# B What is Quantum Interference?

1. Dec 26, 2017

### MichPod

But really, really after this long discussion, if a layman asks what is the quantum interfernce, what answer is possible other than:
"We do have a very powerful theory with which (among the other things) we can CALCULATE such an interference, but otherwise we do not know."
How is this possible answer wrong?

2. Dec 26, 2017

### PeroK

You asked me what is quantum interference and I gave you an answer. So, the answer isn't "I don't know".

If you ask me "why does nature exhibit an intrinsic randomness", then the answer to that is "I don't know".

3. Dec 26, 2017

### MichPod

Btw, I was not the topic starter.

Do I understand you right that the answer is along the following - the nature is random and this radomness is according to some very special sort of pobability theory (i.e. probability amplitudes instead of just probabilities of the regular probability theory) etc. Then how many QM physicists will agree with this explanation?

4. Dec 26, 2017

### PeroK

The "minimal statistical interpretation" is at the heart of QM. That's the core of mainstream QM.

There are also "interpretations" on top of this, which explain further in some way how things work. I learned the Copenhagen interpretation - wave function "collapse" etc.

There is general agreement that the interpretations are different ways for humans to makes sense of QM. It is possible that one interpretation will be proved correct and then our understanding may go deeper.

The statistical nature of quantum interference, though, is not really in doubt.

5. Dec 26, 2017

### Staff: Mentor

This is a pop science book, not a textbook or peer-reviewed paper.

Everyone, please keep the discussion focused on physics, not philosophy, and on acceptable sources--textbooks and peer-reviewed papers--not pop science.

6. Dec 26, 2017

### Staff: Mentor

Even after I explained just how terms like physical reality are very ill defined and loaded you simply don't seem to get it. We know a deeper explanation of solar eclipses than just the patterns they seem to follow that the ancients knew. Does that mean we know the physical reality - of course not.

Physics is a mathematical model - its relation to this thing you called physical reality first needs a definition of physical reality many many of which exist, so many its useless. Think in terms of mathematical models (just like in Euclidean Geometry where you don't argue about what a point or line is 'in physical reality' - you just accept the obvious) - in your example Newton gave us a better mathematical model, Einstein an even better one - that's it - that's all. Do physicists believe we are getting closer to some truth about the world - of course - eg see Wienberg:

But it is not expressed in the terms you use which are very 'contentious' - its expressed in the language of math.

Note the similarity between Wittgenstein that Kuhn eventually degenerates into. Just like Turing Weinberg, correctly IMHO, takes exception to this view - 'All this is wormwood to scientists like myself, who think the task of science is to bring us closer and closer to objective truth.'

But the language of that objective truth is math and its correspondence so experiments can be done to check it, just like Euclidean Geometry, is not philosophical - but pretty easy to see using little more than common-sense and knowledge of the theory.

Thanks
Bill

Last edited: Dec 26, 2017
7. Dec 27, 2017

### vanhees71

Well, if you are asking why the world is as it is or what's "behind the phenomena" it's something at least touching on religious questions, and it's beyond what you can get answered by science, because science restricts itself to that part of human experience which is reproducibly and objectively observable and even quantatively measurable. By construction the outcomes of this method are independent of any opinion or worldview the researchers using it might be. That's also evident from the history of science. E.g., many ideas of the great discoveries in the physics of the 2nd half of the 20th century, mostly about quantum field theory (relativistic as well as non-relativistic) and many-body theory, have been quite independently developed in the eastern and the western part of the world then divided by the Cold War. Of course, both worlds where not completely isolated, but nevertheless many ideas and results were achieved independently in slightly different approaches but leading to precisely the same result. That's also why, by construction, there can never be any real tension between religious believes (be it in terms of one of the "world religions" or atheism or whatever type of believe you might think of) and science: It's just about different realms of human experience.

