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I have read that at high energies, the electromagnetic and weak forces get stronger and the strong force gets weaker, and at higher energies all these forces become indistinguishable from one another.

But I can't wrap my head around why this happens and why the strength of any force depends on energy. The equations I have studied say nothing about energy. Can someone please explain what it means, preferably in an intuitive sense?

The exact words from Stephen Hawking's book, A Brief History of Time, are :-

The basic idea of GUTs is as follows: as was mentioned above, the strong nuclear force gets weaker at high energies. On the other hand, the electromagnetic and weak forces, which are not asymptotically free, get stronger at high energies. At some very high energy, called the grand unification energy, these three forces would all have the same strength and so could just be different aspects of a single force.

PS- I have left out some detail that, at first at energies around 100 GeV, the distinctions between the electromagnetic and weak forces disappear (to form what's known as electroweak unification) and the strength of both becomes the same, but to achieve unification with the strong force even higher energies are needed.

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  • $\begingroup$ This question leads to another. If the strength of the forces because the same, that isn't the same thing as becoming the same force. E.G. An electron has charge and therefore responds to electromagnetic forces. But it has no color charge and so does not respond to the strong force. What happens at Grand Unification temperatures? $\endgroup$
    – mmesser314
    Commented Aug 12 at 19:53
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    $\begingroup$ @mmesser314 we define the energy scale $Q$ as the scale at which $α_1$,$α_2$ and $α_3$ are equal and interpret this to be the unified scale so there are no “electrons”. They already ceased to be a thing at the electroweak scale since they lost their charge and mass anyways :/ $\endgroup$
    – Mike
    Commented Aug 12 at 21:56
  • $\begingroup$ @mmesser314 : The electron is in specific slots of the fermion multiplets at the unification scale, in eqn (8), not acted upon by the color generators. $\endgroup$
    – Cosmas Zachos
    Commented Aug 13 at 16:17

2 Answers 2

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Hawking's popular science statement

On the other hand, the electromagnetic and weak forces, which are not asymptotically free, get stronger at high energies.

is technically correct, read in a certain way, albeit misleading to somebody "following the equations." You have to follow a peculiar winding logical path to there.

Nonabelian gauge theories, such as the strong interactions and a piece of the electroweak interactions (associated with the gauge group SU(2)) are asymptotically free, which is to say their couplings ("charges") weaken at higher energies, whence the emergent forces involved. This is a novel, subtle QFT phenomenon first discovered in 1973 to everybody's surprise. Abelian theories, such as the Hypercharge (and the electromagnetic force), get stronger at high energies (by a little bit). The underlying reason is conspiracies of radiative corrections peculiar to QFT.

However, the two gauge groups of the electroweak interactions (SU(2) and U(1)) get seriously complicated by the Higgs mechanism and are twisted together by electroweak mixing at low energies, so an abelian force (electromagnetism) emerges; and the weak forces (charged and neutral currents) become dramatically short-range at low energies, on account of the masses of the electroweak gauge bosons.

At higher energies, of the order of many-many TeVs, one may shrug off these two effects, and have the "pre-unified" nonabelian interactions resume their asymptotic freedom, and the abelian Hypercharge force its anti-asymptotically free behavior. So, two of the interactions weaken at high energies, and one gets stronger. They meet at around $10^{15}$GeVs.

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The essential answer as to why is due to the nature of gauge theories. Generally, abelian theories get more strongly coupled due to screening and non Abelian theories (QCD & the Weak interaction) get weaker due to the exact opposite of screening — antiscreening. This isn't unfortunately very accessible unless you're a grad student or of a higher role but try Wikipedia here and here.

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  • $\begingroup$ (+1) I am not a grad student, but could you help explain the following please: 1) Is it counter-intuitive that as energy/particle density increases, the strong & weak force actually gets weaker instead of stronger, as gravity & EM would? 2) Relative strength between gravity & EM is $10^{36}$, so clearly they are different forces... Does the relative frequency between EM, strong & weak forces of only $10^2$ and $10^3$ grounds for suspicion that they aren't as "distinct" as gravity & electromagnetism are distinct? 3) Why the absolute need for non-abelian theories, when abelian is simpler? $\endgroup$
    – James
    Commented Sep 12 at 18:02
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    $\begingroup$ @James In some sense yes and no. Classically you'd expect that electric forces tend to get weaker with higher energy scales due to the disruption of the flow of electric charges in a hot fluid of charged particles. At the same time however there exists a screened magnetic interaction that actually grows in hot fluids like these such as flash plasmas. Gravity gets stronger by the way. Things get murky at the quantum scale however. And so it's hard to answer your question since not all interactions have classical analogues. But if we go with classical E/M, esp the electric part,I'd say no! $\endgroup$
    – Mike
    Commented Oct 22 at 15:50
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    $\begingroup$ @James This is roughly the case for the electroweak interactions. And so by common logic,yes,many physicists do extend their logic to strong interactions. In the case of QCD, it's better to look at the evolution of their couplings strengths,which is basically just a number that tells you how strong an interaction is for a given length,energy or momentum scale. It turns out that all the interactions have their couplings meet. But not at equal energy/length scales. Also you mean “relative difference” not “relative frequency”. $\endgroup$
    – Mike
    Commented Oct 22 at 15:58
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    $\begingroup$ @James Not all interactions can be represented by abelian theories of simple groups. Actually only 1 of the interactions can and that's due to,in part,the linearised gauge structure of the theory. $\endgroup$
    – Mike
    Commented Oct 22 at 15:59

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