TOE's getting a little crazy?

  • #1

Main Question or Discussion Point

I'll start off by admitting that just because the "laws of the universe" go against what we might intuit them to be is no grounds to assert their falsehood, but I do have to pose a subjective question:

Do you guys feel that perhaps our current stabs at a ToE are just getting a bit outlandish?

Personally I do. I understand the idealism that "if the math works, then we've got to run with it" but I wonder if the many multi-dimensional ToE's with all sorts of complicated geometries involving string and the like are just throwing layers of math to cover up the initial logic that is being sacrificed. And of course, the more we find out, the more math (and complicated semantic explanation) we need. In short, at gut feeling I believe we just don't know enough about how the universe works right now to be taking stabs in this manner, and we end up laughing at Occam's Razor in the process.

Like I said, this is totally subjective, but does anyone feel me on this?
 

Answers and Replies

  • #2
martinbn
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If the math was working it would be great but I don't think it is the case.
 
  • #3
Pengwuino
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I'm sure this is exactly what they thought when things like QED were being formulated. If you have a better way to explain what is going on, there's a nobel prize waiting for you.
 
  • #4
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I think it may be impossible for us to find the Theory of Everything . even If String theory is experimentally verified and we know everything about it (Which is unlikely ), There will be things that will show up that require further explanation and so on . The more we understand things, the more things that show up that require explanation which may require new math tools and new radical physical ideas .
 
  • #5
I'll start off by admitting that just because the "laws of the universe" go against what we might intuit them to be is no grounds to assert their falsehood, but I do have to pose a subjective question:

Do you guys feel that perhaps our current stabs at a ToE are just getting a bit outlandish?

Personally I do. I understand the idealism that "if the math works, then we've got to run with it" but I wonder if the many multi-dimensional ToE's with all sorts of complicated geometries involving string and the like are just throwing layers of math to cover up the initial logic that is being sacrificed. And of course, the more we find out, the more math (and complicated semantic explanation) we need. In short, at gut feeling I believe we just don't know enough about how the universe works right now to be taking stabs in this manner, and we end up laughing at Occam's Razor in the process.

Like I said, this is totally subjective, but does anyone feel me on this?
It seems to me that the basic idea was to use the top-down method: decide what kind of theory you wanted, then figure out the features that any theory with such properties must have. That narrowed it down to 10^500 theories, but the project seems to have gotten stuck there. Also, there is no assurance that the way the Universe works is in accord with any theory with said desirable properties.

The old bottom-up experimentally driven method may have ended up with a kludgey result, but it works in a broad domain and is reasonably understandable.
 
  • #6
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A TOE would explain where the principles of quantum mechanics come from. I've not seen any main stream research agendas that even attempt this. They all seem to just accept the math because it provide results in some situations, and so they feel justified in applying it to all situations. What needs to happen is to derive QM from the principles of logic alone (IMO). And this might tell us where it applies and under what circumstances we can use it. But it seems as of this date we don't really know that QM should be applied to GR.
 
  • #7
A TOE would explain where the principles of quantum mechanics come from. I've not seen any main stream research agendas that even attempt this. They all seem to just accept the math because it provide results in some situations, and so they feel justified in applying it to all situations. What needs to happen is to derive QM from the principles of logic alone (IMO). And this might tell us where it applies and under what circumstances we can use it. But it seems as of this date we don't really know that QM should be applied to GR.
Agreed. The current trend does not seem to be to look for a physics that makes sense, but to find the equations that work and hope/assume it will make sense sometime. The later is certainly a pragmatic approach, but I still believe in logic, even if it is bizarre logic. If we extrapolate too far without that solid foundation, I fear we endanger the credibility of our equations even if they work.

But yes, even with the many QM interpretations out there, it really does seem to me that a good start would be to attempt verification of one of those theories before we set out on a global ToE. It's like everyone is trying to come up with a single best route to Hawaii, but some of us are starting in Tokyo and others in Canada... ok, it's at least a decent analogy...
 
  • #8
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What alternative is there to the complexity? Do you accept Quantum Mechanics? Do you accept Relativity? They are both heavily mathematical and difficult for the average person to grasp conceptually. If you accept both, you also must accept the fundamental differences between the two.

Finding a way to bring them together is mathematically and conceptually advanced. The TOE will, by nature, be more difficult to understand and formulate than either of its two basic components.

