It’s not useful to tell somebody it is constant without a way to make use of it. Without knowing how it’s defined relative to other things we can’t use it.
The thing about all the absolute physical constants is that they are almost all based on units defined relative to other things. Unitless constants (defined only as a ratio) are extremely rare (like the fine structure constant) - but even then you have to make up units to measure them (although you can still agree on unitless values with somebody else who chose different base units for measurements).
Edit: the most obvious immediate reason Wolfram here is fully wrong is that Cesium frequency is defined as the frequency you measure when light of the correct energy/wavelength is emitted against the atom, to then measure the corresponding returned light of the right energy/wavelength.
To determine what that wavelength should be with your instruments you can measure things like the electric field and charges - which depends on units that are all defined relative to each other, and as soon as you start fixing some units (like when you have measured the energy state differential in the atom) then you will realize you have defined ratios between the units
I was unaware that the person to whom I was replying, who claimed to be intimately familiar with the complete works of Feynman, needed instruction in how to “make use of” a fundamental constant of nature. If that is something you think is necessary, perhaps you should see to their instruction in such matters, as you are so confident in your faculties of condescending instruction.
Furthermore, I am acutely aware of the existence and nature of dimensionless constants, thank you very much.
For somebody who claims to be acutely aware, you really seem to have no idea what goes into calibrating measurement devices to be able to measure physical constants. In particular you have no idea how many other units go into calibrating them, and how you fundamentally can not get an accurate reading of a physical constant without that calibration. And for somebody claiming I’m the condescending one, you’re awfully rude yourself
Just see the definition of the kilogram, and how it’s now defined in relation to time, c, and the planck constant.
While the second is the only base unit to be explicitly defined in terms of the caesium standard, the majority of SI units have definitions that mention either the second, or other units defined using the second. Consequently, every base unit except the mole and every named derived unit except the coulomb, gray, sievert, radian, and steradian have values that are implicitly at least partially defined by the properties of the caesium-133 hyperfine transition radiation. And of these, all but the mole, the coulomb, and the dimensionless radian and steradian are implicitly defined by the general properties of electromagnetic radiation.
When the atom is irradiated with electromagnetic radiation having an energy corresponding to the energetic difference between the two sub-levels the radiation is absorbed and the atom is excited, going from the F = 3 sub-level to the F = 4 one. After some time the atom will re-emit the radiation and return to its F = 3 ground state. From the definition of the second it follows that the radiation in question has a frequency of exactly 9.19263177 GHz, corresponding to a wavelength of about 3.26 cm and therefore belonging to the microwave range.
Oh so now we need to measure electromagnetic fields and charge to be able to hit the atom with light of the right energy to be able to measure time? And to verify the emitted frequency (both in and out) is right we need to define either energy (Joule, circular via either kilogram or Volt) or wavelength (directly circular)? Huh…
Everything meaningful is defined as relative properties, as ratios to other forces and properties of nature.
Again, I think you’re replying to the wrong person. I never disagreed with any of this. I literally learned all of this years ago. I appreciate your attempt to educate, but I’m unclear on its purpose. The dude claimed that the speed of light is defined based on the meter, and that that makes it a tautology. That is simply, provably false. Then the dude tried to move the goalposts. Never did I say that our measurements are anything less than relative. Never did I suggest that our derived units are not based on fundamental constants the nature of which can be only guessed at. Now, you’ve said that the statement I made didn’t tell the dude “how to make use of” dimensionless units, which is a complete non sequitur. If you feel that that lecture is an important one when a dude demonstrates a fundamental misunderstanding of what c even is, that’s your own affair, and I invite you to give this lecture a few comment levels up to the guy who thinks that c is defined based on the meter.
The two constants - the speed at which light moves, and the unperturbed ground-state hyperfine transition frequency of cesium - can be combined to define every measurement of time, length, and velocity. They are the constants by which everything else is defined.
Throw in mass, which is easy - a certain number of atoms of a specific element will also have a universally constant mass. Combine it with the other two constants and you have force, energy, and work, and voila, you can describe nearly everything in classic physics.
The classical behaviour of the electromagnetic field is described by Maxwell’s equations, which predict that the speed c with which electromagnetic waves (such as light) propagate in vacuum is related to the distributed capacitance and inductance of vacuum, otherwise respectively known as the electric constant ε0 and the magnetic constant μ0, by the equation
c = 1/(ε_0*μ_0)
Based on this observation we chose what count of cesium oscillations to use to define the second and meter.
