4 ms·

Related side note: It has always bugged me that the defintion of 1 second, a unit of time, is defined by an atomic oscillation frequency, which is itself a unit

Related side note: It has always bugged me that the defintion of 1 second, a unit of time, is defined by an atomic oscillation frequency, which is itself a unit x/t. A unit of time refers back to itself in its own definition. My lay understanding is imprecise and I'm sure there's an expert in the wings who could fix it. Then again most belief systems have a root paradox somewhere within them. Perhaps this is ours.

beecafe 5y ago
It's more like, 1/time (i.e, frequency), is what has been defined by the observed atomic oscillator frequency, and the second is derived from that. A real weird unit is km/l or miles per gallon, which cancels out to a unit of area.
- kingkawn 5y ago
  What’s to say any two oscillations of the atom are the same length?
  - CamperBob2 5y ago
    It has to do with the assumed constancy of the so-called "fine structure constant." Google that for more info. TL,DR: the only way these atomic resonant frequencies can possibly change is if the fine structure constant varies from place to place, or over time. If that turns out to be the case, the discovery will invalidate, or at least upset, the last 100 years worth of physics and cosmology. It's all but unthinkable.
    - kingkawn 5y ago
      Sounds exciting
  - taejo 5y ago
    You might be interested in the book Inventing Temperature by Hasok Chang which looks at similar questions but for temperature instead of time, both historically and philosophically. For example, you can define a temperature scale using the boiling point of water, but how do you know water always boils at the same temperature without a temperature scale? (And of course, it doesn't -- even at constant pressure, liquid water can exceed 100°C without boiling)
- eesmith 5y ago
  Regarding km/l or mpg, see https://what-if.xkcd.com/11/ https://what-if.xkcd.com/11/ which points out that the area term of the reciprocal - eg, liters per 100 kilometers - has a more direct physical interpretation: > "If you took all the gas you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube [in a car which gets 20 MPG]"
- satori99 5y ago
  > A real weird unit is km/l or miles per gallon, which cancels out to a unit of area. Ohms per square is another weird one. https://en.wikipedia.org/wiki/Sheet_resistance#Units https://en.wikipedia.org/wiki/Sheet_resistance#Units
kragen 5y ago
WP says, "The second is defined as being equal to the time duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental unperturbed ground-state of the caesium-133 atom." I don't see an oscillation frequency in there; rather, I see a number of periods of a particular color of light. Now, normally we do specify colors of light as frequencies in just the way you say, some number of oscillations per second (unless those frequencies are higher than about 10 GHz), but we can't do that in this case, because it would make the definition circular in just the way you say. Instead, the color of light in question is specified in terms of a quantum-physical phenomenon that produces a very precise color. The cesium-133 atom doesn't need to look at a clock to see how fast to resonate. If archaeologists from the planet Plarx land on Earth in the 37th century and are trying to figure out how our culture measured time, and this comment is all that remains from our society, well, all they need to do is build a cesium maser and hook it up to a circuit that counts to 9,192,631,770. (Actually, probably someone on Plarx has already published the spectrum of cesium, so they can just see that the oscillation period of its hyperfine transition corresponds to 0.000000038134825 of their zorps, and then they know that a "second" is 350.5594 zorps long.) We used to do the same thing with the meter: "1650763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum." Usually we give wavelengths in terms of the meter, but in this case we're giving the meter in terms of wavelengths. That's because the wavelength is a physically existing, objective phenomenon, which can be measured by anyone. Now, instead, the meter is defined in terms of the second: a meter is defined as the distance light travels in a vacuum 299,792,458 times in a second. So the Plarxian archaeologists will have to figure out what a "second" is first, if they're working from that definition.
adrian_b 5y ago
There is a difference between primitive physical quantities and physical quantities whose units are base units. The primitive physical quantities are those quantities that in a theory of physics cannot be defined as functions of other previously defined quantities. Therefore any theory of physics starts from a list of primitive physical quantities and the other quantities are defined using the primitive quantities. Sometimes, during the evolution of physics, previously unknown relationships between quantities are discovered, which cause a previously primitive quantity to be defined now using other quantities, so in the updated theory the number of primitive quantities is reduced. The most important examples of such cases are the discovery caused by the Oersted experiment that the magnetism is also produced by the electric charge and not by a distinct magnetic charge and the discovery as a consequence of the atomic theory and of the statistical physics that the temperature is not a primitive quantity but one that can be defined based on the distribution of the kinetic energy of an ensemble of particles. Examples of primitive physical quantities are time, length and force. When you establish a system of units of measurement for the physical quantities, some units are chosen arbitrary and are designated as base units. The other units are derived from them using the relationships that exist between physical quantities during various kinds of experiments. What confuses many people, including you, is that there exists absolutely no relationship between the quantities that are primitive and the quantities whose units are chosen to be base units. In a theory of physics, the number of primitive quantities is fixed, but the number of base units is completely arbitrary. There might be e.g. 10 primitive quantities, but one may choose to have 0, 1, 2, 10, 20 or 50 base units. Having too many base units makes the computations inconvenient, because in each relationship between quantities an extra base unit may introduce an extra arbitrary multiplication factor, a.k.a. "universal constant". The systems with too few base units are disliked by many people because the units for many frequently used physical quantities become either very large or very small in comparison with the usual values, or they just become too different from the traditional units used for those quantities. So the SI is a balance between these 2 conflicting requirements. It has much more base units than necessary but much less than the traditional systems of units that existed before SI. The base units are chosen so that it is possible to make some devices that realize the units with high accuracy and precision. Because of this requirement, the quantities with base units are very seldom also primitive quantities. For a very long time, the length was both a primitive quantity and one whose unit was a base unit, because you could choose some stick or rod as the base unit for length. Because any object has a length that is variable in time when measured with high precision, this had to be abandoned and the length does not have a base unit now (in reality it does not have a base unit, even if the SI definition attempts to preserve the illusion that the length still has a base unit). For time, it was never possible to keep with you a certain time so the base unit has always been not for time but for the period of a periodic system or, equivalently, for its frequency. In the beginning the periodic phenomenon was the rotation of the Earth, then it was the revolution of the Earth around the Sun, then an atomic clock. The unit of time has always been derived from the unit of frequency (or of period). The confusion for those who are not aware how the systems of units of measurement work is greatly enhanced by the definitions of the SI units, which, in an attempt to reduce the confusion (?!) define the units for the same physical quantities that were chosen to have base units at the creation of the SI, even if in fact most of them no longer have true base units. Even at the creation of SI, the time was named as a quantity with a base unit just because it is well known as a primitive quantity, even if the actual definition defined the time unit as derived from the unit of period and later from the unit of frequency. Today, the SI is obtained from a simpler system with much less base units by taking the derived units of various quantities, multiplying them with arbitrary factors chosen so that the new SI units match the older SI units and setting these multiplied units as the base units of the current SI.

