Is string theory a theory?

haushofer

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Apologies this is veering off into metaphysics, but there is another sociological danger with too much reliance on 'falsifiability' and that is what is known as lamp post physics.
The analogy goes as follows:

Suppose you were looking for the proverbial needle in the haystack and you knew it was located somewhere in a dark street. Now at some point in time a street light would turn on, illuminating a small portion of the street. I could make a theory (or a set of theories) describing in detail how the needle (or set of needles) happened to be right where the light would illuminate. A perfectly sound, falsifiable idea.

But in the absence of any other reason to be there, my theory has no new information content even though I have now given myself some percentage of chance for having correctly described the situation (and winning an award). Meanwhile the idea that the needle might be closer to the seamstress's house seems to be a better idea, although of course it is completely unfalsifiable (b/c it stays in the dark).
Don't apologize. These are important questions for physicist. Otherwise we are just sophisticated bookkeepers :P
 

Demystifier

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Same goes for "energy". It's happened over and over again: Study some system in detail and find that energy seems to be lost? Just postulate a new kind of energy! Now energy is just changing form.

"Energy is conserved" is more or less a tautology; it only requires that you define energy appropriately.
A good example is general relativity. There, energy-momentum tensor of matter does not obey global conservation. But then one invents an ugly non-covariant object called energy-momentum pseudo-tensor, which does obey global conservation.

There is also a much cheaper way to resolve the problem of conserved energy-momentum in GR
http://lanl.arxiv.org/abs/1407.8028
but physicists object that it is too useless.

Sorry for the off-topic, but I couldn't resist. :sorry:
 

Demystifier

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Don't apologize. These are important questions for physicist. Otherwise we are just sophisticated bookkeepers :P
Or to paraphrase Rutherford, otherwise physicists risk to become stamp collectors.
 

marcus

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All of these are examples of specific models which are constructed such that their predictions would be testable, and are subsets of much more general frameworks. They are all basically examples of lamppost physics.
You would dismiss this as "lamppost physics"? :

http://arxiv.org/abs/1509.05693
Detailed analysis of the predictions of loop quantum cosmology for the primordial power spectra
Ivan Agullo, Noah A. Morris
(Submitted on 18 Sep 2015)
We provide an exhaustive numerical exploration of the predictions of loop quantum cosmology (LQC) with a post-bounce phase of inflation for the primordial power spectrum of scalar and tensor perturbations. We extend previous analysis by characterizing the phenomenologically relevant parameter space and by constraining it using observations. Furthermore, we characterize the shape of LQC-corrections to observable quantities across this parameter space. Our analysis provides a framework to contrast more accurately the theory with forthcoming polarization data, and it also paves the road for the computation of other observables beyond the power spectra, such as non-Gaussianity.
24 pages, 5 figures
 
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Hm ... was quantum theory derived from a well-defined set of general principles and assumptions in the first place? When I look at the history it rather seems that it was extended ad-hoc in some step-by-step manner.
This was the initial situation. Later it has become a theory. The papers of Heisenberg and Schrödinger, together with the Born rule which clarified that the wave function defines the probability have transformed this vague old "quantum theory" into a real physical theory.

I don't know string theory good enough to judge if it has already reached such a level, but all what I have heard indicates that it has not yet reached this state.
 
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This was the initial situation. Later it has become a theory. The papers of Heisenberg and Schrödinger, together with the Born rule which clarified that the wave function defines the probability have transformed this vague old "quantum theory" into a real physical theory.
That's true. But you cannot change the original derivation of something at a later point in time. If a result was originally derived in a certain way, that will will stay the way it was originally derived until the end of time. It might turn out that there are additional ways to derive the same result, but that does not change the original derivation.
 
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That's true. But you cannot change the original derivation of something at a later point in time. If a result was originally derived in a certain way, that will will stay the way it was originally derived until the end of time. It might turn out that there are additional ways to derive the same result, but that does not change the original derivation.
No. Results about planets have been derived a long time using Newtonian mechanics. Then GR came, and after this all what we think about planets has been rederived based on GR. This will happen again if some better theory of gravity will be found.

The same holds, of course, for quantum results. What has been derived in old quantum "theory" has been rederived later based on quantum theory as we use it today.

And, given that many quantum results are only approximate, they are recomputed all the time if a better approximation method or simply a more powerful computer or computation program appears. And in all these cases, the former derivation are no longer interesting except for history.
 
