Einstein's View of Quantum Mechanics

[bhobba]

Hi All

This is an outgrowth of the following thread:
https://www.physicsforums.com/threads/light-photons-waves-particles-wave-particle-duality.934063/

OK first we need to clear up a few misconceptions about Einsteins view of QM. It is often said Einstein didn't believe in QM. That's really a half truth - he initially didn't and tried many ways to disprove it - his last attempt being the famous clock in a box argument solved by Bohr. For a modern take on it see here:
https://arxiv.org/pdf/1203.1139.pdf

As an aside - the paper says 'At first Bohr didn’t know how to reply to the Einstein’s paradox'. That's a bit of an understatement. Evidently it shook him to his core. Long into the night he labored to resolve it - he was really worried. But finally he resolved it. Einstein was seen sitting there, smiling and literally tipped his hat to Bohr - he knew he was beaten - and by his own equivalence principle at that.

From that point on he never attacked the actual consistency of QM - he accepted it as a correct theory. However until his dying day he believed it incomplete - ie it was just an approximation to a more complete theory, had some hidden variables or something like that. We have versions today he would be happy with such as DBB - although if I remember correctly he thought it was a bit too naive The statements he believed it actually wrong or didn't understand it are incorrect. As I mentioned in my previous post in the other thread he believed Dirac's presentation was the best treatment and kept a copy of his book close at all times. He knew QM very well. He even came up with his own interpretation that got rid of the issues he thought QM had. His main objection was in fact to Copenhagen whose main tenants at that time (it's modern version is likely different because it contains things we now know are strictly speaking wrong such as the wave-particle duality - these days many Copenhagenists have taken on Consistent Histories which is lot more complete and modern) I will detail (from a site that detailed them - there is a bit of variation on exactly what they are) so we can see just what Einstein did not like:

1. A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)
2. The description of nature is essentially probabilistic, with the probability of an event related to the square of the amplitude of the wave function related to it. (The Born rule, after Max Born)
3. It is not possible to know the value of all the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)
4. Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.
5. Measuring devices are essentially classical devices, and measure only classical properties such as position and momentum.
6. The quantum mechanical description of large systems will closely approximate the classical description. (The correspondence principle of Bohr and Heisenberg)

Popularizations concentrate on he didn't like probabilities coming into it. That's not quite right - he made foundational contributions to statistical mechanics and had no trouble with that. No it was something else - in fact it was number 1:
A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)

He did not like this at all, and in fact it was an anathema to his view of an objective reality that Einstein believed science explained - not described - no he thought science explained the world around us:
'I want to know how God created this world. I'm not interested in this or that phenomenon, in the spectrum of this or that element. I want to know His thoughts, the rest are details.'

This is Einsteins real objection - non locality etc is just one of the means he wanted to show it can't be like that. That is the crux of the matter.

Just as an aside both Bohr and Einstein were wrong as Weinberg explains:
http://physicstoday.scitation.org/doi/full/10.1063/1.2155755

What do I believe? I believe the purpose of science is to describe - not explain mind you, although it will often shed light on that - but to describe it. Like for example saying two apples sit on a table is not actually two apples sitting on the table - but just describing it - this is often paraphrased as the map is not the territory.

Are real numbers reality? Well simply look at their definition. Have a look at the least upper bound axiom? Is that real? How would you even test it? No - its not real, like a table that kicks back if you kick it. What it is, is simply, like English, something that has proven useful in describing reality - whatever that is.

Added Later:
I forgot to mention - is the above philosophy - possibly - I will leave it to others to decide that one - but point taken. Feynman was like me - a bit anti philosophy. That in itself is a philosophy - as I said before likely a lot of circularity in these foundational issues.

Thanks
Bill

 

[MathematicalPhysicist]

Life goes in circles...

 

[Buzz Bloom]

We have versions today he would be happy with such as DBB

Hi bhobba:

I searched for what "DBB" stands for on the Internet, but I failed to find it. Please provide the meaning.

Regards,
Buzz

 

[bhobba]

:I searched for what "DBB" stands for on the Internet, but I failed to find it. Please provide the meaning.

De-Broglie Bohm - sometimes called BM or Bohmian Mechanics:
https://arxiv.org/abs/quant-ph/0611032

Thanks
Bill

 

[Stephen Tashi]

Hi All

Popularizations concentrate on he didn't like probabilities coming into it. That's not quite right - he made foundational contributions to statistical mechanics and had no trouble with that.

