What is the difference between cfd and realism?

In summary, the conversation discusses the difference between counterfactual definiteness and realism, as well as their definitions and the confusion between the two concepts in the past. Counterfactual definiteness is the idea that one can do meaningful reasoning about experiments that could have been performed, but were not, while realism is the proposition that if we don't measure, we must still assert that the thing we could have measured is still there. However, the notion of "reality" is not well defined and can have different meanings for different people. The conversation also touches on the relationship between superposition and non-realism, and whether a realistic entity has an unambiguous reality. It is argued that quantum mechanics is not a realistic theory, and the question
  • #1
entropy1
1,230
71
What is the difference between counterfactual definiteness on one side and realism on the other?

And what are their definitions? (references will be welcome if given).
 
Physics news on Phys.org
  • #2
Have you searched for definitions on Google? Is there a specific point of confusion after researching both?
 
  • #3
As far as I interpret it, CFD is the idea that one can do meaningful reasoning about experiments not (yet) performed, and realism the proposition that if we don't measure, we must still assert that the thing we could have measured is still there.

I can't put it to words very accurately, to my regret.

The notions as put in my words above seem to have much in common. I recall (though a PF search yields nothing) that there was some confusion between the two in the past.
 
  • Like
Likes Greg Bernhardt
  • #4
So one of the things I was wondering about is, if superposition is a kind of non-realism, in the sense that a realistic entitity has an unambiquous reality?
 
  • #5
entropy1 said:
CFD is the idea that one can do meaningful reasoning about experiments not (yet) performed

I don't think this is quite correct; I would say CFD is the assumption that one can do meaningful reasoning about experiments that could have been performed, but were not--and therefore cannot now be performed, since the time at which one would have performed them is past. For example, if you measure the spin of an electron in the ##z## direction, CFD is the assumption that one can meaningfully talk about what the result would have been if one had instead measured its spin in the ##x## direction (or any other direction besides ##z##). But that is not the same as talking about what could happen if one were to measure the spin in the ##x## direction at some future time.

entropy1 said:
realism the proposition that if we don't measure, we must still assert that the thing we could have measured is still there

I don't think this really captures the reason why debates about "realism" in QM never get anywhere; the problem is that seemingly innocuous phrase "the thing we could have measured".

entropy1 said:
one of the things I was wondering about is, if superposition is a kind of non-realism, in the sense that a realistic entitity has an unambiquous reality?

If the unambiguous reality is the quantum state, then superposition is perfectly real. The problem is the implications you have to accept if you want to believe that the unambiguous reality is the quantum state. But those problems are problems of interpretation, not theory. In fact, that's probably true of any discussion of realism in a quantum context.
 
  • Like
Likes Demystifier and entropy1
  • #6
Suppose we 'trap' a particle. Could we speak of that the particle is 'really' in the trap, though we haven't (yet) measured it? (even if we did measure it)
 
  • #7
PeterDonis said:
I don't think this really captures the reason why debates about "realism" in QM never get anywhere; the problem is that seemingly innocuous phrase "the thing we could have measured".
The reason is that the notion of "reality" is not well defined. It's some unsharp philosophical idea, with a meaning at least as numerous as people using the word. I think it shouldn't be used in physics discussions at all for this reason.

The culprit most probably is Podolski who is the one who in fact wrote the (in)famous Einstein-Podolski-Rosen paper. Einstein was quite unhappy with this paper, saying that it "buries the main point by erudition" (in a letter to Schrödinger, with whom he discussed these issues in person when they were colleagues in Berlin in the 1920ies and later on via mail). Einstein's criticism against the completeness of QT was rather about the inseparability implied by the formalism by the possibility of entanglement of system parts that are observed at far distant places. He was well aware of all the subtleties concerning this inseparability feature of QT on the one hand and the apparent tension with locality on the other hand. Unfortunately relativistic QFT wasn't well enough understood at the time and Bell's paper came about 10 years after Einstein's death and the first experimental observations of the violation of Bell's inequality only in the late 1970ies/early 1980ies. I'd really like to know how Einstein would have reacted to these ground-breaking results on the foundations of QT.

