What are you reading now? (STEM only)

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In summary, D. J. Tritton's "Physical Fluid Dynamics" is a book that he likes for its structure, beginning with phenomenology before delving into the equations. He also likes the book for its inclusion of experimental results throughout. He recently read J. MacCormick's "Nine Algorithms That Changed the Future" and found it to be very readable. Lastly, he is reading S. Weinberg's "Gravitation and Kosmologie" and Zee's "Gravitation".
  • #666
haushofer said:
I was always dismayed by the lack of interest and often even the aversion against philosophy by quite some of my fellow students and later collegues (and how people can separate philosophy from physics in the first place: where's the "cut"?).
And yet here you are in PF.
 
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  • #667
recently reading Fulton's algebraic curves. maybe seems odd since I am supposed to be an "expert", but find I always learn something from a real expert. e.g. I always thought artin rings (zero dimensional rings) were boring. Just realized after a few pages of Fulton, that they are the rings describing intersections of plane curves!
 
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  • #668
gleem said:
And yet here you are in PF.
Here I am. Because I think. :P
 
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  • #669
haushofer said:
I was always dismayed by the lack of interest and often even the aversion against philosophy by quite some of my fellow students and later collegues (and how people can separate philosophy from physics in the first place: where's the "cut"?). I was also surprised how one could follow many courses on quantum mechanics and QFT in which merely a recipe was explained and no coherent ontology was given about the stuff we spent hours calculating with. Why were so many physicists still positive about the Copenhagen interpretation, even when its similar philosophical paradigm in the guise of logical positivism was long abandoned by philosophers of science? How is it possible to start a PhD in Quantum Gravity without following a single course on the philosophy of science, and why are proposals about treating quantum foundations at journal clubs met with scepticism? And it wasn't just interpretational issues on quantum physics: my own supervisor was very reluctant when I included a historical overview of the hole argument in my PhD-thesis because I wanted to clarify the role of general covariance.
Physicists were well aware of philosophy in the first half of the 20th century. What changed?
 
  • #670
haushofer said:
I've just finished the book, and it took me 5 days. It was a fascinating read, and it coheres with my own experience as a physics student and PhD. I was always dismayed by the lack of interest and often even the aversion against philosophy by quite some of my fellow students and later collegues (and how people can separate philosophy from physics in the first place: where's the "cut"?). I was also surprised how one could follow many courses on quantum mechanics and QFT in which merely a recipe was explained and no coherent ontology was given about the stuff we spent hours calculating with. Why were so many physicists still positive about the Copenhagen interpretation, even when its similar philosophical paradigm in the guise of logical positivism was long abandoned by philosophers of science? How is it possible to start a PhD in Quantum Gravity without following a single course on the philosophy of science, and why are proposals about treating quantum foundations at journal clubs met with scepticism? And it wasn't just interpretational issues on quantum physics: my own supervisor was very reluctant when I included a historical overview of the hole argument in my PhD-thesis because I wanted to clarify the role of general covariance.

Of course, I was aware of the broader historical development leading to these schizophrenic aspects of the field of physics, but this book did a splendid job in filling in many details. It also shows the irrational path science as a human sociological enterprise can take. Highly recommended.
One has to distinguish clearly "philosophy of science" from "history of science". I'm always very sceptical about philosophy of science, because all too often I've read texts from philosophers, stating wrong things about the physics they aimed to make philosophy about. How can this kind of philosophy in any way be valid or of any value if it discusses something but not the correct physics. E.g., once I looked at a book about the "ontology of elementary particles". The introduction summarized the Standard Model of HEP physics, and it was entirely wrong. The author mixed up flavor and color to begin with, let alone describing the Higgs mechanism correctly and so on. I didn't read further, because I don't think that it makes sense to do philosophy about something about which the intrinsic facts are not understood clearly. Don't get me wrong, there are of course also very valuable philosophical texts written about physics (even about the really difficult topic "ontology of elementary particles"), but it's often hard to find these out of all the many really bad ones.

