Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Does the existence of dualities imply a more fundamental structure?

+ 4 like - 0 dislike
2231 views

I was wondering if the existence of some kind of duality in physics always implies the existence of some underlying more fundamental structure/concept?

Let me give a few example from history:

  1. Wave-particle duality$~\Rightarrow~$ Existence of quantum particle.

  2. Heisenberg's Matrix Mechanics $\&$ Schrodinger's wave formulation of QM $~\Rightarrow~$ Existence of Dirac formulation of QM.

  3. Magnetic field $\&$ electric field $~\Rightarrow~$ Existence of an electromagnetic theory.

Similarly, can one conclude that

  1. for example, from AdS/CFT correspondence,

  2. or more generally, because there is an holographic equivalence between quantum gravity in $D+1$ dimensions, and QFT in $D$ dimensions,

then there must be a more fundamental underlying structure that incorporate both sides of the correspondence?

This post imported from StackExchange Physics at 2014-03-17 04:17 (UCT), posted by SE-user Revo
asked Feb 12, 2012 in Theoretical Physics by Revo (260 points) [ no revision ]
Can you please clarify your abbreviations to me?

This post imported from StackExchange Physics at 2014-03-17 04:17 (UCT), posted by SE-user Bernhard
Qm=quantum mechanics. Qft= Quantum field theory. Cft=Conformal field theory. Ads/cft= anti de Sitter/CFT

This post imported from StackExchange Physics at 2014-03-17 04:17 (UCT), posted by SE-user Manishearth
If we have two different descriptions of the same phenomenon, then yeah, we always hope that there is a "unified" picture that tells us why. Logically there's no reason that this must be the case though. Maybe we have a philosopher here who can argue that a thing's thingness depends on it having a unique description.

This post imported from StackExchange Physics at 2014-03-17 04:17 (UCT), posted by SE-user wsc
@wsc I think the answer should be given by a physicist, as Weinberg has said once that philosophy has lots its way long time ago.

This post imported from StackExchange Physics at 2014-03-17 04:17 (UCT), posted by SE-user Revo
@Qmechanic why is this closed?

This post imported from StackExchange Physics at 2014-03-17 04:17 (UCT), posted by SE-user Dilaton
@Dilaton: I closed the question(v1) as not constructive, as it seems formulated too broad to be true in every case. Did you want to add an answer?

This post imported from StackExchange Physics at 2014-03-17 04:17 (UCT), posted by SE-user Qmechanic
Hi @Qmechanic, maybe it is somewhat broad but I thought it nevertheless contains an interesting ordered line of thought which could be adressed by someone (else) knowledgabel enough. I would be interested in seing such an answer too. Maybe Lumo (or Ron :-( ...) could do it.

This post imported from StackExchange Physics at 2014-03-17 04:17 (UCT), posted by SE-user Dilaton
Therefore I was a bit astoished that this is closed and would have prefered it left open ...

This post imported from StackExchange Physics at 2014-03-17 04:17 (UCT), posted by SE-user Dilaton
@Dilaton. It is indeed a nice observation by OP, but I sincerely doubt that an exact answer would be essentially more than what OP have already noted. Would it be an acceptable compromise to urge anyone who wants to answer this question in the future to leave a comment here for the moderators? Else you can bring it up in meta/chat to hear what the community think.

This post imported from StackExchange Physics at 2014-03-17 04:17 (UCT), posted by SE-user Qmechanic
@Qmechanic I agree that this in my opinion deep question is really difficult to answer, if such an answer can be given at present. So maybe your suggestion that anybody who wants to answer can ping a moderator, would be a reasonable compromise. But I hope that the closure of this question does not mean, that other questions laying near the cutting edge of research will be closed soon too. I have once asked a similarly difficult to answer question myself (dont go to dig it our and close it :-D) ... :-/.

This post imported from StackExchange Physics at 2014-03-17 04:18 (UCT), posted by SE-user Dilaton
By the way, Qmechanic I forgot to say that I thought you could of course be among the people who can give an answer to this one too ;-)

This post imported from StackExchange Physics at 2014-03-17 04:18 (UCT), posted by SE-user Dilaton
Dear @Qmechanic, now I have pinged Lumo at TRF and asked him if he could write something nice here since it still picks me somehow ...

