Is Gravity’s Weakness Due to Extra Space Dimensions – And Can We Detect Them?

In 1999, a somewhat astounding hypothesis was proposed to explain why gravity is so relatively weak, i.e. how is it that a simple kitchen magnet can pick up a paper clip – even though the force of gravity is supposed to be holding it down. The hypothesis, advanced by physicist Eric Adelberger of the University of Washington, suggested that gravity only appears weak because it operates in additional spatial dimensions – apart from length, width and height.  The standard Newtonian force of gravitational attraction is defined according to an inverse square law, viz.

F = GMm /r²

Where G is the Newtonian gravitational constant, M is the larger mass, m the smaller mass and r the distance between their centers. It can be seen from this equation that F can only be large on if the mutually attracting masses M and m are large, say on the scale of Earth's mass or even an asteroid's, say 6 x 10 ¹⁷ kg.   What Adelberger is looking for then is a variant  of the classic Newtonian case such that:

      F' = GMm /r²   -   GMm /r^{3+ n}

And F'  < F, where the 2nd term includes the extra dimensions being sought, i.e. in the exponent of r. Thus the first term will generally show Newtonian gravitational effects obtain to a certain scale, and the second term is included - say at a finer scale. Clearly too, if n for the denominator  > 1, the additive term poses a much weaker contribution to F, although the force F itself is diminished (however slightly) over what its Newtonian value might be.

These extra dimensions, to be sure, would be imperceptible in our macro-world but might be detected by devices or instruments which can register gravimetric influence at scales say less than the width of a hair.

A somewhat analogous notion was put forward by C.H. Hinton in 1904. Hinton hypothesized that our four dimensional experience is really five-dimensional. This fifth dimension, according to Hinton, is  actually a thickness - referred to as dI, which existed perpendicularly to time. The problem was that it’s scale size was too minute to be detected by ordinary means.

Back to Adelberger’s hypothesis: if such extra space dimensions do exist, it is conceivable that undiscovered particles and forces might be ‘hiding’ within them.  Given this intriguing thought, Adelberger and colleagues set out to devise a way to detect them.  The solution they arrived at was a torsion balance, such as crudely depicted in my graphic sketch above.

It is basically a table top apparatus that can determine whether gravity breaks down at the minute scales where the extra dimensions might be noticeable.

What is this detector? Basically, it’s comprised of a pendulum – actually a molybdenum ring hanging on an ultra-thin tungsten fiber – and supporting disks driven by motors that can enable rotation, as shown. The pendulum feels the gravitational tug of the two disks below, and the latter are positioned so that their gravitational tugs on the pendulum exactly offset each other. Any unexpected twisting of the pendulum would indicate a violation of the known laws of gravity.

Such a result could suggest the gravitational pull of the two disks is being ‘diluted’ in one or more extra dimensions. Thus far Adelberger’s group has found that gravity behaves as one would expect up to distances of 44 millionths of a meter – meaning that any extra dimensions must be smaller still.

To see a video of Adelberger’s torsion balance in action, check out this link:

https://www.youtube.com/watch?v=YWgtrgk8ebE