"History of science" is an entirely different business. There "historians of science", who usually have studied both the science and the methodology of historians, i.e., they know how to study sources like scientific papers, textbooks as well as correspondence between physicists etc. and how to bring it in relationship with the wider circumstances of its time (within science but also with politics, sociology, and all that). My experience is that papers or books written by historians of science usually get the physics they write about right, and then they put their topic in a solid context in the above sense. I think, it's important to study to a certain extent the history of science to really understand also the purely scientific content of the science.

Then the issue with the "foundations of quantum theory". There you have the history that it was a topic which has been surpressed for some decades by the believers in Copenhagen and only Copenhagen. It was nearly a herasy to question anything that Bohr had said. But this has changed with Bell's work (or at least its scientific part) and the success of the then following experimental work, where the vague EPR speculations were transformed into a clear scientific question, that could be decided as such a scientific question.
 
  • #671
Frabjous said:
Physicists were well aware of philosophy in the first half of the 20th century. What changed?
That the philosophy has become so useless for physics that they don't care anymore ;-).
 
  • #672
Frabjous said:
Physicists were well aware of philosophy in the first half of the 20th century. What changed?
A combination of events: ww2 kicked in, the Manhattan project lead to a huge increase of physicists and technological advances, and with the danger of "heresy against Copenhagen" many physicists thought the debate was settled and weren't that interested. Only in recent decades the situation becomes better. But even now e.g. Bell's theorem is wildly misunderstood, as you can also read in Maudlin or Norsen.

It's quite amazing, but also a bit depressing to read about this history. One surely loses some faith in 'science as a rational activity'.
 
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  • #673
Hope you don't mind I refer a series of videos instead of books. Adam Kashlak from U of Alberta has a great series of videos on Design of Experiments. Rather than just listing the steps to follow, he goes on pretty deeply and pretty clearly , about the material.
 
  • #674
haushofer said:
But even now e.g. Bell's theorem is wildly misunderstood, as you can also read in Maudlin or Norsen.
They misunderstand it or they point out misunderstandings of others?
 
  • #675
martinbn said:
They misunderstand it or they point out misunderstandings of others?
The latter.
 
  • #676
Demystifier said:
The latter.
I haven't read Maudlin, but Norsen definitely misunderstands EPR.
 
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  • #677
Particularly he misunderstands the difference between what many (also in this forum) insist to call "non-locality" (the strong correlations between far-distant parts of quantum systems described by entanglement) and "Einstein locality" as a way (in fact today the only way) to formulate relativistic (classical as well as quantum) theories with dynamics consistent with the causality structur of relativistic spacetime, i.e., the impossibility of faster-than-light signalling.
 
  • #678
martinbn said:
I haven't read Maudlin, but Norsen definitely misunderstands EPR.
Can you point out exactly where?
 
  • #679
vanhees71 said:
Particularly he misunderstands the difference between what many (also in this forum) insist to call "non-locality" (the strong correlations between far-distant parts of quantum systems described by entanglement) and "Einstein locality" as a way (in fact today the only way) to formulate relativistic (classical as well as quantum) theories with dynamics consistent with the causality structur of relativistic spacetime, i.e., the impossibility of faster-than-light signalling.
Can you point to where he misunderstands this exactly? And does he misrepresent Bell then also in his quotes on nonlocality? Or did Bell make the same mistake?
 
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  • #680
martinbn said:
They misunderstand it or they point out misunderstandings of others?
As I read the quotes, quite some physicists claimed that Bell rules out hidden variable theories. I guess his main point of criticism is that it's not stressed that the word "local" is not mentioned.
 
  • #681
haushofer said:
Can you point out exactly where?
Everywhere he writes about Bell. For example the scholarpedia article.
 
