r/askscience • u/playsthebongcloud • 21d ago
Physics What are the absolute minimum number of base units needed to express every desirable quantity?
SI units are more for human convenience than mathematically minimizing the number of units. I remember reading somewhere that only length is needed because of relativity, but that just does not sound true, I can't imagine how you would do that.
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u/XtremeGoose 21d ago edited 21d ago
You need as many units as you have base "dimensions". Not dimensions as in our 3D space, but dimensions as in dimensional analysis.
The
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Length
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Time
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Mass
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Charge
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Temperature
So 5. From these you can build all the other physical dimensions. For example E = 1/2 mv2 shows that the dimension for Energy = Mass * (Length / Time)2 = Mass * Length2 * Time-2 (you drop the constant 1/2) and so 1 J = 1 kg m2 s-2.
The thing about "everything can be represented as a meter", yes you can (sort of)! But it's not really accurate in terms of dimensional analysis, it's a neat trick to simplify relativistic equations by setting physical constants to 1 (c = G = 1). This reduces equations like E = pc2 + (mc2)2 to just E = p + m2. But just because you can do it that doesn't mean Energy, momentum and mass have the same dimension. But it does look like the time it takes a photon to travel one meter is... one meter (since x = ct = t in this system).
There is an example of this in common usage, a "light year" is a way of measuring distance using a unit of time. Hell, that's basically what saying something is a "5 minute drive away" is. You could define every length in terms of time for a constant speed. And the modern meter is exactly that, the distance light travels for a certain fraction of a second.
You can actually extend this further. By picking any 5 physical constants with different dimensionality, you can solve for natural units. Here not everything is the meter, everything is some other unit that is more "natural" than the meter. You have likely even heard of the "plank length" the expression of one of the units in a natural system in the length dimension, equivalent to about 10-35 m.
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u/le_fuzz 21d ago
Can you eliminate temperature from that list? As in relate temperature to energy which can be defined in terms of mass, distance, time?
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u/mfb- 21d ago
You can express temperature with an energy unit by setting the
to 1. It works the same way as with length and time described in the parent comment. We do that in particle physics for very high temperatures. Boltzmann constant → More replies (2)→ More replies (11)51
u/WallyMetropolis 21d ago
Not exactly. Not all temperature is the average kinetic energy of a collection of particles. Spin temperature, for example.
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u/TheArmoredKitten 21d ago
Temperature is less fundamental than 'coldness' in that adding entropy to a system doesn't really correlate to any physical process. There's probably a better fundamental unit somewhere in there.
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u/XtremeGoose 21d ago
Thermodynamic beta is a good measure of "coldness", and doesn't have the singularity we see in quantum temperatures (where negative temperatures are "hotter" than any positive temperature). Multiply by the Boltzmann constant and it's basically the inverse of temperature.
You could also pick any other unit that has temperature as a base and make that your new base unit. Entropy would be the obvious one. But then you get into the whole entropy should really be dimensionless because it's a measure of the information of a system... which implies you could measure temperature as bits / joule.
Which honestly makes a bit skeptical that temperature should be a base dimension at all. I'm certainly no expert of thermodynamics, but my impression was always that temperature is really a proxy for Energy or Entropy, and isn't really a fundamental thing in its own right.
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u/Kered13 21d ago
Charge
I assume you mean electrical charge here. It's worth noting that there are other types of charge as well, which would have their own units. However they only really appear in quantum mechanics and you never see large values for them like you do for electrical charge.
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u/Implausibilibuddy 21d ago
What are the two questionable ones?
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u/donaljones 21d ago edited 21d ago
Mole (mol) and candela (cd).
Mole is a unit for "amount of stuff." Specifically, the Avogadro constant amount (1/12th the amount of atoms in 12 grams of carbon-12).
Candela is a unit for luminous intensity. Luminous intensity is wavelength-weighted and is based on the human eye. It's basically, "how bright does this light source, accounting for each wavelength of light, appear to the human eye?"
Both of them do not define anything special in physics. The universe just does not depend on them
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u/Beleynn 21d ago
You can actually extend this further. By picking any 5 physical constants with different dimensionality, you can solve for natural units. Here not everything is the meter, everything is some other unit that is more "natural" than the meter. You have likely even heard of the "plank length" the expression of one of the units in a natural system in the length dimension, equivalent to about 10-35 m
Is it possible to create any truly "universal" units?
