediaPhoton spin The photon can be assigned a triplet spin with spin quantum number S = 1. This is similar to, say, the nuclear spin of...

Note also that the magnetic field is famously unable to exert a physical force, although some electrical engineering models use virtual work to greatly simply the maths by assuming it does.

EM waves are nothing like Quantum waves, which in turn neither are anything like waves in a material elastic medium.

Unlike the particles in a gas they [photons] cannot transfer momentum between each other.

Sure they can, and the conditions have been created and observed.

https://en.wikipedia.org/wiki/Two-photon_physics
https://atlas.cern/updates/briefing/atlas-observes-light-scattering-light

If it were possible for photons to 'bump' each other in the manner of gas molecules they would also exhibit a spread of energies which is constantly varying.
Consequently monchromatic light would not remain monochromatic.
Every photon of monochromatic light has the same energy, by definition.

[radiolistener]

What EM field ?

when I say "EM field", I mean the electromagnetic field itself. Classical electrodynamics already describes energy and momentum carried by the EM field, including momentum transfer to matter, without introducing photons. QED provides a quantum description of the same field, where photons appear as quantum excitations.

I did not say that classical electrodynamics is unable to account for photon linear momentum transfer I said that quantum effects arise because of the photons spin.
Linear momentum transfer is the reason why a particle explanation (model) is adequate.

I did say quantum effects arise on account of the photon's spin.

I don't think quantum effects can generally be attributed to the photon's spin. Quantum behavior is not simply a consequence of spin. Quantum effects become relevant when we consider interactions between the EM field and charged matter in the quantum limit.

Linear momentum transfer is already described by classical electromagnetism. For example, the Maxwell stress tensor can be used to calculate the force acting on a charged particle. So the transfer of linear momentum is not exclusively a corpuscular property. Photons and QED are not required to describe it.

Likewise, the fact that the photon has quantum properties such as spin does not by itself make it a spacetime corpuscle. In QED, the term "particle" is a way to describe the discrete quantum behavior of the EM field in interactions with charged particles. It does not imply the existence of a small object occupying a definite region of spacetime with its own position, size, and trajectory.

Note also that the magnetic field is famously unable to exert a physical force, although some electrical engineering models use virtual work to greatly simply the maths by assuming it does.

EM waves are nothing like Quantum waves, which in turn neither are anything like waves in a material elastic medium.

A magnetic field can exert a physical force on charged matter - for example, the magnetic part of the Lorentz force acts on a moving charged particle.

And I would be careful with saying that EM waves are "nothing like quantum waves". The classical EM field and the quantum EM field are different descriptions, but classical electromagnetism is what you get from the quantum theory in the classical limit.

[studiot]

What EM field ?

when I say "EM field", I mean the electromagnetic field itself. Classical electrodynamics already describes energy and momentum carried by the EM field, including momentum transfer to matter, without introducing photons. QED provides a quantum description of the same field, where photons appear as quantum excitations.

I did not say that classical electrodynamics is unable to account for photon linear momentum transfer I said that quantum effects arise because of the photons spin.
Linear momentum transfer is the reason why a particle explanation (model) is adequate.

I did say quantum effects arise on account of the photon's spin.

I don't think quantum effects can generally be attributed to the photon's spin. Quantum behavior is not simply a consequence of spin. Quantum effects become relevant when we consider interactions between the EM field and charged matter in the quantum limit.

Linear momentum transfer is already described by classical electromagnetism. For example, the Maxwell stress tensor can be used to calculate the force acting on a charged particle. So the transfer of linear momentum is not exclusively a corpuscular property. Photons and QED are not required to describe it.

Likewise, the fact that the photon has quantum properties such as spin does not by itself make it a spacetime corpuscle. In QED, the term "particle" is a way to describe the discrete quantum behavior of the EM field in interactions with charged particles. It does not imply the existence of a small object occupying a definite region of spacetime with its own position, size, and trajectory.

Note also that the magnetic field is famously unable to exert a physical force, although some electrical engineering models use virtual work to greatly simply the maths by assuming it does.

EM waves are nothing like Quantum waves, which in turn neither are anything like waves in a material elastic medium.

A magnetic field can exert a physical force on charged matter - for example, the magnetic part of the Lorentz force acts on a moving charged particle.