  • #682
haushofer said:
Can you point to where he misunderstands this exactly? And does he misrepresent Bell then also in his quotes on nonlocality? Or did Bell make the same mistake?
I don't know about how he presents Bell, because I don't know, what Bell wanted to say. The only thing I understand is the math, and there it's pretty clear what Bell means by "local realistic theory": realistic means that all observables always take determined values. A probabilistic description is only needed because of incomplete information about these values, maybe related to some "hidden variables" we can't observe. Locality means that measurements on parts of a system at far distant places can be performed in a way that the measurement at one place does not causally influence the outcome of the measurement at the other place. Bell also seems to accept the impossibility of faster-than-light causal influences (at least in the Physica 1 paper). Then reading different other papers by Bell, I'm not so sure anymore, what he wanted to say, but that doesn't matter. The clear mathematical formulation of what he means by "local realistic theory" is enough to see where it's contradicting Q(F)T, i.e., in the assumption of realism. Relativistic QFT in its usual realization as a local theory (local realization of the proper orthochronous Poincare group, microcausality constraints valid for local-observable-operators) excludes faster-than-light influences and thus includes the possibility that measurements at far distant places can be made without mutual causal influence of these measurements by ensuring that the "measurement events", where the measurement results at the far distant places are fixed, are space-like separated.

In Norsen's textbook "Foundations of Quantum Mechanics" Sect. 8.5 he outright and explicitly contradicts these mathematical (not interpretational!!!) facts about local relativistic QFT. It's not the quoted illustrious physicists who are wrong but indeed his interpretation of the EPR argument contradicts mathematical facts of relativistic QFT. It is telling that in the entire book the word "microcausality" doesn't occur at all (at least when searching with my pdf viewer). He also refutes strawmen about relativistic QFT and claims these were the opinions of experts in the field he calls
"most people have not really thought carefully about these kinds of issues".
 
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  • #683
Meow12 said:
Einstein: His Life and Universe by Walter Isaacson
THAT, I can read!
 
  • #684
vanhees71 said:
I don't know about how he presents Bell, because I don't know, what Bell wanted to say. The only thing I understand is the math, and there it's pretty clear what Bell means by "local realistic theory": realistic means that all observables always take determined values. A probabilistic description is only needed because of incomplete information about these values, maybe related to some "hidden variables" we can't observe. Locality means that measurements on parts of a system at far distant places can be performed in a way that the measurement at one place does not causally influence the outcome of the measurement at the other place. Bell also seems to accept the impossibility of faster-than-light causal influences (at least in the Physica 1 paper). Then reading different other papers by Bell, I'm not so sure anymore, what he wanted to say, but that doesn't matter. The clear mathematical formulation of what he means by "local realistic theory" is enough to see where it's contradicting Q(F)T, i.e., in the assumption of realism. Relativistic QFT in its usual realization as a local theory (local realization of the proper orthochronous Poincare group, microcausality constraints valid for local-observable-operators) excludes faster-than-light influences and thus includes the possibility that measurements at far distant places can be made without mutual causal influence of these measurements by ensuring that the "measurement events", where the measurement results at the far distant places are fixed, are space-like separated.

In Norsen's textbook "Foundations of Quantum Mechanics" Sect. 8.5 he outright and explicitly contradicts these mathematical (not interpretational!!!) facts about local relativistic QFT. It's not the quoted illustrious physicists who are wrong but indeed his interpretation of the EPR argument contradicts mathematical facts of relativistic QFT. It is telling that in the entire book the word "microcausality" doesn't occur at all (at least when searching with my pdf viewer). He also refutes strawmen about relativistic QFT and claims these were the opinions of experts in the field he calls
"most people have not really thought carefully about these kinds of issues".
Yes, this is also one of the thing I noticed and to me is not completely clear. But as I understand it, Norsen consciously (!) doesn't distinguish between locality as "no signalling faster than c can occur" and "no (perfect) correlations can exist between spacelike separated events". The success of QFT is, if I understand him and Bell's later papers correctly, despite its failure to incorporate this notion of locality.