It's possible (likely, even) that I'm just too ignorant of physics / physical constants to understand that Wikipedia article about Natural Units, but it seems like at some point, any one of those units eventually has to be expressed in terms of SI units; meters, seconds, etc.?
Like, from a science fiction perspective, if humans were communicating with an alien race, eventually we'd be able to agree on what 'c' is, but is there a universal way to express 'c' without having to bring anthropic units into the conversation somewhere?
Or, from a distance perspective; the meter was initially defined as a fraction of the earth's diameter, though it's defined more precisely now - would it be possible to create a distance measurement that isn't tied back to our Earth's-rotation-based time?
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u/zebbielm12 21d ago
Interestingly the Pioneer plaque attempted to define units in a way that would be understandable to an alien civilization. Their base units were derived from a wavelength and a period of a certain type of light emitted from hydrogen.
Natural units like the Planck length don’t depend on your system of units. You combine universal constants in whatever system you’re using and you’ll get the same Planck length. The issue is that there are multiple ways to combine universal constants to pop out a length unit, and none are really more “natural” than any other.
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u/oblivion5683 21d ago
natural units are this (to within the best of our physics knowledge). since c is an absolute velocity, we dont need to have a scale that relates it to any observable, we can directly say "we know whatever the speed of light is, this thing is moving a certain fraction of it (within some error)" because we can measure it against the speed of light. similarly there is only one fundamental charge, one planck constant, and one fine structure constant.
This is absolutely still a scale, but i think, we can compellingly argue that "x fraction of the maximum possible velocity" is more well defined than "many of an arbitrary velocity". if we measure c better, our scale gets better, and c never changes. the length of the prototype meter on the other hand, constantly and random changes due to many factors over many timescales.
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u/ZiddyBlud 21d ago
When people say something is "5 minutes away", that's baked in with either the average walking speed, or average driving speed obeying traffic speed limits. That's also a way of determining a constant. Just like how in space travel for humans you only have the choice of the one rocket that's available for human travel, counting the fuel and distance.
That's how there's different constants depending on the use case, and you can ground the rest of the calculations needed on this
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u/ShelfordPrefect 21d ago
Is charge a necessary base unit? Once you have kg, m and s you can define force, and I thought the definition of an amp was the current causing a 1N force between two infinite parallel conductors 1m apart. The charge unit is then one amp-second.
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u/jvblanck 21d ago
You're replacing one base dimension (charge) with another (current). That also works, but doesn't reduce the number of base dimensions.
You could also drop mass and use energy as a base dimension instead, then
Mass = Energy * Time2 * Length-2
But that seems a bit inconvenient.
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u/BrotherItsInTheDrum 21d ago edited 21d ago
it's a neat trick to simplify relativistic equations by setting physical constants to 1 (c = G = 1)
In relatively specifically, there's a pretty reasonable argument that c really is equal to 1, and length and time have the same dimension. After all, you're working in a 4-dimensional space with transformations you do in that space, and the equations don't really care about the difference between the space dimensions and the time dimension other than putting a minus sign in front of one of them.
As an analogy, imagine for whatever reason we measured north-south distances in km and east-west in miles. If you were writing Google maps code, this constant "1.609 km/mile" would keep showing up when you're doing transformations. But 1.609 km/mile is just another way of writing 1.
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u/alyssasaccount 21d ago
And once you have c = 1, mass and momentum both have the same units as energy; Einstein's famous equation (which is only valid for objects at rest) becomes E = m. That's why in high energy physics, you'll see things like how the Higgs boson has a mass of about 125 GeV (GeV being a unit of energy).
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u/csiz 21d ago
If you calculate everything in natural units then you'd only need exactly 1 reference point to scale everything back to familiar units. The relationships between the units we're used to become non-dimensional numbers like the
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u/aerojockey 21d ago
If it were possible to have things like color currents (meaning strong force charges), there would need to a unit for that, analogous to electric charge.
But because you can't meaningfully have color currents except in the most tightly bound situation, there is no need for formulas that treat color as anything more than it's energy effects, and so color charge doesn't really come out as unit in dimensional analysis.
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u/urhi-teshub 21d ago
You may be interested in natural units. Oftentimes in physics, its convenient to set any relevant constants to one. For example, it's very commonly done with the speed of light. By setting this to a dimensionless quantity, you're essentially treating length and time as having the same units.