The speed of light is a tautology. We define it via how many meters light travels in a second. And we define the meter by the same measure. It’s just the distance light travels in 1⁄299792458 Of a second.
c is a measurable constant, not some unit that is arbitrarily defined. Like Boltzmann’s Constant, or the ground state hyperfine transition frequency of the Cesium-133 atom… it just… Is.
Therefore, it is a useful tool to define units. You claim it is a tautology because we write it in units of meters per second, while the meter is defined based on c. This is easily disproven, as you can represent the speed of light in any unit of velocity. It is a fundamental constant, derivable through experiment without any units a priori.
It’s not about the units i used. It’s about using something to define itself. The same problem happens when you use c to define empty space since empty space can define c.
Once you decide which units are used in maxwells equations then the electromagnetic permeability and permissivity pops out as a proportions of c.
That may be, and I’ve been meaning to dig into my copy of the Lectures, but that’s moving the goalposts. You said that it was a tautology because it was defined by the meter, and the meter was defined on it. That statement is demonstrably false.
Everything in physics is defined by relative properties. Scale all fundamental units by the same factor and we can not detect any change in behavior whatsoever
I used the meter because that’s generally what is used for measurement in scientific endeavors. There was no goal post moving if the statement applies for all SI measurements.
Literally the entire point of the comment that you’re responding to is that it isn’t true for the metre, and it isn’t true for any SI units.
Your entire claim of tautology rests on the assertion that the speed of light is defined by something external to light itself. That’s false. It remains false irrespective of which SI measurements you swap in.
Just because the speed of light can be expressed in terms of SI units, doesn’t mean its definition depends on them. Which is the point that wolframhydroxide was making.
This directly disproves your original assertion of tautology.
Every metric of speed of light is necessarily relative to other things. Even if you define as 1, now you must be able to know what one unit of time is relative to one unit of distance, and if you do not know that then you do not know that your speed of 1 means.
All fundamental units are defined relative to each other in physics, and all other units are defined relative to the fundamental units.
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).
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.
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.
a second is defined as the time it takes for a caesium atom to oscillate exactly 9192631770 times, at least according to the SI. a meter is then defined, as you said, as the distance light travels in 1/299792458 seconds, which corresponds to some large number of oscillations of those caesium atoms. these numbers are pretty much arbitrary though, we just picked them to match our previous, less precise, definitions of meters and seconds. but using oscillations of caesium atoms and speeds of light in your is completely equivalent to using meters and seconds, except that the latter units are more familiar to us
The speed of light is a tautology. We define it via how many meters light travels in a second. And we define the meter by the same measure. It’s just the distance light travels in 1⁄299792458 Of a second.
c is a measurable constant, not some unit that is arbitrarily defined. Like Boltzmann’s Constant, or the ground state hyperfine transition frequency of the Cesium-133 atom… it just… Is.
Therefore, it is a useful tool to define units. You claim it is a tautology because we write it in units of meters per second, while the meter is defined based on c. This is easily disproven, as you can represent the speed of light in any unit of velocity. It is a fundamental constant, derivable through experiment without any units a priori.
Ergo, it is 1
1 c, yeah.
dumbass
It’s not about the units i used. It’s about using something to define itself. The same problem happens when you use c to define empty space since empty space can define c.
Once you decide which units are used in maxwells equations then the electromagnetic permeability and permissivity pops out as a proportions of c.
Read more Feynman if you don’t believe me.
That may be, and I’ve been meaning to dig into my copy of the Lectures, but that’s moving the goalposts. You said that it was a tautology because it was defined by the meter, and the meter was defined on it. That statement is demonstrably false.
Everything in physics is defined by relative properties. Scale all fundamental units by the same factor and we can not detect any change in behavior whatsoever
I used the meter because that’s generally what is used for measurement in scientific endeavors. There was no goal post moving if the statement applies for all SI measurements.
Literally the entire point of the comment that you’re responding to is that it isn’t true for the metre, and it isn’t true for any SI units.
Your entire claim of tautology rests on the assertion that the speed of light is defined by something external to light itself. That’s false. It remains false irrespective of which SI measurements you swap in.
Just because the speed of light can be expressed in terms of SI units, doesn’t mean its definition depends on them. Which is the point that wolframhydroxide was making.
This directly disproves your original assertion of tautology.
Every metric of speed of light is necessarily relative to other things. Even if you define as 1, now you must be able to know what one unit of time is relative to one unit of distance, and if you do not know that then you do not know that your speed of 1 means.
All fundamental units are defined relative to each other in physics, and all other units are defined relative to the fundamental units.
https://en.wikipedia.org/wiki/SI_base_unit
But isn’t the measurement of the speed of light our own proportion derived from the constant that is 1g of water at 1ATM?
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
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.
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 first rule of tautology club is the first rule of tautology club lol
It’s so meta, even this acronym
a second is defined as the time it takes for a caesium atom to oscillate exactly 9192631770 times, at least according to the SI. a meter is then defined, as you said, as the distance light travels in 1/299792458 seconds, which corresponds to some large number of oscillations of those caesium atoms. these numbers are pretty much arbitrary though, we just picked them to match our previous, less precise, definitions of meters and seconds. but using oscillations of caesium atoms and speeds of light in your is completely equivalent to using meters and seconds, except that the latter units are more familiar to us
This got me thinking if we defined the metre to be a more round number, like 1⁄300000000.
It would shrink the metre by 0.6918mm.
Now I’m curious about what implications that would have.
π would be equal 3. /s
Seriously, any metric unit of a quantity involving the dimension “length” would also change its value slightly.
π doesn’t have the dimension “length”, it’s a dimensionless scalar
I know. I should indicate that with “/s” to make that clear. The “also” refers to anything involving “length” besides the metre itself.
:)
But we defined what a meter was long before we knew the speed of light
The small thing defines the big thing that defines the small thing that defines…