Physical equations generally require exact values for physical parameters: temperature, pressure, or velocity are represented by a constant value. But in reality you cannot determine the numbers with any precision. Measuring instruments produce a small amount of uncertainty, as do random fluctuations from one point to another or over time. In addition to these classic errors, there now exists a third type of uncertainty, the type developed by Jan Korbel and David H. Woolpert of the Center for Complex Sciences in Vienna. They have now been described in the journal Physical Review Research.. As the researchers reported, the values that determine the evolution of the physical system cannot be determined with any precision. In contrast to known sources of error, it is still not entirely clear how this type of error can be taken into account in mathematical procedures, they write.
When describing a real physical experiment mathematically, two types of errors are taken into account. On the one hand, the state of the system is not precisely known. For this reason, the exact measured values are replaced by a probability distribution. On the other hand, interactions with the outside world are described as a random process. The new type of uncertainty now described relates to the evolution of the system over time. It is described by a so-called transition matrix – a set of values that indicates how the system transitions from one state to another. However, Korbel and Wolpert argue that these values cannot be known with any precision. This means that the transition matrix itself and how quickly these transitions occur also contains uncertainty.
This additional uncertainty about the dynamics of the physical system has real consequences, Korbel and Wolpert said. In a press release from the institute Give an example of optical tweezers. Lasers keep small objects suspended. In order to optimally adjust the laser, the state of the system is measured repeatedly, and small fluctuations are a result of measurement inaccuracy. However, according to the researchers, fluctuations could also be the result of unknown system dynamics – and this uncertainty makes it difficult to tune the lasers optimally. In thermodynamic terms, it is an additional source of entropy, and therefore means that more energy must be used for certain processes than previously calculated theoretically.
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