It could well be that Bell himself changed his view about the meaning of "locality" in the almost three decades after he wrote his famour paper. Apparently Bell even considered going back to ethereal theories in an interview in the book "The ghost in the atom". As Norsen states on page 235,

Why did Bell take so seriously these sorts of ideas, which everybody else today regards as completely outmoded and wrong? Because he thinks his theorem (and the associated experimental evidence) proves that nonlocality is a fact of nature, rather than merely a defect of a type of theory we shouldn't believe in.

How I understand his point of view is something like "Look, of course QFT is really succesfull and it incorporates a notion of nonlocality which doesn't violate special relativity explicitly, but that's just because the underlying interpretation of the quantum mechanics refuses to say how those outcomes are realized in the first place. How does the measurement of particle 1 in the EPR experiment causes the outcome of the other? If entanglement is causation rather than mere correlation, why should we then adhere to locality (microcausality, as you call it) in the first place?"

So mathematically it's all good, as it should of course, but I have a feeling that Norsen (and Bell) are not satisfied by this explanation to distinguish between these different notions of locality. They see the Bell results as a hint of nature to take nonlocality more seriously, which explains why Bell adhered to the pilot wave theory which explicitly violates nonlocality.

I guess this is not the topic to discuss these issues, but this is what I make of Norsen's point of view now, and if that's the case, he could have make this distinction more clearly. And to add: I'm also not sure what to make of it myself :P
 
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  • #685
haushofer said:
Yes, this is also one of the thing I noticed and to me is not completely clear. But as I understand it, Norsen consciously (!) doesn't distinguish between locality as "no signalling faster than c can occur" and "no (perfect) correlations can exist between spacelike separated events". The success of QFT is, if I understand him and Bell's later papers correctly, despite its failure to incorporate this notion of locality.

It could well be that Bell himself changed his view about the meaning of "locality" in the almost three decades after he wrote his famour paper. Apparently Bell even considered going back to ethereal theories in an interview in the book "The ghost in the atom". As Norsen states on page 235,
How I understand his point of view is something like "Look, of course QFT is really succesfull and it incorporates a notion of nonlocality which doesn't violate special relativity explicitly, but that's just because the underlying interpretation of the quantum mechanics refuses to say how those outcomes are realized in the first place. How does the measurement of particle 1 in the EPR experiment causes the outcome of the other? If entanglement is causation rather than mere correlation, why should we then adhere to locality (microcausality, as you call it) in the first place?"

So mathematically it's all good, as it should of course, but I have a feeling that Norsen (and Bell) are not satisfied by this explanation to distinguish between these different notions of locality. They see the Bell results as a hint of nature to take nonlocality more seriously, which explains why Bell adhered to the pilot wave theory which explicitly violates nonlocality.

I guess this is not the topic to discuss these issues, but this is what I make of Norsen's point of view now, and if that's the case, he could have make this distinction more clearly. And to add: I'm also not sure what to make of it myself :P
I think many adherents of Bohmian mechanich, Norsen and Bell included (may be @Demystifier as well), do believe that what Bell's theorem implies is that strictly speaking relativity is wrong and there is a preferred frame and so on. For example http://www.scholarpedia.org/article/Bell's_theorem#Non-locality_and_relativity
 
  • #686
haushofer said:
Yes, this is also one of the thing I noticed and to me is not completely clear. But as I understand it, Norsen consciously (!) doesn't distinguish between locality as "no signalling faster than c can occur" and "no (perfect) correlations can exist between spacelike separated events". The success of QFT is, if I understand him and Bell's later papers correctly, despite its failure to incorporate this notion of locality.
That's nonsense. Standard relativistic QFT realized Einstein locality by the microcausality constraint.