Perhaps Einstein should have given up on formulating GR, since Newton's physics were simpler and accurate enough....

That's not the way Occam's Razor works.
 
  • #9
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But it seems as of this date we don't really know that QM should be applied to GR.
Ever heard of the big bang? That is a situation where high density(GR) and very small distances(QM) arise.

Unless you believe the universe is infinite, and then by necessity have a situation where QM won't apply.
 
  • #10
What alternative is there to the complexity? Do you accept Quantum Mechanics? Do you accept Relativity? They are both heavily mathematical and difficult for the average person to grasp conceptually. If you accept both, you also must accept the fundamental differences between the two.

Finding a way to bring them together is mathematically and conceptually advanced. The TOE will, by nature, be more difficult to understand and formulate than either of its two basic components.

Perhaps Einstein should have given up on formulating GR, since Newton's physics were simpler and accurate enough....

That's not the way Occam's Razor works.
By your argument, the basics premise for how evolution works would really be in trouble. Sure our world is highly complex. The interactions of one atom with another to form a molecule aren't quite like how one would play with legos, but the individual fundamentals behind the interaction can be argued as "simple." At least for now, it seems that though our universe is complex, it is an emergent complexity. A ToE may be complicated to sort through, but that does not mean its individual components must themselves be complicated (especially, hopefully, as we are getting to more and more fundamental/core bits of the universe). Thus regardless of how complicated the system as a whole seems, if we understand the behavior of the individual components, I see no reason an individual with slight explanation (not even necessarily an expert) can say "hmm, I guess that makes sense."
 
  • #11
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I don't see how you get from "my argument" to "evolution being in trouble."

I'm not saying that an explanation for something complicated is going to be necessarily complex.

I'm am saying that a union of two fundamentally incompatable and individually complex explanations (GR and QM)will be necessarily complex.
 
  • #12
We may just be arguing semantics here. The way I see it though is that the "merged" system, as you stated, might be complex in that there are many laws and functions which it details built from many individual principles. I think, however, one could suppose a likelihood that the individual components of that system are "simple." In such, I would think that, in matter of perspective alone, treating each model as "complex and incompatible" initially might not be the best place to start. Thus I would agree with friend's line of thinking in that it might be wiser to first get models (i.e. QM) into a build of simple, logical principles that coincides with other models (i.e. CM) in a way that is not inherently incompatible. Then we would would try and build a system on these "simple" principles. To me this is a better ToE. I tend to think that the reason things are "complex" now is because they are not sufficiently understood and much of our work is extrapolation.

If there were a sort of irreducible complexity, however, I would admit this might not be possible, but as of now, I see no reason to believe that is the case.
 
  • #13
marcus
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Let's look at the initial post and try to see what this thread is about:
Do you guys feel that perhaps our current stabs at a ToE are just getting a bit outlandish?

Personally I do...
Like I said, this is totally subjective, but does anyone feel me on this?
Basically in this forum we follow current professional research about BTSM (beyond the standard model) lines of investigation. People ask questions about specific research. Give a link to an online PDF. Or discuss some idea from some recent preprint on the "arxiv.org".

It's not so much about philosophy or feelings. More about definite cases of professional work.

It is not true that BTSM = "ToE"

I haven't been seeing much about "ToE" in the professional literature I follow. For example String research has tended to focus on other stuff, more limited goals, since roughly mid-decade.

A popular research target is developing a quantum theory of the curvature and expansion of spatial geometry. Socalled "quantum gravity" modeling, because basically gravity = geometry. So one wants to have a quantum theory that describes geometry, how it changes etc. how it responds to geometric measurement etc....what actually was happening where the old 1915 (non-quantum) theory of geometry breaks down...

These are not grandiose "ToE" questions. The work currently in progress on them is not "outlandish". It is not even mostly String. It is beginning to connect with ideas for testing by comparison with astronomical observation (e.g. ancient light = CMB)

You might first learn about the prevailing approaches to BTSM physics and provide some links to PDF so we have some concrete examples. Then we could see how we feel. About something real. :smile:
 
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  • #14
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We may just be arguing semantics here. The way I see it though is that the "merged" system, as you stated, might be complex in that there are many laws and functions which it details built from many individual principles. I think, however, one could suppose a likelihood that the individual components of that system are "simple." In such, I would think that, in matter of perspective alone, treating each model as "complex and incompatible" initially might not be the best place to start. Thus I would agree with friend's line of thinking in that it might be wiser to first get models (i.e. QM) into a build of simple, logical principles that coincides with other models (i.e. CM) in a way that is not inherently incompatible. Then we would would try and build a system on these "simple" principles. To me this is a better ToE. I tend to think that the reason things are "complex" now is because they are not sufficiently understood and much of our work is extrapolation.

