Self-interference in double-slit experiments

[Euthan]

In a double-slit experiment, if a beam of photons is fired, an interference pattern composed of photons will result. But, if photons are fired one at a time, an interference pattern will still result. Why is this? The only explanation that I've seen is that the photon interferes with itself. I was talking to a retired-physicist a couple of months ago, and he supported this popular explanation by saying that an interference pattern will only result if the slits are a certain distance away from each other. That strongly implies that the photon is interfering with itself in a wave-like manner, more specifically, it strongly implies that the distance between the slits causes the single photons to undergo destructive, and constructive interference. Thus, even if we fire photons one at a time, an interference pattern will still result, because of the distance between the slits, and ultimately because every single photon does interfere with itself. I conceded to him that this fact alone is strong evidence in favor of the "photon interfering with itself" explanation.

But I think I have a good reason to reject this commonly accepted explanation. I think the explanation of his actually contradicts QM, for it implies that photons are split. If a photon is actually going through both slits, while undergoing destructive, and constructive interference, then that means that the photon is splitting, correct? That is one of my questions. My second question is: is there a better explanation than the "photon interfering with itself" explanation? My third question is: what would it mean for a photon, or electron to interfere with itself?

 

[StevieTNZ]

In a double-slit experiment, if a beam of photons is fired, an interference pattern composed of photons will result. But, if photons are fired one at a time, an interference pattern will still result. Why is this? The only explanation that I've seen is that the photon interferes with itself. I was talking to a retired-physicist a couple of months ago, and he supported this popular explanation by saying that an interference pattern will only result if the slits are a certain distance away from each other. That strongly implies that the photon is interfering with itself in a wave-like manner, more specifically, it strongly implies that the distance between the slits causes the single photons to undergo destructive, and constructive interference. Thus, even if we fire photons one at a time, an interference pattern will still result, because of the distance between the slits, and ultimately because every single photon does interfere with itself. I conceded to him that this fact alone is strong evidence in favor of the "photon interfering with itself" explanation.

But I think I have a good reason to reject this commonly accepted explanation. I think the explanation of his actually contradicts QM, for it implies that photons are split. If a photon is actually going through both slits, while undergoing destructive, and constructive interference, then that means that the photon is splitting, correct? That is one of my questions. My second question is: is there a better explanation than the "photon interfering with itself" explanation? My third question is: what would it mean for a photon, or electron to interfere with itself?

Don't think of photons in the classical sense. Yes, the quantum system interferes with itself.

 

[Cthugha]

Just a small excerpt from a conference proceedings paper by Roy Glauber, Nobel Prize winner for the theory of optical coherence and quantum optics ( https://arxiv.org/pdf/nucl-th/0604021.pdf):

"When you read the first chapter of Dirac’s famous textbook in quantum mechanics, however, you are confronted with a very clear statement that rings in everyone’s memory. Dirac is talking about the intensity fringes in the Michelson interferometer, and he says,

Every photon then interferes only with itself. Interference between two different photons never occurs.

Now that simple statement, which has been treated as scripture, is absolute nonsense. First of all, the things that interfere are not the photons themselves, they are the probability amplitudes associated with different possible histories.[...]"

It indeed makes little sense to claim that photons interfere. In a classical double slit setting you would say that usually fields interfere. Light fields do not translate to photons when you go to the quantum limit. That would be very sloppy language.

 

[Euthan]

Just a small excerpt from a conference proceedings paper by Roy Glauber, Nobel Prize winner for the theory of optical coherence and quantum optics ( https://arxiv.org/pdf/nucl-th/0604021.pdf):

"When you read the first chapter of Dirac’s famous textbook in quantum mechanics, however, you are confronted with a very clear statement that rings in everyone’s memory. Dirac is talking about the intensity fringes in the Michelson interferometer, and he says,

Every photon then interferes only with itself. Interference between two different photons never occurs.

Now that simple statement, which has been treated as scripture, is absolute nonsense. First of all, the things that interfere are not the photons themselves, they are the probability amplitudes associated with different possible histories.[...]"

It indeed makes little sense to claim that photons interfere. In a classical double slit setting you would say that usually fields interfere. Light fields do not translate to photons when you go to the quantum limit. That would be very sloppy language.

