Related papers: Uncomputability and physical law
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to…
Every quantum physical system can be considered the ''shadow'' of a special kind of classical system. The system proposed here is classical mainly because each observable function has a well precise value on each state of the system: an…
In some cases, it is possible to show the conservation of energy by using equations of motion in mechanics. By considering these results, some people can think that the conservation of energy is the result of equations of motion or Newton's…
In the context of a physical theory, two devices, A and B, described by the theory are called incompatible if the theory does not allow the existence of a third device C that would have both A and B as its components. Incompatibility is a…
For any class of operators which transform unary total functions in the set of natural numbers into functions of the same kind, we define what it means for a real function to be uniformly computable or conditionally computable with respect…
An actual infinity of colliding balls can be in a configuration in which the laws of mechanics lead to logical inconsistency. It is argued that one should therefore limit the domain of these laws to a finite, or only a potentially infinite…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
There are reasons to doubt that making sense of the wave function (other than as a probability algorithm) will help with the project of making sense of quantum mechanics. The consistency of the quantum-mechanical correlation laws with the…
When one takes into account gravitation, the measurement of space and time cannot be carried out with infinite accuracy. When quantum mechanics is reformulated taking into account this lack of accuracy, the resolution of the measurement…
Most scientists would hold that science has not established that the cosmos is physically comprehensible - i.e. such that there is some as-yet undiscovered true physical theory of everything that is unified. This is an empirically…
When we want to predict the future, we compute it from what we know about the present. Specifically, we take a mathematical representation of observed reality, plug it into some dynamical equations, and then map the time-evolved result back…
In which a review of the concept of countability is done in mathematics, subjecting review some of the theorems so far accepted, showing their inconsistency and also taking concrete elements on the countability of all the powers of the set…
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
Computation, the use of a computer to solve, simulate, or visualize a physical problem, has revolutionized how physics research is done. Computation is used widely to model systems, to simulate experiments, and to analyze data. Yet, in most…
In this paper I propose a new principle in physics: the principle of "finiteness". It stems from the definition of physics as a science that deals (among other things) with measurable dimensional physical quantities. Since measurement…
Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with…
The procedure used to "do physics" in the macroscopic world is familiar: You take an object, start it off with a particular position and velocity, subject it to known forces (say gravity or friction, or both), and follow its trajectory. You…
For each substance-like quantity, a theorem about its conservation or non-conservation can be formulated. For the electric charge e.g. it reads: Electric charge can neither be created nor destroyed. Such a statement is short and easy to…