For a very thorough analysis about what Einstein really wanted to say in the EPR paper and what he indeed said later in the Dialectica article (quoted in this paper):

D. Howard, Einstein on locality and separability, Studies in History and Philosophy of Science 16, 171 (1985)
https://doi.org/10.1016/0039-3681(85)90001-9
 
  • Like
Likes physika, bhobba and Mentz114
  • #8
To me, it makes sense to call a theory realistic if there is a notion of the state of the universe, and every fact about the universe follows from that state. In contrast, a probabilistic theory is (usually) not realistic in this sense, because there are facts that are not captured by the probability distribution. If you have a probability distribution [itex]\rho(x)[/itex] giving the probability of a particle being at position [itex]x[/itex], then where the particle actually is is a fact above and beyond the probability distribution. The distribution [itex]\rho[/itex] either reflects our knowledge of the particle's position, or it reflects some kind of statistical fact about many systems that are similar to the one we are studying, but it does not reflect (just) facts about our system.

Quantum mechanics is definitely not a realistic theory, and the question was whether there is a realistic theory that gives rise to quantum mechanics in a similar way that Newtonian physics gives rise to statistical mechanics. The answer seems to be "no", if we demand that the realistic theory be local (in the sense of factorizability of the state of the universe into local states that evolve locally).
 
  • #9
vanhees71 said:
The reason is that the notion of "reality" is not well defined. It's some unsharp philosophical idea, with a meaning at least as numerous as people using the word. I think it shouldn't be used in physics discussions at all for this reason.

The culprit most probably is Podolski who is the one who in fact wrote the (in)famous Einstein-Podolski-Rosen paper. Einstein was quite unhappy with this paper, saying that it "buries the main point by erudition" (in a letter to Schrödinger, with whom he discussed these issues in person when they were colleagues in Berlin in the 1920ies and later on via mail). Einstein's criticism against the completeness of QT was rather about the inseparability implied by the formalism by the possibility of entanglement of system parts that are observed at far distant places. He was well aware of all the subtleties concerning this inseparability feature of QT on the one hand and the apparent tension with locality on the other hand. Unfortunately relativistic QFT wasn't well enough understood at the time and Bell's paper came about 10 years after Einstein's death and the first experimental observations of the violation of Bell's inequality only in the late 1970ies/early 1980ies. I'd really like to know how Einstein would have reacted to these ground-breaking results on the foundations of QT.
So perhaps the non-realism in QT is a translation of the conflict between two concepts in physics, that are locality and inseparability?
 
Last edited:
  • Like
Likes morrobay
  • #10
entropy1 said:
So perhaps the non-realism in QT is a translation of the conflict between two concepts in physics, that are locality and inseparability?

No - eg Bell does not deny realism, we simply do not know if QM has realism or not. Bells theorem however does set bounds on it.

But first let's pin down your original question on CFD:
https://arxiv.org/pdf/1212.5214.pdf
Let us define “counterfactual-definite” [14, 15] a theory whose experiments uncover properties that are pre-existing. In other words, in a counterfactual-definite theory it is meaningful to assign a property to a system (e.g. the position of an electron) independently of whether the measurement of such property is carried out. [Sometime this counterfactual definiteness property is also called “realism”, but it is best to avoid such philosophically laden term to avoid misconceptions.]

Once that's understood you may wish to rephrase your question.

Thanks
Bill
 
  • #11
vanhees71 said:
D. Howard, Einstein on locality and separability, Studies in History and Philosophy of Science 16, 171 (1985)
https://doi.org/10.1016/0039-3681(85)90001-9

Nice paper - reading it now.

And indeed its very important to realize Einsteins arguments are not easily dismissed even today - although I am basically with Weinberg that both Bohr and Einstein were, in light of modern knowledge, wrong, there is a tendancy, I have even seen posted on this forum, to say Bohr was more right that Einstein. I do not agree with that - I think its the other way around. Bohr had a bit of a 'wishy washy' side IMHO, with ideas I never actually got like complementarity, however Einstein was always, to my mind, clear and concise in his objections. Many are still valid today, but I think Copenhagen as formulated by Bohr, Heisenberg etc has now morphed a bit in light of current knowledge. For example wave particle duality, which it states as a basic principle, isn't quite thought of the same way today. We know everything is really quantum stuff - its not particle or wave and thinking this way is in fact a myth:
https://arxiv.org/abs/quant-ph/0609163

Understandable in Bohr's day of course - but a lot of water has passed under the bridge since then.