8. Dec 27, 2017

### vanhees71

Physics is not a mathemtical model. A "mathematical model" I'd define as a certain set of axioms (e.g., the axioms of Euclidean geometry) which can be freely invented. Of course you are constrained by the fact that the axioms should not contradic themselves in an obvious way (although according to Gödel for any sufficiently interesting set of axioms you can never prove this consistency within this system of axioms itself), but otherwise you are pretty free to invent anything.

Physics is first of all an empirical science. It's about observation of phenomena in nature that show some regularity and pattern in the sense that you can reproduce these observations in an objective way, i.e., if you find something in a certain arrangement (in experiments that's called "preparation"), then you always find the same observational results (and be it only in a statistical sense). In the history of the modern sciences it turned out that you can make observations quantitative by defining measures for the most importantant quantities involved, starting from the geometrical quantity of length, the duration of times, and mass (as a measure for inertia). Already with this quite limited set you can describe everything what's now called "classical mechanics", and with the work of physicists like Galilei and Newton this could brought into an elegant mathematical system of "Natural Laws", now called Newtonian Mechanics. It's very powerful, giving us all the theoretical tools needed to construct all kinds of machines, including such a phantastic possibility as flying to the moon or landing a little lab at the spot of a tiny comet on the spot after a decade-long journey with some spectacular maneuvres all following Newtons laws as predicted, but nevertheless all this is based on observational facts, and the theory follows these observational facts, reducing the basic ones to an astonishingly simple handful of "fundamental laws" that finally can be cast into symmetry principles.

Of course, from this point on it's very mathematical, nearly like pure mathematics starting from a few axioms and building up a platonic world, but one must not forget that it's just the result of a lot of empirical evidence made ever more precise with the progress of technology of observation. As any empirical finding, it's always bound to be incomplete, and indeed the first evidence that Newtonian Mechanics cannot be the full truth are electromagnetic phenomena, which to a certain extent were found to be quite completely described by another set of fundamental laws, today called "Maxwell's Theory of Electromagnetism". It's plainly contradicting the very fundamental symmetry principles underlying Newtonian spacetime, and indeed after another struggle of about 50 years of many physicists, finally Einstein came to another better mathematical model called Special Theory of Relativity.

It's also true that without these mathematical formulation almost all physics we know to day, and which is crucial for our technological development (particularly quantum theory which is behind almost everything shaping our modern lives, particularly the laptop I'm typing this posting right now, the internet which lets me deliver it to PF where it can be read within a few microseconds or so all around the world), because often you get the idea for new experiments only through the mathematical conclusions within a given model of natural phenomena. In some sense an extreme example is the LHC (as far as I know the 2nd-most expensive experiment ever built up), which is the result of the quest for the final corner stone of the Standard Model of elementary-particle physics, the long-thought Higgs boson, which was predicted almost 50 years before it indeed has been unambigously discovered by ATLAS and CMS. I guess nearly every physicist around the world will remember what he or she did on Jul/04/2012, where the discovery was announced. I remember that we first had a seminar by a guest on another topic and then all watched the announcement of the Higgs discovery via the WWW.

So one must not forget that physics is about reproducible objective observations of nature, leading to astonishingly precise but always incomoplete mathematical models, but it's not math. If there is anything you can call "reality" in the sense of natural sciences it's the objective reproducibility of observations of nature. For sure, the mathematical models are NOT the "reality" in this sense but always incomplete pictures of it. The much I like Penrose's semipopular books (I've read some portions of "Road to Reality"), I cannot agree with his radical neoplatonism. He must have forgotten his time in the introductory and advanced science labs, where he should have learnt that physics is finally an empircal science, not some system of purely mathematical axioms.

9. Dec 27, 2017

### Staff: Mentor

I have a few books on mathematical modelling - its defined as something like what Wikipedia says:
https://en.wikipedia.org/wiki/Mathematical_model
A mathematical model is a description of a system using mathematical concepts and language.

