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DeadWolfe
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And why is it related to pi?
I don't think it does have an exact value. Do you have a reference stating that? I believe it would have been determined experimentally, and to the first 5 or 6 digits, it may work out to be the same first 5 or 6 digits of [tex]4\pi \mbox{ x } 10^{-7}[/tex], but I doubt that if they could perform some perfectly precise and accurate experiment, that they would find that [tex]\mu_{o} \neq 4\pi \mbox{ x } 10^{-7}[/tex], probably just [tex]\mu_{o} \approx 4\pi \mbox{ x } 10^{-7}[/tex].DeadWolfe said:And why is it related to pi?
I believe the French came up with the meter by making a very large measurement and dividing it by some number, and having the result be the meter. Although it is possible that they've changed the definition of the meter.TALewis said:When you see physical constants listed as exact, rather than given to an approximate number of decimals, in my experience this means that the units the constant is given in are defined in some way or another in terms of the constant itself.
For example, my text says that the speed of light in vacuum is exactly:
299792458 meters per second
How can anyone say this is the number, exactly? It's not because they've got a really good stopwatch and meterstick. They can do it because they they define the meter in the following way:
1 meter is equal to the distance traveled by light in vacuum during a time of 1/299792458 second.
The definition of the Ampere seems odd, perhaps "flawed". Since they can never have infinitely long wires, the Ampere isn't really standard. The forces between wires that are 100 m long and wires that are 101 m long may be different, and so the Ampere would have different values.Edit: Through a little more quick research it seems the exact value of the permeability of free space comes from the definition of the Ampere:
The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 Newton per meter of length.
Well, mathematics (including geometry) are deductive axiomatic systems. Although the Pythagorean Theorem is not a definition, it's practicality is essentially irrelevant since it need only apply to mathematical objects which exist "in" mathematics, and need no correspondence to the real world. On the other hand, charge will pass through a wire, whether we define it or construct a logical system that defines it or not. However, to define the basic unit of measurement of the Ampere to something that is necessarily immeasurable is, well, pretty odd.TALewis said:It's the same kind of mathematical idealism that you see in something like the Pythagoream theorem. Sure, I say that a^2 + b^2 = c^2, but I could never physically construct a right triangle so perfect as to be able to say that the measurements of the sides satisfy the equation exactly. There is always uncertainty.
TALewis said:For example, my text says that the speed of light in vacuum is exactly:
299792458 meters per second
How can anyone say this is the number, exactly? It's not because they've got a really good stopwatch and meterstick. They can do it because they they define the meter in the following way:
1 meter is equal to the distance traveled by light in vacuum during a time of 1/299792458 second.
[tex]\mu_0=4\pi\times 10^{-7}\,\mbox{webers/amp-m}[/tex]DeadWolfe said:And why is it related to pi?
H-bar None said:The meter is now defined in terms of light travel time. The second is also defined as 2.999792E8 meters of light travel time.
When did I say that? But anyhow, I'd like you to show me a truly two-dimensional object, a perfectly straight line, etc. We can use mathematical models to very usefully model reality and thus engineers and scientists can actually make use of the theorem. But the theorem proves something about the an object in the "world" of mathematics because it is deduced by the axioms which define the world of mathematics; these axioms do not define reality, and thus the theorem is not a truth of reality, simply mathematics. Mathematics is so great in part because it can model reality so well that we can apply mathematical concepts to reality.TillEulenspiegel said:AKG: Although the Pythagorean Theorem is not a definition, it's practicality is essentially irrelevant since it need only apply to mathematical objects which exist "in" mathematics, and need no correspondence to the real world."
Are you saying that there is no real world correspondence between the theory and the reality?
Any measurement made is subject to errors, so the effects wire length is easily dealt with, as for gravitational attraction, that will be constant with and without applied current, What is measured is a CHANGE in force, thus once again easily dealt with.AKG said:krab
One problem I have, which I pointed out, is that the definition of the Ampere relies on something physically impossible (infinitely long wires). In fact, since there will be gravitational attraction between any two wires as well, it seems the definition of the Ampere is flawed in comparison to, say, the definitions of the second (which depends on a constant and something countable) or the meter (which depends on the constant speed of light).