It appears to me that even though you are rejecting the common explanation of "quantum objects interfering with themselves" you are invoking another explanation that is definitely not a physical one. Mathematical objects such as fields, and probability amplitudes cannot be reasonably said to explain anything about our world. They at best are useful for predicting, and calculating the physical outcomes that are detected. There are many instances in which some physicists will explain everyday phenomena while making use of concepts such as vectors, which are clearly not physical objects, but mathematical representations of real life properties such as velocity, and angular momentum. I realize that it is probably impossible to predict, and/or calculate outcomes in any area of physics without mathematics, but even so, the point still remains clear that making use of mathematical objects does not explain anything physical.

 

[PeterDonis]

Mathematical objects such as fields, and probability amplitudes cannot be reasonably said to explain anything about our world.

We can't stop you from holding this as your personal opinion, but you should be aware that it is not the common opinion among physicists. However, that's not the most important point; see below.

They at best are useful for predicting, and calculating the physical outcomes that are detected.

You are making a distinction between predicting outcomes--which predictions can then be compared with actual outcomes to test a theoretical model--and "explaining" what is going on. But if successfully predicting outcomes does not count as "explaining", then there is no way to experimentally test anything that you would consider an "explanation"--and therefore discussing it is out of scope here. We discuss physics here, not metaphysics or philosophy, and physics consists in constructing models and comparing their predictions with reality. If it can't be tested by experiment, it isn't physics, at least for purposes of discussion here at PF.

 

[Euthan]

We can't stop you from holding this as your personal opinion, but you should be aware that it is not the common opinion among physicists. However, that's not the most important point; see below.
You are making a distinction between predicting outcomes--which predictions can then be compared with actual outcomes to test a theoretical model--and "explaining" what is going on. But if successfully predicting outcomes does not count as "explaining", then there is no way to experimentally test anything that you would consider an "explanation"--and therefore discussing it is out of scope here. We discuss physics here, not metaphysics or philosophy, and physics consists in constructing models and comparing their predictions with reality. If it can't be tested by experiment, it isn't physics, at least for purposes of discussion here at PF.

Why would it imply that because successfully predicting outcomes does not count as "explaining," that then there is no way to experimentally test anything that I would consider an "explanation"? Consider the following scenario: some hypothesis predicts that when I release an object some y distance from the ground, it will accelerate at a constant rate of 9.8 m/s^2. The hypothesis is empirically successful. I consider the relevant meaning of "explanation" to be of the form: some physical phenomena is caused by x. Now consider the explanation that could explain this phenomena that we just discovered. The explanation is: the planet Earth causes this constant rate of acceleration. Now why couldn't we test this explanation, given that the relevant meanings of "explanation" and "hypothesis" are distinct?

 

[vanhees71]

Well, math is the only language which adequately describes the (quantum) world. There's no other way to merely express the content of quantum mechanics.

That said, it's good advice to learn non-relativistic quantum theory before entering the more complicated topic of relativistic quantum field theory. Particularly photons are, in my opinion, the worst starting point from a didactical point of view since photons are very far from anything "particle like" we are used to by our experience of macroscopic objects like billard balls. Photons do not even admit a proper definition of a position observable, i.e., there's no way to localize a single photon in any sense of classical particles at all.

Also, forget the age-old outdated concept of "wave-particle dualism" and phrases like "something interferes with itself" or, even worse, "a particle is at several places at once" etc. The only consistent way to talk about quantum phenomena is a formal mathematical language in terms of Hilbert spaces and operators acting on Hilbert space. The physical meaning is provided by Born's Rule, leading to the probability interpretation of quantum states.

That said, let's look at the interference phenomena with single photons. First of all a single photon is an elementary quantum of the electromagnetic field, and to make a more intuitive picture it's better to think in terms of classical electromagnetic field modes. One complete set of such classical field modes are the plane-wave solutions of the charge-current-free Maxwell equations. It's defined by a wave vector $\vec{k} \in \mathbb{R}^3$ and a polarization vector $\vec{\epsilon}_{\lambda}(\vec{k})$, which for simplicity we can choose also as real $\mathbb{R}^3$-vectors. Elektromagnetic waves are transverse, i.e., you have $\vec{\epsilon}_{\lambda}(\vec{k}) \cdot \vec{k}=0$. Thus there are two linearly independent polarization vectors, i.e., $\lambda \in \{1,2\}$. We choose these vectors conveniently to be unit vectors which are perpendicular to each other and obeying $\vec{\epsilon}_1(\vec{k}) \times \vec{\epsilon}_2(\vec{k})=\vec{k}/|\vec{k}|$. The frequency of the plane wave is $\omega=c |\vec{k}|$, where $c$ is the speed of light (in vacuum).