You and I both know this, but since this is a beginner thread I think its important to explain what is meant by your comment about Euclidean geometry. Kant said Euclidean geometry was a-priori correct. However because in those days Kant was held in such high regard challenging him was something not to be taken lightly. Then Gauss, who in math was at least equally great as Kant, came along and showed not only do other geometries exist (I think some others had already done that as well) but logically they are just as consistent as Euclidean geometry. However because of Kant he did not publish - too scared. Later mathematicians like Riemann, who many thought of as Gauss's successor, had no such qualms, and he laid the foundation for the math Einstein used.

We freely choose which one to use depending on the objectives of our model. So you are 100% correct in pointing out the freely chosen nature of mathematical models. But, and I think this is the key point, how good a model conforms to experiment is its judge ie how good a description is it. That's what makes it science. For everyday things Euclidean geometry is a remarkably good description - but we know its wrong as readily attested to by GPS devices - unless they take into account GR they would not work.

I suspect like some of the concepts in this thread what a mathematical model is may be a bit mutable, so in future when I use it I will be clear what I mean - namely its a mathematical description of some system - how good a description it is, is judged by experiment.

Like just about all you write, both true and expressed well. I think very few agree with Penrose, but its what he thinks, and its seductive - I believed it at one time until I understood what Gell-Mann said:
https://www.ted.com/talks/murray_gell_mann_on_beauty_and_truth_in_physics

One interesting point he makes, that all science advisers on this site know only too well, popularization's (except a few like Feynman) are invariably wrong, even some movies/documentaries about it are wrong. And many are written/done by famous physicists like Brian Greene - go figure.

Thanks
Bill

Last edited: Dec 27, 2017
10. Dec 27, 2017

### vanhees71

As far as I know, Gauss wasn't too afraid of Kant but didn't publish his results on non-Euclidean geometry because he thought he'd shock is contemporaries ;-)). Of course to day we know that physical space is not best described as a Euclidean affine manifold but spacetime as a whole as a pseudo-Riemannian (Lorentzian) one. Another clue about the genius of Gauss is that in fact he tried to check the Euclidicity of physical space by doing a careful triangulation of 3 mountains (indeed Gauss was earning his living as a geodesist precisely making a map of the kingdom of Hanover). He came to the conclusion that he cannot find any deviation from Euclidicity within the accuracy he could achieve with his instruments. Maybe that was another reason to keep silent about his mathematical discoveries concerning non-Euclidean geometry. Of course, he himself published important work on general differential geometry later, after Lobechevsky and Bolyai independently published their work on (I think hyperobolic) non-Euclidean geometry.

11. Dec 27, 2017

### Staff: Mentor

You may be correct, but with his reputation amongst other mathematicians one wonders why he would be worried by that. Gauss was actually secretive in many ways.

It's actually an interesting read about Kant and Gauss - but way off this thread or even this forum. I can give links but it's more philosophy than science. For example the great Poincare had different views again - he believe it or not was more along the lines of Wittgenstein - ie its just convention - amazing

Thanks
Bill

Last edited: Dec 27, 2017
12. Dec 27, 2017

### Lord Jestocost

As a scientist, I have learned to indicate the source when quoting some text. In case you have problems with the quote’s content, please mention your arguments.

13. Dec 27, 2017

### Staff: Mentor

Its not that - its just we prefer reputable textbooks, peer reviewed journals etc. Popularisations, even written by highly reputable scientists, can be rather variable and the mentors, correctly IMHO, keep an eye on such to see if they meet usual science standards. I note you have a PhD, and would undoubtedly have had papers passed to you for peer review. I think the criteria is would you accept it as a reputable scientific source. If yes - then its possibly OK - but we may not always agree with you. BTW since I became a mentor I can assure you of something I didn't know before - before such decisions are made, to for example delete a post as its not from a reputable source, just like peer review, significant discussion goes into it - its not taken lightly.

The issue with your quote is 'no good answers to these questions'. That may be true (I don't agree but that means precisely diddly squat scientifically), or not, depending on what you think a good answer is. Is that science or is it philosophy? Already this thread has degenerated into things rather philosophical instead of scientific.

