B Length, Time, and Velocity -- Which are fundamental quantities?

[Herman Trivilino]

But with the US unit system, a pound (force) is defined as the 'fundamental' unit and thus 'immutable'.

The pound used in the US is defined as 0.453 592 37 kg.

 

[jack action]

The pound used in the US is defined as 0.453 592 37 kg.

I was referring to the British gravitational system where the pound is used to define a force and the slug is used for mass.

 

[jbriggs444]

I was referring to the British gravitational system where the pound is used to define a force and the slug is used for mass.

But if one goes tracing a definition for the pound force in this system, one is likely to find it specified in terms of the avoirdupois pound (mass) and, thus, the kilogram together with an arbitrary number corresponding to one of the standard accelerations of gravity.

 

[Herman Trivilino]

I was referring to the British gravitational system where the pound is used to define a force and the slug is used for mass.

There is no officially-sanctioned definition of the pound force. There used to be an officially-sanctioned definition of the kilogram force which relied on 9.806 65 N/kg as the standard value for the free fall acceleration. No such scheme was ever created for the pound force.

 

[Dale]

There is no officially-sanctioned definition of the pound force.

I have also never seen an official definition of the pound force. The only official definition I have ever seen for the pound was that the pound is exactly 0.45359237 kg. That makes it a unit of mass

 

[jack action]

But if one goes tracing a definition for the pound force in this system, one is likely to find it specified in terms of the avoirdupois pound (mass) and, thus, the kilogram together with an arbitrary number corresponding to one of the standard accelerations of gravity.

Why didn't you write it this way:

«But if one goes tracing a definition for the pound force in this system, one is likely to find it specified in terms of one the standard accelerations of gravity together with an arbitrary number corresponding to the avoirdupois pound (mass) and, thus, the kilogram»

The point was that with this system, the force is considered a "fundamental" unit (whatever that means), and the mass unit (slug) is derived from it. There is no "pound-mass". That is from another system (English Engineering Units) and, yes, if in that other system you defined $1\ lb_m = \frac{1\ lb_f}{g_o}$ then $1\ slug = 32.1740\ lb_m$. And if you defined another system (SI units), where you have established that $1\ lb_m = 0.45359237\ kg$ when comparing those two other systems of units, then $1\ slug = 14.59390\ kg$. But that is completely irrelevant to this system as a whole.

Nobody has created a block of material and declared: "This shall be a slug." They did however create a force and declared «This shall be a pound.» The fact that they used a certain mass at a certain distance from another mass (Earth) to define it is irrelevant. That is 3 variables: The small mass is not more "official" than the other two. Another mass at another distance from another planet could still be the definition of a pound. A specific spring under a certain displacement can also be defined as a pound.

A mass should really be a specific number of protons, neutrons, and/or electrons. That is basically what we are counting. Like 1 kg corresponds to 5.978637407×10²⁶ "protons" or something. But we round it up to an arbitrary number by specifying an arbitrary volume of an arbitrarily selected material.

 

[jbriggs444]

Why didn't you write it this way:

«But if one goes tracing a definition for the pound force in this system, one is likely to find it specified in terms of one the standard accelerations of gravity together with an arbitrary number corresponding to the avoirdupois pound (mass) and, thus, the kilogram»

I consider the "standard" acceleration of gravity to be less well standardized than the size of the avoirdupois pound or the kilogram. So that is where I mostly ascribe the arbitrariness.

But I take your point. Being "fundamental" as you use the word just means that the unit is not defined entirely based on other units already imported into the system. i.e. it is not "derived".

 

[Herman Trivilino]

A mass should really be a specific number of protons, neutrons, and/or electrons. That is basically what we are counting.

That won't work. The mass of a composite body is not equal to the sum of the masses of its constituent particles. What you describe is called the amount of substance. The SI unit is the mole.

 

[Dale]

The point was that with this system, the force is considered a "fundamental" unit (whatever that means), and the mass unit (slug) is derived from it.

What system is “this system”? I am not familiar with it. I know the legal units in the USA, and the English engineering units you mention. Both define the pound as a mass and specifically an exact fraction of a kilogram. So I am not sure what units you are referring to.

 

[jack action]

What system is “this system”? I am not familiar with it. I know the legal units in the USA, and the English engineering units you mention. Both define the pound as a mass and specifically an exact fraction of a kilogram. So I am not sure what units you are referring to.

I'm referring to a weight-based system (British gravitational system) vs a mass-based system (almost any other unit system).

Check my original statement in post #23 for context.

 

[jack action]

That won't work. The mass of a composite body is not equal to the sum of the masses of its constituent particles. What you describe is called the amount of substance. The SI unit is the mole.