In quantum mechanics each free-field mode corresponds to a harmonic oscillator, and you can define a basis of state vectors $|\{N(\vec{k},\lambda)\} \rangle$, where $N(\vec{k},\lambda) \in \mathbb{N}_0=\{0,1,2,\ldots \}$. If all numbers $N(\vec{k},\lambda)=0$ that defines the "vacuum", i.e., no em. fields/photons present. If $\sum_{\vec{k},\lambda} N(\vec{k},\lambda)=1$ you have a one-photon state and so on. This is called the (bosonic) Fock space spanning the Hilbert space of states for the quantized electromagnetic field.

Interference for single is now no brainer anymore: you can superimpose several single-photon states, leading to a new single-photon state. The probability to find a photon at a certain place $\vec{x}$ is simply proportional to the intensity of the em. field, i.e.,
$$I(\vec{x}) \propto \langle \Psi |\hat{\vec{E}}^2(t,\vec{x})|\Psi \rangle,$$
where $\hat{\vec{E}}(t,\vec{x})$ is the electric field (in the Heisenberg picture of time evolution) and $|\Psi \rangle$ the quantum under investigation, e.g., in our discussion a single-photon state.

Nowadays it's pretty easy to prepare single-photon states, but it's not so easy from a historical perspective. One way is parametric down conversion, using a birefringent crystal and a laser to provide true single-photon states, and one can do experiments with it.

The most simple experiment to show that one has prepared a single-photon state is the use of a Mach-Zehnder interferometer

https://en.wikipedia.org/wiki/Mach–Zehnder_interferometer

Just consider a setup without any phase shifter or sample as in Fig. 3 of the Wikipedia article in it (as described inhttps://en.wikipedia.org/wiki/Mach%E2%80%93Zehnder_interferometer#Observing_the_effect_of_a_sample) . First use classical coherent light, nowadays provided easily by a laser, and adjust the beam splitter such that there is full intensity at detector 1 and zero intensity at detector 2. As described by the Wikipedia article due to the Fresnel rules, known from classical wave optics, the intensities at the detectors is due to constructive interference at detector 1 and destructive interference of dectector 2. The interference occurs when combining the partial waves going the one or the other way through the optical setup including the half-silvered mirrors ("beam splitters"). Then putting in the sample leads to some intensity at Detector 1 and some intensity at Detector 2, again due to the interference of the partial beams going either way through the beam splitters. For classical light, one can think indeed in terms of "splitting" of the partial waves going through the apparatus, no matter how dim this light may be. Quantum mechanically such a classical em. wave as provided by a laser is a socalled "coherent state". In terms of photons, as defined above, it's a superposition of state vectors with any number of photons, i.e., the photon number is indetermined. No matter, how dim the laser light may be, there's always a probability to have more than one photon in the apparatus, and it can indeed always happen that you find one photon at detector 1 and one at detector 2 at the same time (or rather "in coincidence"). So with dimmed laser light you cannot prove the existence of single photons, simply because you don't investigate one-photon Fock states but coherent states.

Now consider to use true single-photon states. In the setup that there is no sample in, you always register a single photon at detector one and never one at detector 2, which is no surprise, given that the probabilities to register the photon at detector 1 or 2 is given by the intensity of the classical em. waves. Of course, that this is experimentally really found proves this picture right, i.e., that also in the case of true single-photon states, the constructive interference at detector 1 and the destructive interference of detector 2 holds also for single photons. In a sloppy language one says "the single photon interferes with itself", but it should have become clear that this is indeed only sloppy language, and nowhere in my description was the idea of photons as localized billard-ball-like particles in the apparatus! To the contrary everything is explained in the picture of "quantized fields", and very little by a particle-like picture.