Thanks
Bill

Last edited: Dec 27, 2017
14. Dec 27, 2017

### vanhees71

Well, as usual great mathematicians are often not very good physicists; Poincare is among them. Although he for sure knew everything about what we call special-relativstic spacetime concerning the math, even more than Einstein at the time, he didn't draw the logical conclusions from a physicist's point of view. This was done by Einstein, who appreciated the formal math only 10 years later after struggling for almost the same amount of time with general relativity. I guess it took him so long, because of his aversion against formal mathematics. A theoretical physicist must keep a good balance between mathematical formalism and physical intuition.

Another example is von Neumann, who was for sure superior in the math of QT, bringing the non-relativistic theory quickly in a rigorous mathematical form, including the comlicated eigenvalue problem for unbound operators, but he did more harm than good concerning the physical interpretation, inventing the infamous Princeton Interpretation.

Then there is also Weyl, who better than nearly all physicists of his time new the use of group theory and their representations for mathematical physics, and he also wrote a brillant textbook on GR early on (Raum, Zeit, Materie; I think the 1st edition was already in 1918, i.e., very quick after Einstein's and Hilbert's final breakthrough in formulating GR), but his intuition totally failed him concerning his unfortunate try to combine GR and electromagnetism by geometrizing electromagnetism by gauging the scale invariance of the free gravitational field, as we would call it. Ironically this theory, which is physically "not even wrong" (as Pauli acidly put it, and Einstein with one glance disproved it by the simple argument that obviously the length of a yardstick doesn't depend on its electromagnetic history, which is very fortunate for our everyday use of them), gave the name "gauge theory" to (Q)FTs with a local symmetry group.

15. Dec 27, 2017

### Staff: Mentor

Yes, great Polymaths like Poincare and Von-Neumann are really interesting when looked at from the vantage of the specialty they are venturing into. Maybe it's the fact they are Polymaths and try to take a view wider than they really should. Poincare was like that - he also wrote widely on the philosophy of science, but was also a practical and professionally qualified mining engineer of some note. These guys are simply enigmas. But at least they cant be accused of, in writing about the Philosophy Of Science, of not knowing what they were writing about - its just they reached strange views. Wittgenstein was also like that - before being a philosopher he was an aeronautical scientist of some note. As a scientist you would expect him to side with Turing - but he didn't. Even Russell found him an enigma - but later came to think he was correct. It goes without saying I think his and Poincare's views utter balderdash - but such are not what we worry about here.

Thanks
Bill

Last edited: Dec 27, 2017
16. Dec 27, 2017

### vanhees71

Indeed, and von Neumann was the founding father of modern informatics too!

17. Dec 27, 2017

### stevendaryl

Staff Emeritus
We're getting off-topic, but could you summarize in a sentence or two what views Poincare and/or Wittgenstein held that you consider balderdash?

18. Dec 27, 2017

### stevendaryl

Staff Emeritus
It seems to me that if Einstein could so easily disprove Weyl's theory, then it was wrong, rather than "not even wrong".

19. Dec 27, 2017

### Staff: Mentor

They believed geometry for example had no objective reality - it was simply a convention we have - just a construct we adhere to. Turing countered, since it is used in deigning bridges etc it must have some kind of objective truth or bridges could fall down etc. Wittgenstein, and I presume Poincare, simply said - so what. If they fall down, they fall down and we adjust our conventions.

http://www.chass.utoronto.ca/~jrbrown/PhilosophyofPhysics.V.ppt

Thanks
Bill

20. Dec 27, 2017

### Staff: Mentor

Its just Pauli's well known acid tongue. He even said to Einstein - you know what Prof Einstein says isn't totally silly or something like that. He did similar put-downs of many great scientists eg Landau, who while one of my heroes basically treated everyone else like a fool. He was well-known to be utterly merciless with colleagues that he considered to be lesser intellects than himself. The only person, who supposedly matched him in arrogance was Wolfgang Pauli. After explaining his work to a skeptical Pauli, he angrily asked whether Pauli thought that his ideas were nonsense. ‘Not at all, not at all,’ came the reply. ‘Your ideas are so confused I cannot tell whether they are nonsense or not’.

