# What is the relation between uncertainty and information obtained from a measurement?

For ex. if a measurement gives a position with twice the uncertainty as another measurement, how much less information regarding position are you getting? In other words, if uncertainty doubles, is the information gained cut in half? What is the relationship? Also, does infinite uncertainty equate to 0 information?

Edit: David, I am referring to measurement in terms of the uncertainty principle. If you choose to increase the frequency of the photon used to locate an electron, the uncertainty of momentum will obviously increase. My question is, if uncertainty in an observable rises or falls between 2 measurements, what effect does that have on the information obtained for each observable? Put explicity, if you do a measurement that gives you a more precise particle location, doesnt that mean you are getting more information about that observable? If you tell me my seat in a hockey arena is in “section 104/row E/seat 16 “, isnt that more information than telling me my seat is “somewhere in the stadium”?

• How do you define information? – my2cts Aug 4 '18 at 19:12
• My information concept is based on the tenet information cannot be created or destroyed. – user21909 Aug 4 '18 at 21:28