### Challenge: Create a Periodic Table of Physical Measurements

Discover and Underlying Order

Mendeleev created the periodic table to organize what was then known about the elements. By doing so he was able to predict properties of undiscovered elements as well as guide chemists to develop theories of atomic structure. Gell-Mann and Zweig organized the known subatomic particles into a table by their properties. By doing this they were able to discern the existence of quarks from the underlying properties of the table. Here we propose that the known measurable properties of physics be organized into a table based on their properties. The least we would expect from this would be the creation of a very handy reference guide for students of physics. But is it possible that we might discover something more? Could such a periodic table of the measurable universe lead to discoveries of underlying structures, or properties not yet measured? That is the challenge of this page.

 Part 1: The Challenge Part 2: Musing about force constants

Last update: October 2012

this project has already been started!

The obvious starting point for making a periodic table of physical measurements would be to organize the table by fundamental units. Our chart needs to include key information about each measure. Is it a vector, scalar, or statistical? Is it conserved? Is there a known minimum or maximum possible value? Below we show two pieces to motivate the organizational structure. The first page involves all units of time and distance with no units of mass (exponent of mass equals zero.)
In terms of organization, moving to the right on the table involves increasing the exponent of distance, moving to the left involves decreasing the exponent of distance. Mathematically, this means that moving left involves taking the derivative with respect to distance. Moving right involves taking the integral with respect to distance and considering the boundary value conditions. Moving down the table involves decreasing the exponent for time. Mathematically speaking, moving down means taking the derivative with respect to time. The organization is easy to see under D1. Velocity is the time derivative of distance. Acceleration is the time derivative of velocity.

 M0 d0 d1 d2 t0 (Unitless ratios) Distance - vector Wavelength -vector Planck length = smallest Area Surface area t-1 Frequency Highest = 1/ Planck time Angular velocity - vector Velocity - vector Wave velocity Fastest = speed of light (c) t-2 Acceleration - vector Gravity - vector E/m conversion constant (c2)

page 2

 M1 d0 d1 d2 t0 Mass - scalar Conserved with energy t-1 Momentum - vector conserved Angular momentum - vector conserved t-2 Force - vector Energy - scalar / statistical Conserved Torque -vector

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With this structure we can create an organized list of all the known measurements used in physics. This would make for a great reference guide. But does the chart have some underlying structure that will teach us more? We can look for hints.
To the right of the block for mass we have a blank. The structure of the chart suggests that block would be filled as mass integrated across distance. Can we determine any useful purpose for integrating mass across distance? The block could also be seen as the derivative of momentum with respect to time. For a whole system, since momentum is conserved, this value should always be zero. But could it have meaning when examining components of a system?
We might find information in other ways of moving around the chart. Side to side is to differentiate or integrate with respect to distance, up and down would be time. But physical constants take us in other directions. We can move from frequency to energy by multiplying by the Planck constant, h. Can all moves across the chart in the same direction be made, in a physically meaning full manner, using the Planck constant? Would Planck's constant take us from velocity to another measure with units m1*d3/t2? Similar questions may be raised for the gravitational constant, G, the electrical constant, e, the magnetic constant, m, and the speed of light, c.
Finally, if the fundamental constants do work like vectors across this table, this would suggest the table could be transformed like a vector space. Would this lead to new useful ways to organize these properties and hint at unseen relationships between them?

Summation
An organized table makes for a great reference. Creating this table would be a great step forward for education in physics. But might something more be discovered from the table? We challenge you to find out.

#### Part 2: Musing from the implications of periodicity

We can arrange the three physical force constants - Gravity: G, electric: e, and magnetism: u - to see if the order suggests anything. Our starting point is to find pattern or relationships within their fundamental units. Once arranged to group their units, we notice that one appears to be missing. The pattern would be complete if we add another constant which has mass (1/kg) like gravity, and distance (m) like magnetism.

 Characteristic units m^3 / S^2 m kg/c^2 1/e: kg/c^2 * m^3/S^2 u: kg/c^2 * m 1/ kg G: 1/kg * m^3/S^2 Tbd: 1/kg * m

This missing piece in the pattern makes one wonder whether a force of nature remains undiscovered (or un-discussed.) We can predict the value of this unknown by setting it equal to one in terms of Planck units, then converting back to common units. If we predict the value of this constant by following the Planck unit pattern the value would be about 7.42*10^-28 kg-m. The units and position on our chart imply that the force would be related to motion like magnetism.
Reasoning from that, if this force were real, it would be about 10^18 times weaker than the electric force in a particle accelerator. In the large scale, if a 1 kg object flew roughly 2000 Mph within 1 meter of earth, the force would be about 1 newton, or roughly 1/10th the force of gravity on that object. Thus, the only place we would expect to see this force large enough to be significant would be in with very large close fast objects (eg: brown dwarves circling each other), or sub-atomic distances.
Does such a force exist? Should its constant be added to the list of known physical constants? How would we find out? Is it reasonable to believe that this force exists? When we look at the mass equation from relativity we might guess that extremely fast objects should have a higher gravitational field. But the field would have to be dependent on relative motion. By analogy, magnetic fields around moving charged particles depend on relative motion. So the idea makes sense.
At the subatomic scale this new undiscovered force may be about the same magnitude as weak force. It doesn't appear to have the correct units to match the weak force. But the weak force is attractive at extremely close sub-atomic distances, and repulsive farther out. Again, using the magnetism analogy the force on a moving charged particle is opposite just outside a toroid from what it is inside. Perhaps it does make sense to suggest this for is real and has already been observed.
On the very large scale could some of the unusual motions in space be attributed to this force that depends on relative motion? Could dark energy actually be a relative motion force?
This musing shows how a periodic organization of physical properties might lead to new insights for physics.

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