And I would be careful with saying that EM waves are "nothing like quantum waves". The classical EM field and the quantum EM field are different descriptions, but classical electromagnetism is what you get from the quantum theory in the classical limit.

It would be better if you actually read what I wrote rather than simply repeating yourself endlessly.

And I stand by what I said about EM waves being quite different from Quantum Waves.
I have already state the reason.

If you require more mathematical detail, first go back to what I said about the dimensions of the quantum wave function in the Schroedinger equation.
This varies according to the number of spatial dimensions you are working in but is fractal in all.

EM wave equations, vector or tensor, are linear in having integer spatial dimensions for their wave function.

FYI the wave function is the name given to the mathematical dependant variable.

The reason the Schroedinger equation is called a wave equation is lost in time but I think it was because it is an equation of motion that connects space and time as separated variables.

[radiolistener]

It would be better if you actually read what I wrote rather than simply repeating yourself endlessly.

And I stand by what I said about EM waves being quite different from Quantum Waves.
I have already state the reason.

If you require more mathematical detail, first go back to what I said about the dimensions of the quantum wave function in the Schroedinger equation.
This varies according to the number of spatial dimensions you are working in but is fractal in all.

EM wave equations, vector or tensor, are linear in having integer spatial dimensions for their wave function.

FYI the wave function is the name given to the mathematical dependant variable.

The reason the Schroedinger equation is called a wave equation is lost in time but I think it was because it is an equation of motion that connects space and time as separated variables.

I did read what you wrote, but I don't see how the dimensionality of the wavefunction shows that EM waves and quantum waves are fundamentally unrelated.

The Schrodinger equation is linear, just as Maxwell's equations are (in vacuum), and a single-particle wavefunction and the EM field are both defined on ordinary 3D space. So I don't understand where you see fractal dimensions.

[studiot]

It would be better if you actually read what I wrote rather than simply repeating yourself endlessly.

And I stand by what I said about EM waves being quite different from Quantum Waves.
I have already state the reason.

If you require more mathematical detail, first go back to what I said about the dimensions of the quantum wave function in the Schroedinger equation.
This varies according to the number of spatial dimensions you are working in but is fractal in all.

EM wave equations, vector or tensor, are linear in having integer spatial dimensions for their wave function.

FYI the wave function is the name given to the mathematical dependant variable.

The reason the Schroedinger equation is called a wave equation is lost in time but I think it was because it is an equation of motion that connects space and time as separated variables.

I did read what you wrote, but I don't see how the dimensionality of the wavefunction shows that EM waves and quantum waves are fundamentally unrelated.

The Schrodinger equation is linear, just as Maxwell's equations are (in vacuum), and a single-particle wavefunction and the EM field are both defined on ordinary 3D space. So I don't understand where you see fractal dimensions.

In 3 dimensions the dimensions of the wave function is L^-3/2        (Sorry I haven't yet figured out how to configure my Mathtype for this site)

This means that as I said, at least one of the dimensions of the space in this system is fractal.

https://www.damtp.cam.ac.uk/user/tong/qm/qmhtml/S2.html

In classical mechanics a harmonic oscillator has the dimensions L^3 in 3 dimensions.

In phase space this number may be different depending upon the number of variables

The result of this is to paraphrase Mr Al  it doesn't wave in space(time), but in an abstract space.

[radiolistener]

In 3 dimensions the dimensions of the wave function is L^-3/2        (Sorry I haven't yet figured out how to configure my Mathtype for this site)

This means that as I said, at least one of the dimensions of the space in this system is fractal.

https://www.damtp.cam.ac.uk/user/tong/qm/qmhtml/S2.html

In classical mechanics a harmonic oscillator has the dimensions L^3 in 3 dimensions.

In phase space this number may be different depending upon the number of variables

The result of this is to paraphrase Mr Al  it doesn't wave in space(time), but in an abstract space.

As I understand, L^-3/2 is the physical dimension of the wavefunction.

The wavefunction is a mathematical concept used to describe the probabilities of measurement outcomes. This should not be confused with the physical state of a classical object.

For example, we can describe the probabilities of a coin landing heads or tails without implying that the coin itself is in some physically intermediate state before we look at it.