Added Latter:
Finished reading it. Einstein had an absolute conviction in the existence of a reality out there independent of us. To him the wave-function had to be real or the theory, almost by definition, was incomplete. Clearly and exactly stated - I don't necessarily agree with it, but won't go into what I think here, the point is its unambiguous. Then we have his actual EPR type objection - its based on separability. Kind of reminds me of Weinberg statement of the Cluster Decomposition property:
https://www.physicsforums.com/threads/cluster-decomposition-in-qft.547574/

Not exactly the same of course - but you get the feeling Einsteins famous intuition was still there pointing to future developments.

Thanks
Bill
 
Last edited:
  • Like
Likes Demystifier and vanhees71
  • #12
entropy1 said:
What is the difference between counterfactual definiteness on one side and realism on the other?

And what are their definitions? (references will be welcome if given).

The details of the definitions will ultimately control the answer to your first question. But in any context in which they are mentioned together, there is no practical difference.
 
  • Like
Likes vanhees71, atyy, fresh_42 and 1 other person
  • #13
bhobba said:
Nice paper - reading it now.

And indeed its very important to realize Einsteins arguments are not easily dismissed even today - although I am basically with Weinberg that both Bohr and Einstein were, in light of modern knowledge, wrong, there is a tendancy, I have even seen posted on this forum, to say Bohr was more right that Einstein. I do not agree with that - I think its the other way around. Bohr had a bit of a 'wishy washy' side IMHO, with ideas I never actually got like complementarity, however Einstein was always, to my mind, clear and concise in his objections. Many are still valid today, but I think Copenhagen as formulated by Bohr, Heisenberg etc has now morphed a bit in light of current knowledge. For example wave particle duality, which it states as a basic principle, isn't quite thought of the same way today. We know everything is really quantum stuff - its not particle or wave and thinking this way is in fact a myth:
https://arxiv.org/abs/quant-ph/0609163

Understandable in Bohr's day of course - but a lot of water has passed under the bridge since then.

Added Latter:
Finished reading it. Einstein had an absolute conviction in the existence of a reality out there independent of us. To him the wave-function had to be real or the theory, almost by definition, was incomplete. Clearly and exactly stated - I don't necessarily agree with it, but won't go into what I think here, the point is its unambiguous. Then we have his actual EPR type objection - its based on separability. Kind of reminds me of Weinberg statement of the Cluster Decomposition property:
https://www.physicsforums.com/threads/cluster-decomposition-in-qft.547574/

Not exactly the same of course - but you get the feeling Einsteins famous intuition was still there pointing to future developments.

Thanks
Bill
To be honest, I never understood Bohr's writings on the subject, particularly his response to the EPR paper (with the same title) is a complete enigma to me. I wonder, what he really wanted to say.

In contradistinction to that, Einstein was absolutely clear about what he thought to be a "complete physical theory", and indeed for him QT (and also modern relativistic QFT) is not complete because of the inseparability, described by entanglement. In this respect, I think he was wrong, as is confirmed by all the fancy Bell experiments successfully done in the recent few decades. I can only speculate about what Einstein would have to say about it, but since he was very close to experiment (he even did experiments himself sometimes, but not with too much success, as the famous example of the Einstein-de Haas effect shows) I think, at least he would have become more convinced about the fact that QT is not incomplete because of inseparability, but that inseparability is a successful prediction of the theory.

Of course QT is not complete as long as nobody has found a satisfactory way to incorporate gravitation.

Concerning the socalled "interpretational problems", I think QT in the minimal interpretation is what all physical theories are, namely a mathematical description of what we can observe in nature by objective quantitative measurements, no more no less. There is no necessity for any "interpretation" in an ontic sense beyond the minimal one since I don't even know, where should be a problem. As long as QT describes all observed facts we can objectively measure, there is no problem.

Last but not least: If you want religion, go to church; you won't find it in any physics lecture hall, and in fact you shouldn't find it there!
 
  • Like
Likes Demystifier, fresh_42 and bhobba
  • #14
vanhees71 said:
To be honest, I never understood Bohr's writings on the subject, particularly his response to the EPR paper (with the same title) is a complete enigma to me. I wonder, what he really wanted to say.

I am pretty sure I was not Robinson Crusoe there. Einstein and Bohr were friends so I think he understood what Bohr was getting at, but I sure didn't.