Isn't mass the quantity of matter in a physical body? I kind of based my statement on the definition found on Wikipedia, where the simplest version is matter is made up of atoms:

Based on protons, neutrons and electrons

A definition of "matter" more fine-scale than the atoms and molecules definition is: matter is made up of what atoms and molecules are made of, meaning anything made of positively charged protons, neutral neutrons, and negatively charged electrons.[14] This definition goes beyond atoms and molecules, however, to include substances made from these building blocks that are not simply atoms or molecules, for example electron beams in an old cathode ray tube television, or white dwarf matter—typically, carbon and oxygen nuclei in a sea of degenerate electrons. At a microscopic level, the constituent "particles" of matter such as protons, neutrons, and electrons obey the laws of quantum mechanics and exhibit wave–particle duality. At an even deeper level, protons and neutrons are made up of quarks and the force fields (gluons) that bind them together, leading to the next definition.

 

[Herman Trivilino]

I consider the "standard" acceleration of gravity to be less well standardized than the size of the avoirdupois pound or the kilogram. So that is where I mostly ascribe the arbitrariness.

Good, because there is no standard value for the free fall acceleration. In the past BIPM adopted a value of 9.806 65 N/kg to define the kilogram force, but they abandoned that practice decades ago. Plus, there is no place on Earth where $g$ has a value that constant. It's invention was just a way to use units of force to measure mass. A practice that continues with the pound force. Today and throughout history there are several different pounds, all of them units of mass.

 

[Herman Trivilino]

Isn't mass the quantity of matter in a physical body?

No. Mass also includes the energy content of a body. It's been known for well over a century that mass is not the quantity of matter in a body.

 

[gmax137]

What system is “this system”?

Well I have no idea if it even has a name. But in the US over the past century or so, thousands of chemical plants, refineries, power plants, factories, etc. were designed and built using pounds-mass per second for mass flow rates and pounds-force per square foot or per square inch for pressures. The "system" also uses gallons for volumes (sometimes) and Btu for energy (there are at least three or four different "Btu" unit values). Time is variously measured in seconds, minutes, hours -- thank the Babylonians and the Mayans.

Are there problems with this system? Yes, plenty of pitfalls and traps for the unwary. Are other systems easier to deal with? Yes. But in the end, it is just units, which are necessarily arbitrary. To me, saying one system is "better" than another is like someone saying they like Ariel better than Helvetica.

 

[Dale]

I'm referring to a weight-based system (British gravitational system) vs a mass-based system (almost any other unit system).

Check my original statement in post #23 for context.

Cool! I didn’t know about this system. I am not seeing an “official” definition of the units. So I think there is no organization that “owns” these units like the BIPM owns the SI.

 

[Herman Trivilino]

But in the US over the past century or so, thousands of chemical plants, refineries, power plants, factories, etc. were designed and built using pounds-mass per second for mass flow rates and pounds-force per square foot or per square inch for pressures.

True. And you left out missions that put men on the moon, explored other worlds, put telescopes in space, and lots of other missions.

But there is still no officially sanctioned definition of the pound force. NASA defines it as the product of 0.453 592 37 kg and 9.806 65 N/kg. They get a result with far too many digits, there being no way to justify them all.

 

[gmax137]

But there is still no officially sanctioned definition of the pound force.

Is that really true? If so, that's interesting. I thought all of the units were laid out in excruciating detail in the front of the 1967 ASME steam tables (one example of a widely used document using pound-force per square inch). I can't seem to find my copy of them now. Maybe that doesn't count as "official"?

Sorry for sidetracking this thread.

 

[Herman Trivilino]

I thought all of the units were laid out in excruciating detail in the front of the 1967 ASME steam tables (one example of a widely used document using pound-force per square inch). I can't seem to find my copy of them now. Maybe that doesn't count as "official"?

That document is easy enough to find online: https://che.k-state.edu/docs/imported/SteamTable.pdf

I don't see any definitions of units there. You can go to the ASME website and look there for a definition, but I didn't see any definitions of units.

By law, and by international treaty, units must be defined in terms of SI units. So, for example, we can use the inch because we define it as 0.0254 m, exactly. There is no such definition of the pound force. The pound used in the US is a unit of mass equal to exactly 0.453 592 37 kg.

 

[jbriggs444]

NIST Special Publication 811 has a conversion factor between the pound force and the Newton. However they include the caveat about the standard acceleration of gravity.

If the local value of the acceleration of free fall is taken as $g_n = 9.80665 m/s^2$ (the standard value), the exact conversion factor is 4.448 221 615 260 5 E+00

 

[gmax137]

Thanks @Mister T but that link is for the (very) abbreviated steam tables (published by my former employer!). I haven't been able to locate the ASME publication online. It is probably 300 pages including all of the definitions and curve fits used to represent the data.

 

[David Lewis]

Will any measurement be possible of a background in which there are no comparable differences?

It doesn't matter whether you can make the measurement in practice. To exist, a physical quantity only has to be hypothetically measurable.

Putting an engineer's hat on, we do not care whether the meter is fundamental, and the speed of light is derived or whether the speed of light is fundamental, and the meter is derived.

If the vacuum permittivity of free space is defined as a fundamental quantity, which has some advantages, I'm sure engineers would find the system unwieldy.