A similar example is the complex representation of a real wave signal, using cos and sin projections of a rotating vector. The mathematical representation contains both positive and negative-frequency components, which are extremely useful for calculations and signal processing, but in the real signal this does not mean that the signal consists of two separate components. They are simply part of the mathematical model. In the real signal, the positive and negative-frequency components are superimposed.

[MrAl]

I am not sure what you are saying about a 'thought'.  Who was talking about a thought, or did I say something that sounded like I was talking about a thought?

I brought up the thought analogy to explain why a photon does not need to have a position, size, or trajectory in spacetime. A thought is a useful analogy because it shows how something can be a perfectly meaningful and useful concept for reasoning, while not existing as a separate object in spacetime.

In other words, I am using a thought as an example of how a concept can be useful without being a spacetime object and why trying to interpret such a concept as an object in spacetime is a mistake.

For me, a probability is the closest we can get to reality at least for now.  The reason for this is that there simply is nothing else.

We can never know where anything is, we can only know the probability of where it might be.  This gets very deep too.
If we throw a coin over a wall and it lands on the ground where we can't see over the wall, we don't know how the coin landed.  It is heads up or tails up.  We don't know, and we cannot assume that it is either heads or tails (or on edge as some people like to throw in there).  It is in a state of in between.  It's neither heads nor tails, but something else that could be heads, tails, on edge, or something else in between.

Why is that so.  It's because our reality depends hugely on observation.  Everything we see and measure depends on observation, so everything we know is based on observation. We base all of our knowledge on what we have observed in the past.  Nature does not seem to care about how we observe something, it does what it wants to do.  In common knowledge, what we observe is usually what we get, but it's not always like that.  If nature wants to do something or have properties that we can't ever observe, there's not much we can do about it, and it turns out that is what nature does sometimes, unfortunate as it is for us when we try to understand it.

I agree that physics does not give us a God's-eye view of reality. But I think there is an important distinction between uncertainty in our knowledge and indeterminacy in the physical system itself.

For example, if a classical coin has fallen behind a wall, the fact that we don't know whether it is heads or tails does not mean that the coin is physically in some intermediate state. Our description is uncertain, but the coin itself is not in an intermediate state.

A quantum state is not a classical spacetime object with a definite position, size, and trajectory. And there is no need to replace every statement about reality with "we only know probabilities".

A model can tell us exactly which concepts and quantities are meaningful within that model. So we don't have to decide what the "ultimate reality" is before deciding whether a particular concept belongs to a particular description.

Hi again,

I quote this statement you wrote because this is a good illustration of where we diverge from our view of everything:
START QUOTE
For example, if a classical coin has fallen behind a wall, the fact that we don't know whether it is heads or tails does not mean that the coin is physically in some intermediate state. Our description is uncertain, but the coin itself is not in an intermediate state.
END QUOTE

Here is my view of that statement, for better or worse...
First, there is no such thing as a "classical coin".  We have coins, that's it.  That's reality and there is no way around that.  We can talk about a classical coin, but that means we have automatically fallen under some assumptions about reality, when what we are trying to determine all along is what reality is or what we know about it.  We want the bottom-line truth.
This is why I think you are looking too hard for comfort in physics when there is none really.
The point I made about observation is that since EVERYTHING we see and know is based on observation, then we look at everything through a sort of "observation" filter.  Something appears, but we don't see it, we only see it AFTER it passes through that observation window.  It's completely out of view until it passes though, and unfortunately once it passes through we lose detail, detail that we may never get back.

The coin is in a superposition of states behind the wall because we can't observe it.  This comes from a chain of reasoning that is part of quantum physics.  This is really the way reality is.  The only reason we BELIEVE it is in one state or the other is due to PAST observations that told us that "coins always land heads or tails" (excluding the edge case for simplicity).  But that observation set was done in the PAST, and that pushes it right into the statistical average category where we rely on common observations over time.  That does not mean that it is REALLY heads or tails, it just SUGGESTS that it is PROBABLY heads or tails.  We have never seen it in a state other than that, that's what makes us BELIEVE it will be again.  In quantum physics though, the down to earth hard and very uncomfortable truth, is that belief is just a heuristic, although it is a very good one for our common experience and our survival.  The QM statistics says that the probability that it will be in some other state is very, very low, BUT it's NOT ZERO.  Again uncomfortable, but true.