If there were a sort of irreducible complexity, however, I would admit this might not be possible, but as of now, I see no reason to believe that is the case.
What is simple to you? Even if we were to formulate the TOE(which we could call any theory of Quantum Gravity) solely with arithmetic, the questions of consistency within number theory researchable by Peano's Axioms would arise.

You cannot develop a simpler logical system than one formulated solely from arithmetic, and yet this would still not be "simple"

Our current models are "complicated" because the nature of our universe is complicated. Subatomic particles do not behave in a manner that can be modeled with highschool mathematics. The geometry of space and time cannot be constructed within Euclidean geometry.

If what you are calling the "Theory of Everything" seems a little too crazy, then you are simply not familiar enough with current research. If an extra dimension, or 7, arises from our studies, then so what? Who are we to say this seems unreasonable? 80 years ago Space was static and flat.
 
  • #15
Let's look at the initial post and try to see what this thread is about:


Basically in this forum we follow current professional research about BTSM (beyond the standard model) lines of investigation. People ask questions about specific research. Give a link to an online PDF. Or discuss some idea from some recent preprint on the "arxiv.org".

It's not so much about philosophy or feelings. More about definite cases of professional work.

It is not true that BTSM = "ToE"

I haven't been seeing much about "ToE" in the professional literature I follow. For example String research has tended to focus on other stuff, more limited goals, since roughly mid-decade.

A popular research target is developing a quantum theory of the curvature and expansion of spatial geometry. Socalled "quantum gravity" modeling, because basically gravity = geometry. So one wants to have a quantum theory that describes geometry, how it changes etc. how it responds to geometric measurement etc....what actually was happening where the old 1915 (non-quantum) theory of geometry breaks down...

These are not grandiose "ToE" questions. The work currently in progress on them is not "outlandish". It is not even mostly String. It is beginning to connect with ideas for testing by comparison with astronomical observation (e.g. ancient light = CMB)

You might first learn about the prevailing approaches to BTSM physics and provide some links to PDF so we have some concrete examples. Then we could see how we feel. About something real. :smile:
Thank you for giving a considerate and supported reply. Off of what you said, I looked back up at the forum rules, and it seems there may be a better place to move this thread (I have no intention of hiding any subjectivity in my post). As to what I was referring to, I strictly meant when efforts (as you discussed) are touted as a ToE. Sure this is not what you find in many (most) specific pieces of literature, but this is often what is fed to public media (if even not intentionally). You could reword my intentions as a strong feeling to be more cautious in letting the association "ToE" be cast with current theories, especially in personal opinion (as admitted) when having a complex premise and a somewhat ambiguous foundation (in terms of intuitive logic).
 
  • #16
What is simple to you? Even if we were to formulate the TOE(which we could call any theory of Quantum Gravity) solely with arithmetic, the questions of consistency within number theory researchable by Peano's Axioms would arise.

You cannot develop a simpler logical system than one formulated solely from arithmetic, and yet this would still not be "simple"

Our current models are "complicated" because the nature of our universe is complicated. Subatomic particles do not behave in a manner that can be modeled with highschool mathematics. The geometry of space and time cannot be constructed within Euclidean geometry.

If what you are calling the "Theory of Everything" seems a little too crazy, then you are simply not familiar enough with current research. If an extra dimension, or 7, arises from our studies, then so what? Who are we to say this seems unreasonable? 80 years ago Space was static and flat.
I believe you largely misunderstand me, but I think my statement about explaining a system to someone might be why. Take that from the context of whether or not a system seems complicated at face value and move it to the context of what is being proposed for unknown facets of a system. Perhaps that makes my point clearer. It is no issue that extra dimensions "seem a complicated idea." That is our human/cultural/knowledge bias. When I say something is simple or complex I refer to the number of new ideas needed to accommodate a new theory (without fully supporting empirical evidence). For a very crude interpretation of meaning, a theory just involving strings or just involving extra dimensions would be simpler while a theory needing both is more complex. It's all in the amount of material that must be given at one time (without "conclusive" backing of previous suppositions) which I define more complicated. This is perfectly reasonable, as the simpler the theory while still explaining all parameters, the better. I am, subjectively (as I know no way to quantify the amount of requirements for each theory) suggesting that, given our current knowledge, ToE agendas seem somewhat complex because many new ideas must simultaneously be proposed (while each, individually, is not yet fully backed).