The particle-like properties of single-photon states comes, however, into the game if we looking at the situation with the sample in place, where there's some non-zero intensity on both detectors for the classical waves. Now using single photons, these intensities provide the probabilities (and nothing else!) to find the single photon either at detector 1 or detector 2. There's no way to predict, where a specific single photon will end up, but what's found with very high accuracy is that indeed one never ever measures coincident countings at both detectors! Only either detector 1 or detector 2 registers the photon. Using very many single photons, you'll find precisely the statistics predicted by the above given modern description of single photons in terms of quantized electromagnetic fields. The only particle-like property is that the single-photon states indeed imply that these "tiniest lumps of electromagnetic fields at a given frequency" cannot be split in two such quanta. This is impossible already by the simple fact of energy conservation. Each single photon has an energy of $\hbar \omega$, and you simply cannot create two photons of the same frequency, because then you'd have $2\hbar \omega$ energy, and this cannot happen in a "passive" apparatus like the Mach-Zehnder interferometer. On the other hand, all we know are the probability that the photon gets registered either at detector 1 or at detector 2, and these probabilities are given by the intensity of the corresponding classical em. wave. Only in this sense there's some kind of "wave-particle duality" left in this modern picture of quantum optics provided by the theory of quantized fields, i.e., quantum electrodynamics (QED).

It's long overdue that textbooks do not provide anymore the old-fashioned picture of photons as billard-ball-like particles!

 

[PeterDonis]

Why would it imply that because successfully predicting outcomes does not count as "explaining," that then there is no way to experimentally test anything that I would consider an "explanation"?

Because the only thing you can experimentally test is whether your model correctly predicts outcomes. So if you don't consider successfully predicting outcomes to count as "explaining", which you said you didn't, then whatever you do think "explaining" is, it isn't the only thing you can experimentally test.

why couldn't we test this explanation

Does dropping objects above the Earth and seeing them fall at 9.8 m/s^2 count as testing the explanation "Earth causes objects to fall"? If it does, then successfully predicting outcomes does count as explanation, contrary to what you claimed. If not, how would you test the explanation "Earth causes objects to fall"?

 

[PeroK]

. Mathematical objects such as fields, and probability amplitudes cannot be reasonably said to explain anything about our world.

Mathematics, in my experience of learning physics, explains a lot. In many cases, it is the only explanation. Nature, for her own reasons, has decided to act in accordance with certain mathematical laws.

You can say, for example, that opposite charges attract. But, if you want to expand on this vague generality, you need Coulomb's law. And that can only be stated mathematically.

 

[vanhees71]

It's among the most fascinating results of the scientific endeavor that math is so much to the point to describe Nature. Wigner once called it the "Unreasonable effectiveness of mathematics":

https://onlinelibrary.wiley.com/doi/pdf/10.1002/cpa.3160130102

 

[Euthan]

Because the only thing you can experimentally test is whether your model correctly predicts outcomes. So if you don't consider successfully predicting outcomes to count as "explaining", which you said you didn't, then whatever you do think "explaining" is, it isn't the only thing you can experimentally test.
Does dropping objects above the Earth and seeing them fall at 9.8 m/s^2 count as testing the explanation "Earth causes objects to fall"? If it does, then successfully predicting outcomes does count as explanation, contrary to what you claimed. If not, how would you test the explanation "Earth causes objects to fall"?

You test the explanation "Earth causes objects to fall" by testing the predictions that are implicated by the explanation. But, successfully predicting outcomes still does not count as explanation. Explaining things has a different meaning than merely predicting things. The Earth scenario that I constructed shows that the kind of "explanation" that I had in mind can be tested by experiment. It does not follow that successfully predicting an outcome counts as an explanation. Predicting an outcome does not necessarily tell us the "why," but making an explanation does necessarily tell us the "why," and that is the crucial distinction between making predictions and making explanations. I am not able to reply to all of your statements one by one in an orderly fashion, because I do not know how to quote in such a way.

 

[Boing3000]

You test the explanation "Earth causes objects to fall" by testing the predictions that are implicated by the explanation.

This is no more an "explanation", that : "the wave fonction" cause the probability for an observation to be such at such. You have no idea how the Earth does that, nor Newton, nor even Einstein. Nobody does. We just can describe it accurately.

You also have made identical contradictory claim by stating that "vector" are abstract, and velocity is "real". That's very surprising, because velocity is a totally abstract notion (actually it is a vector), that only of few percentage of a specific species on Earth more or less understand.

Explaining things has a different meaning than merely predicting things.

Maybe you should reconsider your explanation of what explanation means. Physics discribes and predict.
A very wise men explained it quite beautifully.

 

[Nugatory]

I think the explanation of his actually contradicts QM, for it implies that photons are split. If a photon is actually going through both slits, while undergoing destructive, and constructive interference, then that means that the photon is splitting, correct?

