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 ...

  Did anybody ever claim that a unified Lagrangian exists?

+ 1 like - 0 dislike
828 views

Continuing the issue raised by Klaus 1 month ago, I have a question. Is there a unified Lagrangian that combines particle physics and general relativity? The answer probably is: we do not know.

So here is the next question: Did anybody ever state in writing that such a unified Lagrangian must exist? 

Is there an argument in favor (or against)?

There are so many people working on string theory, on loop quantum gravity and on other ideas.

Did anybody working on any idea for unification ever claim that unification is achieved using a Lagrangian?

What are the expectations?

asked Mar 21, 2023 in Theoretical Physics by Jean [ revision history ]
edited Mar 23, 2023

One can write down putative Lagrnagians, but one doesn't know how to solve the corresponding quantum field theory without introducing infinitely many renormalization parameters. That's why it remains an open problem.

@Arnold I'd like to read about these putative Lagrangians!

@Arnold I like the Christian part of your website.

@Jean: The variation of the Lagrangian of classical gravity coupled to the Dirac and the electromagnetic field produces the Einstein–Maxwell–Dirac equations. They describe the dynamics of a single Dirac particle coupled to classical gravity and a classical electromagnetic field. To obtain quantum gravity one would have to quantize these equations. Nobody knows how to do it. Coupling to the standard model rather than electrodynamics is analogous; I don't know whether anyone has written it down explicitly, but there is no difficulty doing so.

@Arnold Ok, so we know at least one person who believes that there is a unified Lagrangian! (Even though your link goes to a strange wikipedia page.)  Could you maybe provide another link with the Einstein-Maxwell-Dirac Lagrangian? Thank you in advance for all your help and patience.

@Jean: See, e.g., equation (14) in the paper

Jakubiec, A., & Kijowski, J. (1985). On interaction of the unified Maxwell-Einstein field with spinorial matter. letters in mathematical physics, 9, 1-11.

@Arnold Thank you. In fact, equation (8) is an even simpler version. Interesting!

The opposite seems to apply.

The entropy of black holes suggests that they are composed of distinct components. These components are shared by both space and particles, as black holes can be described as either curved space or compressed matter. Based on black hole thermodynamics, these shared components are estimated to be of Planck size. Their behaviour is crucial in defining the unified theory - which is still unknown.

Combining general relativity with quantum theory suggests that the Planck scale represents the smallest measurable length in nature. This limitation indicates that the common constituents, regardless of their specific details, cannot be described using a Lagrangian. Consequently, the unified theory of relativistic quantum gravity cannot be described by a Lagrangian either, independent of the specific type of common constituents. 

Mere suggestions are not answers.Moreover, ChatGTP is well-known for producing spurious comments to even simple scinetific questions.

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$\hbar\varnothing$sicsOverflow
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
...