I will admit ignorance in many cases, but in this regard I think even Hawking, being as highly ambitious as he is in theoretical work, would not find cautiousness in these terms at least reasonable.
 
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  • #17
qsa
345
1
I'll start off by admitting that just because the "laws of the universe" go against what we might intuit them to be is no grounds to assert their falsehood, but I do have to pose a subjective question:

Do you guys feel that perhaps our current stabs at a ToE are just getting a bit outlandish?

Personally I do. I understand the idealism that "if the math works, then we've got to run with it" but I wonder if the many multi-dimensional ToE's with all sorts of complicated geometries involving string and the like are just throwing layers of math to cover up the initial logic that is being sacrificed. And of course, the more we find out, the more math (and complicated semantic explanation) we need. In short, at gut feeling I believe we just don't know enough about how the universe works right now to be taking stabs in this manner, and we end up laughing at Occam's Razor in the process.

Like I said, this is totally subjective, but does anyone feel me on this?
I do agree with your gut feeling (there must be a better way), but I also think current theories are on some path to the final theory. However, this path is a very long route, but that was dictated by many reasons.

IMO all forces have the same origin. I disagree with Marcus in the strongest terms possible. But he refuses and side steps my objections all the time. I repeat here

The whole idea of QUANTUM gravity is just that to take GR away from geometry (in the metric sense) and show its quantum origin (similar to QM) which should have united it with other forces. and to finally show us how all these forces arise naturally together with matter being the center of it all. none of the QG theories has come to anything close. Besides, one of the great achievements have been the development of " effective theories for gravity", so why should it be any different fundamentaly at high energy.
 
  • #18
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I'll start off by admitting that just because the "laws of the universe" go against what we might intuit them to be is no grounds to assert their falsehood,...
Indeed so. Our brain has been evolved to understand macroscopic aspects of reality, we may call it classical physics. There is no reason why our brain would be wired to have an intuitive grasp of the laws of nature outside this domain, such as quantum mechanics. Fortunately the laws of nature can be cast in the language of mathematics, and this allows to get us a handle on them.

Thus, arguments whether some theories are against "common sense" or "gut feeling", "outlandish", and "too mathemaical", are worth nothing.

What people often overlook is that there are usually pretty good reasons to invoke certain mathematical structures, namely quite definite and oiften highly non-trivial computational results. For example, strings are not just invented ad hoc, rather it can be shown by explicit computation that they lead to gravity at low energies.
 
  • #19
Indeed so. Our brain has been evolved to understand macroscopic aspects of reality, we may call it classical physics. There is no reason why our brain would be wired to have an intuitive grasp of the laws of nature outside this domain, such as quantum mechanics. Fortunately the laws of nature can be cast in the language of mathematics, and this allows to get us a handle on them.

Thus, arguments whether some theories are against "common sense" or "gut feeling", "outlandish", and "too mathemaical", are worth nothing.

What people often overlook is that there are usually pretty good reasons to invoke certain mathematical structures, namely quite definite and oiften highly non-trivial computational results. For example, strings are not just invented ad hoc, rather it can be shown by explicit computation that they lead to gravity at low energies.
You should go back and reread the last post in this thread where I already explained this wasn't quite what I meant in the OP.

All the same, I do disagree with you on at least one facet. Our human instinct and intuition are certainly not always reliable, and they can by no means be used to argue a final conclusion in any situation. However, the worth of "gut feelings" should not be discarded entirely. That cautionary feeling of "Hmm, something's odd here, maybe we should go back and check this" may not be unbiased (or sufficient), but that non-linear thinking helps me (and I'd argue most of the world) out quite often. At least it helps me from forgetting my car keys. :) It is worth noting though that our "training" to see the world one way isn't just training. It really means the world is that way on many many many levels. The fact that such emerging theories don't match up with this is definitely a reason to at least say "Hmmmm" first. It just simply isn't a reason to continue to retreat from them after multiple tests and the evidence still holding.
 
