Measuring Objects using Dissimilar Units

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Discussion Overview

The discussion revolves around the measurement of speed, particularly the implications of using dissimilar units such as distance and time. Participants explore whether speed can be meaningfully quantified and the logical consistency of operations involving these units, with a focus on both classical and quantum perspectives.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants question the logic of dividing seconds into feet when measuring speed, suggesting it creates a conceptual dilemma.
  • Others argue that it is logical to consider how many feet an object travels in one second, indicating that such measurements are meaningful.
  • One participant points out that while addition and subtraction of quantities with different units are not meaningful, multiplication and division can be logically defined.
  • Another participant discusses the idea of division as an acceptable operation for mixed units, contrasting it with addition, which they claim lacks meaning when combining different units.
  • There is a query about the term "quantumly measured" in relation to speed, with a mention of the uncertainty principle affecting measurements of momentum and position.

Areas of Agreement / Disagreement

Participants express differing views on the logical consistency of measuring speed with dissimilar units. There is no consensus on whether speed can be meaningfully quantified in this manner, and the discussion remains unresolved.

Contextual Notes

Participants highlight limitations in understanding the operations involving mixed units, particularly regarding the validity of division versus addition. The discussion also touches on the implications of quantum mechanics for measurement, which remains an area of contention.

Tom Bruce
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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.
 
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Tom Bruce said:
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?
 
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mfig said:
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.
 
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Tom Bruce said:
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.
 
Tom Bruce said:
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.
 

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