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In my opinion, the information within a limited volume of space is infinite. ...Can this be true in in Quantum Mechanics ?
From which follows that there should be a maximum amount of entropy in a given volume of space. Leading to the conclusions of Beckenstein and on to the holographic principle. This ties together entropy and information theory.
Quote from: NilakIn my opinion, the information within a limited volume of space is infinite. ...Can this be true in in Quantum Mechanics ?Mathematically speaking, you could measure the position and velocity of every fundamental particle to infinite precision, which would produce an infinite amount of data.However, quantum theory tells us that:- The position and velocity of subatomic particles is a bit "fuzzy", so you can't actually measure it to infinite precision- If you did try to measure to great precision, the measurement process itself would disturb the trajectory of the particles you are measuring- Measurement requires energy, and measurement to infinite precision would require infinite energy; expending infinite energy in a finite volume of space would represent a severe disturbance to this volume of space!So there is an effective maximum amount of information that could (in principle) be extracted from a given volume of space.