But those constants are also defined relative to the others;
Expressed in terms of SI base units, it has the unit kg⋅m⋅s−2⋅A−2. It can be also expressed in terms of SI derived units, N⋅A−2, H·m−1, or T·m·A−1, which are all equivalent.
The new definition of the ampere fixes the value of e instead of μ0, and as a result, μ0 must be determined experimentally [BIPM 2016]. Similarly, the permittivity of vacuum ε0 = 1/μ0c2 must be determined experimentally (as it was before c was fixed in 1983). The product ε0μ0 = 1/c2 remains exact.
After Maxwell published his theory of electromagnetism, it became possible to calculate the speed of light indirectly by instead measuring the magnetic permeability and electric permittivity of free space. This was first done by Weber and Kohlrausch in 1857. In 1907 Rosa and Dorsey obtained 299,788 km/s in this way. It was the most accurate value at that time.
Many other methods were subsequently employed to further improve the accuracy of the measurement of c, so that it soon became necessary to correct for the refractive index of air since c is light’s speed in a vacuum. In 1958 Froome obtained a value of 299,792.5 km/s using a microwave interferometer and a Kerr cell shutter. After 1970 the development of lasers with very high spectral stability and accurate caesium clocks made even better measurements possible. Up until then, the changing definition of the metre had always stayed ahead of the accuracy in measurements of the speed of light. But by 1970 the point had been reached where the speed of light was known to within an error of plus or minus 1 m/s. It became more practical to fix the value of c in the definition of the metre and use atomic clocks and lasers to measure accurate distances instead. Nowadays, the speed of light in vacuum is defined to have an exact fixed value when given in standard units. Since 1983 the metre has been defined by international agreement as the distance travelled by light in vacuum during a time interval of 1/299,792,458 of a second. This makes the speed of light exactly 299,792.458 km/s. (Also, because the inch is now defined as 2.54 centimetres, the speed of light also has an exact value in imperial units.) This definition only makes sense because the speed of light in vacuum is measured to have the same value by all observers;
Observe how every measurement of c measures it relative to something else!
The very fundamental constants in which we define c requires experimental measurements which we only can perform by already having other units defined and measuring things like forces relative to them! Even our choice to fix our units so c has a value more precise than we can measure simply means we choose to transfer the measurement errors into the less precise units, the non-fixed units
This does not make our measurements of c perfectly precise, it still retains measurement errors of c, but whenever we increase the accuracy in measuring c we choose to force that deviation from prior measurements into the other units depending on it. Similar to how you could first make an inaccurate calculation with Pi = 3.14 and then repeat it with hundreds of decimals, you choose to not let other numbers change Pi and let Pi change every else
You’re also, separately, wrong about mass because it depends on measuring the gravitational force. The definition of mass has changed;
The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of c and ΔνCs.
The Joule and Newton and Planck constant are all defined relative to each other!
… But you can also define Joule in terms of Ohm, in turn defined by Volt, defined by… The meter, second, Ampere (defined as a given number of charges per second), and… The kilogram.
And if you look at vacuum permeability again, which defines the speed of light, that too depends on the damn Newton which once again is defined circularly as ratios to other measured constants!
Tldr: Yes some properties of spacetime are absolute.
However, they are absolute RATIOS defined relative to each other. We took something we could measure reliably and then fixed some of these values relative to our most accurate measurements, and then derived all other values from those based on our measurements of what the ratios must be.
It’s not useful to tell somebody it is constant without a way to make use of it. Without knowing how it’s defined relative to other things we can’t use it.
The thing about all the absolute physical constants is that they are almost all based on units defined relative to other things. Unitless constants (defined only as a ratio) are extremely rare (like the fine structure constant) - but even then you have to make up units to measure them (although you can still agree on unitless values with somebody else who chose different base units for measurements).
https://en.wikipedia.org/wiki/Dimensionless_physical_constant
Edit: the most obvious immediate reason Wolfram here is fully wrong is that Cesium frequency is defined as the frequency you measure when light of the correct energy/wavelength is emitted against the atom, to then measure the corresponding returned light of the right energy/wavelength.