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No. Results about planets have been derived a long time using Newtonian mechanics. Then GR came, and after this all what we think about planets has been rederived based on GR. This will happen again if some better theory of gravity will be found.

The same holds, of course, for quantum results. What has been derived in old quantum "theory" has been rederived later based on quantum theory as we use it today.

And, given that many quantum results are only approximate, they are recomputed all the time if a better approximation method or simply a more powerful computer or computation program appears. And in all these cases, the former derivation are no longer interesting except for history.
If the result changes, then we are not speaking of rederivation anymore.

You can rederive the same results as many times as you want: The rederivation never becomes the original derivation.
 

marcus

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Video of the talks to be given at next week's conference on issues like these will be available free on line (according to the organizers)
http://www.whytrustatheory2015.philosophie.uni-muenchen.de/program/index.html
===quote==
Monday (7 December)
Time Topic
09:30 - 09:50 Opening
09:50 - 10:30 David Gross: What is a Theory?
10:30 - 11:10 Carlo Rovelli: Has Theoretical Fundamental Physics become Sterile?
11:10 - 11:35 Coffee Break
11:35 - 12:15 Richard Dawid: Non-empirical Confirmation
12:15 - 12:55 Massimo Pigliucci: Post-empirical Physics, Falsificationism, and the Public Perception of Science
12:55 - 14:35 Lunch
14:35 - 15:15 Radin Dardashti: Physics without Experiments?
15:15 - 15:55 Helge Kragh: Fundamental Theories and Epistemic Shifts: Can History of Science serve as a Guide?
15:55 - 16:35 Peter Achinstein: Scientific Speculation
16:35 - 17:00 Coffee Break
17:00 - 18:30 Panel I (Host: Stephan Hartmann): Why Trust a Theory?
Tuesday (8 December)
Time Topic
09:30 - 10:10 Björn Malte Schäfer: Dark Gravity, Dark Fluids, and Dark Statistics
10:10 - 10:50 Chris Smeenk: Gaining Access
10:50 - 11:20 Coffee Break
11:20 - 12:00 Gordon Kane: String/M-Theories about our World are Testable in the Traditional Physics Way
12:00 - 12:40 Joseph Silk: The Limits of Cosmology, Post-Planck
12:40 - 14:30 Lunch
14:30 - 15:10 Fernando Quevedo: Achievements and Challenges for String
Phenomenology/Cosmology

15:10 - 15:50 Chris Wüthrich: Considering the Role of Information Theory in
Fundamental Physics

15:50 - 16:30 Viatcheslav Mukhanov: Is the Quantum Origin of Galaxies Falsifiable?
16:30 - 17:00 Coffee Break
17:00 - 18:30 Panel II (Host: Johanna Erdmenger): How far do we get with Empirical Data?
19:15 Dinner (Cafe Reitschule)
Wednesday (9 December)
Time Topic
09:30 - 10:10 George Ellis: Limits in testing the Multiverse
10:10 - 10:50 Joseph Polchinski: String Theory to the Rescue
10:50 - 11:20 Coffee Break
11:20 - 12:00 Elena Castellani: Scientific Methodology: A View from Early String Theory
12:00 - 12:40 Dieter Lüst: Aspects of Quantum Gravity
12:40 - 14:30 Lunch
14:30 - 15:10 Sabine Hossenfelder: Lost in Math
15:10 - 15:50 Karim Thebault: What can we learn from Analogue Experiments?
15:50 - 16:30 Georgi Dvali: Secret Quantum Lives of Black Holes and Dark Energy
16:30 - 17:00 Coffee Break
17:00 - 18:30 Panel III (Host: Daniele Oriti): Has Physics changed? – and should it?
Abstracts
...
...

[endquote]
 
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marcus

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Sample abstracts of some of the talks to be given at the conference:
==quote==
Massimo Pigliucci: Post-empirical Physics, Falsificationism, and the Public Perception of Science
Trouble, as explicitly hinted at in the title of a recent book by Lee Smolin, has been brewing for a while within the fundamental physics community. Ideas such as string theory and the multiverse have been both vehemently defended as sound science and widely criticized for being “not even wrong,” in the title of another book, by Peter Woit. Recently, George Ellis and Joe Silk have written a prominent op-ed piece in Nature, inviting their colleagues to defend the very integrity of physics. To which cosmologist Sean Carroll has responded that physics doesn’t need "the falsifiability police,” referring to the famous (and often misunderstood or badly applied) concept introduced by Karl Popper to demarcate science from pseudoscience. The debate isn’t just “for the heart and soul” of physics, it has spilled onto social media, newspapers and public radio. What is at stake is the public credibility of physics in particular and of science more generally — especially in an era of widespread science denial (of evolution and anthropogenic climate change) and rampant pseudoscience (antivax movement). Since philosophers of science have been invoked by both sides, it is time to take a look at the “physics wars” from a detached philosophical perspective, in my case informed also by my former career as an evolutionary biologist, a field that has peculiar similarities with what is going on in fundamental physics, both in terms of strong internal disputes and of perception by a significant portion of the general public.