The traditional viewpoint of statistical mechanics is that it deals with "ensembles". The "ensemble" point of view in classical thermodynamics seems to be an attempt to circumvent probabilities by replacing them with actual observed frequencies. By analogy, instead of thinking of the probability of 1/2 that a fair coin lands heads, we would think of "the ensemble" of all fair coin tosses and say half them them result in heads.

In the classical context I, myself, don't find that approach to "ensembles" convincing. In the first place, the ensemble would have to be a finite set in order to have a definite frequency associated with it. The definition of an ensemble isn't precise. For example, in the case of a fair coin, are we thinking of all possible tosses of a fair coin that have occurred in history? Do we include tosses that will be done in the future? Do we only include tosses done in laboratory setting? Also, when analyzing experiments, they are modeled by assuming the member(s) of the ensemble used in the experiment are chosen at random from those in the ensemble - so probably renters the picture.

The current Wikipedia article on the ensemble interpretation of QM https://en.wikipedia.org/wiki/Ensemble_interpretation says:

Einstein perhaps sometimes seemed to interpret the probabilistic "ensemble" as a preparative ensemble, recognizing that the preparative procedure does not exhaustively fix the properties of the system; therefore he said that the theory is "incomplete".

( The phrase "perhaps sometimes seemed" isn't very assertive!) Did Einstein think that the ensemble point of view naturally leads to existence of hidden variables? For example, in the ensemble of fair coin tosses, if we think them as already existing, we could trivially assign a hidden variable R taking values "H" or "T" to each toss.

 

[bhobba]

Did Einstein think that the ensemble point of view naturally leads to existence of hidden variables? For example, in the ensemble of fair coin tosses, if we think them as already existing, we could trivially assign a hidden variable R taking values "H" or "T" to each toss.

I think he did - but there is no way to be sure. It had to be modified slightly as well in light of the Kochen-Specker theorem - this was done by Ballentine - but with our current knowledge of decoherence, in the ignorance ensemble interpretation (which is just a slight modification of the ensemble to include decoerence) it's more like Einstein envisaged.

Your probabilistic type arguments are as old as probability has been around for. The ensemble, based of course on the Strong Law Of Large Numbers, must be infinite to work. That of course is physically unrealizable. What you usually do is something like is done in the intuitive presentation of the calculus with thinking of dx as so small - but not actually zero - you can FAPP take it as zero - you imagine something so large - a googleplex^googleplex say, but still finite, that for all practical purposes behaves like an infinite one. That of course will be argued against - but really is something that has never been resolved so everyone agrees on the answer. As John Baez says many issues on interpreting QM are really just rehashes of the same issues in probability:
http://math.ucr.edu/home/baez/bayes.html

Copenhagen is more like the Bayesian interpretation of probability - Ensemble more like the frequentest. Einstein strongly believed in an objective reality out there and saw no place for the subjective entering into physics. This was his objection and why he chose the Ensemble. He likely would have had the same issues with the Bayesian view of probability.

Thanks
Bill

 

[Buzz Bloom]

http://www.spaceandmotion.com/quantum-mechanics-richard-feynman-quotes.htm

"I think it is safe to say that no one understands Quantum Mechanics."​

I have always felt that Feynman meant by this that there is a fundamental property concerning quantum mechanics which prevents any complete explanation using any natural language about what is actually happening regarding quantum mechanics phenomenon.

 

[jerromyjon]

I have always felt that Feynman meant by this that there is a fundamental property concerning quantum mechanics which prevents any complete explanation using any natural language about what is actually happening regarding quantum mechanics phenomenon.

I take that a step further, QM prevents any complete explanation using natural comprehension of physics. Neither the language of English nor mathematics (to date) can fully describe quantum phenomena completely.

 

[PeterDonis]

I have always felt that Feynman meant by this that there is a fundamental property concerning quantum mechanics which prevents any complete explanation using any natural language about what is actually happening regarding quantum mechanics phenomenon.

I don't think he necessarily meant such an explanation was impossible, just that nobody actually knew one.

 

[bhobba]

I take that a step further, QM prevents any complete explanation using natural comprehension of physics. Neither the language of English nor mathematics (to date) can fully describe quantum phenomena completely.

In terms of everyday pictures - yes. But mathematically? I think we have that down pat.