This post imported from StackExchange Physics at 2014-03-17 04:18 (UCT), posted by SE-user Dilaton
@Qmechanic could you, as we agreed upon, reopen this for a while such that I can put down what Lumo said about this issue on TRF as I asked him in the form of a CW answer? He did not have an outline of an underlying structure, but he explained what he thinks about it.

This post imported from StackExchange Physics at 2014-03-17 04:18 (UCT), posted by SE-user Dilaton
... thanks @Qmechanic :-)

This post imported from StackExchange Physics at 2014-03-17 04:18 (UCT), posted by SE-user Dilaton

2 Answers

+ 2 like - 0 dislike

I think AdS/CFT went the other way. People knew about the unifying concept (string theory) first and "derived" AdS/CFT from worldsheet duality in string theory. But I guess it could've gone the other way in an alternate history.

This post imported from StackExchange Physics at 2014-03-17 04:18 (UCT), posted by SE-user josh
answered Feb 12, 2012 by josh (205 points) [ no revision ]
+ 2 like - 0 dislike

I asked Lumo if he has an answer to this question. He did not like the question too much... ;-) Nevertheless he gave some nice clarifying comments and explained what is wrong with it and how he thinks about the issues mentioned. I think his comments make a very decent answer here anyway (and hope he does not mind that I post them here). So here we go:

\begin{quote}

Dualities are obviously important and unify several seemingly different descriptions. This is by definition of dualities. In this most general sense, they are analogous to the wave-particle dualism and unification of pictures in quantum mechanics and perhaps other things (unification of electricity and magnetism is substantially different).

The quantum particle is the same thing as the object displaying both wave and particle properties, so the "two" concepts related by the arrow on that line are really the same concept, and the whole relationship claim is vacuous or tautological.

In the same way, the matrix and wave mechanics may be unified but the unification is nothing else than the Dirac formalism for quantum mechanism so the two parts of the relationship are - assuming that the relationship between the pictures is found - a priori equivalent, too. We already have this description for dualities in string theory, sort of, too. One may discuss physics in the description-invariant way. The problem is that we don't have a universal definition of the "Hamiltonian" or "action" but we may still write the general equations with a Hamiltonian or an action that is duality-invariant. This situation differs from the simplest models of quantum mechanics where the Hamiltonian could have been written down "exactly". In string theory, the expressions for the "Hamiltonian" or whatever defines the dynamics depends on the description and it is often incomplete, so the dualities can't be formulated as a sharp mathematical claim at this moment. They're still perfectly true according to all the evidence and tests we may do and assuming it is indeed the case, and it seems to be the case beyond any reasonable doubt, the equivalence is the same equivalence as the equivalence between pictures (Heis/Schr) in quantum mechanics or representations (position/momentum) in quantum mechanics.

Electromagnetism is a bit different because the electromagnetic field contains both the electric vector and the magnetic vector as independent degrees of freedom, so electromagnetism isn't about 2 views on the same 1 thing. It is about 2 things that naturally collaborate and are linked by symmetries and transform into each other under the Lorentz transformations. It's a different relationship than the equivalence in dualities.

\end{quote}

Here you can read Lumo's original nice comment.

answered Mar 20, 2013 by Dilaton (6,240 points) [ revision history ]
I made this answer CW because it contains what Lumo said; so everybody who agrees with his comments can freely upvote and I dont need to have a bad concience for any upvotes that may occur :-)

This post imported from StackExchange Physics at 2014-03-17 04:18 (UCT), posted by SE-user Dilaton
Hi @Dilaton: Do you have an Internet link to the above quote by Lubos Motl?

This post imported from StackExchange Physics at 2014-03-17 04:18 (UCT), posted by SE-user Qmechanic
@Qmechanic not directly, it is in the comments below a TRF article and at these comments I can not link directly ... I can at most link to the corresponding TRF post.

This post imported from StackExchange Physics at 2014-03-17 04:18 (UCT), posted by SE-user Dilaton
... ok, it is the second comment below this TRF article.

This post imported from StackExchange Physics at 2014-03-17 04:18 (UCT), posted by SE-user Dilaton
Ok. Link good enough for now.

This post imported from StackExchange Physics at 2014-03-17 04:18 (UCT), posted by SE-user Qmechanic
@Dilaton: You can click on the timestamp on the link to the comment: e.g. motls.blogspot.com/2012/12/…

This post imported from StackExchange Physics at 2014-03-17 04:18 (UCT), posted by SE-user Dimensio1n0

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ys$\varnothing$csOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...