It is no contradiction to causality that perfect correlations exist between space-like separated "measurement events", because the correlations described by entanglement are inherent to the states, i.e., if you create an entangled photon pair by, e.g., parametric downconversion, and there's no severe interaction with something on their path to detectors, which can be arbitrarily far away from the source as well as from each other, the 100% correlations due to entanglement can be (and in fact are) observed. There's nowhere a contradiction to Einstein causality in the description of the creation and measurement processes on these photons when relativistic QFT (in this case QED) is used by construction.
haushofer said:
It could well be that Bell himself changed his view about the meaning of "locality" in the almost three decades after he wrote his famour paper. Apparently Bell even considered going back to ethereal theories in an interview in the book "The ghost in the atom". As Norsen states on page 235,
How I understand his point of view is something like "Look, of course QFT is really succesfull and it incorporates a notion of nonlocality which doesn't violate special relativity explicitly, but that's just because the underlying interpretation of the quantum mechanics refuses to say how those outcomes are realized in the first place. How does the measurement of particle 1 in the EPR experiment causes the outcome of the other? If entanglement is causation rather than mere correlation, why should we then adhere to locality (microcausality, as you call it) in the first place?"
The outcomes are realized by the interaction between the measured system and the measurement device. The outcome is inherently random, i.e., there's no cause for the specific outcome of a single measurement (which is of course also an interpretation, but I think it's the only interpretation that is consistent with both the formalism of Q(F)T and all observations we have made so far). The measurement of particle 1 does not cause anything for the outcome of measurements on particle 2 (for sure, if these measurements are space-like separated). The 100% correlation when, e.g., measuring the polarization state of the photon in the same direction, is described by the two photon being prepared in an entangled state. Although the single outcomes are completely random (the single photons are simply ideally unpolarized) the 100% correlations are there due to the entanglement.
haushofer said:
So mathematically it's all good, as it should of course, but I have a feeling that Norsen (and Bell) are not satisfied by this explanation to distinguish between these different notions of locality. They see the Bell results as a hint of nature to take nonlocality more seriously, which explains why Bell adhered to the pilot wave theory which explicitly violates nonlocality.
But pilot-wave theory works for non-relativistic QT, which of course is in no sense of the word local. Even classical Newtonian mechanics is non-local. To the contrary, interactions are described by actions at a distance.
haushofer said:
I guess this is not the topic to discuss these issues, but this is what I make of Norsen's point of view now, and if that's the case, he could have make this distinction more clearly. And to add: I'm also not sure what to make of it myself :P
Also I think the way Norsen expresses it in a textbook is not a good scientific style. If you claim that the standard point of view is wrong, in pretty offending language btw, then at least you also have to give the reasons of these people following (and partially having established) the standard point of view and carefully disprove these reasons. Just telling, the standard point of view were wrong, only because it contradicts you personal world view, is a bit weak. In addition the Einstein locality of standard relativistic QFT is a mathematical property, i.e., it cannot be disputed away by some interpretational metaphysics.
 
  • #687
martinbn said:
I think many adherents of Bohmian mechanich, Norsen and Bell included (may be @Demystifier as well), do believe that what Bell's theorem implies is that strictly speaking relativity is wrong and there is a preferred frame and so on. For example http://www.scholarpedia.org/article/Bell's_theorem#Non-locality_and_relativity
Yes. That QFT still contains spooky action at a distance, which still needs an explanation. Of course, this depends on your "philosophical" stance: realist, anti-realist/instrumentalist, etc.

So contrary what @Vanhees71says about Norsen's paragraph 8.5, the issue is, I think, not mathematical, but interpretational.
 
  • #688
martinbn said:
I think many adherents of Bohmian mechanich, Norsen and Bell included (may be @Demystifier as well), do believe that what Bell's theorem implies is that strictly speaking relativity is wrong and there is a preferred frame and so on. For example http://www.scholarpedia.org/article/Bell's_theorem#Non-locality_and_relativity
Not sure whether saying "relativity is wrong" is the right way to put it. The suggestion that general relativity might be emergent is attractive, not just for Demystifier. And the conviction that there would be no "preferred frame" is not as clear cut as it may appear to the layman either:
gentzen said:
Even your example with the Earth is not as clear cut as it may appear to the layman (i.e. myself some month ago, before I dived a bit into the most basic introductions to cosmology and general relativity). It seems that we are moving relative to the universe at the speed of ~ 600 km/s. This is the speed of our galaxy relative to the cosmic microwave background. Maybe you object that me defending the “cosmic microwave background rest frame” as the preferred frame of reference is the sort of pointless debate your example tried to highlight.