Einstein for example had zero problems with the math of QM, in fact greatly admired Dirac's very beautiful presentation, carrying his textbook with him at all times. The only issue he had is - what does the math mean? He had his own view of that - the Ensemble Interpretation, but of course not everyone agrees (to put it mildly). But just like Copenhagen is still around today, so is the Ensemble - both have changed a bit of course in light of current knowledge - but basically are still viable - although many Copenhagenst's have moved to Decoherent Histories (which interestingly was Feynman's choice towards the end) and I personally update the Ensemble with decoherence giving the Ignorance Ensemble. The issues are still with us. Interestingly Ballentine, the modern champion of the Ensemble, doesn't think decoherence is important as far as interpretations go - it of course is very important in things like actually implementing a quantum computer - but for interpretations of no real value:
https://link.springer.com/content/pdf/10.1007/s10701-008-9242-0.pdf

With all due respect to him, and his beautiful textbook I disagree - but it would be remiss not to present his views.

Thanks
Bill

 

[Zafa Pi]

From that point on [1930] he never attacked the actual consistency of QM - he accepted it as a correct theory.

In 1935 EPR claimed the Heisenberg Uncertainty Principle was invalid. That seems like an attack.

it contains things we now know are strictly speaking wrong such as the wave-particle duality

Wave-particle duality to me is that some measurements of a photon make it seem wave like and other measurements make it seem particle (bullet) like. For instance, the double slit experiments. What's wrong with that? Admittedly, I don't know what it means to say a photon is simultaneously both a wave and a particle.

he [Einstein] accepted it as a correct theory

But Weinberg in the article you linked to said, "Einstein’s rejection of quantum mechanics contributed, in the years from the 1930s to his death in 1955, to his isolation from other research in physics"
I think you are correct and Weinberg is not. Furthermore Weinberg criticism of Bohr does not fault Copenhagen.In the previous thread you said, "Although I never understood much of what Bohr wrote, especially Complementary, his ideas while subtle, were not, well I won't mince my words, mystical gibberish."
Complementarity to me says, for a certain observable A on a subspace there is another B on the same subspace with [A,B] (commutator) ≠ 0, and perhaps with maximal norm. E.g. position and momentum operators, or PauliX and PauliZ.

Bohr's response to the EPR paradox was something like, "There are no values for experiments not made." To me (with modern terminology) they disagreed over the validity of counterfactual definiteness. And Bell proved that if locality holds then CFD does not.

 

[Zafa Pi]

The ensemble, based of course on the Strong Law Of Large Numbers, must be infinite to work

Not necessary. See Nelson.

 

[bhobba]

In 1935 EPR claimed the Heisenberg Uncertainty Principle was invalid. That seems like an attack.

The quote I think you are referring to is:
'The essence of the paradox is that particles can interact in such a way that it is possible to measure both their position and their momentum more accurately than Heisenberg's uncertainty principle allows, unless measuring one particle instantaneously affects the other to prevent this accuracy, which would involve information being transmitted faster than light as forbidden by the theory of relativity ("spooky action at a distance"). This consequence had not previously been noticed and seemed unreasonable at the time; the phenomenon involved is now known as quantum entanglement.'

Notice the out 'unless measuring one particle instantaneously affects the other to prevent this accuracy'. He was trying to show that it was not complete - rather than actually wrong. But interestingly in another thread it was pointed out to me something I didn't know - you learn somthing all the time - see attached.

It seems even though his name was on the paper, it wasn't necessarily his view - his real objection was separability.

But point taken - it is a bit of a fine line saying he accepted QM but thought it incomplete not incorrect. I think it was like stochastic mechanics - its real basis is classical mechanics - one uses statistical methods as a practical matter.

Wave-particle duality to me is that some measurements of a photon make it seem wave like and other measurements make it seem particle (bullet) like. For instance, the double slit experiments. What's wrong with that? Admittedly, I don't know what it means to say a photon is simultaneously both a wave and a particle.

Did you read the section about it in the myths paper - its in there.

But Weinberg in the article you linked to said, "Einstein’s rejection of quantum mechanics contributed, in the years from the 1930s to his death in 1955, to his isolation from other research in physics" I think you are correct and Weinberg is not. Furthermore Weinberg criticism of Bohr does not fault Copenhagen.

What I was referring to is the following:
http://physicstoday.scitation.org/doi/full/10.1063/1.2155755
'All this familiar story is true, but it leaves out an irony. Bohr’s version of quantum mechanics was deeply flawed, but not for the reason Einstein thought. The Copenhagen interpretation describes what happens when an observer makes a measurement, but the observer and the act of measurement are themselves treated classically. This is surely wrong: Physicists and their apparatus must be governed by the same quantum mechanical rules that govern everything else in the universe. But these rules are expressed in terms of a wavefunction (or, more precisely, a state vector) that evolves in a perfectly deterministic way. So where do the probabilistic rules of the Copenhagen interpretation come from?'