Helge Kragh: Fundamental Theories and Epistemic Shifts: Can History of Science serve as a Guide?
Epistemic standards and methodologies of science inevitably reflect the successes and failures of the past. In this sense, they are in part of a historical nature. Moreover, the commonly accepted methodological criteria have to some extent changed over time. Faced with the problem of theories that cannot be tested empirically, perhaps not even in principle, it may be useful to look back in time to situations of a somewhat similar kind. Roughly speaking, previous suggestions of non-empirical testing have not fared well through the long history of science. Ambitious and fundamental theories of this kind have generally been failures, some of them grander than others. So, is there any reason to believe that they will not remain so in the future? Can we infer from history that empirical testability is a sine qua non for what we know as science? Not quite, for it is far from obvious that older scientific theories can be meaningfully compared to modern string theory or multiverse physics. History of science is at best an ambiguous guide to present and future problems, yet it does provide reasons for scepticism with regard to current suggestions of drastic epistemic shifts which essentially amounts to a new “definition” of science.

George Ellis: Limits in testing the Multiverse
Our ability to test cosmological models is severely constrained by visual horizons on the one hand, and physical horizons (limits on testing physical theories) on the other. Various arguments have been given to get round these limitations. I will argue that these amount to philosophical choices, which may or may not correspond to physical reality, and hence resulting claims do not amount to established scientific results. This holds in particular to a variety of claims of physical existence of infinities of galaxies, universes, or beings like ourselves in a multiverse. We need a strong philosophical stance to distinguish which of these claims should indeed be regarded as proven science,and which not.

Carlo Rovelli: Has Theoretical Fundamental Physics become Sterile?
Fundamental physics has changed from a field capable of spectacular successful predictions (electromagnetic waves, black holes, antiparticles, just to name a few...) to a depressing sequence of failed predictions: low-energy supersymmetry being the most recent and burning. Why? I will consider the possibility that the last generation of theoretical physicists has modified the practice of scientific method. Unproductively.
...
...
[endquote]
 
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I look forward to hear this:

Peter Achinstein: Scientific Speculation
Throughout the history of science controversies have emerged regarding the legitimacy of speculating in science. Three very strong views about the general practice of speculating have emerged: One, very conservative, says “never do it, or at least never publish it.” It is the official doctrine of Isaac Newton: “hypotheses have no place in experimental philosophy.” (Of course, he violated his official doctrine on several occasions). Another, more moderate position is the official doctrine of hypothetico-deductivists such as Whewell, Popper, and Hempel: speculate freely but verify before publishing. The third, the most liberal, is suggested by Feyerabend’s principle of proliferation: speculate like mad, and publish, even when you have no idea how to test your speculations.

In my talk I want to reject all three of these views. They are too simple-minded. Some speculations are good ones, some not so good. I will ask how a speculation is to be evaluated. In the process of doing so, I will consider two historically important speculations: James Clerk Maxwell’s kinetic theory speculations from 1860 to 1875, and a speculation that has been put forward by some string theorists, as well as by others, viz. that there is a “theory of everything” (whether or not it is string theory). The first, I will argue, deserves praise, the second does not.

Sabine Hossenfelder: Lost in Math
I will speak about the role of social and cognitive biases in hypotheses pre-selection, and reflect on the rationale behind the concepts of naturalness, simplicity and beauty.

