Famous, highly relevant numbers are everywhere.
Square root of 2
Base of Natural Logarithms
Pi
AND THEY ARE IRRATIONAL NUMBERS.
But what about
c = the speed of light.
IS C A RATIONAL NUMBER?
Question by Fhree
2006-07-07 21:22:57 · 21 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
C = The speed of light
has been shown to be a Universal Constant.
WHAT KIND OF NUMBER IS IT?
Is there any sort of proof, or has any research been done - mathematically?
2006-07-07 21:42:53 · update #1
Don't know, it is an experimentally derived result. However ANY experiment can only yield rational numbers (you can't measure something with infinite precision so you can't measure something as being irrational as that REQUIRES infinite precision. This is something like the difference between .333333 (note the end of the decimal expansion) and .333333333... (note the lack of end of decimal expansion) they are similar but not the same. Hopefully that makes sense. You FUNDAMENTALLY can't arrive at an irrational unit of measure when you measure something in the real world that uses purely rational units of measure.
Be wary of people that are giving you answers w/o explanations.
2006-07-07 21:36:57 · answer #1 · answered by Anonymous · 1⤊ 0⤋
As others have pointed out, the value of c depends on your units. It is very common in advanced physics to choose units where c=1. In that case, c is clearly rational. In terms of meters/second, c has a *defined* value which is rational. This value helpes to set the definition of a meter.
A somewhat more interesting question would be whether various dimensionless constants are rational or irrational. For example, the fine structure constant, e^2/(2*epsilon_0 *hc) is a constant of nature that does not depend on the system of units being used. Unfortuantely, it is probably simply meaningless to ask whether a *physical* constant is rational or irrational becuse the value of such a thing can only be measured to a certain degree of accuracy and no degree of accuracy will distinguish between rational and irrational numbers. This is very different from the constants you mentioned which are purely mathematical constants and can be defined without any knowledge of the physical world.
2006-07-08 09:13:25 · answer #2 · answered by mathematician 7 · 0⤊ 0⤋
It's a rational number and it does not depend on the units. You can't convert a rational number into an irrational number by changing the units. (Changing the units is just multiplying it by a constant. That doesn't turn a rational number into an irrational number.)
But why is it rational? Because the universe is quantized. At the smallest scales, there there is a minimum lenght (the Plank length). There is also a minimum time scale (the Plank time). So light must move X Plank lengths in Y Plank times. Dividing X and Y will give you a rational number.
2006-07-16 23:00:11 · answer #3 · answered by C. C 3 · 0⤊ 0⤋
The speed of light is not a constant, because it changes depending on the medium in which the light passes. If you fire an electron in a vacuum at 99% of the speed of light into and through some glass, the speed of light in that medium will be less than when it was fired, and the electron does not have a chance to slow down. This will actually cause the electron to move faster than the speed of light in that medium, causing a visible flash of light (like a sonic boom)!
The constant c that is used is a theoretical speed limit for light passing through a true vacuum. It has been measured with some degree of accuracy. The constant that is used is not irrational. It is approximately 186,282 miles per second.
2006-07-16 18:20:45 · answer #4 · answered by Dr. Rob 3 · 0⤊ 0⤋
This is an open question because it really depends upon what units you are using, since the Speed of Light is a Measured Quantity. So there really isn't a hard and fast answer.
One can measure it in Miles per Second, Meters per Second, or any proportion consisting of units of length/units of time.
Also the Speed of Light is only constant within a vacuum. The speed of light is slower in a medium such as an Atmosphere, or Liquid.
(There is even some debate whether or not the speed of light is truly constant or changes slowly over time as the universe expands.)
Many Cosmologists simply set the speed of light in Vaccuum to 1. and drill on through their calculations.
2006-07-08 11:52:54 · answer #5 · answered by bostonterrier_97 1 · 0⤊ 0⤋
Universal constants or measured quantities are irrational numbers in general UNLESS they can be computed as a ratio of two other rational numbers. So calculated quantities may be rational - but fundamental quantities would not be.
At the present time, it appears based on our understanding of physics that the speed of light is a fundamental quantity that cannot be calculated based on the ratio of two rational numbers. So it would be irrational.
But that is subject to change because our understanding of physics is not complete.
At some point in the future, we may discover that the speed of light is dependent on some underlying physical properties that we do not yet understand, and its is actually a calculated quantity from two rational numbers.
However, remember that the irrational numbers are infinitely more likely than the rational numbers!
2006-07-08 11:50:07 · answer #6 · answered by volume_watcher 3 · 0⤊ 0⤋
Speed of light is not a number but a physical quantity.
A physical quantity is expressed as a number PLUS A UNIT.
The numerical value depends on the unit you choose.
In SI units, speed of light is approx. 2.998.10^8 m/s, but there is nothing special about this number. In fact, we can only discover more precise information about it through experiment.
The distinction between rational and irrational numbers is only meaningful if we know the numbers without any error. Physical constants cannot be measured without error.
Best I can say here: if you pick arbitrary units, and you could measure c with infinite precision, the probability that it is irrational is 100% -- but it is still possible that it is rational. (Follows from the fact that Q has zero measure in R.)
2006-07-21 11:39:22 · answer #7 · answered by dutch_prof 4 · 0⤊ 0⤋
Actually eventhough the C is not an irrational number or whatsoever, the main concern is that the said Formula is never been proven, because we have no such Jetplane or spacecraft that can Fly with the Speed of light. And if even we can travel on a speed of light, No, we can't go back in time, we can go only forward as what Eintein's says. But as what ive said - Its Not Yet been Proven, maybe after Gogoplex of years.
2006-07-21 06:55:31 · answer #8 · answered by DOC AGA 2 · 0⤊ 0⤋
The speed of light (in a vacuum I assume) may or may not be a rational number. Thus far the speed has only been determined experimentally, however it is possible that the value will be determined mathematically. For example, various properties of sub atomic properties were originally only derived experimentally, but can now be derived mathematically from string theory. It is possible this may happen for the speed of light some day and we will see if it is rational or not :)
2006-07-08 05:12:41 · answer #9 · answered by blair f 1 · 0⤊ 0⤋
The speed of light is not exactly 3 x 10^8 m/s.
If u check out the definition of metre - 1 m is the distance travelled by light in vaccum in 1/2.9979...*10^8 of a second.
As u can see, the denominator is the exact speed of light and is a never ending decimal number and hence not an integer...
2006-07-08 04:40:46 · answer #10 · answered by Srikanth 2 · 0⤊ 0⤋