I

n the previous thread you said, "Although I never understood much of what Bohr wrote, especially Complementary, his ideas while subtle, were not, well I won't mince my words, mystical gibberish."
Complementarity to me says, for a certain observable A on a subspace there is another B on the same subspace with [A,B] (commutator) ≠ 0, and perhaps with maximal norm. E.g. position and momentum operators, or PauliX and PauliZ. Bohr's response to the EPR paradox was something like, "There are no values for experiments not made." To me (with modern terminology) they disagreed over the validity of counterfactual definiteness. And Bell proved that if locality holds then CFD does not.http://physicstoday.scitation.org/doi/full/10.1063/1.2155755

Of course Borhr did not sprout mystical gibberish - he made a deep and subtle attempt to come to grips with QM. My issue with complementary is for me its trite and vacuous. Take a coin. Over where I live you have a picture of the queen on one side and an animal of some sort on the other. So it can be like a queen or an animal depending on which side is up. But really its money. It's true - but so - I just don't get it - it says - well to me nothing. But I am no Bohr - one of the true greats. We know what a coin is - the rest IMHO is trite and useless. Just my view of course. Bohr obviously had something in mind that I just do not get. QM is QM - a coin is a coin - that's it. He could mean something like what you say - but if that's what he meant that's what he should have said. But like I said he was subtle - as you can guess I think the central issue is I am not.

Thanks
Bill

 

[vanhees71]

I take that a step further, QM prevents any complete explanation using natural comprehension of physics. Neither the language of English nor mathematics (to date) can fully describe quantum phenomena completely.

Where does this impression come from? It's not true since there's no phenomenon known yet that contradicts QT. The only big trouble we have is that we cannot describe gravity in a fully consistent quantum theory. Finally one should be aware that math is not only the most adequate but the only language to express what physics and thus all other natural sciences are about. Without math you cannot even talk about physics, at least not in a fully comprehensive way.

 

[jerromyjon]

But mathematically? I think we have that down pat.

Where does this impression come from?

I was referring to my belief and I'm pretty sure Einstein believed QM is incomplete. I simply mean that math predicts what can be known (observables), but there must be something going on "behind the scenes" that the theories are silent about, not to get off on a tangent about locality, reality, gravity and whatnot. I have no doubts that quantum physics models reality to stunning accuracy, but I do believe there is more to be uncovered.

 

[jerromyjon]

In terms of everyday pictures - yes. But mathematically? I think we have that down pat.

What of renormalization? I'm sure many just shut up and calculate and it works, but doesn't that seem to indicate something is missing? I'm curious what Einstein thought of it. (Trying to stay on topic)

 

[jerromyjon]

He [Einstein] had his own view of that - the Ensemble Interpretation

But the Ensemble doesn't solve this problem, explained as a quote from the "Kochen-Specker" wikipedia:
"The theorem proves that there is a contradiction between two basic assumptions of the hidden variable theories intended to reproduce the results of quantum mechanics: that all hidden variables corresponding to quantum mechanical observables have definite values at any given time, and that the values of those variables are intrinsic and independent of the device used to measure them."
If you can't say what happens between observations, other than waves of probabilistic intensity, then something on the macroscopic determinism is lost in the grey space, don't you think?

 

[Stephen Tashi]

I personally update the Ensemble with decoherence giving the Ignorance Ensemble.

When I search for "ignorance ensemble", I find only posts by you. So, from the horse's mouth, what exactly is the ignorance ensemble?

 

[jerromyjon]

what exactly is the ignorance ensemble?

I think that is one of his "catch-phrases".
https://www.physicsforums.com/threads/can-someone-explain-the-ignorance-ensemble-theory.747446/

 

[vanhees71]

I was referring to my belief and I'm pretty sure Einstein believed QM is incomplete. I simply mean that math predicts what can be known (observables), but there must be something going on "behind the scenes" that the theories are silent about, not to get off on a tangent about locality, reality, gravity and whatnot. I have no doubts that quantum physics models reality to stunning accuracy, but I do believe there is more to be uncovered.

That's always true. As I said, the great unsolved problem of contemporary physics is to find a consistent QT of gravitation. I've no clue what the solution of this problem might be (or whether there is a solution at all), but I'm sure about one thing: It will not come from esoterical philosophical gibberish but hard theoretical and experimental work, as has been the case for all the great successes of modern science starting from Galileo and Newton!