Helge Kragh: Fundamental Theories and Epistemic Shifts: Can History of Science serve as a Guide?
Epistemic standards and methodologies of science inevitably reflect the successes and failures of the past. In this sense, they are in part of a historical nature. Moreover, the commonly accepted methodological criteria have to some extent changed over time. Faced with the problem of theories that cannot be tested empirically, perhaps not even in principle, it may be useful to look back in time to situations of a somewhat similar kind. Roughly speaking, previous suggestions of non-empirical testing have not fared well through the long history of science. Ambitious and fundamental theories of this kind have generally been failures, some of them grander than others. So, is there any reason to believe that they will not remain so in the future? Can we infer from history that empirical testability is a sine qua non for what we know as science? Not quite, for it is far from obvious that older scientific theories can be meaningfully compared to modern string theory or multiverse physics. History of science is at best an ambiguous guide to present and future problems, yet it does provide reasons for scepticism with regard to current suggestions of drastic epistemic shifts which essentially amounts to a new “definition” of science.
 
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in germany we have a hard debate about this theme. It is time for such a conference.
especially particle physicists are now more and more aggressive and see that they lost the game

Here they pray sarcastically against Ed Witten

"Witten unser, der Du bist in Princeton,
Publiziert werde Dein Name,
Dein Bran komme, Deine Theorie bestehe
Wie in Dimensionen Also auch auf Erden
Unsern täglich’n Einfall gib uns heute,
Und vergüt’ uns uns’ren Kult,
So wie auch wir nur geben unsren Huldigern.
Und führe uns nicht zu Versuchen
Sondern erlöse uns von der Prüfung
Denn Dein ist der String, und die Kraft
Und die Unwiderlegbarkeit
In Ewigkeit. Amen."
 

Haelfix

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You would dismiss this as "lamppost physics"? :
The first paper you linked to is, the second you linked to is not. The second is some work related to scanning the parameter space within loop quantum cosmology, where clearly some of the models within that set have testable predictions and some do not. The first paper on the other hand is lamppost physics by definition. In fact it is an attempted proof that there is a lamppost at all! Inflation has a tendency to wipe out most primordial imprints of quantum gravity, so the paper is making the point that at least a small portion of the parameter space can leave an imprint in the CMB.

Anyway I think you misunderstand me, there is nothing necessarily wrong with lamppost physics, there are many great models that are constructed as such (indeed some have won Nobel prizes). Most physicists write many such things within their lifetime, I certainly have. Indeed it is important to look where you can, and we do the best we can under the situation. However the point of the analogy is that there is often very good models/ideas that are NOT falsifiable right from the getgo and just because something is falsifiable, does not necessarily endow it with some special virtue in and of itself as the needle in the haystack example tries to show. For that you typically need to look at the details of the model.
 

marcus

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in germany we have a hard debate about this theme. It is time for such a conference.
...
...

"Witten unser, der Du bist in Princeton,
Publiziert werde Dein Name,
Dein Bran komme, Deine Theorie bestehe
Wie in Dimensionen Also auch auf Erden
Unsern täglich’n Einfall gib uns heute,
Und vergüt’ uns uns’ren Kult,
So wie auch wir nur geben unsren Huldigern.
Und führe uns nicht zu Versuchen
Sondern erlöse uns von der Prüfung
Denn Dein ist der String, und die Kraft
Und die Unwiderlegbarkeit
In Ewigkeit. Amen."
heh heh :oldbiggrin:
I found an English translation in google books--- from Unzicker "Bankrupting Physics"
https://books.google.com/books?id=dcgTAAAAQBAJ&pg=PA183&dq="Our+witten+who+art+in+Princeton,+published+be+thy+name.+Thy+brane+come"&hl=en&sa=X&ved=0ahUKEwif_sC9zcHJAhVI82MKHQoFCV8Q6AEIHTAA#v=onepage&q="Our witten who art in Princeton, published be thy name. Thy brane come"&f=false

A different version in English is here:
http://resonaances.blogspot.com/2007/01/cern-th-2007.html
 

haushofer

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I'm excited about this conference and didn't know about it! My personal view is that too much emphasis in our field has shifted from philosophy and conceptual interpretation towards doing calculations. I agree e.g. with the amazement of Bell about why people haven't paid more attention to Bohmian mechanics and the critics it gets from 'opponents'. Also populair science books don't devote much space to philosophy.

And to be honest, I don't understand in many cases when topics here are closed with the argument that it is 'metaphysics' or 'philosophy'. That's a sidermark, but it shows the distinction people make between mathematical models and their interpretations.

For me this is one important reason to be interested in string theory. Its very existence raises a lot of interesting questions and possible answers to these issues in a concrete way.
 

marcus

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Hi Haelfix, thanks for your reply. I was just getting off to bed,will respond in the morning.
 