I think Landau would have greatly benefited from meeting Feynman - but that never happened. Feynman, like Pauli would have put him in his place. Feynman did meet Pauli, but as far as I know, wisely IMHO, kept his put-downs in check. Feynman was known to mostly be pretty tolerant, argumentative yes - telling greats like Bohr etc you are crazy and what not, but I have heard of only a few occasions where he was into the actual put-down. He hated arrogance of any type - it is said his mask was that of a kid from the boondocks who saw through the ways of city slickers. Pauli or Landau in put-down mode would have really made him mad.

Thanks
Bill

21. Dec 27, 2017

### stevendaryl

Staff Emeritus
Okay, thanks.

Geometry shows up in equations of motion through the appearance of additional velocity-dependent terms:

$m (\frac{d^2 x^\mu}{ds^2} + \Gamma^\mu_{\nu \lambda} \frac{dx^\nu}{ds} \frac{dx^\lambda}{ds}) = F^\mu$

I suppose you are free to move the terms to the other side and interpret them as velocity-dependent forces:

$m \frac{d^2 x^\mu}{ds^2} = F_{eff}(m, v)$

where $F_{eff}(m,v) = - m \Gamma^\mu_{\nu \lambda} v^\nu v^\lambda + F^\mu$

Kaluza-Klein models go the other way; they reinterpret forces (electromagnetism, in the original model) as being due to geometry. So maybe even if geometry is not completely conventional, we may not be able to empirically distinguish geometrical explanations from other types of explanations. So our observations may not uniquely determine the geometry

22. Dec 27, 2017

### Staff: Mentor

That's true. But a conversationalist would counter something, gravitions maybe, simply makes flat space-time act as if its curved - it isn't really - its flat. I asked Steve Carlip about this and he said there is no way to tell the difference. Its just the way it is. Its simply convention based on simplicity that we choose curved space-time. But an actual quantum theory of gravity below the Plank scale may change that - who knows.

The same with LET and SR. Both are equally valid scientifically - we just choose SR because its simpler, more beautiful and elegant, generalizes more easily to QFT - all sorts of reasons. But LET may be true. However IMHO you would need rocks in your head to choose it - all our current knowledge supports SR over LET. I think it's rubbish, personally, to consider theories that are simply contrived for the purpose of demonstrating some philosophical position. As Einstein said - nature is subtle, but never malicious. Can I prove it - of course not.

Thanks
Bill

23. Dec 27, 2017

### vanhees71

I think, in this case both views are right but in different senses. Geometry, as a mathematical axiomatic system, is of course convention. You can invent any system of axioms you like to define a geometry. As long as you don't run into some contradictions, it's each a valid mathematical theory. As a description of physical observation it's subject to experimental/observational testing, and one has to verify how accurate the description coincides with observations, and there indeed Euclidean geometry has been found to be only a good approximation, neglecting gravity. Gravity is a very weak interaction, and thus the approximation in our everyday world is very good, because we are surrounded only by quite tiny amounts of matter (the Earth and even the Sun are pretty small masses, and it's hard to find the deviations from Euclidean geometries, like the classical tests of GR, i.e., perihelion shift of Mercury and the deflection of light by the Sun). In this sense, as a physical model of Nature geometry is not pure convention but an empirical finding.

24. Dec 27, 2017

### Staff: Mentor

The trouble is we have theories like LET that are experimentally indistinguishable from SR. Why would anyone but 'cranks' choose LET? Conventional scientists know it just fits better with our other knowledge like QFT. It isn't experiment that chose's it - it's some sense we have of right and wrong - maybe what Gell-Mann was getting at.

This is really my last comment. We are getting way off its purpose. Please can we simply stick to its purpose. Really - if we don't it will be shut down.

Thanks
Bill

Last edited: Dec 27, 2017
25. Dec 27, 2017

### Staff: Mentor

We will go ahead and close this thread at this point. It has gone out of physics and into philosophy.