 

[vanhees71]

What of renormalization? I'm sure many just shut up and calculate and it works, but doesn't that seem to indicate something is missing? I'm curious what Einstein thought of it. (Trying to stay on topic)

Renormalization is a very well understood procedure to evaluate scattering matrix elements within perturbative quantum field theory. I don't know, whether Einstein ever looked at the developments of early renormalization theory (which started around 1948 with the famous Shelter Island and Pocono conferences). For a brillant book on the history of particularly this subject, see S. Schweber, QED and the Men who Made it.

 

[jerromyjon]

It will not come from esoterical philosophical gibberish but hard theoretical and experimental work, as has been the case for all the great successes of modern science starting from Galileo and Newton!

I'm not sure how to understand the word "esoteric" or how it might pertain exclusively to philosophical types, but I agree that it will take clever experiments and brilliant minds to unravel the mysteries. Beyond the obvious need for gravity to be unified there are still yet unanswered mechanics involved in QM.

 

[bhobba]

I was referring to my belief and I'm pretty sure Einstein believed QM is incomplete.

Einstein strongly believed in aa reality independent of us. Conceptional Copenhagen cast doubt on that so Einstein 'rebelled'. That's it in a nutshell.

I simply mean that math predicts what can be known (observables), but there must be something going on "behind the scenes"

That's the crux isn't it. You like Einstein obviously strongly believe that. But as Bohr said to Einstein - stop telling God what to do. Despite how you feel about it nature does not have to oblige - there may be nothing behind the math - that may be all there is. You probably will not like that - and jump up and down etc - but its true - it could just be like that. Want to argue the point? We do not discuss that here - go over to the philosophy forums if that is you intent - here we simply accept it - nature is as nature is - that's it. We have various interpretations - and understanding what they say is fair game here -but without experimental evidence any could be correct - even very minimal ones like I believe in such as the Ensemble. There may be nothing deeper.

Thanks
Bill

 

[bhobba]

What of renormalization? I'm sure many just shut up and calculate and it works, but doesn't that seem to indicate something is missing? I'm curious what Einstein thought of it. (Trying to stay on topic)

It was sorted out by Wilson and he got a Nobel for it.

I also wrote an insight article explaining it at the very basic level:
https://www.physicsforums.com/insights/renormalisation-made-easy/

But basically we know:
1. Its cause - likely the result of our perturbative approach to QFT. It's solved by realizing in that approach some constants such as the electric field coupling are cutoff dependent.
2. You can do it without re-normalization if you want - no infinities at all arise in that approach - its just not as common. There is a textbook that does QED that way - can't recall its name - some others might like ot chime in.

I think Uris's series on QFT explains it all - but he is a mathematical physicist and you require considerable mathematical sophistication to follow it. I have a degree in math, and have read quite a bit beyond that - it stretches me to my limit. But is still one of my favorite insight series.

Thanks
Bill

 

[bhobba]

When I search for "ignorance ensemble", I find only posts by you. So, from the horse's mouth, what exactly is the ignorance ensemble?

See:
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf

Go to section 3.1 - see the ignorance interpretation:
Ignorance interpretation: The mixed states we find by taking the partial trace over the environment can be interpreted as a proper mixture. Note that this is essentially a collapse postulate.

I simply add that to the Ensemble - hence Ignorance Ensemble.

For a more detailed account see:
https://www.amazon.com/dp/3540357734/?tag=pfamazon01-20

Schlosshauer carefully examines the measurement problem. It has three parts I will not detail here - see the book. The key one is how does an improper mixed state become a proper one - that we do not know. My interpretation is simple - somehow.

Thanks
Bill

 

[bhobba]

IBeyond the obvious need for gravity to be unified there are still yet unanswered mechanics involved in QM.

That's your view about the mechanics - gravity is 100% correct - its a big unsolved problem.. On this forum we are humble enough to say - we don't know if there are unanswered questions or not. I personally, with regard to standard QM, do not think there is. But I may be wrong.

To be honest you will get a lot further in physics by taking my attitude ie I think I know the answer but I may be wrong. In fact that's the essence of science as explained by the master himself - Feynman:


Science is guess, experiment, guess, over and over. If experiment does not say what your guess says - then its wrong. It's that simple. You can have all sorts of opinions such as 'there are still yet unanswered mechanics involved in QM.' - but unless you can put them to the test then its so much hot air.

There is an old joke in physics. Whatever happened to so and so - he looked so promising. He became primarily concerned with what QM means. The response was - then he is lost. If you become overly worried by that you too will be lost.. That's why Einstein was lost in his later years - he had a certain view that may indeed be correct - but it was not testable so he really got nowhere - at least by his lofty standards - of course he still wrote interesting and provocative papers - but they didn't really lead anywhere, except in one case - Bell. I often wonder just what other great things he could have accomplished if he had more of the attitude I suggest.