Thanks
Bill
 
  • Like
Likes vanhees71
  • #15
entropy1 said:
So perhaps the non-realism in QT is a translation of the conflict between two concepts in physics, that are locality and inseparability?
Since I still don't know, what the term "reality" means in clearly defined operational or theoretical way, I say only that much: For me reality is what can be objectively observed and quantitatively measured, and in this regards, there's not a single reproducible observation that disproves QT.

There is also no conflict between locality and inseparability. Any relativistic local and microcausal QFT is, as the name says, both local and at the same time allows for entanglement ob observables between far-distant observations on quantum systems. In this sense QFT includes, as any QT, inseparability. E.g., a polarization-entangled biphoton as produced by parametric downconversion is one quantum system, no matter how far distant the photons are registered. Not long ago there was a big press hype about photons being entangled over astronomical distances. There's no problem with that concerning locality. QED by construction has only local interactions, and all observations are in accordance with it. Also note that the linked-cluster theorem by construction holds true for all these theories.

I recently got a copy of

A. Duncan, The conceptual framework of quantum field theory, Oxford University Press, Oxford, 2012.

It's the best textbook on QFT after Weinberg's masterpiece, and it's complementary, discussing many subjects not mentioned by Weinberg! There you can find a very clear discussion on locality, the linked-cluster theorem, causality, and all that.

BTW: Oxford University Press has a seasonal sale with 50% off (code: HOLIDAY17).
 
  • Like
Likes Demystifier, entropy1 and bhobba
  • #16
vanhees71 said:
after Weinberg's masterpiece
Is that "The Quantum Theory of Fields", of Steven Weinberg?
 
  • #17
Yes, it's

S. Weinberg, Quantum Theory of Fields, 3 vols., Cambridge University Press
 
  • Like
Likes entropy1
  • #18
vanhees71 said:
To be honest, I never understood Bohr's writings on the subject, particularly his response to the EPR paper (with the same title) is a complete enigma to me. I wonder, what he really wanted to say.

I never understood that either. Always seems a bit hand-wavy as a response to EPR.
 
  • Like
Likes Demystifier and bhobba
  • #19
entropy1 said:
What is the difference between counterfactual definiteness on one side and realism on the other?
Hard to say about difference but there certainly is similarity - different people attach different meanings to both terms.

entropy1 said:
And what are their definitions? (references will be welcome if given).
https://arxiv.org/abs/quant-ph/0607057 - here are the list of possible definitions of "realism"
https://en.wikipedia.org/wiki/Counterfactual_definiteness - wikipedia gives two different meanings in first sentence and if you take the meaning of the term "counterfactual" from Counterfactual thinking you have even the third meaning.
 
  • Like
Likes entropy1
  • #20
entropy1 said:
What is the difference between counterfactual definiteness on one side and realism on the other?

And what are their definitions? (references will be welcome if given).

CFD = Values = object property.
no object -> no values -> no reality..
 
  • #21
DrChinese said:
I never understood that either. Always seems a bit hand-wavy as a response to EPR.

Its glad to know I am not the only one that feels that way about Bohr. To me his response is - how to express it - a bit mumbo jumbo'ish - like much of Bohr's writings are to me. Maybe its a bit like David Bohm. When he was good he was very very good - when he was, let's say not quite exact as in his implicate order writings, he was - well terrible. In his defense though I think Einstein understood Bohr - his objections were I think more wryly stated when he said - nearly everyone's refutation of it was different.

Really interesting was when Dirac visited Bohr - totally different in style:
http://www.ams.org/notices/201109/rtx110901278p.pdf

Actually to me Dirac was clearer than Bohr.

Added Later.

To see what me, Dr Chinese and Vanhees mean see the following:
https://philpapers.org/rec/WHITEP
For many years after Bohr's response to the EPR argument, Bohr was considered to have provided an authoritative rebuttal of the ideas of the paper, and more generally of Einstein's stance on quantum theory. More recently, however, there has been great difficulty even in achieving general agreement on Bohr's meaning. Two recent papers, by Dickson, and by Clifton and Halvorson, have sought to establish the structure of Bohr's argument. In the present paper, the papers of EPR and Bohr are re-assessed in the light of these recent papers, and also in light of the development and presentation of quantum information theory.

