Challenge: Create a Periodic Table of Physical Measurements D
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.
Draft January 2012
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.
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M0
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d0
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d1
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d2
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t0
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(Unitless ratios) |
Distance - vector |
Area |
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t-1
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Frequency Angular velocity - vector |
Velocity - vector |
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t-2
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Acceleration - vector |
E/m conversion constant (c2) |
page 2
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M1
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d0
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d1
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d2
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t0
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Mass - scalar
Conserved with energy |
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t-1
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Momentum - vector
conserved |
Angular momentum - vector
conserved |
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t-2
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Force - vector
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Energy - scalar / statistical
Conserved Torque -vector |
Related pages at this site
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, , the magnetic constant, , 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.
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