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I'm excited about this conference and didn't know about it! My personal view is that too much emphasis in our field has shifted from philosophy and conceptual interpretation towards doing calculations. I agree e.g. with the amazement of Bell about why people haven't paid more attention to Bohmian mechanics and the critics it gets from 'opponents'. Also populair science books don't devote much space to philosophy.

And to be honest, I don't understand in many cases when topics here are closed with the argument that it is 'metaphysics' or 'philosophy'. That's a sidermark, but it shows the distinction people make between mathematical models and their interpretations.

For me this is one important reason to be interested in string theory. Its very existence raises a lot of interesting questions and possible answers to these issues in a concrete way.
I can understand why physicists don't want speculations because all the last 70 years we had much speculations about quantumtheory and their interpretation. Heisenberg saw this long before and said that we only should calculate and don't want to see in the black box (although he was much more afraid of the positivistic lame middleintelligent physicists who only take all for granted what he was talking about without thinking by themself) . But you cannot forbid to look in the black box and then a lot of esoteric religions, believing systems developed over the time. Evene the religions itselves are now argueing with quantumtheory for their believing system (free will, probability etc.)
And now we have a lot of physicists who are religious in some kind also and want to defend this established physics for their believing system too. Big bang with creator, Quantumtheory for free will etc.
We have now similar situation as it was in old greek before Platon.

On the other hand we have now the first possibility with string theory to get a theory which cannot be misused for religious believing system because it is explicitely without a creator, without indeterministic interpretations. This makes a lot people afraid.

Freud explained this behaviour and thinking behind of such physicists and religious people psychologically that it is a narzistic violation. We had it all the time in science history.
It was with the end of ptolomaic worldview. With darwins evolutiontheory and now we get it with modern physics of multiverses especially which makes most afraid.
 

fresh_42

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On the other hand we have now the first possibility with string theory to get a theory which cannot be misused for religious believing system because it is explicitely without a creator, without indeterministic interpretations.
You bet?
 
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I would never bet ;-) You can create a religion out of Harry Potter also lol

But Stringtheory means in many views a complete paradigm change for all established religions and especially for esoteric believing systems. And most will not follow them. Hopefully! Otherwise we can say that they are currupted lol

For christians (jews, muslim) it would be a complete change and they have no fundament anymore they can say that it is also proved by science what they believe (creator, free will ...). And this is most important I think.
 
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But Stringtheory means in many views a complete paradigm change for all established religions
How conforting it feels for me to think that science can eventually describe the "Godly" occurrences or "miracles", as a basic example, if a God could and would perform such a feat. String theory is only one possible "theory of everything" that leads humans towards Godly powers so at some point you get off the hype and look at it realistically and see that science and religion don't "have" to conflict. It is all human interpretation of stories, written by fallible humans. Fallible in science as well. To suppose all the atoms are vibrating strings which oscillate with deterministic interference undermining our ability to physically alter the universe seems like the most far-fetched science/religion theory, to date, in my humble opinion.
 
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How conforting it feels for me to think that science can eventually describe the "Godly" occurrences or "miracles", as a basic example, if a God could and would perform such a feat. String theory is only one possible "theory of everything" that leads humans towards Godly powers so at some point you get off the hype and look at it realistically and see that science and religion don't "have" to conflict. It is all human interpretation of stories, written by fallible humans. Fallible in science as well. To suppose all the atoms are vibrating strings which oscillate with deterministic interference undermining our ability to physically alter the universe seems like the most far-fetched science/religion theory, to date, in my humble opinion.
yes maybe you are right. Some see in the mathematics/theoretical physics the way to touch godly power like Paul Halmos
"I am not a religious man, but it’s almost like being in touch with god when you’re thinking about mathematics."
 

fresh_42

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yes maybe you are right. Some see in the mathematics/theoretical physics the way to touch godly power like Paul Halmos
"I am not a religious man, but it’s almost like being in touch with god when you’re thinking about mathematics."
I'm more and more in doubt about "the beauty of math". Of course it exists, I can see it, too. We all have a sense of beauty and aesthetic. One of my favorites is the infinity of primes for you can tell every school kid how it is proved. Same with Cantor's diagonal argument. Or the concept of normal subgroups. All of them have a kind of inner beauty. However, when I remember, e.g. Galois' original text which you can hardly follow. (I've found it by chance in an old book beneath a bunch of old books the library wanted to get rid of because they feared the work to be done to catalog all of them.) And next how Artin wrote his textbook about Galois Theory and then how Bourbaki would have done it - then all three describe the same thing in a completely different way and language. Doesn't that mean that what's regarded as beautiful simply changes as times go by? Personally I find the AdS explanation not very convincing but couldn't this just change when we once get used to it (if proven suitable.)?
 