beecafe 5y ago

It's more like, 1/time (i.e, frequency), is what has been defined by the observed atomic oscillator frequency, and the second is derived from that. A real weird unit is km/l or miles per gallon, which cancels out to a unit of area.

kingkawn 5y ago
What’s to say any two oscillations of the atom are the same length?
- CamperBob2 5y ago
  It has to do with the assumed constancy of the so-called "fine structure constant." Google that for more info. TL,DR: the only way these atomic resonant frequencies can possibly change is if the fine structure constant varies from place to place, or over time. If that turns out to be the case, the discovery will invalidate, or at least upset, the last 100 years worth of physics and cosmology. It's all but unthinkable.
  - kingkawn 5y ago
    Sounds exciting
- taejo 5y ago
  You might be interested in the book Inventing Temperature by Hasok Chang which looks at similar questions but for temperature instead of time, both historically and philosophically. For example, you can define a temperature scale using the boiling point of water, but how do you know water always boils at the same temperature without a temperature scale? (And of course, it doesn't -- even at constant pressure, liquid water can exceed 100°C without boiling)
eesmith 5y ago
Regarding km/l or mpg, see https://what-if.xkcd.com/11/ https://what-if.xkcd.com/11/ which points out that the area term of the reciprocal - eg, liters per 100 kilometers - has a more direct physical interpretation: > "If you took all the gas you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube [in a car which gets 20 MPG]"
satori99 5y ago
> A real weird unit is km/l or miles per gallon, which cancels out to a unit of area. Ohms per square is another weird one. https://en.wikipedia.org/wiki/Sheet_resistance#Units https://en.wikipedia.org/wiki/Sheet_resistance#Units