This is not just weird as all heck to us, it's weird as all heck to everyone.

[studiot]

For example, if a classical coin has fallen behind a wall, the fact that we don't know whether it is heads or tails does not mean that the coin is physically in some intermediate state. Our description is uncertain, but the coin itself is not in an intermediate state.

A quantum state is not a classical spacetime object with a definite position, size, and trajectory. And there is no need to replace every statement about reality with "we only know probabilities".

A model can tell us exactly which concepts and quantities are meaningful within that model. So we don't have to decide what the "ultimate reality" is before deciding whether a particular concept belongs to a particular description.

Here is my view of that statement, for better or worse...
First, there is no such thing as a "classical coin".  We have coins, that's it.  That's reality and there is no way around that.  We can talk about a classical coin, but that means we have automatically fallen under some assumptions about reality, when what we are trying to determine all along is what reality is or what we know about it.  We want the bottom-line truth.
This is why I think you are looking too hard for comfort in physics when there is none really.
The point I made about observation is that since EVERYTHING we see and know is based on observation, then we look at everything through a sort of "observation" filter.  Something appears, but we don't see it, we only see it AFTER it passes through that observation window.  It's completely out of view until it passes though, and unfortunately once it passes through we lose detail, detail that we may never get back.

The coin is in a superposition of states behind the wall because we can't observe it.  This comes from a chain of reasoning that is part of quantum physics.  This is really the way reality is.  The only reason we BELIEVE it is in one state or the other is due to PAST observations that told us that "coins always land heads or tails" (excluding the edge case for simplicity).  But that observation set was done in the PAST, and that pushes it right into the statistical average category where we rely on common observations over time.  That does not mean that it is REALLY heads or tails, it just SUGGESTS that it is PROBABLY heads or tails.  We have never seen it in a state other than that, that's what makes us BELIEVE it will be again.  In quantum physics though, the down to earth hard and very uncomfortable truth, is that belief is just a heuristic, although it is a very good one for our common experience and our survival.  The QM statistics says that the probability that it will be in some other state is very, very low, BUT it's NOT ZERO.  Again uncomfortable, but true.

This is not just weird as all heck to us, it's weird as all heck to everyone.

Model is a good word so is meaning.

Both only have validity within their domain of definition, something mentioned once in lectures and then forgotten.

Probability is more difficult but you have obviously understood and remembered that the word has more than one meaning (something taught in the UK high school basic statistics syllabus and promptly forgotten)

Reality is an even more difficult word.

Talking of low probability and quantum theory

  Eddington
A random fluctuation could produce a system which thinks it is you or I at this or that instant, with a full set sensory impressions, memories and expectations of the future

[radiolistener]

I quote this statement you wrote because this is a good illustration of where we diverge from our view of everything:
START QUOTE
For example, if a classical coin has fallen behind a wall, the fact that we don't know whether it is heads or tails does not mean that the coin is physically in some intermediate state. Our description is uncertain, but the coin itself is not in an intermediate state.
END QUOTE

Here is my view of that statement, for better or worse...
First, there is no such thing as a "classical coin".  We have coins, that's it.  That's reality and there is no way around that.  We can talk about a classical coin, but that means we have automatically fallen under some assumptions about reality, when what we are trying to determine all along is what reality is or what we know about it.  We want the bottom-line truth.
This is why I think you are looking too hard for comfort in physics when there is none really.
The point I made about observation is that since EVERYTHING we see and know is based on observation, then we look at everything through a sort of "observation" filter.  Something appears, but we don't see it, we only see it AFTER it passes through that observation window.  It's completely out of view until it passes though, and unfortunately once it passes through we lose detail, detail that we may never get back.

The coin is in a superposition of states behind the wall because we can't observe it.  This comes from a chain of reasoning that is part of quantum physics.  This is really the way reality is.  The only reason we BELIEVE it is in one state or the other is due to PAST observations that told us that "coins always land heads or tails" (excluding the edge case for simplicity).  But that observation set was done in the PAST, and that pushes it right into the statistical average category where we rely on common observations over time.  That does not mean that it is REALLY heads or tails, it just SUGGESTS that it is PROBABLY heads or tails.  We have never seen it in a state other than that, that's what makes us BELIEVE it will be again.  In quantum physics though, the down to earth hard and very uncomfortable truth, is that belief is just a heuristic, although it is a very good one for our common experience and our survival.  The QM statistics says that the probability that it will be in some other state is very, very low, BUT it's NOT ZERO.  Again uncomfortable, but true.

