Measured vs calculated quantities

[Kiril]

Hello everyone,

My general goal is to understand why and how certain physical formulas came to be written, a specific way and not another - so as to judge their correspondence with reality. My specific interest in this thread is to understand the link between a formula(calculated or complex quantities) - for example G/momentum/energy(kinetic) and reality; as contrasted with measured quantities - length, weight, time - where the link is immediate and obvious(or where a single unit is involved).

What I understand by the term quantity or measure-of, in physics:
The number of times something(A) can be divided, by a thing/object(B) possessing the attribute/property(of interest) of (A) to a lesser extent.

-In the case of length, we are dealing with the directly perceivable attribute of length and we can divide this by a stick or our fingers(just imagine 12 kirilfingers :) ) - also on the perceptual level.
-In the case of weight, we are dealing with the physical experience of mass, we divide it by anything, a rock, car(that would be too large), etc also possessing mass.
-In the case of time we are measuring our perception of difference(change eg. seasons) and we divide it by specific(regular) changes, like the sun rising(night and day).

In all these cases we are dealing with the directly perceivable and therefore the axiomatic - therefore we can be safe in our certainty that we are quantifying real quantities via a rational method.

But when we have calculated, so called quantities, like, F=ma, W=Fd let alone G - I can't apply the definition above - by what thing, possessing what attribute should I divide by, and what? In other words, I can't reduce them back to sensible information; I cannot deny that somehow these calculation apply to reality, but I can't justify the link.

With regard to concept formation it is possible to concretize abstract concepts like "justice", by checking the referents of the hierarchy of sub-concepts it subsumes -- I don't know how to do this for physical formulas which describe quantities? Are there any very fundamental resources which describe the theory of how and why, starting from immediate perception, men moved from simple measurements to complex-measurements(multiple units)?

Thanks in advance, I will greatly appreciate your understanding that its difficult for my to describe the problem and therefore difficult to keep it short.

Kiril




The origin of the idea of modern form of formulas or quantities

 

[SpecialKM]

To clarify, you want to know the relationship between measured quantities and calculated quantities in which how each is seen in reality?

 

[Kiril]

To clarify, you want to know the relationship between measured quantities and calculated quantities in which how each is seen in reality?

Hi SpecialKM,

Yes, however the keyword is "seen". I will appreciate any assistance, as per your interpretation of the questions.

 

[SpecialKM]

I will try my best to give some insight.

Well, the main reason they're given the terms measured and calculated, is because most calculated quantities have some type of derived quantity in them. A derived quantity is something like velocity. In that case it's the amount of distance traveled divided by the type, two measured quantities to form a calculated (derived) quantity.

In essence, you could change the units from m/s to sticks/season, now you have two things you can measure and see, while having a calculated quantity.

Something like G would be far too complex, to relate to measured quantities, something you can see because of the sole reason that you can't see the force. Physicists are trying to see there are particles linked to gravity, called gravitons, but you still can't see them.

The fact is, that the idea of calculated quantities came with our tendency to want to know. Horsepower is another thing where these come together. I think it's something like the amount of work done by a horse for 1m carrying a 1kg mass divided by the time was the official term, back in the day? (I am not sure on this).

Hopefully, I shed some light on this for you. I must say, it's awfully profound question to be thinking about.

 

[Kiril]

SpecialKM, thanks for your efforts.

I have taken from your answer, the idea of something being derived, even though without a formal(Genus–differentia) definition - and the theory behind it - it cannot be seen as anything more then a synonym of "calculated"; so that the following question could be posed without getting much further: "What is the physical status of derived quantities?"

"Something like G would be far too complex, to relate to measured quantities, something you can see because of the sole reason that you can't see the force[...]"
In the case of such complexity what makes us certain we are dealing with reality? By what justified method can such a formulation be considered rational? And what are its limits?
For me, this problem is similar to the current status of induction in epistemology - it works, but, why/how/when?

Side tracking a little:
It is true that 'force' is not visually sensible, but does this make odor and texture any less real; or the physical sensation of a paper cut(pain/pleasure)?
I'd like to suggest that force is directly perceivable - is axiomatic - and this is so because of our experience of discomfort/pain in the process of exerting motion. This is the only experience in reality that could give meaning to the various similar ways people use the term - but which is seldom identified in words(in this respect temperature is also axiomatic).
But the interesting problem is, that got me started with these questions - by what rational method(and related premises), was one able to quantify it in terms of the multiplication of two numbers(and later, because experience tells us that continued exertion(force) is required to move things through a distance, to denote, this, by a another formula W=Fd)?

Here is a quote, which sums up my general attitude and goal:
"Our problem is the double one of understanding what we are trying to do and what our ideals should be in physics, and of understanding the nature of the structure of physics as it now exists. " (P.W.Bridgman, The Logic of Modern Physics)

 

[SpecialKM]

Your reply left me intrigued, so I went out and did some research on how these equations actually came to be. Your questions are absolutely valid, how did these equations originate, what led scientists to believe that a mathematical equation is directly related to nature?

Namely, F=ma, if you search up how Issac Newton actually came up with it, it will make sense to you somewhat. It has to do with complex math and patterns. In nature, patterns are everywhere. Even something called the golden ratio, an irrational number which is a ratio, that is seen in nature! The origins of formulas, may have come from these patterns that brilliant scientists have taken and related it indirectly to reality.

Perhaps if you venture far enough into this, you'll find your answer. Unfortunately, I don't have much understanding on this topic yet, but if you find answers, be sure to fill me in.

 

[Studiot]

Namely, F=ma, if you search up how Issac Newton actually came up with it, it will make sense to you somewhat. It has to do with complex math and patterns. In nature, patterns are everywhere. Even something called the golden ratio, an irrational number which is a ratio, that is seen in nature! The origins of formulas, may have come from these patterns that brilliant scientists have taken and related it indirectly to reality.

People in Newton's time did not work in terms of equations.

At that time comparison (and ratios) was much used. Newton investigated many diverse phenomena where the comparison on one of direct proportionality. Many of the statements of the time were couched in terms of proportionality or other comparison.

This is, incidentally, one good way to approach the subject.

go well

 

[Kiril]

People in Newton's time did not work in terms of equations.

At that time comparison (and ratios) was much used. Newton investigated many diverse phenomena where the comparison on one of direct proportionality. Many of the statements of the time were couched in terms of proportionality or other comparison.

This is, incidentally, one good way to approach the subject.

go well

Thanks for the tip. Its just what I was hoping to come across: an intermediary method, which as a rule must exist.

 

[SpecialKM]

Try and search up the Cavendish Experiment, it was the first time anyone had measured
the big G constant (universal gravitational constant). It was done during the 18th century and this experiment enabled Cavendish to measure G to an accuracy of 1% (which was amazing for the time).