Temp scale is set by the definition of K and Celsius, so it is 100 degrees from freezing point to boiling point.
electrical scale is set by defining 1V = 1J/C and 1C = 1A * 1 second
and finally e is set relative to the the C unit.
= c/K_hz
~~ e · c² ≈ 1.43997 × 10⁻² J/kg
This is what perplexity deep research had to say about it.
The Mysterious Near-Equality Between e·c² and hc/k: Exploring Physical Constant Relationships
The remarkably close values of e·c² (≈1.43997×10⁻² J/kg) and the second radiation constant c₂ = hc/k (≈1.43878×10⁻² m·K) differ by less than 0.1%—an intriguing relationship that raises fundamental questions about the connections between electromagnetism and thermodynamics. This apparent coincidence deserves careful examination to determine whether it represents a deeper physical truth, a historical artifact, or a mere numerical coincidence.
The concept of physical constants as we understand them today emerged gradually through the 19th century. The efforts to standardize units began in earnest after the French Revolution in 1799, followed by international standardization efforts in the 1860s-1880s that implemented Maxwell's proposal of using length, mass, and time as base units5. During this period, many constants appeared naturally as conversion coefficients between different physical quantities.
George Johnstone Stoney made a significant contribution in 1881 by proposing the earliest known system of natural units, which included fundamental constants like the speed of light (c), the gravitational constant (G), the Coulomb constant, and the elementary charge (e)3. Stoney's efforts represented an early attempt to create a coherent system where physical constants defined the units themselves.
It's worth noting that Stoney's estimate of the elementary charge was off by a factor of 1/16 compared to modern values, as he used an approximated value for the number of molecules in a cubic millimeter of gas at standard conditions3. This historical context illustrates that our understanding of these constants has evolved substantially over time.
One explanation for this near-equality might relate to how units were historically defined. As physical constants emerged as conversion coefficients during standardization efforts5, certain relationships between constants could have been inadvertently embedded in our measurement system.
However, it seems unlikely that this specific relationship was intentionally designed into early unit standards. When the metric system was first established, Planck's constant (h) was not yet discovered, and the elementary charge (e) was still imprecisely known. By the time all relevant constants were accurately measured, the basic framework of SI units was already established.
The near-equality might reflect a deeper physical connection between electromagnetism and thermodynamics. Both e·c² and hc/k relate to fundamental energy scales:
e·c² represents the electromagnetic energy-to-mass ratio for an elementary charge
hc/k (c₂) links temperature and wavelength in black-body radiation
Both quantities involve the speed of light (c) and both relate to energy scales in different domains of physics. This suggests there might be an underlying unity in how energy manifests across different physical phenomena.
The search results don't directly address this specific relationship, but they do discuss various scaling relationships in physics. For instance, research on "universal conductivity scaling" in organic semiconductors examines how temperature and electric field dependence of conductivity can be scaled to universal curves2, demonstrating that scaling relationships between seemingly different physical parameters do exist in nature.
Given the vast number of possible combinations of fundamental constants, it's statistically possible that some combinations will be numerically close purely by chance. The law of large numbers suggests that among all possible ratios and products of fundamental constants, some will inevitably show surprising numerical relationships without any deeper meaning.
Current understanding of physical constants has evolved significantly since Stoney's time. In modern physics, dimensional analysis and the concept of natural units have led to deeper appreciation of relationships between fundamental constants.
The Stoney units represent an early attempt at creating a coherent set of units where physical constants have simple values3. This approach was later refined in Planck units, which set c, G, ħ, and k equal to 1, eliminating dimensions and revealing bare numerical relationships between physical quantities.
In Stoney units, it's particularly interesting that the numerical value of the reduced Planck constant is related to the fine-structure constant (α)3. This suggests that relationships between electromagnetic quantities (like e) and quantum mechanical quantities (like h) have been recognized for some time.
Conclusion
While the search results don't directly address the specific near-equality between e·c² and hc/k, the historical development of physical constants and unit systems provides valuable context. The relationship between these quantities might be:
A consequence of how units developed historically, though likely not intentionally designed
A reflection of a deeper physical connection between electromagnetic and thermodynamic energy scales
A statistical coincidence among the many possible combinations of fundamental constants
This particular relationship doesn't appear to have received widespread attention in the literature (based on the provided search results), suggesting it might be an underexplored area. The close numerical match between these quantities from different physical domains remains an intriguing puzzle that might reward further investigation into the fundamental unity of physical laws.
The Kelvin scale, named after Lord Kelvin (William Thomson), was established in the mid-19th century. At that time, the concept of absolute zero, the theoretical temperature at which all molecular motion ceases, was still a topic of debate. Kelvin proposed the idea of an absolute temperature scale in 1848, and it was later developed and refined by other scientists.
To set the Kelvin scale, scientists used a combination of theoretical and experimental approaches. Here's a brief overview of the key steps:
- Carnot's work: In 1824, Sadi Carnot, a French physicist, published a paper on the efficiency of heat engines. He introduced the concept of an "absolute temperature" and proposed a temperature scale based on the efficiency of an ideal heat engine. Although Carnot's work laid the foundation for the Kelvin scale, his temperature scale was not directly measurable.