Incorrect, because the intermediate conclusion you've drawn (that the photon actually goes through both slits) is seriously misleading. It would be just as accurate to say that it goes through neither slit; that "goes through both slits" and "goes through neither slit" are about equally correct is a very strong hing that neither is a good starting point for understanding what quantum mechanics actually says.

The "very wise man" that @Boing3000 mentions in the previous post has also written a book "QED: The strange theory of light and matter" that does a pretty good job of explaining at a layperson level what quantum mechanics does say about the behavior of photons. It's all about how we can accurately calculate what photons will do and how the phenomena that we take for granted (reflection, beams of lights, shadows, ...) emerge from these calculations. Whether you consider this an "explanation" or not is a matter of personal taste; but whether you like it or not, that's as good as it gets in physics.

 

[PeterDonis]

You test the explanation "Earth causes objects to fall" by testing the predictions that are implicated by the explanation.

Yes.

But, successfully predicting outcomes still does not count as explanation.

Then, by your definition, "explanation" is not something that science does, and is therefore off topic for this forum. Here we discuss science, not philosophy or metaphysics.

The rest of us prefer to use a definition of "explanation" by which having a theory that makes accurate predictions counts as an explanation.

 

[Carpe Physicum]

Yes.

Then, by your definition, "explanation" is not something that science does, and is therefore off topic for this forum. Here we discuss science, not philosophy or metaphysics.

The rest of us prefer to use a definition of "explanation" by which having a theory that makes accurate predictions counts as an explanation.

Excellent link someone sent me was to a discussion about Epistemology vs Ontology. You two are mixing the two. Predicting outcomes is epistemology. Explaining something in the sense of Euthan is ontology. In this forum, I've found out, ontology is off limits since in the past of this forum it only lead to rampant personal speculation. I can see the logic in curbing that for a forum like this. But it is interesting in light of the book I'm reading suggested by another member of this forum. It explains how there are two camps in the QM debate. One camp is okay with epistemology only. One is not. Not a judgment, just an observation.

 

[PeterDonis]

Excellent link someone sent me was to a discussion about Epistemology vs Ontology. You two are mixing the two. Predicting outcomes is epistemology. Explaining something in the sense of Euthan is ontology.

And all of this is philosophy, not physics, and is off topic here. If making accurate predictions doesn't count as "explanation" to you, that's fine, you don't have to accept our definition of the word "explanation". But as I said before, that just means "explanation" by your definition is out of scope for discussion here.

It explains how there are two camps in the QM debate. One camp is okay with epistemology only. One is not.

Since all QM interpretations make the same predictions about experiments, one could argue that the QM debate itself is philosophy, not physics. However, there is another aspect, since different QM interpretations also suggest different potential experiments to run, which might possibly give results different from the predictions of standard QM, and therefore point the way to a more comprehensive theory that includes our current QM as a special case. Historically, science often progresses this way, and that's fine. One just has to be careful not to treat an interpretation one personally favors, that might someday lead to a better theory, as though it were an actual better theory. It isn't an actual better theory until it is confirmed by actual experiments to make accurate predictions in a domain where our current theory does not.

 

[Buzz Bloom]

Well, math is the only language which adequately describes the (quantum) world.

Hi vanhees::

It could well be that I misunderstand the meaning of the word" describes". One usage seems to be that the Copenhagen Interpretation (CI) "describes" what is happening regarding a QM phenomenon. The CI used words such as "collapse" regarding the wave function as what happens when a "measurement" occurs. Do you disagree with this, or did you have a different meaning in mind for "describes".

Regards,
Buzz

 

[Nugatory]

Hi vanhees::

It could well be that I misunderstand the meaning of the word" describes". One usage seems to be that the Copenhagen Interpretation (CI) "describes" what is happening regarding a QM phenomenon. The CI used words such as "collapse" regarding the wave function as what happens when a "measurement" occurs. Do you disagree with this, or did you have a different meaning in mind for "describes".

Regards,
Buzz

I'm not vanhees, but if we're debating the meaning of the word "describes" and whether the math "describes" or "predicts the behavior of" the quantum world, that seems to me a pretty strong hint that we should be paying more attention to the math and less attention to the natural-language words wrapped around it.

 

[Buzz Bloom]

you don't have to accept our definition of the word "explanation".