  • #20
marcus
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==excerpt from previous==
My post #13:...I haven't been seeing much about "ToE" in the professional literature I follow. For example String research has tended to focus on ... more limited goals, since roughly mid-decade.

A popular research target is developing a quantum theory of the curvature and expansion of spatial geometry. Socalled "quantum gravity" ...

These are not grandiose "ToE" questions. The work currently in progress on them is not "outlandish". It is not even mostly String. It is beginning to connect with ideas for testing by comparison with astronomical observation (e.g. ancient light = CMB)

You might first learn about the prevailing approaches to BTSM physics and provide some links to PDF so we have some concrete examples. Then we could see how we feel. About something real.

Altrus post #15:... Off of what you said, I looked back up at the forum rules, and it seems there may be a better place to move this thread (I have no intention of hiding any subjectivity in my post). As to what I was referring to, I strictly meant when efforts (as you discussed) are touted as a ToE. Sure this is not what you find in many (most) specific pieces of literature, but this is often what is fed to public media (if even not intentionally). You could reword my intentions as a strong feeling to be more cautious in letting the association "ToE" be cast with current theories, especially in personal opinion (as admitted) when having a complex premise and a somewhat ambiguous foundation (in terms of intuitive logic).
==endquote==

Compliments on your thoughtfulness and reasonableness. And steady focus.

So the topic is not so much the current science itself but the "hyperscience" in the media. It is about encouraging sober integrity in what is fed to the public. But how shall the debauched be restrained? :biggrin:

Could Brian Greene be persuaded to wear some kind of chastity belt?
 
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  • #21
Compliments on your thoughtfulness and reasonableness. And steady focus.

So the topic is not so much the current science itself but the "hyperscience" in the media. It is about encouraging sober integrity in what is fed to the public. But how shall the debauched be restrained? :biggrin:

Could Brian Greene be persuaded to wear some kind of chastity belt?
Thanks Marcus. And I'm afraid books on "hyperscience" are what sell and make money while hardline theoretical work by itself doesn't hah.... so good luck on Greene. You're roughly right on what I meant, though I wouldn't exclude it only to public domain. One doesn't necessarily have to be talking to a reporter to get overzealous on what we "know." In short, our current theories are indeed complex and indeed (as surprised mentioned) quite contrary to conventional thinking, and because of this, we should always maintain necessary humility. Any of the current theories may well be an exact truth, but in the meantime we still need more empirical data (if it is obtainable hah). Thus gearing up to talk about any current theory as a "theory of everything" or even the "reality" of the universe for that matter is difficult (personal opinion, "crazy"). We're coming up with some impressive mathematical models, but in order to espouse them as I just mentioned...well, we're just not there yet I think. :)
 
  • #22
marcus
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...You're roughly right on what I meant, though I wouldn't exclude it only to public domain. One doesn't necessarily have to be talking to a reporter to get overzealous on what we "know."​
In that case please give examples where a reputable scientist on record before colleagues (not the public) shows overzealous hubris. It probably happens but I'm not sure how common.

...we should always maintain necessary humility.​
I want to be very sure I am not being shown a "straw man" of the Arrogant Scientist. The culture of science is supposedly one of doubt and of recognizing one's ignorance. When one speaks at peer-group meeting one's reputation/credibility is on the line. You are supposed to lose points if you don't properly qualify your statements. Can you give an example of some representative top scientist currently maintaining that some theory or other is a "Theory of Everything"?


Any of the current theories may well be an exact truth,​

Are you kidding? I don't know any theoretical physicist who claims to believe that some current theory is the exact truth. It sounds as if you think you are granting a concession to somebody.

Thus gearing up to talk about any current theory as a "theory of everything" ... is difficult (personal opinion, "crazy").​

You really should give examples. Who specifically talks about what current theory as a ToE? Give us a recent quote, like from 2010-2011. You seem to be losing focus. What are you talking about that is "difficult" or (personal opinion) "crazy"?

We're coming up with some impressive mathematical models, but in order to espouse them...​

Who is "we" and what models do you have in mind? Of what? You might give us a link to a PDF of some equations that impressed you---IOW not just hearsay. As I understand it, one does not "espouse" mathematical models. Models are made to be tested. You are not expected to believe. You calculate, predict, test, judge how much provisional reliance to place, derive and study consequences.

