Years ago when I took physics in college, every time a new unit of measurement was introduced it was defined in terms of other units. The only exceptions were the few fundamental units. For example, mass and distance are expressed as fundamental units but energy and force are not.
When we got into thermodynamics, the Kelvin was introduced without it being expressed in terms of other units. When I asked about this, I was told it is a fundamental unit.
It seemed to me at the time that temperature should be expressible in terms of other units, perhaps as heat energy divided by volume. We know that heat is caused by molecular motion. We know that when the molecules move faster in a given volume, the temperature goes up. We know that adiabatic compression causes a temperature increase, and adiabatic expansion causes a temperature decrease.
Since we know what factors cause temperature to increase or decrease, and these factors are expressible in terms of other fundamental units, why is the Kelvin considered to be a fundamental unit?
Any unit can be expressed in terms of other units. We can measure distance from point A to point B by traveling that distance at a fixed speed, and doing the calculation.
Or we can get a ruler.
Mass and temperature are other things very easy for us to measure directly. And time.
Conversely, how do we measure speed? By calculating based on measured time and measured distance.
Well temperature is an indicator or average kinetic energy, so no it’s not a fundamental constant. The use of Kelvins comes from the nature of its scale. It starts at 0 J Energy = 0 K. Other scales start all over the place.
No there are a few fundamental units and all other units derive from this. There is no way to get an equation with ‘second’ on one side and other units on the other. The fundamental ones (SI form) second (time) length (meter) mass (kilogram) charge (columb) and probably a few others I am missing. For example a Newton is a combination of distance time and mass (kgm/s^2), a Joule is (kgm/s^2*m), Ampere is (Columb/s) these are not fundamental units.
Actually we have no way of measuring an objects mass we only can measure the effect of the mass.
As to the OP you can define temperature in terms of other fundamental units but its easier to just assign it a unit and be done with it. I suspect it wasn’t defined in other units becuase it would mostly be a waste of time to do so. I am thinking of how it would be defined in other units and you would need to use molar mass, mass and velocity at the very least.
We can express time as equal to distance divided by speed, though. So while the way I put it specifically was (probably*) wrong, the example I gave is valid. For the purpose of the OP, why isn’t speed the fundamental measure, rather than time? Because time’s easier to measure, is the supposition. You’re still not answering his ‘why’, which is what I’m attempting to do.
Well, I know of at least one way of directly measuring mass, it just so happens to be very simplistic, and only works on our planet.
It’d definitely be a hodge-podge of other units, and it’d be very awkward to express. I still suggest that temperature is a fundamental unit because of the ease with which it is measured.
*Time isn’t able to be converted to something else by anything in my knowledge of physics, but I wouldn’t rule out the possibility of it being able to be converted.
Temperature for ordinary materials in ordinary situations is roughly proportional to the average kinetic energy per particle, but that’s not always the case. A black hole, for instance, has a temperature, despite not being made of particles at all. And even for ordinary materials, the constant of proportionality can be different: It’s different for a monatomic gas and a diatomic gas, for instance.
Nonetheless, it is sometimes convenient to treat temperature as though it has units of energy. What you’re dealing with there is not actually T, but k[sub]b[/sub]T, where k[sub]b[/sub] is Boltzmann’s constant (a constant of nature with units of energy/temperature). Effectively, what you’re doing when you give T units of energy, is you’re choosing a system of units such that k[sub]b[/sub] = 1, which can be very convenient when k[sub]b[/sub] is showing up a lot.
Likewise, if one is doing relativity, c shows up a lot, so it’s convenient to set c = 1, in which case length and time have the same units. If it’s general relativity (thus involving gravity), one typically also sets G = 1, in which case length, time, and mass all have the same units. If one is doing quantum mechanics, then one typically sets hbar = 1, meaning that energy and frequency have the same units. If one goes so far as to set hbar, G, and c all equal to 1, then not only is everything the same units, they’re dimensionless. That is, you could say that you have a mass of 10, or a length of one million, without specifying any units.
No you can’t. s=(m)/(m/s) reduces down to s=s so you haven’t defined anything. Time isn’t a fundamental unit becuase its easy to measure its a fundamental unit becuase you can’t get any reduced equation where you get s=something.