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I'm more and more in doubt about "the beauty of math". Of course it exists, I can see it, too. We all have a sense of beauty and aesthetic. One of my favorites is the infinity of primes for you can tell every school kid how it is proved. Same with Cantor's diagonal argument. Or the concept of normal subgroups. All of them have a kind of inner beauty. However, when I remember, e.g. Galois' original text which you can hardly follow. (I've found it by chance in an old book beneath a bunch of old books the library wanted to get rid of because they feared the work to be done to catalog all of them.) And next how Artin wrote his textbook about Galois Theory and then how Bourbaki would have done it - then all three describe the same thing in a completely different way and language. Doesn't that mean that what's regarded as beautiful simply changes as times go by? Personally I find the AdS explanation not very convincing but couldn't this just change when we once get used to it (if proven suitable.)?
It was always the same in mankind history that we saw the beauty in mathematics, when we find a lot of descriptions from different views on the same thing. Then we "see" something which is behind or is underlying and especially when we "see" kind of reality we can find in the real world. The most powerful beauty lies in the stringtheory that we have a lot of equivalences ( think of T duality) , which we are used to in General Relativity too (acceleration/gravity). And the best is, that out of this model there were many problems in mathematics proved/solved like topologies and their axiomatik, which makes sense now and is not anymore any assumption.

We always learn at school that we live in an euclidic world and know that two parallel lines have always the same distance and cannot cross. It was a hard principle like a dogma. Since Einstein (although we knew that the earth is not flat ;-) ) we know it can and is a princple of spacetime in universe. It was not so convincing for the most. An old naiv believing system was completely vanished since 100 years now. Now it is for us not a problem anymore to believe that parallel lines can even cross. The same will be with AdS in time.

The old Idea of natural numbers like the pythagoreer had, that it must be an underlying reason for the numbers we have now since Plato in ideas and know since Wittgenstein that we are playing games with mathematical language. We are always since old greek in this tensionfield between Platos ideas and wittgensteins game of mathematical language to see the sun directly out of the cave.

btw FYI A new nice book if you can read german.
Thomas Bedürftig /Roman Murawski -
Philosophie der Mathematik - De Gruyter Verlag
 
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fresh_42

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I feel very comfortable with my Platonism, despite Zorn, Goedel, constructivism, Bohr, Einstein and Schrödinger; or Wittgenstein. The latter doing with words what Pythagoras did with numbers: esoteric nonsense. I even subsume musical compositions and all concepts of religion under Plato's ideas dropping thus the question about existence. I admit this might be a little lazy. :cool:

But back to AdS. What does a hyperbolic curvature prefer to a elliptic one? (Assuming both are locally flat, with some very large charts in spacetime.)
 
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I feel very comfortable with my Platonism, despite Zorn, Goedel, constructivism, Bohr, Einstein and Schrödinger; or Wittgenstein. The latter doing with words what Pythagoras did with numbers: esoteric nonsense. I even subsume musical compositions and all concepts of religion under Plato's ideas dropping thus the question about existence. I admit this might be a little lazy. :cool:

But back to AdS. What does a hyperbolic curvature prefer to a elliptic one? (Assuming both are locally flat, with some very large charts in spacetime.)
you seem to have a widespread humanistic education. ;-) That's great. :-) In our days not many have this anymore. :-(

But to the musical composition and kind of religion as philosophy I must say that this was included in the the thinking of the Pythagoreer too. Platon took that over from them in his ideas. With ratio of course and not so esoteric anymore because he found them criminal to hide their knowledge about the principles of mathemtics and nature and who made an esoteric cult out of it. Plato was a rebell in his time and wanted to teach all his knowledge for all people who were intellectual able to understand it in his academia.

hyperbolic is for some reasons more attractiv. We see e.g. how it works better for gravity in an additional spacedimension and we see hyperbolic structures in black holes as hint. On the other side we can explain much better phenomens like accelerating expansions in spacetime. I think these are the main reasons so far. If we calculate for möbius transformations in compactified space then it could be also that elliptic could be a good approximation too, but I don't know really. Never looked it up. String theory is now over time a good in itself extremely consistant model and is working with hyperbolic space.
 

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