A mathematical model is not analogous to a religious belief, if that's where you are coming from.
But presumably you already make that obvious distinction so I shouldn't have to say.
 
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  • #23
I can not cite my personal experience, nor do I need Individual A purporting a certain belief to argue against the belief. Were I arguing that a large number of people do this, this would be true, but it is not. If one disagrees in the extent of this occurrence, then maybe there is no need for the argument (but it does not affect the validity of it). Your terminology "arrogant scientist" and "overzealous hubris" seems to reflect a rather adverse (and somewhat abrasive) reaction to more meager statements on my own part. Being critical keeps us from coming to wrong conclusions, but when we really are talking about something subjective, it's really ok to relax, speak conversationally and generally (as long as such conversation is not held as the "final word" on any matter). In such cases general experience is at least worth its comment. I have offered the moving of this thread if this is not the place for such type of discussion, but otherwise I uphold my opinion here.

I have already stated an example in response to immortal's comment to reference what I meant by complexity of new theories (i.e. string theory). Furthermore, I did not (or at least I did not meant to) accuse that anyone is mistakenly saying "This is a theory of everything," but rather our current candidates have a lot of work to do, are quite complex and unconventional, and still require extensive empirical footwork to add to the theoretical --> Thus the notion of any of these as a candidate (individually or merged together) for a theory of everything seems beyond what we can do at the current time (subjectively, I would say a "crazy" notion). And heck, even if by mainstream media alone we see this, the rumor of it is enough that I don't need to drudge up papers and press releases to simply suggest that the notion itself isn't the best one.

As a quick aside, when I said "exact truth" I simply was being over-generous for the sake of that argument, not attesting that this is the generalized claim.
 
  • #24
marcus
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TOE's getting a little...out-of-date?

You need to give examples of current professional work and inhouse opinion NFPC ("not for public consumption") in order for me to learn anything and for you to learn anything from this kind of discussion.

Feelings aren't necessarily to be dismissed (we all have, of course) but they should not be mere feelings about your own fantasies (like "ToE" research, however you picture it). Feelings about something real we can learn from and you can learn from by talking about it. That's my opinion anyway.

"ToE" has faded some of late, a little out of style so to speak. But you can probably still find some if you look. Extra dimensions too, a bit muted and upstaged by other stuff.

No new firsttime faculty hires for String/M theorists this year, in either Usa or Canada. A short time back it might have been a dozen. Other types of high energy theorists yes.

At the annual Strings conf. this year (in Sweden) it was noticed how few speakers actually dealt with string/brane. One of the few exceptions commented on it at the beginning of his presentation.

Theorists still doing string/brane stuff are tending to find applications that are NOT "ToE".

A lot more work by theorists these days seems to be focused on 4D---actual four-dimensional spacetime---and real stuff like what the collider is probing. Or anyway that is my impression. It wouldn't be surprising if that were the case.

I could be wrong of course but I'd say you are voicing rather out-of-date complaints and are maybe 5 or 10 years too late with it. It sounds like you have a made-up fantasy of how things are and are expressing your feelings about your fantasy.

sources:
2011 high energy theory hires http://particle.physics.ucdavis.edu/rumor/doku.php?id=archive:2011
Next year (prelim,) http://particle.physics.ucdavis.edu/rumor/doku.php
Faculty hires 2004-2010 http://www.physics.utoronto.ca/~poppitz/Jobs94-08
Comment http://www.math.columbia.edu/~woit/wordpress/?p=3715
Annual conf http://www-conference.slu.se/strings2011/ [Broken]
https://www.akademikonferens.se/list.jsf?conf=strings2011-S [Broken]

If you would like more specific sources about something in particular, please ask! I or someone else will try to supply some. These are rather general ones I just happened to have handy.
===================

However we know we have a problem with the "hyperphysics" in the media! Pop-string, pop-multiverse, Kaku-jazz, celebrity-cult corrupting science, misleading speculation. Boggle for boggle's sake. Whatever sells or gets attention. I'm far from expert on pop-sci. I have to rely on others to report. So tell us about the sins of pop-sci hyperphysics if you want, just don't let the diatribe slop over onto actual current research trends unless you offer examples so we know it is not just made up but is about what real people are doing/writing. I'm sure you understand my concern. :smile:
 
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  • #25
qsa
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What about lubo's acusation of the lqg camp amounting to fraud
 

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