To determine what that wavelength should be with your instruments you can measure things like the electric field and charges - which depends on units that are all defined relative to each other, and as soon as you start fixing some units (like when you have measured the energy state differential in the atom) then you will realize you have defined ratios between the units
I was unaware that the person to whom I was replying, who claimed to be intimately familiar with the complete works of Feynman, needed instruction in how to “make use of” a fundamental constant of nature. If that is something you think is necessary, perhaps you should see to their instruction in such matters, as you are so confident in your faculties of condescending instruction.
Furthermore, I am acutely aware of the existence and nature of dimensionless constants, thank you very much.
For somebody who claims to be acutely aware, you really seem to have no idea what goes into calibrating measurement devices to be able to measure physical constants. In particular you have no idea how many other units go into calibrating them, and how you fundamentally can not get an accurate reading of a physical constant without that calibration. And for somebody claiming I’m the condescending one, you’re awfully rude yourself
Just see the definition of the kilogram, and how it’s now defined in relation to time, c, and the planck constant.
https://en.wikipedia.org/wiki/Caesium_standard
Oh so now we need to measure electromagnetic fields and charge to be able to hit the atom with light of the right energy to be able to measure time? And to verify the emitted frequency (both in and out) is right we need to define either energy (Joule, circular via either kilogram or Volt) or wavelength (directly circular)? Huh…
Everything meaningful is defined as relative properties, as ratios to other forces and properties of nature.
Again, I think you’re replying to the wrong person. I never disagreed with any of this. I literally learned all of this years ago. I appreciate your attempt to educate, but I’m unclear on its purpose. The dude claimed that the speed of light is defined based on the meter, and that that makes it a tautology. That is simply, provably false. Then the dude tried to move the goalposts. Never did I say that our measurements are anything less than relative. Never did I suggest that our derived units are not based on fundamental constants the nature of which can be only guessed at. Now, you’ve said that the statement I made didn’t tell the dude “how to make use of” dimensionless units, which is a complete non sequitur. If you feel that that lecture is an important one when a dude demonstrates a fundamental misunderstanding of what c even is, that’s your own affair, and I invite you to give this lecture a few comment levels up to the guy who thinks that c is defined based on the meter.
The two constants - the speed at which light moves, and the unperturbed ground-state hyperfine transition frequency of cesium - can be combined to define every measurement of time, length, and velocity. They are the constants by which everything else is defined.
Throw in mass, which is easy - a certain number of atoms of a specific element will also have a universally constant mass. Combine it with the other two constants and you have force, energy, and work, and voila, you can describe nearly everything in classic physics.
You can’t measure the cesium frequency without having other units defined.
https://en.wikipedia.org/wiki/Speed_of_light
Based on this observation we chose what count of cesium oscillations to use to define the second and meter.
But those constants are also defined relative to the others;
https://en.wikipedia.org/wiki/Vacuum_permeability
https://en.wikipedia.org/wiki/Vacuum_permittivity
https://pmc.ncbi.nlm.nih.gov/articles/PMC5907514/
And here;
https://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/measure_c.html
Observe how every measurement of c measures it relative to something else!
The very fundamental constants in which we define c requires experimental measurements which we only can perform by already having other units defined and measuring things like forces relative to them! Even our choice to fix our units so c has a value more precise than we can measure simply means we choose to transfer the measurement errors into the less precise units, the non-fixed units
This does not make our measurements of c perfectly precise, it still retains measurement errors of c, but whenever we increase the accuracy in measuring c we choose to force that deviation from prior measurements into the other units depending on it. Similar to how you could first make an inaccurate calculation with Pi = 3.14 and then repeat it with hundreds of decimals, you choose to not let other numbers change Pi and let Pi change every else
You’re also, separately, wrong about mass because it depends on measuring the gravitational force. The definition of mass has changed;
https://en.wikipedia.org/wiki/Kilogram
The Joule and Newton and Planck constant are all defined relative to each other!
… But you can also define Joule in terms of Ohm, in turn defined by Volt, defined by… The meter, second, Ampere (defined as a given number of charges per second), and… The kilogram.
And if you look at vacuum permeability again, which defines the speed of light, that too depends on the damn Newton which once again is defined circularly as ratios to other measured constants!
Tldr: Yes some properties of spacetime are absolute.
However, they are absolute RATIOS defined relative to each other. We took something we could measure reliably and then fixed some of these values relative to our most accurate measurements, and then derived all other values from those based on our measurements of what the ratios must be.