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

[Keith Koenig]

We think of length and time as the first fundamental quantities and velocity as the first derived quantity but any two determine the third so we would be completely justified in defining velocity as a fundamental quantity and one of length or time as the other, with the remaining being the first derived quantity. Indeed, it may make sense to do so.

Suppose we earthlings are about to join a federation of planets, and we would like to compare our physics with other members. We learn that this federation uses the VA (Vulcan Academy) system of units, where the speed of light has the value of 1c. This is agreeable to all members of the federation, since all members agree on the speed of light. Similarly, the VA defines the peak CMB wavelength, another value all members can agree on, as having the value of 1λ. The first derived quantity is the Sarek (S), where 1S = 1λ/1c.

The greater point is that time without length and speed is meaningless.

 

[PeroK]

The SI unit of time is defined by a caesium clock. The unit of length is defined as the distance light travels in a given time. See:

https://physics.nist.gov/cuu/Units/current.html

 

[Keith Koenig]

The SI unit of time is defined by a caesium clock. The unit of length is defined as the distance light travels in a given time. See:

https://physics.nist.gov/cuu/Units/current.html

I get that, but I was trying to provoke a bit of introspection on basic assumptions that physics makes. Always a good idea, and fun imho.

 

[DaveC426913]

we would be completely justified in defining velocity as a fundamental quantity

Sure. We define the common velocity to be zero (I.e. sharing A common frame of reference) , and then our time and length measurements all agree.

Change our velocity (wrt) the Vulcans, and our measurements change too.

 

[Keith Koenig]

Having a common value of zero for anything is meaningless. I could claim a quantity exists called "smeorf" that has a default value of zero, but if you multiply your velocity at any point by the proper value of smeorf you obtain another quantity that is proportional to the meaning of life.

 

[DaveC426913]

Having a common value of zero for anything is meaningless.

Quite the opposite. This entire thread is premised on the acknowledgment that it is not meaningless.

Only when my velocity wrt you is zero (and when yours is zero wrt to me) do we agree on length and time.

To the extent that, if your length and time measurements agree with mine to an arbitrary level of precision, we can conclude that our velocity wrt each is zero.

 

[Keith Koenig]

OK, my bad, frankly I did not carefully translate wrt to "with respect to", at which point it becomes clear you are thinking relativistically, in which case I agree, with the caveat that it applies most at large velocities. It is interesting that your concern is with defining the value of 0, whereas mine is in defining the value of 1. Both of course are necessary. Good call. Still, it does not address my original point which is that we really can't think that anyone of length, time, or velocity has meaning in and of itself, without the other 2. Something is not long (far if you prefer) unless it takes a long time to get there at some speed. Maybe this is well known and often thought about. I think it has deeper meaning.

Not sure if the usual would be to create a new post or edit this one but I am going with the latter. What exactly is the definition of zero for length and time. We already know it is fuzzy for velocity. Thanks DaveC426913.

 

[Halc]

Velocity of light is not constant. Speed of light (in a vacuum) is. I actually like this universal unit.

Similarly, the VA defines the peak CMB wavelength, another value all members can agree on, as having the value of 1λ.

This is an incredibly poor choice for a universal standard length since it changes over time and (being a non-local measurement) varies from one location to the next, even for frames in which it is isotropic.
The resonant frequency of caesium is a far better choice for a universal standard of local time since it is one of the most stable intervals known.

That makes the 3rd thing, length, a function of the other two. Since the resonant frequency of caesium is about 9.19 GHz, light moves about 3.26 cm in once cycle, which is a nice unit with which to measure something.

 

[Keith Koenig]

OK, I'll give you that, but it could be that caesium is extremely rare elsewhere in the universe but certainly a choice can be made using a similar oscillation. And let's give the period and wavelength of the chosen oscillation values of 1. This uniquely determines the value of all speeds in the universe, including of course c, the speed of light. Defining the value of 1 for any of the two uniquely determines all values of the third. No exceptions.

 

[PeroK]

OK, I'll give you that, but it could be that caesium is extremely rare elsewhere in the universe but certainly a choice can be made using a similar oscillation. And let's give the period and wavelength of the chosen oscillation values of 1. This uniquely determines the value of all speeds in the universe, including of course c, the speed of light. Defining the value of 1 for any of the two uniquely determines all values of the third. No exceptions.

You seems to be confused by 1) physical quantities, such as length, time, mass and derived quantities such as velocity and energy; 2) the units we use for these quantities, such as the second, kilogram and metre; 3) numbers, such as 0 and 1, which are defined mathematically.