Hi Peter:

I am wondering what you mean by "our" in this statement. I am guessing you might mean that you personally along with a large number of other physicists agree on the usefulness of the previously presented definition. But I am also guessing you do not intend that this definition is now accepted by all or nearly all physicists. I have been reading Adam Becker's "What is Real?", and that until Bell's Theorem in 1964 it seems likely it would be reasonable to say that almost all physicists agreed with the Copenhagen Interpretation. But nowadays it seems there are quite a few alternate interpretations, and the issues are quite controversial.

Regards,
Buzz

 

[PeterDonis]

I am wondering what you mean by "our" in this statement.

I meant the people in this thread who have been using the definition of "explanation" that I gave. Don't overthink.

 

[Buzz Bloom]

I meant the people in this thread who have been using the definition of "explanation" that I gave.

Hi Peter:

I do appreciate your response, but I note that your definition and the usage in the OP do not agree.

The only explanation that I've seen is that the photon interferes with itself.

If making accurate predictions doesn't count as "explanation" to you, that's fine

As I read it, Euthan is describing an explanation of the double-slit experiment which is something beyond the observation that the math makes accurate predictions.

Regards,
Buzz

 

[PeterDonis]

As I read it, Euthan is describing an explanation of the double-slit experiment which is something beyond the observation that the math makes accurate predictions.

And, if you read the thread, you will see that his understanding as given in the OP is wrong. Also see my response to him in post #5, where I specifically talked about the term "explanation".

 

[vanhees71]

Hi vanhees::

It could well be that I misunderstand the meaning of the word" describes". One usage seems to be that the Copenhagen Interpretation (CI) "describes" what is happening regarding a QM phenomenon. The CI used words such as "collapse" regarding the wave function as what happens when a "measurement" occurs. Do you disagree with this, or did you have a different meaning in mind for "describes".

Regards,
Buzz

I strongly disagree with the collapse hypothesis. We are lucky to live in times where the Copenhagen doctrine comes out of fashion more and more. I always warn against to use of too much philosophy, and Heisenberg and Bohr where too much on the philosophical side and have confused generations of physicists more than necessary about QT.

In my opinion the aim of physics is to describe nature in regard of reproducible objective observations (experimental physics) and to find mathematical models and theories that order these observations by finding fundamental rules (natural laws) that allow to mathematically derive predictions for observations, using as few "irreducible assumptions" (usually called postulates or axioms).

In QT all we have are probabilistic predictions about the outcome of measurements, and that's the only meaning of the formalism that does not lead to problems with fundamental laws of physics such as the relativistic space-time and causality structure related with it. Particularly the collapse hypothesis violates this fundamental principles and it even usually doesn't describe what happens in a real-world experiment. There are very few examples, where a von Neumann filter measurement is possible, and there you can use FAPP the collapse hypothesis, but you should keep in mind that it is just a handwaving description for a preparation procedure.

Since relativistic local and microcausal QFT, the fundamental starting point for the Standard Model of elementary particle physics, obey the linked-cluster theorem, there cannot be any instantaneous collapse, and there is no "spooky action at a distance" as Einstein called it. Einstein understood much more about QT as usually is claimed in popular writings about QT, and what he indeed criticized is not so much QT itself but parts of the CI, which indeed are contradicting fundamental basic laws of physics and are at the same time not necessary to "interpret" QT. Any theory needs "interpretation" in the sense that you have to relate the mathematical formalism to real-world observations (measurements), but you don't need more "interpretation" than to make this link. Particularly you cannot expect to find natural laws that satisfies any of your preferred world views or prejudices. To the contrary, you want to find out, what really happens in Nature and not to confirm your prejudices.

 

[Lord Jestocost]

I strongly disagree with the collapse hypothesis. We are lucky to live in times where the Copenhagen doctrine comes out of fashion more and more.

"Second, many physicists and philosophers see the reduction of the wave function as an important part of the Copenhagen interpretation. But Bohr never talked about the collapse of the wave packet. Nor did it make sense for him to do so because this would mean that one must understand the wave function as referring to something physically real. Bohr spoke of the mathematical formalism of quantum mechanics, including the state vector or the wave function, as a symbolic representation."

Jan Faye, "Copenhagen Interpretation of Quantum Mechanics", https://plato.stanford.edu/entries/qm-copenhagen/

 

[vanhees71]

Indeed, Bohr was much more careful than, e.g., Heisenberg. However, both are notouriously overcomplicating things in their writing. Rather stick to Dirac or Pauli ("Don't make so many words") if you want to read about quantum theory from the original sources founding fathers.

