So­lu­tion com­mutec-a


This sounds se­ri­ous! If I am dri­ving my car, the po­lice re­quires me to know my speed (lin­ear mo­men­tum). Also, I would like to know where I am. But nei­ther is pos­si­ble ac­cord­ing to quan­tum me­chan­ics.


On sec­ond thought, maybe I can re­lax.

Ac­cord­ing to the un­cer­tainty re­la­tion­ship, the un­cer­tain­ties could be as small as, for ex­am­ple, 0.5 10$\POW9,{-10}$ m in po­si­tion and 10$\POW9,{-24}$ kg m/s for lin­ear mo­men­tum. I am not go­ing to miss my exit if I am mis­taken by half an Å in where the car re­ally is.

Also, 10$\POW9,{-24}$ kg m/s of lin­ear mo­men­tum for a 1 100 kg car cor­re­sponds to an un­cer­tainty in ve­loc­ity of 2 10$\POW9,{-27}$ mph. I don't think the po­lice is go­ing to ticket me for go­ing 2 10$\POW9,{-27}$ mph over the speed limit, since their laser dis­plays do not have the 29 dig­its re­quired to read off 75.000 000 000 000 000 000 000 000 002 mph.

The re­quire­ments of un­cer­tainty that give rise to the very size of the atoms are im­mea­sur­ably small for the ob­jects that pop­u­late the macro­scopic world.