Only recently o0)o0)o0)o0)o0)o0)

Oh dear. I won't spell out what that suggests to me - my respect for the scientists involved is far too great. Suffice to say perhaps similar to Von-Neumann's proof of no hidden variables that everyone seemed to agree with, but hardly anyone took the time to check. Or think about it clearly enough - I didn't know of Bell etc when I read his book - Mathematical Foundations of QM and didn't see the error - bad boy, bad boy :nb):nb):nb):nb):nb):nb):nb).

Thanks
Bill
 
Last edited:
  • Like
Likes DrChinese
  • #22
Sure, Dirac was the typical no-nonsense math physicist. You can take his papers and bind them together to a textbook, and his own textbooks are all masterpieces (not only the most famous one, The Principles of Quantum Mechanics, but also his very brief but concise GR book). In the early days of QT there were indeed these two types of physicists: namely the ones using the math and presenting a physical theory (Born, Jordan, Pauli, Sommerfeld, Dirac, also Schrödinger, but with a flawed interpretation of the quantum state) and the more philosophically inclined type tending to blurr the subject by gibberish statements about some kind of "deeper meaning" of QT (Bohr, Heisenberg, partially also von Neumann, whose interpretational part is completely flawed, while his work on the mathematical foundations of non-relativistic QT is a cornerstone of the theorie's development). Bohm is somewhat in between: On the one hand he has written a very good textbook on the subject (not to mention his original work, including the Aharonov-Bohm effect) on the other hand he has presented his non-local pseudo-deterministic additions, now called "Bohmian Mechanics". I consider this also as flawed since the claimed trajectories of particles are not observable, and anything that is observable is equivalent to standard QT. For relativistic QFT, the Bohmian approach is at least difficult, if not self-contradictory.
 
  • Like
Likes DrChinese and bhobba
  • #23
I think there is GREAT value both in cleaning up the mathematical formalisms, AND understanding the constructing principles that led to current formalisms, and that might lead us to improvements in the formalisms.

I always enjoyed BOTH the more formal "right to the point" books, to learn the theories, and the "behind the scenes" thinking especially of the original founders.
From the point of view of mastering an established theory you can surely skip what you call "gibberish", and read the "cleaned up" writings. But if you have the ambition to undersand they theory conceptually in order to find the right angle to solve some of the open questions such as unification and quantum gravity, the gibberish of the original founders might well be gold worth as well.

vanhees71 said:
To be honest, I never understood Bohr's writings on the subject, particularly his response to the EPR paper (with the same title) is a complete enigma to me. I wonder, what he really wanted to say.

In contradistinction to that, Einstein was absolutely clear about what he thought to be a "complete physical theory", and indeed for him QT (and also modern relativistic QFT) is not complete because of the inseparability, described by entanglement. In this respect, I think he was wrong, as is confirmed by all the fancy Bell experiments successfully done in the recent few decades.
As I understand it, I think Bohr's point in the 1935 paper is to try to convey why the idea of Einsteins local realism is fallacious when applied to "atomic physics" as bohr calls it. And the reason is complementarity that as per the "quantum of action" that is significant for "atomic physics", and that implies that it is impossible to actually make a proper "preparation" in a way that fulfills the local realist description - without disturbing the system.

Sure, it is obvious, given history that this is hard to grasp for many physicists. I am my view, Bohr takes the concept of "measurement theory" truly seriously.In this sense i think no one ever was more clear than Bohr. IMO bohr takes on the minimalist stance here, and suggest that if we are to consistently talke about measurement theory, even the "preparation" is a kind of measurement. And there is not really any room for the old style realism. It is fundamentally incompatible with what Bohr thinks is the "essence of QM", and i fully share that view!
vanhees71 said:
Of course QT is not complete as long as nobody has found a satisfactory way to incorporate gravitation.
Bohr has an interesting remark in the end of his paper where he compares the "complementarity" with "relativity". I can't tell from that paper alone how deep insight he had about this, but I think that association is probably just the right way to TRY to adress things to Einstein, as beeing the father of relativity in the first place. The possible parallell here is that relativity, with its observer associated frames of reference, conceptually could be expanded to consider more general "observers", where the machian relativity ideas, could well be applied also to measurements.

Somehow i would be curious to hear what Bohr and Einstein would say about todays situation, and about stuff like "GR=QM", "EPR=ER". I sometimes get the feeling that there in history are "lost ideas" that was just grossly misunderstood by contemporary scientists. After all, people grow old, and even a genious can only do so much progress in a lifetime.

