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In my physics classes, I remember it being repeated a few times that gravity is a much weaker force than the other three fundamental forces, and being told this is an open problem in physics. However, I don't understand why this is a problem. I see no intrinsic reason why the four fundamental forces should have similar strengths in the first place.

So why then is the fact that gravity is many orders of magnitude weaker than the other fundamental forces a problem?

Note: I've attempted to read the Wikipedia article on the Hierarchy problem, but it is far too technical for me.

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Let's look at the forces in nature, there are four of them as far as we know (note that I am not very precise in the numbers I give, but for the comparison I make this is enough):

  • the strong force is very strong, it's coupling constant (which is a measure for its strength) is about 0.1
  • the weak force is not actually all that weak. It can be unified with
  • electromagnetism, the force we know best. Together, the electroweak interactions have coupling constants on the order of 0.01, about 10 times less than the strong force.

Finally we have gravity, which has a coupling constant around $$0.000 000 000 000 000 000 000 000 000 000 000 000 01 = 10^{-38}$$ For the other forces nature chose coupling values that are smaller than one, but still comparable. For gravity, the coupling constant is ridiculousely small (a magnet sticks to your fridge, even though the whole mass of earch pulls it down!).

There are attempts at explaining how this coupling constant got so small. Most notably, extra dimensions say that gravity, unlike the other forces can go into all spacetime dimensions and therefore just appears weak in our 4D perspective, while it is of similar strength to the other forces in the larger picture.

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    $\begingroup$ To me, this just raises the similar question "Why is gravity's coupling constant being relatively small a problem?" I don't have much understanding of coupling constants, is there something I'm missing there? $\endgroup$
    – DPenner1
    Nov 5, 2014 at 6:40
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    $\begingroup$ "Problem" is a relative term. We won't get trouble by it, it's just a puzzle not solved $\endgroup$ Nov 5, 2014 at 6:41
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    $\begingroup$ @DPenner It becomes a problem if you want a theory that "unifies" all the forces, by unify I mean that all forces are different aspects of some underlying "field". That is what physicists would like to have, a unified view of all forces. Otherwise, there is no problem at all. $\endgroup$
    – user65081
    Nov 5, 2014 at 9:44
  • $\begingroup$ @julianfernandez If I understand correctly, you're saying that the Hierarchy problem is a "problem" insofar as it makes it difficult to come up with a TOE? $\endgroup$
    – DPenner1
    Nov 5, 2014 at 17:04
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    $\begingroup$ @DPenner no, I just chose the one example that looks to me the simplest to explain in a comment. Because in the end we call it a "problem" if it doesn't fit our expectations based on theoretical assumptions of various kinds and attempts to fit everything in the same framework. $\endgroup$
    – user65081
    Nov 5, 2014 at 17:12
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It is not a problem in the sense that it bothers anybody or causes trouble in certain calculations. In physics, however, we would like to find out whether there is an explanation for certain phenomena. In this case, the phenomenon is that there is a huge gap between the scales of interaction strengths of gravity and the other forces. This has no explanation in terms of the standard model and general relativity, but the question why this happens to be the way it is might be answered in a different framework. The question is also known as a so-called "Hierarchy problem".

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I believe you are "jumping to conclusions." The reason gravity is "an open problem in physics," is not because it is several orders of magnitude smaller than the others. It is only a problem for those trying to unify gravity with the other three forces, to come up with a TOE.

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So why then is the fact that gravity is many orders of magnitude weaker than the other fundamental forces a problem

The problem is not that gravity is a weaker force but the open problem is that we do not know at present if there exist some relation between gravitational and other forces and probably if we are able to a new picture and dimension of everything from micro world to macro world may come before us.

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