There have been a number of excellent texts mentioned here. Just get the Feynman Lectures - study it and put your personal concerns to one side - and you will make progress - don't and you will get basically nowhere - just like everyone else who went down that path - even the great Einstein.

Thanks
Bill

 

[bhobba]

Not necessary. See Nelson.

That interesting - but I will need to study it. Getting the time is the issue.

I wish it was true because it would solve a lot of issues explaining the Ensemble interpretation.

I saw a proof of it in my undergrad years - but it was hard. Terry Tao has I think a better proof:
https://terrytao.wordpress.com/2008/06/18/the-strong-law-of-large-numbers/

Thanks
Bill

 

[vanhees71]

2. You can do it without re-normalization if you want - no infinities at all arise in that approach - its just not as common. There is a textbook that does QED that way - can't recall its name - some others might like ot chime in.

Bill

You can't do it without renormalization since renormalization is an empirical fact. E.g., the running of the electromagnetic coupling is measured. At a scale of $M_Z \simeq 90 \; \text{GeV}$ the fine structure constant bekomes about 1/128 instead of 1/137 at low momenta ("on-shell" scheme). The same holds for the running of the strong coupling $\alpha_{\text{s}}$, which proves asymptotic freedom (i.e., it gets smaller at higher scales rather than larger as in non-Abelian QED).

What you mean is that you can do without illdefined diverging integrals, and that's called the Epstein-Glaser or causal approach. The cuplrit of the infinities is not the physical theory but our sloppy treatment of distribution valued operators. If you use "smeared operators", everything is finite, but as Wilson's point of view makes evident, the parameters of the theory (wave-function normalization, masses, couplings) depend on the renormalization scale, and this is physics not an artifact of the formalism. The great importance of Wilson's work is this insight, i.e., that renormalization is not sweeping the garbage under the rug (as Feynman criticized the renormalization procedure he helped to discover in the late 1940ies) but has a physical meaning (not only in scattering theory of a few particles ("vacuum QFT") but the more and in some sense more intuitive in statistical many-body theory, where coarse graining is at the heart of the entire formalism, and there you have to choose the adequate "resolution" of your observables to begin with; the consistency between looking at the system at different "resolution scales" is provided by the renormalization group, and Wilson's reformulation of it from this point of view is the ingeneous insight which lead to his well deserved Nobel prize.

A good book on Epstein-Glaser renormalization is

G. Scharf, Finite Quantum Electrodynamics, Springer-Verlag, 1989.

I personally prefer the more pragmatic BPHZ renormalization, which also doesn't need a regularization procedure, but reads the Feynman diagrams simply as the integrands of the loop integrals, does the subtractions (at a chosen renormalization scale or in a chosen renormalization scheme) on the level of the integrands and only then performs the integration. Also in this approach only well-defined finite integrals occur, and the idea of the renormalization-scale dependence is built in in a very intuitive way from the beginning. Of course the use of the "smeared operators" in the EG approach also inevitable introduces a scale which has directly the Wilsonian physical meaning.

Of course for practical purposes, an intermediate regularizaion is a very convenient tool (at least for strictly perturbative calculations). The most convenient one is dimensional regularization, which has the pedagogical drawback of hiding the Wilsonian meaning of the introduction of the renormalization scale somewhat, because in dim. reg. it's simply introduced to keep the dimensions of the parameters of the QFT models the same in all space-time dimensions, and then you analytically continue to analytic functions of space-time dimensions, which is a rather abstract way, but of course you get the same results as with any other technique, and often in a much more convenient way, keeping the regularized theory always gauge invariant (provided it's a gauge theory you deal with).

 

[Demystifier]

You can't do it without renormalization since renormalization is an empirical fact. E.g., the running of the electromagnetic coupling is measured.

Well, we don't really measure running of coupling constants. In fact, we don't even measure coupling constants. (This is one of the things explained greatly in the Zee's QFT, that you hate.) What we measure are cross sections and their dependence on energy. The running of coupling constant is our interpretation of measured energy dependence of cross sections, stemming from our choice to interpret everything in terms of tree-level amplitudes.

 

[vanhees71]

Of course, we measure cross sections and parametrize them with our models, confirming the predictions of the RG solutions for the running coupling. That's what I'd call "measuring the coupling constant". Of course Zee may write as many things in his confusing book as he likes...