This is not just weird as all heck to us, it's weird as all heck to everyone.

I would draw the line between uncertainty in our knowledge and quantum superposition. A coin being behind a wall does not put it into a quantum superposition simply because we cannot observe it. If the coin has landed heads or tails, our lack of knowledge about which one it is does not by itself establish that its physical state is indefinite.

Returning to the example of the mathematical model of a wave using a rotating vector. The projection of that vector onto an axis can describe the measured real signal extremely well but this does not mean that the signal is physically represented by a rotating vector. It may be a very useful and valid mathematical description but the fact that a model accurately describes the observed behavior does not by itself prove that the model is literally what exists in reality.

So I think we should be careful not to confuse a mathematical model with a statement about what reality ultimately is. Claiming that the mathematical description itself is literally the underlying reality goes beyond what the model and the observations alone establish. Without experimental evidence distinguishing that interpretation from other possibilities that becomes a philosophical claim rather than a scientific conclusion.

We may have several models that work within certain limits but we tend to choose one and treat it as reality. Yet reality may be described by a completely different model that we have not discovered yet. 

[studiot]

In 3 dimensions the dimensions of the wave function is L^-3/2        (Sorry I haven't yet figured out how to configure my Mathtype for this site)

This means that as I said, at least one of the dimensions of the space in this system is fractal.

https://www.damtp.cam.ac.uk/user/tong/qm/qmhtml/S2.html

In classical mechanics a harmonic oscillator has the dimensions L^3 in 3 dimensions.

In phase space this number may be different depending upon the number of variables

The result of this is to paraphrase Mr Al  it doesn't wave in space(time), but in an abstract space.

As I understand, L^-3/2 is the physical dimension of the wavefunction.

Yes

The wavefunction is a mathematical concept used to describe the probabilities of measurement outcomes.

No

 This should not be confused with the physical state of a classical object.

The term state has many shades meaning and should be used only in its domain of definition

For example, we can describe the probabilities of a coin landing heads or tails without implying that the coin itself is in some physically intermediate state before we look at it.

A similar example is the complex representation of a real wave signal, using cos and sin projections of a rotating vector. The mathematical representation contains both positive and negative-frequency components, which are extremely useful for calculations and signal processing, but in the real signal this does not mean that the signal consists of two separate components. They are simply part of the mathematical model. In the real signal, the positive and negative-frequency components are superimposed.

You are the one who keeps introducing mathematics for support and then saying it doesn't count.
You can't have it both ways.

[studiot]

It seems to me that this thread has wandered off topic arguing about different models.

The question was why do photons travel in straight lines or alternatively how does the photon model lead lead to spherical radiation patterns ?

I have tried to slant replies towards this objective.

The geometrical optics model v the wave optics model faces the same issue and the user chooses the most appropriate for his purpose.

Radio waves can be focused so are not always spherical eg the standard hertzian dipole, just as light is focused by suitable lenses.

A good treatment can be found in the Manchester Physics series published by Wiley : Read  "Electromagnetic Radiation".   A simpler treatment also appears in the sister book in the series by Grant and Philips  "Electromagnetism", though the second reference concentrates more on the relationship between waves and relativity over wave and quantum physics.

Here is an extract from Read which shows that this is not an uncommon question.  Note the paragraph I have starred.

[radiolistener]

The wavefunction is a mathematical concept used to describe the probabilities of measurement outcomes.

No

what exactly do you mean by "No"?
That the wavefunction is a mathematical concept, or that it is used to calculate probabilities of measurement outcomes? 🤔

You are the one who keeps introducing mathematics for support and then saying it doesn't count.
You can't have it both ways.

I think you are conflating two different claims. I am not saying that the mathematics “doesn't count”. Quite the opposite: the mathematical properties of the wavefunction are essential to the theory.

My point is that a mathematical property of the representation does not by itself establish a corresponding physical property of what is being described. Saying that the wavefunction has dimension L^-3/2 tells us about the mathematical representation and its normalization. It does not by itself tell us that the wavefunction is a physical field with that dimension.