No you don’t. You know how to measure the effect of two masses have on each other i.e. their gravatational attraction.
Your using circular reasoning, Its only because you’ve defined speed as m/s. If we made speed a fundamental unit p, then s = t/p and would be expressed in seconds per <speed unit>
Fine lets use velocity as a fundamental unit. So we have time=distance/velocity lets say I have 0 velocity does this mean time is undefined? If you define time like this it means that it is physically impossible for an object to have a 0 velocity which we know is not true.
The reason time is a fundamental unit is becuase you can’t break the equation seconds=change in time down any further. Any unit you define as velocity will have to be a change in distance/change in time and as such must be a combination of two other units. Its also impossible to measure velocity directly. Any measurement you make of velocity will have to use some sort of change in distance and change in time.
The fundamental quantities are the base for every other other measurement we make. For example if we measure distance time and mass we can generate any number of other quantities such as velocity, acceleration, work, force, pressure, area etc etc. The fundamental units are the units we assign to these fundamental quantities of the universe.
Hope I’ve explained that better or hopefully a physicist (Chronos!) can help with the explanation.
But the concept of speed is the amount of distance covered during a certain time. You can’t divorce time from speed. And all units of time can be reduced to seconds, so no matter how you express speed, seconds are - or can be - involved.
I would have said there are n (I’m not sure how many) base units, but it’s arbitrary WHICH you use. I don’t think time has a fundamental and velocity doesn’t, or velocity does but time doesn’t, just that if you’ve defined length, then you need to pick a unit of time OR velocity, and derive the other one.
Of course, we all have to use the same units, so there are universally accepted fundamental units, of which I think K is one, but you can’t decide that just by arguing about which quantities are ‘more’ fundamental.
Its not an arbitrary choice though there are consequences for that choice. Use my example from above if you define time=distance/velocity you physically can not have a 0 velocity and have time be defined. Since it is possible to have a 0 velocity there is a problem with your definition. If you define velocity=distance/time and you have a 0 time then your velocity is not defined which is consistent with what we measure i.e. we can’t measure velocity without some time passing.
But I’m talking about units. You can say “let a metre be the length of this bar in paris” and “let one m/s be one three hundred millionth of the speed of light” and then define a second as the the time it takes something going at 1 m/s to go one m.
(In fact, we use the speed of light to define a metre (iirc) so perhaps speed should be a fundamental unit. But it doesn’t really matter so long as we choose and stick to it.)
I’m not sure how constant speed of X being distance traveled by X divided time taken fits in.
Yes but your choice of units implies a physical impossibility. If I take a photograph of a ball in flight it is impossible for you to determine its velocity. Time is zero therefore your velocity (distance/time) is undefined which is consistent with you not being able to determine velocity. If you define time as (distance/velocity) it implies that if you have a 0 velocity then your change in time is undefined which isn’t true. I can sit here with a stop watch and measure my change in time despite my velocity being zero.
I suppose you could do that but then you run into the problem of not being able to directly measure velocity. The reason the meter, second, kg, columb etc. are fundamental units is becuase they represent fundamental quantities. We can go out and measure each of these fundamental quantities and then derive any other value such as force from these measurements. It is impossible to measure the velocity of something independent of time and distance. It is impossible to measure the energy of something without measuring its mass.
Given the equation distance=velocity x time the quantities that you can measure are distance and time. If I go and measure time and distance the units I use for time and distance define what units velocity has. The argument that velocity is a fundamental unit breaks down becuase there is no way to directly measure velocity.
While your velocity is zero, and time marches on, that doesn’t mean everything’s velocity is zero during that time. As long as something is moving over some distance, the relation holds. Aside from that, your velocity isn’t zero, ever. You’re on a planet, moving through space, etc.
Assuming one could reach a velocity = zero situation, then the distance becomes zero as well - some the time based on that object would be zero divded by zero, or undefined, that’s true - but that would only signify that we couldn’t determine the passage of time based on observation of the motion of the object in question - because the object in question isn’t moving. I can’t tell time from a broken clock.
Is there some Deja Vu in here? Didn’t I say this several posts ago? Didn’t you attempt to refute me at the time?