 

[MathematicalPhysicist]

Of course Zee may write as many things in his confusing book as he likes...

:-D LOL

 

[Zafa Pi]

I wrote, "Wave-particle duality to me is that some measurements of a photon make it seem wave like and other measurements make it seem particle (bullet) like. For instance, the double slit experiments. What's wrong with that? Admittedly, I don't know what it means to say a photon is simultaneously both a wave and a particle."
And you responded:

Did you read the section about it in the myths paper - its in there.

Myths paper? Is there something wrong with what I wrote?

So where do the probabilistic rules of the Copenhagen interpretation come from?'

In QM they come from the definition of a measurement as a random variable (probability of getting an eigenvalue), and in the lab measuring a polarized photon with a polarization analyzer.
Nothing in Copenhagen need be said about what transpires to obtain those values or what evolution the state of the photon goes through to its post measurement state (collapse).
Bohr should have remained silent about an observer and the status of the device, as did Newton when asked how masses pull off their mutual attraction.
It is not testable whether decoherence provides the answer. That the combined system of photon and device satisfy the deterministic unitary evolution of QM is all well and good, yet like a classical coin flip no one can predict the outcome so it is modeled stochastically.

 

[Zafa Pi]

Science is guess, experiment, guess, over and over. If experiment does not say what your guess says - then its wrong. It's that simple. You can have all sorts of opinions such as 'there are still yet unanswered mechanics involved in QM.' - but unless you can put them to the test then its so much hot air.

Even for me this is a bit simplistic. There has been an infinity of bad experiments, if you include the social sciences then the cardinality is c. Recently the Italians showed the relativity guess was wrong, since neutrinos go faster than light. And speaking of infinity,

I saw a proof of it in my undergrad years - but it was hard. Terry Tao has I think a better proof:
https://terrytao.wordpress.com/2008/06/18/the-strong-law-of-large-numbers/

His proof involves infinite sequences of r.v.s, which is what I thought you want to avoid.

 

[bhobba]

A good book on Epstein-Glaser renormalization is G. Scharf, Finite Quantum Electrodynamics, Springer-Verlag, 1989.

That's the book. Thank's for clarifying that - you read in places things like: Scharf presents a textbook for a course on quantum field theory that uses the causal method developed by Stückelberg and Bogoliubov during the 1950s, to make sure that no infinity appears. On refection you realize that's not quite the same thing as no re-normalization - but without thinking you can be fooled.

I also read in Dirac page 311 that he managed to do it without re-normalization in - Lectures On Quantum Field Theory. But he used the Heisenberg picture - and said - I quote - The calculation of the Lamb shift and anomalous magnetic moment are rather complicated. I hate to think of a calculation Dirac would call 'rather complicated' - the mind boggles. Any idea how he avoided it? I suspect he didn't - just had some sleight of hand so speak to circumvent it explicitly - but of course only conjecturing.

I personally prefer the more pragmatic BPHZ renormalization, which also doesn't need a regularization procedure, but reads the Feynman diagrams simply as the integrands of the loop integrals, does the subtractions (at a chosen renormalization scale or in a chosen renormalization scheme) on the level of the integrands and only then performs the integration. Also in this approach only well-defined finite integrals occur, and the idea of the renormalization-scale dependence is built in in a very intuitive way from the beginning. Of course the use of the "smeared operators" in the EG approach also inevitable introduces a scale which has directly the Wilsonian physical meaning.

I have read of others such as what one book called standard re-normalization and it consisted of shuffling infinities around. Didn't understand it, thought it total bunkum, and still think it's bunkum. Then it said there is another, totally equivalent method called BPHZ re-normalization - instantly everything was clear. It's the only method I understand. Others simply leave me cold. Have zero idea how they show its equivalent to the usual re-normalization since to me its totally bogus - but that's the claim.

Thanks
Bill

 

[bhobba]

Myths paper? Is there something wrong with what I wrote?

I think I posted what Copenhagen was about the time of Bohr - but for completeness will do it again:

1. A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)
2. The description of nature is essentially probabilistic, with the probability of an event related to the square of the amplitude of the wave function related to it. (The Born rule, after Max Born)
3. It is not possible to know the value of all the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)
4. Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.
5. Measuring devices are essentially classical devices, and measure only classical properties such as position and momentum.
6. The quantum mechanical description of large systems will closely approximate the classical description. (The correspondence principle of Bohr and Heisenberg)

Now let's look specifically at principle 4 - wave-particle duality:
Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.

