If we follow an ancient Greek philosopher saying "there is no perfect
circle in our world", every physical value must be rational number.
However I thought the light speed only is irrational, and our
(classical) world is composed of Q(c) (i.e. rational number field Q
adding the light speed c). And I found Minkowski metric was very
naturally induced on Q(c). For details, visit;

http://www.geocities.com/tontokohiro...ic/complex.htm

"tontoko" wrote in message
ups.com...
If we follow an ancient Greek philosopher saying "there is no perfect
circle in our world", every physical value must be rational number.

Even the diagonal of a square of unit size?

However I thought the light speed only is irrational,

Since it can be made any value at all depending on units shown it is
obviously neither rational or irrational.

Bill

and our
(classical) world is composed of Q(c) (i.e. rational number field Q
adding the light speed c). And I found Minkowski metric was very
naturally induced on Q(c). For details, visit;

http://www.geocities.com/tontokohiro...ic/complex.htm

Even the diagonal of a square of unit size?

Anyway we have to approximate the square root by rational number if it
is irrational. Can you state every figure of square root of 2?

Since it can be made any value at all depending on units shown it is
obviously neither rational or irrational.

Mathematically the number in Q(c) is expressed as x = a+bc where a and
b are rational numbers and c is irrational number.

"tontoko" wrote in message
oups.com...
Even the diagonal of a square of unit size?

Anyway we have to approximate the square root by rational number if it
is irrational.

We do not have to approximate sqrt 2 any more than we need to approximate
the rational number 1/googolplex - yet both would be intractable to exact
manipulation. It is the choice of doing tractable calculations that
determines if we approximate anything.

Can you state every figure of square root of 2?

Can you write down all the digits of the decimal expansion of the rational
number - 1/googolplex?


Since it can be made any value at all depending on units shown it is
obviously neither rational or irrational.

Mathematically the number in Q(c) is expressed as x = a+bc where a and
b are rational numbers and c is irrational number.

In natural units c = 1 thus your b would be 0.

Bill

tontoko wrote:
If we follow an ancient Greek philosopher saying "there is no perfect
circle in our world", every physical value must be rational number.
However I thought the light speed only is irrational, [...]

No. The value for the speed of light depends on one's choice of units.
Using the current SI units, the speed of light is exactly 299,792,458
meter/second. That is quite clearly an INTEGER. This is, quite
literally, the definition of the meter in terms of the second and a
light beam.


Tom Roberts

This is, quite
literally, the definition of the meter in terms of the second and a
light beam.

I agree with that. So we can express time with meters. If we measure
the point in space-time, say t = 5 meters (in time) and x = 3 meters
(in space), then the Lorentz invariant is 5^2-3^2 = 16 (meter^2). It is
decomposed as 16 = 4^2. I insist generally such decomposition is
unavailable, i.e. the time measured by the unit of meter is always
irrational. In this case we can never measure the time = 5 (meters).

Dear tontoko:

"tontoko" wrote in message
oups.com...
This is, quite
literally, the definition of the meter in terms of the
second and a light beam.

I agree with that. So we can express time with
meters. If we measure the point in space-time,
say t = 5 meters (in time) and x = 3 meters
(in space), then the Lorentz invariant is
5^2-3^2 = 16 (meter^2). It is decomposed as
16 = 4^2. I insist generally such decomposition
is unavailable, i.e. the time measured by the
unit of meter is always irrational. In this case
we can never measure the time = 5 (meters).

We can, and it *is* rational, namely: 5 / 299,792,458 seconds

As Bill Hobba has tried to point out to you, it is our choice of
*SI units* that provides rationality/irrationality. You don't
need to add to the list of people that believe in magic numbers,
and how they will "revolutionize" physics.

David A. Smith

tontoko wrote:
This is, quite
literally, the definition of the meter in terms of the second and a
light beam.

I agree with that. So we can express time with meters. If we measure
the point in space-time, say t = 5 meters (in time) and x = 3 meters
(in space), then the Lorentz invariant is 5^2-3^2 = 16 (meter^2). It is
decomposed as 16 = 4^2. I insist generally such decomposition is
unavailable, i.e. the time measured by the unit of meter is always
irrational. In this case we can never measure the time = 5 (meters).

This is physics, not math. Nothing is ever measured precisely.

We model space and time as continua, as we observe no quantization of
them. So the math used is reals, not rationaals or integers. The proof
is in the pudding, and reals permit differentiation which is absolutely
essential in modern theories of physics.


Tom Roberts