So I am not saying "mathematics doesn't count". I am saying that we should distinguish mathematical properties of the model from ontological claims about physical reality.

If you consider the mathematical model sufficient to conclude that reality is actually structured that way, I would be interested to understand how you arrive at that conclusion?

[SteveThackery]

The coin is in a superposition of states behind the wall because we can't observe it.  This comes from a chain of reasoning that is part of quantum physics.  This is really the way reality is. 

I hope you don't mind an ignoramus interjecting with a basic question. This description of the coin behind the wall is just another version of Schrodinger's cat.

Schrödinger did not propose that the cat was genuinely in a quantum superposition of alive and dead. He offered it as a thought experiment intended to expose what he regarded as a serious problem with the Copenhagen interpretation of quantum mechanics. If you simply extend quantum theory to the entire system, you appear to arrive at a cat that is simultaneously alive and dead. And Schrödinger thought that was "ridiculous" (he used that word).

He did not claim that the cat is both alive and dead. He said it would definitely be either one or the other, therefore (he argued) quantum theory does not work for macro-scale objects (like the coin behind the wall).

With his thought experiment, Schrödinger was mostly interested in understanding the transition between the scale at which quantum theory works perfectly and the macro world where it doesn't.

So the coin really will be heads-up or tails-up, even when we haven't looked at it.

[studiot]

The coin is in a superposition of states behind the wall because we can't observe it.  This comes from a chain of reasoning that is part of quantum physics.  This is really the way reality is. 

I hope you don't mind an ignoramus interjecting with a basic question. This description of the coin behind the wall is just another version of Schrodinger's cat.

Schrödinger did not propose that the cat was genuinely in a quantum superposition of alive and dead. He offered it as a thought experiment intended to expose what he regarded as a serious problem with the Copenhagen interpretation of quantum mechanics. If you simply extend quantum theory to the entire system, you appear to arrive at a cat that is simultaneously alive and dead. And Schrödinger thought that was "ridiculous" (he used that word).



He did not claim that the cat is both alive and dead. He said it would definitely be either one or the other, therefore (he argued) quantum theory does not work for macro-scale objects (like the coin behind the wall).

With his thought experiment, Schrödinger was mostly interested in understanding the transition between the scale at which quantum theory works perfectly and the macro world where it doesn't.

So the coin really will be heads-up or tails-up, even when we haven't looked at it.

Good afternoon Steve.

Schroedinger was a Swiss Professor of Mathematics.
Yes his cat is famous and does indeed show the ridiculous woo that some people turn to when they are unwilling to admit that "They just don't know"
Although famous for his equation, he actually only wrote one maths book "Space-Time Structure"  Cambridge University Press, which was about Relativity and Differential Geometry rather than Quantum Theory.
In fact the equation named after him was two equations, one linear, one nonlinear not one, called Shrodinger's first and second equations.

But it is not the same as the coin.
In the case of the cat you can simply leave the box sealed for a long time, say a hundred years, before opening it.
Then the cat will definitely be dead.

There is no equivalent with the coin, unless you are prepared to believe in the repeating holographic cosmological interpretation of Copenhagen.

[studiot]

The wavefunction is a mathematical concept used to describe the probabilities of measurement outcomes.

No

what exactly do you mean by "No"?
That the wavefunction is a mathematical concept, or that it is used to calculate probabilities of measurement outcomes? 🤔

You are the one who keeps introducing mathematics for support and then saying it doesn't count.
You can't have it both ways.

I think you are conflating two different claims. I am not saying that the mathematics “doesn't count”. Quite the opposite: the mathematical properties of the wavefunction are essential to the theory.

My point is that a mathematical property of the representation does not by itself establish a corresponding physical property of what is being described. Saying that the wavefunction has dimension L^-3/2 tells us about the mathematical representation and its normalization. It does not by itself tell us that the wavefunction is a physical field with that dimension.

So I am not saying "mathematics doesn't count". I am saying that we should distinguish mathematical properties of the model from ontological claims about physical reality.

If you consider the mathematical model sufficient to conclude that reality is actually structured that way, I would be interested to understand how you arrive at that conclusion?

You don't seem able to decide whether you think the wavefunction is a mathematical concept or a something with a physical dimension.

I said No because the quantum wavefunction does  not directly yield a probability.
Probability is just a number it has no physical dimensions.