kragen 5y ago

WP says, "The second is defined as being equal to the time duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the fundamental unperturbed ground-state of the caesium-133 atom." I don't see an oscillation frequency in there; rather, I see a number of periods of a particular color of light. Now, normally we do specify colors of light as frequencies in just the way you say, some number of oscillations per second (unless those frequencies are higher than about 10 GHz), but we can't do that in this case, because it would make the definition circular in just the way you say. Instead, the color of light in question is specified in terms of a quantum-physical phenomenon that produces a very precise color. The cesium-133 atom doesn't need to look at a clock to see how fast to resonate. If archaeologists from the planet Plarx land on Earth in the 37th century and are trying to figure out how our culture measured time, and this comment is all that remains from our society, well, all they need to do is build a cesium maser and hook it up to a circuit that counts to 9,192,631,770. (Actually, probably someone on Plarx has already published the spectrum of cesium, so they can just see that the oscillation period of its hyperfine transition corresponds to 0.000000038134825 of their zorps, and then they know that a "second" is 350.5594 zorps long.) We used to do the same thing with the meter: "1650763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum." Usually we give wavelengths in terms of the meter, but in this case we're giving the meter in terms of wavelengths. That's because the wavelength is a physically existing, objective phenomenon, which can be measured by anyone. Now, instead, the meter is defined in terms of the second: a meter is defined as the distance light travels in a vacuum 299,792,458 times in a second. So the Plarxian archaeologists will have to figure out what a "second" is first, if they're working from that definition.

adrian_b 5y ago

There is a difference between primitive physical quantities and physical quantities whose units are base units. The primitive physical quantities are those quantities that in a theory of physics cannot be defined as functions of other previously defined quantities. Therefore any theory of physics starts from a list of primitive physical quantities and the other quantities are defined using the primitive quantities. Sometimes, during the evolution of physics, previously unknown relationships between quantities are discovered, which cause a previously primitive quantity to be defined now using other quantities, so in the updated theory the number of primitive quantities is reduced. The most important examples of such cases are the discovery caused by the Oersted experiment that the magnetism is also produced by the electric charge and not by a distinct magnetic charge and the discovery as a consequence of the atomic theory and of the statistical physics that the temperature is not a primitive quantity but one that can be defined based on the distribution of the kinetic energy of an ensemble of particles. Examples of primitive physical quantities are time, length and force. When you establish a system of units of measurement for the physical quantities, some units are chosen arbitrary and are designated as base units. The other units are derived from them using the relationships that exist between physical quantities during various kinds of experiments. What confuses many people, including you, is that there exists absolutely no relationship between the quantities that are primitive and the quantities whose units are chosen to be base units. In a theory of physics, the number of primitive quantities is fixed, but the number of base units is completely arbitrary. There might be e.g. 10 primitive quantities, but one may choose to have 0, 1, 2, 10, 20 or 50 base units. Having too many base units makes the computations inconvenient, because in each relationship between quantities an extra base unit may introduce an extra arbitrary multiplication factor, a.k.a. "universal constant". The systems with too few base units are disliked by many people because the units for many frequently used physical quantities become either very large or very small in comparison with the usual values, or they just become too different from the traditional units used for those quantities. So the SI is a balance between these 2 conflicting requirements. It has much more base units than necessary but much less than the traditional systems of units that existed before SI. The base units are chosen so that it is possible to make some devices that realize the units with high accuracy and precision. Because of this requirement, the quantities with base units are very seldom also primitive quantities. For a very long time, the length was both a primitive quantity and one whose unit was a base unit, because you could choose some stick or rod as the base unit for length. Because any object has a length that is variable in time when measured with high precision, this had to be abandoned and the length does not have a base unit now (in reality it does not have a base unit, even if the SI definition attempts to preserve the illusion that the length still has a base unit). For time, it was never possible to keep with you a certain time so the base unit has always been not for time but for the period of a periodic system or, equivalently, for its frequency. In the beginning the periodic phenomenon was the rotation of the Earth, then it was the revolution of the Earth around the Sun, then an atomic clock. The unit of time has always been derived from the unit of frequency (or of period). The confusion for those who are not aware how the systems of units of measurement work is greatly enhanced by the definitions of the SI units, which, in an attempt to reduce the confusion (?!) define the units for the same physical quantities that were chosen to have base units at the creation of the SI, even if in fact most of them no longer have true base units. Even at the creation of SI, the time was named as a quantity with a base unit just because it is well known as a primitive quantity, even if the actual definition defined the time unit as derived from the unit of period and later from the unit of frequency. Today, the SI is obtained from a simpler system with much less base units by taking the derived units of various quantities, multiplying them with arbitrary factors chosen so that the new SI units match the older SI units and setting these multiplied units as the base units of the current SI.