# Laws of Physics and Resolution of Measurement

1. Any 'physical' quantity is expressed as (generally) a Real Number. Real Numbers are abstract mathematical constructs.

2. Laws of Physics are written as mathematical equations; where these real numbers are equated to each other (By now we have already left the world of physics and are purely in mathematics)

3. But when we 'measure' any physical quantity we can only measure up to a level of precision. (And this is due to resolution of the measurement instrument - I'm not talking of quantum effects etc.)

Say for e.g. distance ($$d$$), speed ($$s$$) and time ($$t$$) $$d = s*t$$ (I know this is a definition and not a law but explains the point try to make here)

But when I measure $$s$$, $$d$$ and $$t$$ and plug those values in - I will never get an equality only an approximation.

I will never know (i.e. measure) what is the value of real number $$d$$ which represents distance for me (and similarly for any other physical quantities). If I can never know $$d$$ - What's the point of putting them in equations?

Does this put some fundamental limitation?

Apologies if I'm unable to frame my question well - even I'm not very clear on what am I finding difficult to grasp. Any pointers would be helpful please

• Actually, very few quantities are expressed as real numbers. For example, $2$ is a real number, but what about $4\:\rm kg$? It’s not a real number; they are incompatible for addition. Oct 30, 2020 at 3:32

It is also usually uneconomical to attempt to make measurements to extremely high degrees of precision (of course in some cases the intention is to push the limit, for example in particle colliders). In the example you gave, the mathematical relationship $$s=d/t$$ is exact, but if the numbers you are using in the equation ($$d$$ and $$t$$) have some degree of experimental error then you will not get an exact number. What you will get is a range within which the value of $$v$$ is guaranteed to lie - not a single, exact value.