Information is an approximation: it does not exist in nature
How computers block progress in fundamental physics
In fundamental physics, people have become used to talk about information. We all know what information is in everyday life: it is a quantity measured in bits. We are used to measure information exchange or information content, and even talk about the entropy of information and much more.
The people working on quantum computers speak about quantum information, about qubits, and about many related topics. All this is interesting. And all this is correct in everyday life. But in fundamental physics, the situation is different.
Information is a series of bits, i.e., a set of yes/no questions. Is nature a set of yes/no questions? It only takes a few lines to deduce that it is not.
There is nothing faster than light; there is no action below Planck’s quantum of action ℏ; there is nothing more compact than a black hole. All observations confirm these three limits. The three limits are without doubt.
The three limits of nature can be combined. Take the maximum speed v≤c, the minimum action W≥ℏ, and a black hole limit of general relativity, such as the maximum force F≤c⁴/4G.
Insert the limits into the dimensional definition for action W (the quantity that measures the change of a system and that appears in the principle of least action) which is given by
W =F d t =F d²/v ,
where F is force, d is distance, t is time, and v is speed. After inserting the limits for force, action and speed, we get
d ≥ √(4Gℏ / c³) ≈ 3⋅10-35 m.
In other words, the combination of the three observed limits implies that nature has a minimum length. It is given by twice the Planck length.
A smaller length does not exist, in the same way that nothing faster than light exists, no mass smaller than a black hole of that same mass value exists, and no change smaller than Planck's quantum of action exists.
The smallest length is also the smallest length measurement error. And this second limit has drastic consequences. It means that nowhere in nature it is possible draw a precise boundary between two regions, things, or quantities.
Precise distinctions are impossible in nature. In other words, there are no yes/no situations in nature. Nowhere. Never.
Yes/no alternatives assume that exact distinctions are possible. Alas, nature is not made in this way. Nature does not contain such alternatives. All yes/now alternatives are made up by humans. They are, at best, approximations. But exact alternatives do not exist in nature.
Therefore, the concept of information is an approximation. It is only valid in everyday life. It does not apply to fundamental physics. Information does not exist at the Planck scale.
Thinking in terms of information or in terms of bits prevents progress in fundamental physics.
One can state that the concept of information neglects gravity. In other words, computers do not help us to think about the foundations of nature. The story and its many further consequences – for example, minimum measurement errors imply that nature has no axioms and that all math is approximate – are told in detail in the last appendix of this preprint. Enjoy.
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