It is often said that the square of the wavefunction is the probability, but things are not as simple as that.

The wavefunction is part of a class of functions that are 'square integrable'.
In order to obtain a probability we have to the wave function by its conjugate and then integrate it over all the independent variables and set that integral equal to 1.
You may be familiar with the procedure with complex conjugates.

The wavefunction itself is of course the dependant variable in equations like Schrodinger 1 or 2 or Dirac or the KDV or whatever.

I am quite happy to explain what I know about QM but in another thread as I don't see it has any bearing on the photon model in question.

Of course QM is very very important in electronics, our pcs and screens wouldn't work without quantum tunnelling for instance

[radiolistener]

You don't seem able to decide whether you think the wavefunction is a mathematical concept or a something with a physical dimension.

I said No because the quantum wavefunction does  not directly yield a probability.
Probability is just a number it has no physical dimensions.

It is often said that the square of the wavefunction is the probability, but things are not as simple as that.

The wavefunction is part of a class of functions that are 'square integrable'.
In order to obtain a probability we have to the wave function by its conjugate and then integrate it over all the independent variables and set that integral equal to 1.

I never said that "the wavefunction is the probability". I said that the wavefunction is a mathematical concept.

The L^-3/2 dimension follows from the normalization of the probability distribution. So why should this dimension be taken as evidence that the wavefunction itself is a physically existing field?

The question is: does \$\Psi\$ itself represent a physically existing field?

[studiot]

You don't seem able to decide whether you think the wavefunction is a mathematical concept or a something with a physical dimension.

I said No because the quantum wavefunction does  not directly yield a probability.
Probability is just a number it has no physical dimensions.

It is often said that the square of the wavefunction is the probability, but things are not as simple as that.

The wavefunction is part of a class of functions that are 'square integrable'.
In order to obtain a probability we have to the wave function by its conjugate and then integrate it over all the independent variables and set that integral equal to 1.

I never said that "the wavefunction is the probability". I said that the wavefunction is a mathematical concept.

The L^-3/2 dimension follows from the normalization of the probability distribution. So why should this dimension be taken as evidence that the wavefunction itself is a physically existing field?

The question is: does \$\Psi\$ itself represent a physically existing field?

Well I suppose that has got to depend on what you mean by
Physically
Existing
Field.

Bear in mind that Physicists and Mathematicians have very different definitions of a field.

[radiolistener]

Well I suppose that has got to depend on what you mean by
Physically
Existing
Field.

Bear in mind that Physicists and Mathematicians have very different definitions of a field.

That's fair. Then what do you mean by a "physically existing field" in this context and what makes you conclude that \$\Psi\$ is one rather than a mathematical representation of the quantum state?

[studiot]

Well I suppose that has got to depend on what you mean by
Physically
Existing
Field.

Bear in mind that Physicists and Mathematicians have very different definitions of a field.

That's fair. Then what do you mean by a "physically existing field" in this context and what makes you conclude that \$\Psi\$ is one rather than a mathematical representation of the quantum state?

I try to avoid the use of these terms unless I specify what I mean, but you have linked 3 controversial words together, which is why I asked you.

In Physics a Field is something which has a value at every point in some specified region.

I say value as a general term as it may be a number or it may be something else.

Take for instance a fluid flowing.

At every point in that fluid has a pressure, a temperature, and a direction, which all have values.

Each one of these constitute a field but are any of these fields physical and what do you mean by saying that a pressure field or a temperature field or a direction field exists ?


In mathematics a field is a set of elements with two defined binary operations, one of which forms a group and the other forms a group with the zero element removed.

The set of integers does not form a field, the set of rational numbers does, as does the set of real numbers and complex numbers  (and many other sets besides)

Does this give the numbers existence or make them physical  ?


I prefer to use the terms material and non material rather than physical to distinguish things like shadows and holes which are abstract.

As regards existence the best test I know is the ask can it affect other objects, shadows and holes can certainly affect material things.

[radiolistener]

I try to avoid the use of these terms unless I specify what I mean, but you have linked 3 controversial words together, which is why I asked you.

In Physics a Field is something which has a value at every point in some specified region.

I say value as a general term as it may be a number or it may be something else.

Take for instance a fluid flowing.

At every point in that fluid has a pressure, a temperature, and a direction, which all have values.