I suspect that Einsteins take on "realism" would be different today, and probably more reflect the reality of law as opposed to evolution of law. I also wonder what Einstein would think today about the idea that his field equations are to be seen as an equation of state.

Conceptually these things are all very closely related to the original topic in the epr paper, and its a pity we can't hear their what their opinions today would be. And which should not be hard to understand, these conceptual issues - at this immature point - are not yet clear mathematical problems simply because we do not know (except i know some of you beg to differ) how current theory needs to be deformed or changed in order to realize the presumed vision bohr is hinting at to unifty "complementarity" and "relativity" in the observer-observer sense.

/Fredrik
 
  • #24
vanhees71 said:
To be honest, I never understood Bohr's writings on the subject, particularly his response to the EPR paper (with the same title) is a complete enigma to me. I wonder, what he really wanted to say.
"Truth and clarity are complementary."
- Niels Bohr
 
  • Like
Likes bhobba and vanhees71
  • #25
vanhees71 said:
I recently got a copy of

A. Duncan, The conceptual framework of quantum field theory, Oxford University Press, Oxford, 2012.

It's the best textbook on QFT after Weinberg's masterpiece, and it's complementary, discussing many subjects not mentioned by Weinberg! There you can find a very clear discussion on locality, the linked-cluster theorem, causality, and all that.
For my taste, Duncan is even better than Weinberg. I particularly like how Duncan demystified the Haag's theorem.
 
  • Like
Likes vanhees71
  • #26
I think the problem is that Bohr hadn't a "translator" who transformed his ingenious insights to clear mathematical analyses. For Heisenberg that role has been played by Pauli. Pauli's and Heisenberg's approach to physics and their entire livestyle were indeed "complementary", and together they brougth (quantum) physics a huge step forward, while the entangled pair "Heisenberg-Bohr" amplified the mysticism of each other.
 
  • Like
Likes bhobba and Demystifier
  • #27
Demystifier said:
For my taste, Duncan is even better than Weinberg. I particularly like how Duncan demystified the Haag's theorem.
It's not better but fills the gaps in Weinberg's treatment. I've been always a bit mystified about the fact, why Weinberg doesn't even mention the problems addressed by Haag's theorem.

My present recommendation for how to learn relativistic QFT is

Start with working through M. Schwartz, QFT and the Standard Model to learn the physics and how to really calculate S-matrix elements, including renormalization. Then read Weinberg's books to understand why QFT looks the way it looks from the point of view of first principles (symmetries + causality requirements) and finally study Duncan for the finer details of the mathematics behind it, including all the trouble with LSZ, Haag, etc.
 

1. What is the definition of CFD and realism?

CFD stands for Computational Fluid Dynamics, which is a branch of fluid mechanics that uses numerical methods to solve and analyze fluid flows. Realism, on the other hand, refers to the degree to which something accurately represents reality.

2. How do CFD and realism differ in terms of application?

CFD is primarily used in engineering and scientific research to simulate fluid flows and predict the behavior of fluids in various environments. Realism, on the other hand, is more commonly associated with art, literature, and other forms of media where the goal is to accurately depict real-life situations or events.

3. What are the key differences in the underlying principles of CFD and realism?

The underlying principles of CFD are based on mathematical equations and numerical methods, while realism relies on observation, perception, and interpretation of the real world. CFD is more focused on quantitative analysis and prediction, while realism is concerned with capturing the essence of reality in a subjective manner.

4. Are there any similarities between CFD and realism?

While CFD and realism may seem very different, they both involve the use of models to represent real-world phenomena. CFD uses mathematical models to simulate fluid flows, while realism uses artistic or literary techniques to create a representation of reality.

5. How is the accuracy of CFD and realism determined?

CFD is typically evaluated based on its ability to accurately predict fluid behavior and compare results to experimental data. Realism, on the other hand, is more subjective and can be evaluated based on the level of detail, believability, and emotional impact it conveys to the audience.

Similar threads

  • Quantum Physics
Replies
9
Views
1K
Replies
2
Views
1K
Replies
12
Views
1K
Replies
10
Views
2K
Replies
7
Views
1K
Replies
2
Views
1K
Replies
6
Views
2K
  • Quantum Physics
4
Replies
120
Views
10K
  • Quantum Physics
Replies
10
Views
2K
  • Quantum Physics
Replies
3
Views
1K
Back
Top