Have there been any attempts at unifying gravity and electromagnetism at least at classical level since Hermann Weyl's idea of gauge principle (1918)? We now have Standard Model which is very successful and many other theories. But gravity and electromagnetism are long range in nature and classical as well. Can these two be unified independent of weak and strong forces?

  • $\begingroup$ Trivia: There is an unfortunate history regarding Weyl's reception--exemplified in the famous words Pauli sent to Weyl: "Before me lies the April edition of Proc. Nat. Acad. [the journal that pre-published Weyl's 1929 paper]. Not only does it contain an article from you under "Physics" but shows that you are now in a "Physical Laboratory": from what I hear you have even been given a chair in "Physics" in America. I admire your courage; since the conclusion is inevitable that you wish to be judged, not for your successes in pure mathematics, but for your true but unhappy love for physics." $\endgroup$ – Dvij Mankad Feb 21 '19 at 21:32
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    $\begingroup$ Here you can find an involved discussion : physics.stackexchange.com/questions/27689/… $\endgroup$ – my2cts Feb 21 '19 at 21:40
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    $\begingroup$ Since you mentioned the long-range nature of the two phenomena, I would like to mention that although not unified, (most theoretical physicists would agree that) we understand why electromagnetism and gravity MUST be described by the Yang-Mills theory and GR respectively at large distances in the light of the basic principles of quantum mechanics and special relativity. Nima explains this wonderfully in this talk: youtu.be/_k_V8TNWTHg?t=1207 $\endgroup$ – Dvij Mankad Feb 22 '19 at 8:44
  • $\begingroup$ @DvijMankad you have taken the OP into many dimensions;) Testing extra dimensions experimentally is a challenge unless there are compelling indirect evidences. $\endgroup$ – user31694 Feb 22 '19 at 10:12

Yes, classically, we can unify gravity with electromagnetism. The theories that do so are the famous Kaluza-Klein theories. They are theories of pure gravity in $4+1$ dimensions rather than our usual $3+1$ dimensions. When such theories are viewed from a $3+1$ dimensional perspective, the effects of gravity in the fourth unseen dimension appear in the lowered $3+1$ universe as electromagnetism! This is really amazing (the Professor who taught me GR titled the topic on the Kaluza-Klein theory as The Kaluza-Klein Miracle in his notes!). Now, the lesson physicists learned from the KK miracle is that what makes this miracle possible is the fact that pure gravity in additional dimensions appears as gauge-fields in lower dimensional universes. The more evolved version of the spirit of the KK miracle is survived in string theoretic theories which naturally (and inevitably) unite electromagnetism (and all other forces) with gravity--in addition, these theories are inherently quantum mechanical too.

Now, of course, we don't yet have explicit experimental evidence for any of the string theoretic theories (we also don't know which string theoretic theory reproduces the standard model). But yes, theoretically, we can construct consistent theories that unite electromagnetism with gravity.


Of course, KK theories are not a part of the "done-deal" physics, among various reasons that I am not well-educated in, the major reason is that we don't have experimental evidence for the extra dimensions. Nonetheless, KK theories are a part of textbook physics and for very good reasons. They do provide an internally consistent classical framework to unite electromagnetism and gravity and teach us how pure gravity in a higher dimension can give rise to gauge-fields in lower dimensions as I already mentioned. And this insight is now a part of the daily toolkit for theoretical physicists.

  • $\begingroup$ Can the downvoter elaborate? $\endgroup$ – Dvij Mankad Feb 21 '19 at 20:09
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    $\begingroup$ Isn’t Kuluza-Klein theory unstable in the sense that the radius of the fifth dinension wouldn't stay constant? And isn’t that why this theory has never been accepted as a successful classical unification of gravity and electronagnetism? $\endgroup$ – G. Smith Feb 21 '19 at 20:11
  • $\begingroup$ @G.Smith The main reason I am aware of as to why KK theories have not been fully accepted is that we don't have any experimental verification of the extra dimension. I am vaguely aware of instability phenomena in certain KK manifolds but I am largely unaware. If you can suggest me some review article (or similar), I would be grateful. Thanks. $\endgroup$ – Dvij Mankad Feb 21 '19 at 20:20
  • $\begingroup$ So the kk theory is not "fully accepted". In short, not accepted. $\endgroup$ – my2cts Feb 21 '19 at 21:10
  • $\begingroup$ @my2cts Rather than arguing over the basic scientific differences amongst "not fully accepted", "not accepted", and "never accepted", I have edited my answer to convey more explicitly what I want to convey. $\endgroup$ – Dvij Mankad Feb 21 '19 at 21:23

Most physicists are not interested in unifying just gravity and electromagnetism, because electromagnetism is already fully unified with the weak nuclear force. They’re now sometimes just called the electroweak force.

Furthermore, the strong nuclear force has closer similarities to the electroweak force than gravity does, and Grand Unification of the strong and electroweak forces may be an easier next step.

Most physicists also have no interest in classical unification, when quantum physics is a more successful explanation of reality than classical physics. Classical electromagnetism isn’t even a correct theory, so why would we want to unify it with anything?

  • $\begingroup$ -1: This doesn't answer the question OP asked. $\endgroup$ – Dvij Mankad Feb 21 '19 at 19:42
  • $\begingroup$ I would be interested regardless. $\endgroup$ – my2cts Feb 21 '19 at 21:09

There is no acceptable field theory of gravity, which should describe gravity as a field defined on Minkowski space like electromagnetism, and there is no acceptable theory that describes electromagnetism as a curvature of space . It will take one or the other to make a unified theory at all possible.

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    $\begingroup$ There is little truth in what you say, if you judge this outside quantum physics. Even the Kaluza-Klein model was classical, not to mention Weyl's. $\endgroup$ – DanielC Feb 21 '19 at 18:23
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    $\begingroup$ 1. There is nothing but a field theory of gravity. GR is a field theory of the metric. To provide rather social proof, Landau discusses GR entirely in his second volume, "The Classical Theory of Fields". 2. Theory of electromagnetism is a gauge theory. And there are indispensable geometric structures associated with a gauge theory. So, to say that there is no geometric theory of electromagnetism is misleading. 3. Classically, Kaluza-Klein theories are precisely the theories that unite electromagnetism with gravity. The reason they can do so is based on my previous two points. $\endgroup$ – Dvij Mankad Feb 21 '19 at 19:28
  • $\begingroup$ There is an answer by @DvijMankad already posted $\endgroup$ – Aaron Stevens Feb 21 '19 at 20:50

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