However, there is something deeper going on. Your argument just looks at the physical laws, and ignores the importance of the initial state. The big bang at the beginning of time (of our universe) is that initial state in our case. It is very special and defines a preferred direction of time, namely away from that initial singularity. An the spatial directions “orthogonal” to it are the preferred rest frame, i.e. the CMB rest frame in our case.
My thinking went away from the "initial state" to "boundary conditions" in the meantime, but the point remains the same: A symmetry of the physical laws is not necessarily also a symmetry of the world around us.

My "most basic introduction to cosmology and general relativity" in that case was Jan-Markus Schwindt "Universum ohne Dinge", which also exists in English, but seems to be ridiculously overpriced at the moment. The thinking in that book shows clear traces at certain points of the author's academic supervisor, Christof Wetterich.
 
  • #689
vanhees71 said:
That's nonsense. Standard relativistic QFT realized Einstein locality by the microcausality constraint.

It is no contradiction to causality that perfect correlations exist between space-like separated "measurement events", because the correlations described by entanglement are inherent to the states, i.e., if you create an entangled photon pair by, e.g., parametric downconversion, and there's no severe interaction with something on their path to detectors, which can be arbitrarily far away from the source as well as from each other, the 100% correlations due to entanglement can be (and in fact are) observed. There's nowhere a contradiction to Einstein causality in the description of the creation and measurement processes on these photons when relativistic QFT (in this case QED) is used by construction.
No, it's not "nonsense": you misunderstand me (probably also due to how to use the word "locality"). With "this notion of locality" I mean the sort of locality, or "realism" if you want to call it that way, Einstein had in mind in order to explain away his problems with EPR. I guess critics would find your phrasing "the correlations described by entanglement are inherent to the states" merely descriptive, and not explanatory: the correlation is described, but not explained. I understand what quantum mechanics says and how it describes entanglement, but the whole point of EPR and Bell was to criticize the fact that it doesn't explain anything according to them.

Of course I understand that the relativistic notion of locality is build in in second quantization. That's part of a first course in QFT and not the issue here.

vanhees71 said:
The measurement of particle 1 does not cause anything for the outcome of measurements on particle 2 (for sure, if these measurements are space-like separated). The 100% correlation when, e.g., measuring the polarization state of the photon in the same direction, is described by the two photon being prepared in an entangled state.
Again: that's how quantum mechanics describes it. But the whole EPR paper was, as I understand it, to say that entanglement shows that for a realist this is not an explanation.
vanhees71 said:
Also I think the way Norsen expresses it in a textbook is not a good scientific style. If you claim that the standard point of view is wrong, in pretty offending language btw, then at least you also have to give the reasons of these people following (and partially having established) the standard point of view and carefully disprove these reasons. Just telling, the standard point of view were wrong, only because it contradicts you personal world view, is a bit weak. In addition the Einstein locality of standard relativistic QFT is a mathematical property, i.e., it cannot be disputed away by some interpretational metaphysics.
Again: nobody disputes the (as you call it) "locality of standard relativistic QFT" as one imposes in the quantization procedure of QFT (I'd call it "relativistic locality", because I doubt whether Einstein would be satisfied by it, but that's merely a guess).

Look, I'm not asking you to agree with me; I'm not even sure what to think of all this stuff myself. But I have a feeling that you miss the point of Norsen here (also because you claim the essence here is mathematics, not interpretations), and just labels it as his misunderstanding. But anyway, I don't need to defend other physicists here on issues I myself don't have a strong opinion about. I'm merely suggesting that you misread him, that's all.
 