 

[Keith Koenig]

You seems to be confused by 1) physical quantities, such as length, time, mass and derived quantities such as velocity and energy; 2) the units we use for these quantities, such as the second, kilogram and metre; 3) numbers, such as 0 and 1, which are defined mathematically.

I don't think I am at all confused. I am concerned with the definition of the units of fundamental quantities, from which the units of all derived quantities are obtained. To stick with mechanics and leave out charge, the fundamental units are defined to be length, time, and mass. Fundamental also meaning immutable. The first derived quantity is velocity, with units length/time. The next are momentum (mass*length/time) and acceleration(length/time/time). Next of course we have Force (mass*length/time/time) and Energy (mass*length*length/time/time). Surely you agree with that.

Surely you would not dispute that every "length/time" in the above enumeration of physical quantities and their units in mechanics could be replaced with velocity.

So far as I am aware, and please correct me if I am wrong, but there is no principal by which we are compelled to define length and time as fundamental, especially since time is always measured with something that is moving, in other words has velocity, usually an oscillation.

We could instead define the fundamental units as length and velocity. Then the first derived quantity is time, with units length/velocity. The next are momentum (mass*velocity) and acceleration(velocity/time = velocity/length/velocity = velocity*velocity/length. Next of course we have Force (mass*velocity/time = mass*velocity*velocity/length) and Energy (mass*velocity*velocity). Surely you agree with that.

 

[PeroK]

So far as I am aware, and please correct me if I am wrong, but there is no principal by which we are compelled to define length and time as fundamental,

SI units take take the speed of light as fundamental. Length is derived from that.

We could instead define the fundamental units as length and velocity.

Yes, but time and velocity (in SI) is preferred, for practical purposes.

 

[jack action]

I am concerned with the definition of the units of fundamental quantities, from which the units of all derived quantities are obtained. To stick with mechanics and leave out charge, the fundamental units are defined to be length, time, and mass. Fundamental also meaning immutable.

I'm not sure what is meant by fundamental here. What does it mean for a quantity to be immutable?

There is obviously a relationship between length, time, and velocity. When two of them are defined, so is the third one. But I don't see how that means that one is more fundamental (whatever that means) than the others.

We could instead define the fundamental units as length and velocity.

Why do you choose length instead of time as fundamental?

Do we now live in a "spacevelocity" continuum? So instead of telling you «Let's meet in two hours, in the park», it would be better to say «Let's meet at 25 km/h in the park»? And just like "the park" has an implied direction (displacement is a vector), velocity must also have an implied direction, which wouldn't be the same for both persons. Very confusing.

The only reason I can think of for choosing length and time as "fundamental" units is that they are quantities that are easier to measure, easier to conceive, easier to relate to.

 

[Dale]

the fundamental units are defined to be length, time, and mass.

Mass, length, and time are dimensions, not units. So you should say that the fundamental dimensions are defined to be mass, length, and time.

This is true in SI units, but different unit systems use different dimensions. SI units also include current and a couple of other fundamental dimensions, but cgs units do not have a separate electrical dimension. Many of the formulas of electromagnetism are different in cgs than in SI units because the electrical units have different dimensions in the two systems. This idea of reducing the fundamental dimensions is taken to its extreme in geometrized units where the only dimension is length.

So it is already well known that the fundamental dimensions are an arbitrary choice that is part of what defines a system of units.

 

[Vanadium 50]

This thread seems to be philosophy, and not very good philosophy at that. Until there is a commonly agreed upon measure of fundamentalness, this is just personal preference.

 

[Ibix]

Until there is a commonly agreed upon measure of fundamentalness

I vote that the SI unit of fundamentalness be the Point (P), so when we can't specify its value the topic can be said to be Pointless.

 

[Melbourne Guy]

This thread seems to be philosophy, and not very good philosophy at that. Until there is a commonly agreed upon measure of fundamentalness, this is just personal preference.

I'm also wondering if it essentially the same conceptually as this recent thread, @Vanadium 50 :

​

https://www.physicsforums.com/threads/replacing-the-measurement-standards-si-units.1011468/​

Measuring things is fundamental, but deciding what the units are seems entirely arbitrary!

 

[gmax137]

We could instead define the fundamental units as length and velocity.

OK, but what would change other than some words?

I am also not sure how to construct a velocity "meter" that doesn't use a ruler and a clock. Maybe I am just not very creative today.

 

[Vanadium 50]

I am also not sure how to construct a velocity "meter" that doesn't use a ruler and a clock.

Doppler Radar.

 

[Keith Koenig]

Mass, length, and time are dimensions, not units. So you should say that the fundamental dimensions are defined to be mass, length, and time.

