Re: universal constants in cryptography?

As you known the physical ssciences have a set of what one might call
universal constants. Example "c" the speed of light, that turn up on
manay places. As far as I can understand these constants are useful as
a means of deciding whether a proposed theory or construction might be
correct. For example, A theory of electomagnetism might show that "c'"
is a consequence of the theory.

c is a units conversion "constant". Historically, people, not knowing
relativity, measured time and space with different units. It would be like
measuring horizontal distances in kilometres and vertical in inches. Since
they are really the same thing, one needs a conversion constant. In the

You can only use "they really are the same thing" only so far.
Using c as a conversion constant implies that there is one speed,
and that's rarely the case for cars on a freeway. If the value of
c comes up in traffic court related to a speeding charge, someone
is doing something stupid. Also, there are laws of conservation
of energy and momentum, but there is no law of conservation of time
after you get through converting things to death.

example that conversion constant is inches/km. In the case of time and
space it is m/sec. Similarly hbar converts metres to inverse momentum, or time
to inverse energy.

One problem with this is that the constants are not known to 100%
accuracy. If you ever get a more accurate version of the constant,
and this isn't uncommon, you need to go back and fix the measurements
that were made of one type of unit but not the other. Keep the
units. Don't try to collapse them into dimensionless mush.

Dimensional analysis is very useful in physics. If you are calculating
how far up a bullet will go if you fire it into the air (police are
notifying everyone locally that there's a $4000 fine for doing that,
and it's NOT safe) and you get an answer of 9 seconds, you've screwed
up the formulas. You do not multiply by c to convert it to distance.

And G/c^2 converts mass to distance. Ie, they have no physical
significance, but are purely a correction factor to account for historical
accident.

Although in theory a kilogram of rice provides a huge amount of
energy, much more than enough to blow up a Japanese city, it doesn't
provide nearly that much energy when I eat it and run a marathon.


Now there are some other constants. 1/137... for the charge^2 of the
electron,4x10^(-23) for the mass of an electron (in natural units), pi for
the ratio of circumference to diameter of a circle, etc. which are natural
constants.

Yes, there are a few dimensionless constants like pi.

What you are describing is dimensional analysis, where one guesses for a
physical process that its depenence is on mass, legths and time (in
theories where their separate specification makes sense) and sticks in
appropriate conversion factors to take care of the mismatch in dimensions,
and assumes that in "absolute" units, the answer is approximately 1.

Any time you start having to "just stick in" conversion factors
between dimensionally different quantities, you've probably goofed
something up. Quantities like mass, force, time, distance, velocity,
temperature, energy, momentum, currency, charge, etc. are all
different dimensionally and if you need to "convert" distance to
time, you need to use an appropriate velocity, not assume that the
only velocity is c. Yes, there are times when you need to convert
energy units to mass units and vice versa but only when describing
something that actually involves conversion of energy to mass and
vice versa.

.

Relevant Pages

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