 

[Euthan]

This is no more an "explanation", that : "the wave fonction" cause the probability for an observation to be such at such. You have no idea how the Earth does that, nor Newton, nor even Einstein. Nobody does. We just can describe it accurately.

You also have made identical contradictory claim by stating that "vector" are abstract, and velocity is "real". That's very surprising, because velocity is a totally abstract notion (actually it is a vector), that only of few percentage of a specific species on Earth more or less understand.Maybe you should reconsider your explanation of what explanation means. Physics discribes and predict.
A very wise men explained it quite beautifully.

To say that vectors are abstract, and that velocity is real, is not a contradiction. The words "abstract," and "real" are not mutually exclusive.

 

[vanhees71]

Well, what "real" means is an enigma to me. You have to ask philosophers about it, but be warned, from two philosophers you get at least 4 answers and no clear definition. For physicists it's pretty simple: Any reproducible objective, preferably accurately quantifiable, phenomenon is real.

 

[Carpe Physicum]

Well, what "real" means is an enigma to me. You have to ask philosophers about it, but be warned, from two philosophers you get at least 4 answers and no clear definition. For physicists it's pretty simple: Any reproducible objective, preferably accurately quantifiable, phenomenon is real.

Like epicycles, right? ;)

 

[Stephen Tashi]

The Earth scenario that I constructed shows that the kind of "explanation" that I had in mind can be tested by experiment. It does not follow that successfully predicting an outcome counts as an explanation.

As far as I can see, the only distinction you are making between "prediction" and "explanation" is the scope of applicability of the predictive model. If you have a model of gravitation that implies the model for a falling object near the surface of the Earth as a special case , you call that "explaining" the behavior of a falling object, but the model of gravitation doesn't "explain" why there is gravity.

 

[Stephen Tashi]

Like epicycles, right? ;)

Perhaps we have to distinguish between "phenomena" and "properties of phenomena". If specifying a phenomena exactly requires describing all its properties, we are out of luck - yet we do it approximately all the time. For example, "my cat".

 

[Carpe Physicum]

Perhaps we have to distinguish between "phenomena" and "properties of phenomena". If specifying a phenomena exactly requires describing all its properties, we are out of luck - yet we do it approximately all the time. For example, "my cat".

Maybe. My point was, it's not so simple as the holier-than-philosophers poster implied.

 

[vanhees71]

Like epicycles, right? ;)

Epicylces are no observation but a (by the way correct though not very efficient!) description of planetary motion.

 

[Carpe Physicum]

Epicylces are no observation but a (by the way correct though not very efficient!) description of planetary motion.

Epicycles are phenomenon observed in nature, just like orbits. Or so they thought. My point is, they were considered real in their time until it was realized they weren't. Same with circular orbits. Point being, they were considered real, and in a sense reproducable, albeit by "the creator" or the sun.

 

[Stephen Tashi]

Epicylces are no observation but a (by the way correct though not very efficient!) description of planetary motion.

The formalism of QM speaks of measurements and their association with linear operators. If the result of a "measurement" is single number, then how do we formalize "observations" that are more complicated - such as "The particle was detected at 3 points that lie in a straight line" or "the planet moves in an elliptical orbit"?

In a hand-wavy manner, I could say that "observations" are merely elaborate sets of measurements, each of whose result is a single number. However, can we handle the mathematical technicalities of assigning probabilities to observations? - meaning can we handle them by the standards of mathematics - measure theory as opposed to intuitive physical arguments.

 

[vanhees71]

"The particle was detected at 3 points that lie in a straight line". Where has this been ever observed. You observe particles as single point-like events in a detector (of course with always finite position resolution). "The planet moves in and elliptical orbit" is described with overwhelming accuracy by classical mechanics (and be it general relativistically if it comes to high accuracy). Why this is a good description is understandable from quantum statistics (particularly decoherence through interaction with the "environment").

Mathematics is the language we use to describe our observations and theories about them. In my opinion the relation between probabilities and observations is given by the usual frequentist interpretation, and that's how probabilistic predictions as those from QT are tested by observations. An important addition to "classical probability theory" (e.g., a la Kolmogorov) are the notions of information theory (a la Shannon and Jaynes).