Second of all, it is said that any time less than the Planck time is meaningless. We can take this to suggest that, for all meaningful intents and purposes, time is quantized. Charge, too, is quantized. Current measures the rate of flow of charge with respect to time. But if current depends on [itex]\mu_{o}[/itex] which depends on [itex]\pi[/itex] which is irrational, then doesn't that contradict the fact that current is based on quantum measurements (sorry if I'm using the wrong terminology). A second must be a multiple of the Planck time, I would think, since, if, say a second was 100.5 Planck times (I know that's way off) that would mean 0.5 Planck times would have some meaning, but it doesn't, as far as I know. So, if an amp is charge/time, then it must be some_natural/some_natural x some units, giving some rational with units, whereas pi is irrational. Is this not contradictory?
The Ampere was originally defined as the amount of current that would deposit a certain weight of silver in an electrolytic cell in a given amount of time. The definition was later changed to be a tad bit more precise. Anyway, even with the current (haha pun) definition, it's very possible to have wires so long that they are "close enough" to infinitely long that our equipment will never tell the difference. I mean, really, how many decimal points do you need? I believe something like 30 decimals of [tex]\pi[/tex] is sufficient to calculate the circumfrence of the universe to within the radius of a proton - surely this is sufficient.AKG said:One problem I have, which I pointed out, is that the definition of the Ampere relies on something physically impossible (infinitely long wires). In fact, since there will be gravitational attraction between any two wires as well, it seems the definition of the Ampere is flawed in comparison to, say, the definitions of the second (which depends on a constant and something countable) or the meter (which depends on the constant speed of light).
H-bar None said:The vibration of a cesium atom is constant. A cesium atom electons are excited and gives of light. From Q.M. the energy of photon also reveals the frequency. So the second is the inverse of the frequency of cesium atom
vibrations.
rogerperkins said:What if I told you that the permeability of free space was increasing due to the expansion of the universe? That would mean that the speed of light is also increasing.
rogerperkins said:What if I told you that the permeability of free space was increasing due to the expansion of the universe? That would mean that the speed of light is also increasing. Which would mean that light emitted from distance stars billions of years ago would actually be traveling faster now than when it was first emitted, and therefore appear to be red shifted more to the red than it actually would be just due to the expansion of the universe alone.
The permeability of free space, denoted by the symbol μ0, is a fundamental physical constant that describes the ability of a vacuum to support the flow of magnetic fields. This value is exact because it is defined based on the International System of Units (SI), which is a globally accepted system of measurement for physical quantities. The value of μ0 is determined by experiments and is not subject to change.
The exact value of μ0 is determined through a variety of experiments, including the measurement of the force between two current-carrying wires, the behavior of a magnet in a coil of wire, and the deflection of a charged particle in a magnetic field. These experiments allow scientists to calculate the value of μ0 with a high degree of accuracy.
The permeability of free space is considered a constant because it does not vary with any external factors such as temperature, pressure, or magnetic field strength. This means that the value of μ0 remains the same regardless of the conditions in which it is measured. This makes it a reliable and fundamental constant in the study of electromagnetism.
The value of μ0 plays a crucial role in many equations and formulas in the field of electromagnetism. It is used to calculate other physical quantities such as the magnetic field strength, the force between two electric charges, and the speed of light in a vacuum. Having an exact value for μ0 allows for precise calculations and predictions in various scientific fields.
The value of μ0 is considered a fundamental constant, meaning it is an unchanging and immutable quantity. As of now, there is no scientific evidence to suggest that the value of μ0 could change in the future. However, as our understanding of the universe and its fundamental laws continues to evolve, it is possible that new discoveries may lead to a re-evaluation of this constant in the future.