# Measuring Objects using Dissimilar Units

• B
• Tom Bruce
In summary, the conversation discusses the possibility of measuring speed in quantum terms and the dilemma of calculating objects with different units. It is argued that adding and subtracting quantities with different units is not meaningful, but multiplication and division are precisely defined operations. The question is raised about measuring speed in quantum terms and the trade-off between accuracy in measuring momentum and position.f

#### Tom Bruce

Quantumly speaking: Can speed be measured? If so, why? If not why?
This is a serious question. Speed involves a distance unit and a time unit. For example .. "ft/sec" .. and it is illogical to divide seconds into feet. Having made this point can speed be quantumly measured and how do you resolve this dilemma i.e calculating objects defined by using dissimilar units.

t is illogical to divide seconds into feet

This is the part where I think you need more work. What is illogical about wondering how many feet an object travels in 1 second?

• russ_watters
This is the part where I think you need more work. What is illogical about wondering how many feet an object travels in 1 second?
... or the difference between a carton that holds 12 eggs and a carton that holds 18 eggs? Or the amount that my paycheck will increase if I put in another hour this week (zero, at the pay scale for Physics Forums staff, but that's neither here nor there), or ...

Adding and subtracting quantities expressed in different units is not meaningful, but multiplication and division are precisely defined operations with logical meanings.

• russ_watters
it is illogical to divide seconds into feet.
It works for sharing sweets amongst n kids and it works for sharing feet out amongst the n seconds that are available.
Division is an 'allowed' mixed unit or mixed quantity operation. Addition is not; 3 miles + 1 hour has no meaning and 3 miles+1km is not convenient.

Quantumly speaking: Can speed be measured? If so, why? If not why?
This is a serious question. Speed involves a distance unit and a time unit. For example .. "ft/sec" .. and it is illogical to divide seconds into feet. Having made this point can speed be quantumly measured and how do you resolve this dilemma i.e calculating objects defined by using dissimilar units.
What do you mean by "quantumly measured"?

You can measure the momentum of a particle as accurately as you like, but the more accurately you measure the momentum the less accurately you can measure it's position.