To examine it more carefully let's see what that paper says:

In introductory textbooks on QM, as well as in popular texts on QM, a conceptually strange character of QM is often verbalized in terms of wave-particle duality. According to this duality, fundamental microscopic objects such as electrons and photons are neither pure particles nor pure waves, but both waves and particles. Or more precisely, in some conditions they behave as waves, while in other conditions they behave as particles. However, in more advanced and technical textbooks on QM, the wave-particle duality is rarely mentioned. Instead, such serious textbooks talk only about waves, i.e., wave functions ψ(x, t). The waves do not need to be plane waves of the form ψ(x, t) = e^i(kx−ωt) but, in general, may have an arbitrary dependence on x and t. At time t, the wave can be said to behave as a particle if, at that time, the wave is localized around a single value of x. In the ideal case (see the equation in the paper - it involves that dreaded Dirac Delta Function) then the position x of the particle has a definite value x The state is the eigenstate of the position operator, with the eigenvalue x. Typically, the wave attains such a localized-particle shape through a wave-function collapse associated with a measurement of a particle position. Moreover, the wave may appear as a point like particle for a long time if the particle position is measured many times in sequence with a small time interval between two measurements. This makes the wave to appear as a classical particle with a trajectory, which occurs, e.g., in cloud chambers. However, the position operator is just one of many (actually, infinitely many) hermitian operators in QM. Each hermitian operator corresponds to an observable, and it is widely accepted (which, as we shall see later, is also one of the myths) that the position operator does not enjoy any privileged role. From that, widely accepted, point of view, there is nothing dual about QM; electrons and photons always behave as waves, while a particle like behavior corresponds only to a special case. In this sense, the wave-particle duality is nothing but a myth. But why then the wave-particle duality is so often mentioned? One reason is philosophical; the word “duality” sounds very “deep” and “mysterious” from a philosophical point of view, and some physicists obviously like it, despite the fact that a dual picture is not supported by the usual technical formulation of QM. Another reason is historical; in early days of QM, it was an experimental fact that electrons and photons sometimes behave as particles and sometimes as waves, so a dual interpretation was perhaps natural at that time when quantum theory was not yet well understood. From above, one may conclude that the notion of “wave-particle duality” should be completely removed from a modern talk on QM. However, this is not necessarily so. Such a concept may still make sense if interpreted in a significantly different way. One way is purely linguistic; it is actually common to say that electrons and photons are “particles”, having in mind that the word “particle” has a very different meaning than the same word in classical physics. In this sense, electrons and photons are both “particles” (because we call them so) and “waves” (because that is what, according to the usual interpretation,they really are). Another meaningful way of retaining the notion of “wave-particle duality” is to understand it as a quantum-classical duality, because each classical theory has the corresponding quantum theory, and vice versa. However, the word “duality” is not the best word for this correspondence, because the corresponding quantum and classical theories do not enjoy the same rights. Instead, the classical theories are merely approximations of the quantum ones.

BTW in the above wave does not mean an actual wave - it is short for wave-function.

Now look again at the wording:
Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.

You are correct in saying sometimes it seems like a particle, and sometimes it seems like a wave. To be even plainer - there is nothing wrong with it at all. But that isn't what the above says - especially the bit: in some experiments both of these complementary viewpoints must be invoked to explain the results. It never needs to be invoked - period. A wave-function is simply the representation of a state in terms of position eigenvectors. That's all that needs to be invoked - nothing at all to do with wave-particle duality - its simply how some results 'seem' that way, as you say but only in very special circumstances. In virtually all circumstances it acts neither like a particle or a wave. Its OK to talk about this stuff in popularization's and/or beginner texts (although I wouldn't) but once one becomes more advanced it confuses more than illuminates because you now deal with all sorts if things - like a particle in a well, the hydrogen atom., the harmonic oscillator - none of which it acts like a particle or a wave. Yet student have been told it does. If you go back and correct that to something like you say - OK - but why bother - simply don't use it in the first place. Its a concept that is simply not needed.

Its not a founding principle of QM (merely what QM says in some special circumstances), its simply a left over form the early days of QM before it was understood as well as it is now, I would argue ever since Dirac published his textbook it should have been banished - but has hung on, and on, and on.

Yes - I agree Bohr should have remained silent about the status of the measuring device - but IMHO Bohr should have remained silent about a lot of things since I think much of what he says confuses rather than illuminates. That's just my view - he obviously was one of the greatest physicists that ever lived and grappled with QM as well as anyone could at the time - except maybe Dirac. But then again for Dirac it was - the math ma'am, just the math. Many do not have that attitude.

Thanks
Bill