# Are properties quantities or do properties have quantities?

The title pretty much says it all, but let me elaborate on the source of confusion. VIM defines quantity as:

property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference
Other definitions I found are extremely circular. They typically go like this, "a physical quantity is a property that can be quantified". In other words, they explain quantity with quantity. When you add the fact that a unit of measurement is a quantity itself, no definition seems explanatory!

So far, my understanding is that properties that can be measured (e.g. weight, length, etc.) are referred to as quantities. More subjective properties like taste and smell are not quantities, since they can't be compared to any accepted standard. Would it be safe to say that psychologists generally deal with properties, while physicists with quantities?

To summarize, are quantities assignable to properties or is a quantity a property in its own right?

A clear separation between the terms you use would be much appreciated. Thank you!

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Well quantity can relate to language social sciences and other places but I guess what you mean is in the field of physics.Or natural sciences.
Now a place to read would be

http://en.wikipedia.org/wiki/Physical_quantity
For starters.

Now a quantity can be something that is a property of a system so they are in atleast some sense similar words for the same thing.The question then become how small of a quantity can you measure.Quantities of light would be it's wavelength/frequency and intensity.That's it only two , you cannot make more to light atleast not from a human perspective.
Well there is redshift for example but that's not a property of light itself rather of gravity when interacting with light.
A quantity is basically a measure of some part of the system, and some do have many parts some only a few some only one.

""""To summarize, are quantities assignable to properties or is a quantity a property in its own right?""""

To answer your question I would say yes you can assign them because it depends on at what scale you look at a certain system.But a system that has like one property and that property is "A" cannot have in the same time a quantity "B". Because for that other quantity "B" to be there it has to come from somewhere and if it comes from the system then it is a property of the system and then the system becomes a system with two instead of one properties.
But there is one thing to add , a system can have properties but those properties can and usually are broken down to smaller pieces that you would call quantities.
Because if you view a macro system like a car it has certain properties but when you break it to it's parts each of those parts may have different properties and each of the properties of each of the parts can have it's own quantities, like for example a engine makes the property for a car to move and accelerate, now when you take the engine apart you see pistons , camshafts , and other stuff each of them have their own property but usually a single part has like one property in terms of what it does to the engine but it can have multiple quantities itself like weight , size, temperature , wear , chemical composition , and so on.Basically it depends from what scale you look upon them from a classical or a quantum because the deeper you go the more quantities emerge for a single otherwise few macro quantity object.

But there is one thing to add , a system can have properties but those properties can and usually are broken down to smaller pieces that you would call quantities.
Because if you view a macro system like a car it has certain properties but when you break it to it's parts each of those parts may have different properties and each of the properties of each of the parts can have it's own quantities...
Thanks a lot for your answer. You state that you would call properties that are broken down into smaller pieces, quantities. In other words, you describe quantity as a product of property analysis. But where do properties end and quantities begin?

To use your example, a car engine is a single unit, or it has a quantity of 1 engine, measured in engines. An engine can itself have four cylinders, or you could say the engine has a quantity of 4 cylinders, measured in cylinders. On the smaller scale, a simple element may have a weight of 5g. Even though weight is just one aspect of that body, however, it is considered a quantity.

How do you differentiate between a property and a quantity, if they are not the same thing?

Doc Al
Mentor
How do you differentiate between a property and a quantity, if they are not the same thing?
What is the point of your query? Sounds like you are trying to attach some exact meaning to the term "property". What problem are you trying to solve?

Well even though this is no official way of explaining I would say the word quantity has the base "quanta" in it now quantum physics is called quantum because it deals with the microscopic side of everyday objects , it literally breaks big objects apart and tries to observe and explain the most basic , fundamental things that make the bigger one.And it goes down to pieces so small that there cannot be any smaller after that, like in the case of an electron which is portrayed in our models as a point structure.With no inner mechanism in it.

As I said a system can have many properties when looked upon a macro level and it also has many quantities and not always properties go 1:1 with quantities, a car can break down which is a property of every mechanism due to processes like wear and other unpredictable situations but breaking down is not a quantity of a mechanism. the lower you go to more smaller scales the properties decrease as the scope does too.Now when you get to the lowest possible level we currently know - subatomic particles the properties become practically 1:1 with quantity , for example the electron it has only a few quantities like mass, electric charge, spin. But when you go higher and put the electron in the picture of being outside the nucleus now more quantities start to emerge and they turn into properties of the system that is now building up, just like bricks turn into houses when you put alot of them one above the other.
Now the electron starts to interact with the nucleus because it has negative charge and the nucleus has a positive one.
So the "moral" of this is that when you have only one smallest possible "brick" it has a few quantities but not many properties as it is only a single brick you can't do much wit it but as you go higher and get more of them you start to see the bigger picture and now those few quantities from each of the sub parts start to merge into a bigger mechanism which has now different quantities than the single ones had before they were put together and now system with properties emerge.
So basically properties are the same as quantities for classical large scale systems but as you go deeper they can separate.Because with a term property we usually understand something that is a mechanism and works in a certain way but in quantum physics things are weird and mechanisms can break down to single points or point like structures and fields that make those structures which each have a different and only few quantities but let them interact and you will see new quantities emerging which will dictate the properties of the bigger system.

What is the point of your query? Sounds like you are trying to attach some exact meaning to the term "property". What problem are you trying to solve?
I guess language may be the culprit, and the problem itself is probably somewhat philosophical. To answer your question, I am trying to wrap my head around what "quantity" is. Normally, I would figure out the meaning of a concept quite quickly, but in this particular case, I couldn't find a single satisfactory explanation -- and I've read a lot on the subject. Is quantity an intrinsic property of things that exists independently or is it a product of comparison? The very fact that quantities are expressed only in terms of other quantities makes matters extremely difficult to disentangle. For example, we refer to a pack of cigarettes, as having a quantity of 20 cigarettes, but we don't say it just has a quantity. We may measure an object in centimeters, but a meter is pegged to the speed of light. See, when we describe quantity, there is always a different quantity it is compared to, ad infinitum. Quantity itself is always obscured. Yet, when we look at an object it looks like having a composition. How would you describe quantity without referring to a different quantity?

Now when you get to the lowest possible level we currently know - subatomic particles the properties become practically 1:1 with quantity , for example the electron it has only a few quantities like mass, electric charge, spin. But when you go higher and put the electron in the picture of being outside the nucleus now more quantities start to emerge and they turn into properties of the system that is now building up, just like bricks turn into houses when you put alot of them one above the other.
I am glad you put it this way. I agree that there's an interdependence between properties and quantity, but as you implied yourself, they are not one the same. For instance, let's take the height of a box. Height is a very abstract property; it only has one dimension. The height of that particular box we could say has a certain quantity, if it is compared against the height of another object we take as a standard unit. Both objects have the same property of being higher than ground level, but their respective heights seem to have different quantities.

My point is, properties like dimensions and mass tend to have a certain quantity, not the other other way round. Why then is quantity defined as a property itself?!

If this sounds circular, it is. :((

What are you guys on to?
I can hardly imagine anything simpler than quantity, or property.
Quantity is simply something that can be expressed by number.
Property has nothing to do with quantity,(except when quantity is property :) )

Dale
Mentor
I guess language may be the culprit, and the problem itself is probably somewhat philosophical.