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

RUSH- the Science Illiterate

Today, Rush Limbaugh waxed long and hard about Mars and the recent landing of the Phoenix and the fact Mars possessed an atmosphere of 95% carbon dioxide – and yet there was no global warming!

Fancy that! All that CO2 and little heat to show for it! Meanwhile, Earth doesn't even have a half of a percent CO2 and we are supposed to believe there's a connection to global warming!

Hello! Calling all dingbats! First, Mr. Limbaugh, Mars is more than 1.5 times further from the Sun than Earth. As any basic physics student knows, the intensity of radiation (including heat and light received) falls off as the inverse square of the distance.

Thus, relative to the Earth (1360 watts/ m^2 received), on Mars one would have:

(1360 W/m^2) x 1 / (1.5)^2 = 1360 W/ m^2/ 2.25 = 604 W/M^2

or less than half the intensity of radiation, heat.

This means that before CO2 even enters the picture Mars is much colder than Earth.

Added to that is the fact that the atmospheric pressure on Mars is barely 0.0056 of that on Earth. In other words, just over five thousandths of an atmosphere. This is less atmosphere than one would encounter on Everest.

The low density of atmosphere means that CO2 occurs in too low a density to matter, in terms of effecting any climate change or in this case – global warming.

By analogy, the higher one goes up a mountain on Earth, the less air there is to absorb heat.(What we call 'heat' is really energy associated with motion and positionsof molecules in a material. The conversion of radiant energy - say from the Sun- is really a conversion of large scale energy, e.g. in electro-magnetic waves- to internal or microscopic energy.

In effect, if air is thin, as it is at the top of a mountain (or on Mars), there isn't enough MASS present to enable or facilitate energy transfer to the medium. Hence, it feels 'cold' to the human observer.

The thermal capacity is defined by the quantity:

W = mc

where m is the mass and c, the specific heat capacity. It is a measure of how difficult it is to increase the temperature of a medium by one degree (e.g. 1K or 1 Kelvin).

Again, the higher one is above the Earth, the lower the atmospheric density & pressure, and the lower the thermal capacity of the medium – so the smaller the amount of heat that can be retained, or measured.The lower one goes in altitude, the greater the number of particles, and the greater retention of heat- especially if water vapor is also included (since water has a large specific heat capacity ~ 4200 Joules/ kg K).

The low atmospheric pressure combined with the distance and low solar insolation means the CO2 present on Mars affords no measure of countervailing forcing factor for warming, such as the presence of CO2 does on Earth. Which, despite its low percentage in the atmosphere (< 0.04%) harnesses much more forcing on account of the atmosphere being 178 times more dense, and the Earth 1.5 times closer to the Sun.

This is why CO2 plays a vastly more critical and important role in controlling Earth’s climate, as opposed to Mars’.

Limbaugh finished his Mars’ piece by huffing to the effect: “Take that, you global warming idiots!”

But he’d do better to look at himself in a mirror when he babbles similar codswallop in the future.

Perhaps, he'd do even better by removing the penchant for "chaos" he is seeking to fulminate in the real world.