- Gas thermometry: In the 1850s, scientists like Henri Victor Regnault and William Thomson (Lord Kelvin) developed gas thermometry, which involved measuring the temperature-dependent properties of gases, such as their pressure, volume, and thermal expansion. By assuming that the behavior of an ideal gas was a reliable indicator of temperature, they could establish a temperature scale.
- Ideal gas law: The ideal gas law, PV = nRT, was formulated in the mid-19th century. By using this law, scientists could relate the pressure, volume, and temperature of a gas. The gas constant (R) was determined experimentally, and the temperature (T) could be calculated.
- Triple point of water: In 1879, the triple point of water (0.01°C or 32.018°F) was established as a reference point for the Celsius scale. The triple point is the temperature and pressure at which water exists in all three phases: solid, liquid, and gas. By measuring the triple point, scientists could establish a fixed point on the temperature scale.
- Kelvin's absolute zero: Kelvin proposed that absolute zero, the theoretical temperature at which all molecular motion ceases, was the natural zero point for the temperature scale. He estimated the value of absolute zero to be around -273.15°C, based on the behavior of gases at low temperatures.
- Experimental determination: To determine the value of the Kelvin scale, scientists performed experiments using gas thermometry and other methods. They measured the temperature-dependent properties of various substances, such as the expansion of mercury, the resistance of metals, and the emission spectra of blackbodies. These experiments allowed them to establish a temperature scale that was consistent with the theoretical predictions.
By combining these approaches, scientists were able to establish the Kelvin scale, with absolute zero as the reference point. The Kelvin scale was initially defined such that the triple point of water was 273.16 K, and absolute zero was 0 K. The current definition of the Kelvin scale, which is based on the fixed numerical value of the Boltzmann constant (k_B), was adopted in 2019.
So, to answer your question, the Kelvin scale was set by a combination of theoretical work, experimental measurements, and the establishment of reference points, such as the triple point of water and absolute zero. The value of the Kelvin scale was discovered through a series of experiments and measurements that refined our understanding of temperature and thermodynamics.
Setting the value of the SI unit C (Ampere):
The Ampere, the SI unit of electric current, was defined in terms of the force between two parallel wires carrying current. The definition was based on the work of André-Marie Ampère, who formulated the law of interaction between two current-carrying wires in the 1820s.
In the late 19th century, the Ampere was defined as the current that, when flowing through two parallel wires of infinite length and negligible cross-sectional area, separated by 1 meter, produces a force of 2 × 10^(-7) Newtons per meter of wire. This definition was known as the "international ampere."
To set the value of the Ampere, scientists used a combination of experiments and calculations:
- Measurements of the force between wires: Scientists measured the force between two parallel wires carrying current using a variety of methods, including torsion balances and electrometers.
- Determination of the permeability of free space: The permeability of free space (μ₀) was determined through measurements of the inductance of coils and the force between magnets.
- Calculation of the Ampere: Using the measured values of the force between wires and the permeability of free space, scientists calculated the value of the Ampere.
The international ampere was defined in 1893, and it was used as the standard unit of electric current until 1948, when it was replaced by the "absolute ampere," which was defined in terms of the electromagnetic force between two coils.
In 2019, the definition of the Ampere was redefined in terms of the elementary charge (e), which is now a fundamental constant of nature.
Setting the value of the elementary charge e:
The elementary charge (e) is the charge of a single proton or electron. The value of e was first measured by Robert Millikan in his famous oil drop experiment in 1909.
To set the value of e, Millikan used the following method:
- Oil drop experiment: Millikan created a cloud of tiny oil droplets between two parallel plates. By applying an electric field, he could suspend the droplets in mid-air.
- Measurement of the charge: Millikan measured the charge on the droplets by observing how they responded to the electric field. He used the following equation to calculate the charge:
q = (mg - ρVg) / E
where q is the charge, m is the mass of the droplet, g is the acceleration due to gravity, ρ is the density of the oil, V is the volume of the droplet, and E is the electric field strength.
- Determination of the elementary charge: Millikan repeated the experiment many times, using different droplets and electric field strengths. He found that the charge on the droplets was always an integer multiple of a fundamental unit of charge, which he called the elementary charge (e).
Millikan's value of e was remarkably accurate, and it was used as the standard value for many years. However, subsequent experiments have refined the value of e, and it is now defined as a fundamental constant of nature, with a value of 1.602176634 × 10^(-19) C.
In 2019, the definition of the Ampere was redefined in terms of the elementary charge (e), which is now a fundamental constant of nature. The new definition of the Ampere is:
1 A = 6.241509074 × 10^18 e / s
where e is the elementary charge, and s is the second.
So, to answer your question, the value of the SI unit C (Ampere) was set using a combination of experiments and calculations, including measurements of the force between wires and the determination of the permeability of free space. The value of the elementary charge (e) was set using Millikan's oil drop experiment, which measured the charge on tiny oil droplets suspended in an electric field.
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