{"id":4263,"date":"2026-05-11T09:01:30","date_gmt":"2026-05-11T09:01:30","guid":{"rendered":"https:\/\/greekablessingindisguise.com\/philoquantum-book-2\/i-avevaioita\/"},"modified":"2026-08-31T15:05:51","modified_gmt":"2026-08-31T15:05:51","slug":"i-avevaioita","status":"publish","type":"page","link":"https:\/\/greekablessingindisguise.com\/en\/philoquantum-book-2\/i-avevaioita\/","title":{"rendered":"Uncertainty"},"content":{"rendered":"\t\t
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\r\n <\/i>\r\n Quantum Nugget #26 \u2014 Uncertainty\r\n <\/h2>\r\n\r\n
\r\n \"Quantum\r\n <\/div>\r\n\r\n
\r\n\r\n

\r\n <\/i>\r\n Not One, but Three Different Ideas\r\n <\/p>\r\n\r\n

\r\n Terms of the Day:<\/strong>
\r\n \r\n Probability \u2014 Indeterminacy \u2014 Measurement Uncertainty\r\n <\/em>\r\n <\/p>\r\n\r\n

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\r\n The word \u201cuncertainty\u201d appears frequently when we discuss\r\n Quantum Physics.\r\n <\/p>\r\n\r\n

\r\n It does not, however, always mean the same thing.\r\n <\/p>\r\n\r\n

\r\n It may refer to:\r\n <\/p>\r\n\r\n

    \r\n
  1. Uncertainty in an experimental measurement.<\/li>\r\n
  2. \r\n The probabilistic outcome of a quantum measurement.\r\n <\/li>\r\n
  3. \r\n The fundamental uncertainty relation between\r\n particular pairs of physical quantities.\r\n <\/li>\r\n <\/ol>\r\n\r\n

    \r\n If we confuse them, Quantum Physics begins to resemble\r\n a world in which \u201cnothing can be known.\u201d\r\n <\/p>\r\n\r\n

    \r\n <\/i>\r\n If we distinguish them, we discover something very\r\n different: a theory that knows with extraordinary precision\r\n \r\n the probabilities and limits of its own knowledge\r\n <\/strong>.\r\n <\/p>\r\n\r\n

    \r\n\r\n

    \r\n <\/i>\r\n 1. Ordinary Measurement Uncertainty\r\n <\/p>\r\n\r\n

    \r\n Every experimental measurement carries some uncertainty.\r\n <\/p>\r\n\r\n

    \r\n An instrument has limited resolution.\r\n <\/p>\r\n\r\n

    \r\n Temperature may fluctuate.\r\n <\/p>\r\n\r\n

    \r\n Noise affects the signal.\r\n <\/p>\r\n\r\n

    \r\n Repeated measurements display some variation.\r\n <\/p>\r\n\r\n

    \r\n <\/i>\r\n This is not unique to quantum mechanics.\r\n It occurs throughout science.\r\n <\/p>\r\n\r\n

    \r\n Measurement uncertainty expresses the range of values\r\n that could reasonably be attributed to the quantity\r\n being measured.\r\n <\/p>\r\n\r\n

    \r\n With improved instruments, better calibration and more\r\n data, it can often be reduced.\r\n <\/p>\r\n\r\n

    \r\n <\/i>\r\n It is not identical to a \u201cmistake.\u201d It is a quantitative\r\n statement of how well a value is known.\r\n <\/p>\r\n\r\n

    \r\n\r\n

    \r\n <\/i>\r\n 2. The Probability of a Quantum Outcome\r\n <\/p>\r\n\r\n

    \r\n A quantum system may be prepared in exactly the same way\r\n many times, while the same measurement produces different\r\n allowed outcomes.\r\n <\/p>\r\n\r\n

    \r\n The quantum state does not always tell us which result\r\n will appear in an individual measurement.\r\n <\/p>\r\n\r\n

    \r\n It gives us the probabilities of the possible results.\r\n <\/p>\r\n\r\n

    \r\n When the experiment is repeated many times, the frequencies\r\n of the outcomes approach the theoretical probabilities\r\n with remarkable accuracy.\r\n <\/p>\r\n\r\n

    \r\n Quantum mechanics therefore does not say:\r\n <\/p>\r\n\r\n

    \r\n <\/i>\r\n \u201cWe know nothing.\u201d<\/em>\r\n <\/p>\r\n\r\n

    \r\n It says:\r\n <\/p>\r\n\r\n

    \r\n <\/i>\r\n \r\n \u201cWe cannot always predict the individual outcome,\r\n but we can precisely predict the statistical\r\n distribution of outcomes.\u201d\r\n <\/em>\r\n <\/p>\r\n\r\n

    \r\n Within its standard formulation, this probability cannot\r\n simply be removed by using a more powerful microscope.\r\n <\/p>\r\n\r\n

    \r\n\r\n

    \r\n <\/i>\r\n 3. The Uncertainty Principle\r\n <\/p>\r\n\r\n

    \r\n Heisenberg showed that certain pairs of physical quantities\r\n cannot simultaneously have arbitrarily narrow spreads\r\n within the same quantum state.\r\n <\/p>\r\n\r\n

    \r\n For position x<\/strong> and momentum\r\n p<\/strong>:\r\n <\/p>\r\n\r\n

    \r\n \u0394x \u00b7 \u0394p \u2265 \u210f\/2<\/strong>\r\n <\/p>\r\n\r\n

    \r\n The more narrowly localised a particle\u2019s position is,\r\n the greater the spread in its momentum must be \u2014\r\n and vice versa.\r\n <\/p>\r\n\r\n

    \r\n <\/i>\r\n This is not merely a defect in our instruments, nor is\r\n it caused only by the measurement \u201cdisturbing\u201d the particle.\r\n <\/p>\r\n\r\n

    \r\n It follows from the mathematical structure of the quantum\r\n state and from the fact that the corresponding quantities\r\n are represented by non-commuting operators.\r\n <\/p>\r\n\r\n

    \r\n\r\n

    \r\n <\/i>\r\n Uncertainty Is Not Lawlessness\r\n <\/p>\r\n\r\n

    \r\n Quantum Physics does not say that \u201canything can happen.\u201d\r\n <\/p>\r\n\r\n

    \r\n The possible outcomes and their probabilities are strictly\r\n constrained by:\r\n <\/p>\r\n\r\n