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  • #690
Maybe we should ask Norsen himself :P
 
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  • #691
haushofer said:
Again: that's how quantum mechanics describes it. But the whole EPR paper was, as I understand it, to say that entanglement shows that for a realist this is not an explanation.
But physical theories don't explain anything but "only" describe.
haushofer said:
Again: nobody disputes the (as you call it) "locality of standard relativistic QFT" as one imposes in the quantization procedure of QFT (I'd call it "relativistic locality", because I doubt whether Einstein would be satisfied by it, but that's merely a guess).

Look, I'm not asking you to agree with me; I'm not even sure what to think of all this stuff myself. But I have a feeling that you miss the point of Norsen here (also because you claim the essence here is mathematics, not interpretations), and just labels it as his misunderstanding. But anyway, I don't need to defend other physicists here on issues I myself don't have a strong opinion about. I'm merely suggesting that you misread him, that's all.
Maybe than I don't understand Norsen right. I read his rattle against the standard view as saying that "relativistic locality" in fact must be violated, but that bluntly contradicts the mathematics of relativistic QFT. Of course, it's hard to understand vague philosophical ideas generally. So maybe Norsen doesn't say, what I understand him to say.
 
  • #692
haushofer said:
Maybe we should ask Norsen himself :P
Maybe someone could move this off topic discussion to another thread.
 
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  • #693
 Something Deeply Hidden  by Sean Carroll. It's a non-mathematical intro to Quantum Mechanics.
 
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  • #694
Meow12 said:
 Something Deeply Hidden  by Sean Carroll. It's a non-mathematical intro to Quantum Mechanics.
Well, its first part is "the best" introduction to the Many Worlds Interpretation (and Sean Carroll's perspective on it), and the second part is an introduction to Sean's own work on QFT and gravity emerging from QFT.
 
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  • #695
vanhees71 said:
But physical theories don't explain anything but "only" describe.
I agree with Demystifier that this is offtopic and should be relocated, but I'll just give one last reply, because I think this sentence is at the essence of the discussion: what's the difference between explaining and describing?

Physics does more than "only describing". "Only describing" is what a black box does: you get the right output, but you don't really understand what's under the hood. On top of that, in physics we use causal explanations. E.g., a pole of height 1 m casts a shadow on the ground of length 2,7 m. That follows from simple goniometry. But we don't read that equation "tangent of the angle is length of pole divided by length of shadow" always causally. E.g., we don't interpret this equation "length of shadow is length of pole divided by tan(20)" causally: it doesn't explain the length of the pole.

I guess people like Einstein considered the wavefunction in the EPR-experiment in a similar way: it's a useful calculational tool, but it doesn't give a causal explanation of why there is this perfect correlation between the particles.

Anyway, I'll leave it with this. I'd be happy to hear your thoughts in a separate topic at some later time. Which I would have opened myself if I had the time right now, but I'm busy finishing my next popular science book which is published this summer and needs my attention right now :P
 
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  • #696
I just started

"Mathematics for Machine Learning" by Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong

I look forward to demystifying all the complex machinery behind machine learning and understanding it from a mathematical point of view.

Personal Anecdote: After graduating with a masters in physics I had trouble breaking into tech/data science so I enrolled in one of those "Data Science Bootcamps". It was stupid so I quit, none of the mathematical details were divulged, just superficial banalities about "Bias vs. Variance trade-off" (which is a real thing but it's not like they actually explained it). I actually had to explain the concept of a partial derivative to one of the bootcamp instructors when doing "multilinear regression". I said "f this I'm out".

I feel like this book will help me actually grasp AI/ML on a level that isn't superficial/deluded/pretentious.

/soapbox

Also it's available for free by the Authors via Github if anyone is interested

https://mml-book.github.io/book/mml-book.pdf
 
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  • #697
Presently reading The Trouble with Physics by Lee Smiling.
 
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  • #698
Jodo said:
Presently reading The Trouble with Physics by Lee Smiling.
Haha Smiling. Sorry Lee Smolin
 
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  • #699
pinball1970 said:
THAT, I can read!
There's one written by Isaac Walterson in a reverse universe.
 
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  • #700
Information Theory by Cover.
 

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