Each one of these constitute a field but are any of these fields physical and what do you mean by saying that a pressure field or a temperature field or a direction field exists ?


In mathematics a field is a set of elements with two defined binary operations, one of which forms a group and the other forms a group with the zero element removed.

The set of integers does not form a field, the set of rational numbers does, as does the set of real numbers and complex numbers  (and many other sets besides)

Does this give the numbers existence or make them physical  ?


I prefer to use the terms material and non material rather than physical to distinguish things like shadows and holes which are abstract.

As regards existence the best test I know is the ask can it affect other objects, shadows and holes can certainly affect material things.

Hm... I agree that \$\Psi\$ is a field in the physics sense you defined: it assigns a value to every point in the relevant domain. The question is whether this field itself exists independently of the mathematical model.

Using your own criterion for existence "can it affect other objects?", what is the physical mechanism by which \$\Psi\$ itself affects something?

[studiot]

I try to avoid the use of these terms unless I specify what I mean, but you have linked 3 controversial words together, which is why I asked you.

In Physics a Field is something which has a value at every point in some specified region.

I say value as a general term as it may be a number or it may be something else.

Take for instance a fluid flowing.

At every point in that fluid has a pressure, a temperature, and a direction, which all have values.

Each one of these constitute a field but are any of these fields physical and what do you mean by saying that a pressure field or a temperature field or a direction field exists ?


In mathematics a field is a set of elements with two defined binary operations, one of which forms a group and the other forms a group with the zero element removed.

The set of integers does not form a field, the set of rational numbers does, as does the set of real numbers and complex numbers  (and many other sets besides)

Does this give the numbers existence or make them physical  ?


I prefer to use the terms material and non material rather than physical to distinguish things like shadows and holes which are abstract.

As regards existence the best test I know is the ask can it affect other objects, shadows and holes can certainly affect material things.

Hm... I agree that \$\Psi\$ is a field in the physics sense you defined: it assigns a value to every point in the relevant domain. The question is whether this field itself exists independently of the mathematical model.

Using your own criterion for existence "can it affect other objects?", what is the physical mechanism by which \$\Psi\$ itself affects something?

One such process is called photon downconversion.

[radiolistener]

One such process is called photon downconversion.

But how does this demonstrate that \$\Psi\$ itself exists independently of our mathematical description?

The fact that a physical process can be described mathematically using \$\Psi\$ does not by itself show that \$\Psi\$ is something that physically exists or has causal efficacy of its own.

[studiot]

One such process is called photon downconversion.

But how does this demonstrate that \$\Psi\$ itself exists independently of our mathematical description?

The fact that a physical process can be described mathematically using \$\Psi\$ does not by itself show that \$\Psi\$ is something that physically exists or has causal efficacy of its own.

I believe this is called "Let me Google this for U"

https://www.edinst.com/resource/what-is-upconversion/

This reverence is upconversion but the principle is the same.

There are a whole gaggle of  learned article from MIT, Arizona UNI, US Bureau of standards etc etc.

Do you understand differential equations ?

You have never acknowledged my references to dependent and independent variables.

Psi is the dependent variable which comes from the energy levels - so it must be a physical variable

[radiolistener]

I believe this is called "Let me Google this for U"

https://www.edinst.com/resource/what-is-upconversion/

This reverence is upconversion but the principle is the same.

There are a whole gaggle of  learned article from MIT, Arizona UNI, US Bureau of standards etc etc.

Do you understand differential equations ?

You have never acknowledged my references to dependent and independent variables.

Psi is the dependent variable which comes from the energy levels - so it must be a physical variable

Being a dependent variable in a differential equation does not by itself make a mathematical function a physically existing thing.

For example, x(t) is the dependent variable in a classical equation of motion, but the mathematical function x(t) is not a separate physical thing. Likewise, solving an equation for \$\Psi\$ does not by itself establish that \$\Psi\$ physically exists.

Also, in the Schrodinger equation, \$\Psi\$ and the energy eigenvalues are obtained together from the eigenvalue problem. It is not simply that \$\Psi\$ "comes from the energy levels".

So I still don't see the missing step - what is the evidence that distinguishes "\$\Psi\$ is a physically existing thing" from "\$\Psi\$ is a mathematical representation of the quantum state"?