This is true in SI units, but different unit systems use different dimensions. SI units also include current and a couple of other fundamental dimensions, but cgs units do not have a separate electrical dimension. Many of the formulas of electromagnetism are different in cgs than in SI units because the electrical units have different dimensions in the two systems. This idea of reducing the fundamental dimensions is taken to its extreme in geometrized units where the only dimension is length.

So it is already well known that the fundamental dimensions are an arbitrary choice that is part of what defines a system of units.

That may be a matter of semantics. A quick google search for "fundamental properties of physics" gives this as the first hit: https://www.texasgateway.org/resource/13-language-physics-physical-quantities-and-units#:~:text=In physics, there are seven,of substance, and luminous intensity.

My understanding of the definition of immutable is that it cannot be broken down into smaller parts, though a quick google search of that term yields "unchanging over time or unable to be changed."

Using the former definition, a Newton for example is not immutable since it can be broken down dimensionally to $kg \cdot \frac{m}{s^2}$

The point I was trying to make, and perhaps Vanadium 50 is correct in that this is more philosophical than anything, is that we cannot really think that time exists independently of length and velocity. In a "heat death" universe where everything is at absolute zero and all motion has stopped, there would be no time, imho. It seems an interesting concept. Not earth-shattering, but interesting nonetheless.

 

[Dale]

That may be a matter of semantics.

Indeed, but when communicating complicated concepts it is helpful to use the standard semantics.

we cannot really think that time exists independently of length and velocity

Why would we think that anything exists independently of anything else? Designating a set of fundamental units doesn’t have that implication at all.

In a "heat death" universe where everything is at absolute zero and all motion has stopped, there would be no time, imho.

That isn’t at all in keeping with current cosmology. Time doesn’t end at heat death according to any reputable source I have read

 

[Melbourne Guy]

In a "heat death" universe where everything is at absolute zero and all motion has stopped, there would be no time, imho.

Not sure it follows that time stops in a heat death universe, @Keith Koenig. Do we understand what time is in the first place to make that determination? We commonly describe it as progression of events, often using terms such as 'past' and 'present' and 'future', and in that sense, heat death would result in the apparent cessation of time, but is that the same thing as "there would be no time"?

 

[jack action]

Using the former definition, a Newton for example is not immutable since it can be broken down dimensionally to $kg \cdot \frac{m}{s^2}$

But with the US unit system, a pound (force) is defined as the 'fundamental' unit and thus 'immutable'. The mass is a slug, which can be broken down dimensionally to $lb \cdot \frac{s^2}{ft}$.

That is what people here are trying to show you: It all depends on what you define as 'fundamental'.

 

[valenumr]

Would it be reasonable to say that dimensional units are basically meaningless unless we are comparing two quantities?

 

[jim mcnamara]

They are not useless. If I ask 'please make 1 of 1 NaCl' (1L of 1.0M NaCl) -- it is unintelligible. You will notice that all of the advisors are always asking newbies to use units. There are many good reasons to do this.

PS: same goes for cooking using recipes, purchases of gasoline, milk, cheese ... ad nauseum.

 

[Anko]

I think what this thread might be about is the difference between knowing there are physical units, and being able to measure them.
If there is a heat death of the universe, will temperatures be measurable even when they still exist? Will any measurement be possible of a background in which there are no comparable differences?

Physics is possible because it's relatively easy to compare measurements, at least it is in this era.

 

[Dale]

Believe me, just because a measurement is boring doesn’t mean that it cannot be done.

 

[David Lewis]

The distinction between fundamental and derived quantities is arbitrary. The universe doesn't prefer one system over another, so we generally choose whatever is easiest to comprehend and work with, a.k.a. whatever keeps engineers happy.

 

[jbriggs444]

The distinction between fundamental and derived quantities is arbitrary. The universe doesn't prefer one system over another, so we generally choose whatever is easiest to comprehend and work with, a.k.a. whatever keeps engineers happy.

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.

We care whether our meter sticks and calipers are going to have to be swapped out due to a change in units.

 

[Herman Trivilino]

So far as I am aware, and please correct me if I am wrong, but there is no principal by which we are compelled to define length and time as fundamental, especially since time is always measured with something that is moving, in other words has velocity, usually an oscillation.

It is more precise to define things the way BIPM does. This is the science of metrology, not physics. Theoretically you could have velocity as a fundamental unit, but that would be a less precise way of defining units of measure.

Something is not long (far if you prefer) unless it takes a long time to get there at some speed.

If I have two sticks at rest wrt me, I can compare their lengths and tell you which one is longer and by how much. I don't need to refer to a unit of time or of velocity.

When we measure a length we are simply comparing that length to the standard.

 

[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.