arXiv subjects

Per Östborn

Publications and source records attributed to Per Östborn.

6 recordsLinked to original sources

arXiv2024

A cognitive basis for physical time

The treatment of time in relativity does not conform to that in quantum theory. In the context of quantum gravity this is called "the problem of time". A crucial difference is that time $t$ may be seen as an observable in relativity theory, just like position $x$, whereas in quantum theory $t$ is a parameter, in contrast to the observable $x$. Aiming to resolve the discrepancy, a formalization of time in the spirit of Kant's Copernican revolution is suggested, where it is required that the treatment of time in physics agree with our cognition. This leads to reconsideration of the notions of identity and change of objects, as well as the nature of physical states and their evolution. The formalization has two components: sequential time $n$ and relational time $t$. The evolution of physical states is described in terms of $n$, which is updated each time an event occurs. The role of $t$ is to quantify distances between events in space-time. There is a space-time associated with each $n$, in which $t$ represents the knowledge at time $n$ about temporal distances between present and past events. A universal ordering of events in terms of $n$ can be postulated even though distances $t$ are relativistic. In short, it is argued that time as a sequential flow of events should be separated from time as a measure of distance between events. In physical models, these aspects of time can be expressed as one evolution parameter and one observable, respectively.

physics.hist-ph↗

arXiv2024

Generally covariant evolution equations from a cognitive treatment of time

The treatment of time in relativity does not conform to that in quantum theory. To resolve the discrepancy, a formalization of time is introduced in an accompanying paper, starting from the assumption that the treatment of time in physics must agree with our cognition. The formalization has two components: sequential time $n$ and relational time $t$. The evolution of physical states is described in terms of $n$. The role of $t$ is to quantify distances between events in space-time. There is a space-time associated with each $n$, in which $t$ represents the knowledge at time $n$ about temporal distances between present and past events. This approach leads to quantum evolution equations expressed in terms of a continuous evolution parameter $σ$, which interpolates between discrete sequential times $n$. Rather than describing the evolution of the world at large, these evolution equations provide probabilites of a set of predefined outcomes in well-defined experimental contexts. When the context is designed to measure spatio-temporal position $(x,t)$, time $t$ becomes an observable with Heisenberg uncertainty $Δt$ on the same footing as $x$. The corresponding evolution equation attains the same symmetric form as that suggested by Stueckelberg in 1941. When the context is such that the metric of space-time is measured, the corresponding evolution equation may be seen as an expression of quantum gravity. In short, the aim of this paper is to propose a coherent conceptual basis for the treatment of time in evolution equations, in so doing clarifying their meaning and domain of validity.

quant-ph↗

arXiv2024

Born's rule from epistemic assumptions

Born's rule is the recipe for calculating probabilities from quantum mechanical amplitudes. There is no generally accepted derivation of Born's rule from first principles. In this paper, it is motivated from assumptions that link the ontological content of a proper physical model to the epistemic conditions of the experimental context. More precisely, it is assumed that all knowable distinctions should correspond to distinctions in a proper model. This principle of "ontological completeness" means, for example, that the probabilistic treatment of the double slit experiment with and without path information should differ. Further, it is assumed that the model should rely only on knowable ontological elements, and that failure to fulfill this principle of "ontological minimalism" gives rise to wrong predictions. Consequently, probabilities should be assigned only to observable experimental outcomes. Also, the method to calculate such probabilities should not rely on the existence of a precise path of the observed object if this path is not knowable. A similar principle was promoted by Born, even though he did not apply it to probability. Another crucial assumption is that the proper rule to calculate probabilities should be generally valid. It should be applicable in all experimental contexts, regardless the setup that determines which attributes of the studied object are observed, together with the probability to observe each of the associated attribute values. There is no need to refer to the Hilbert space structure of quantum mechanics in the present treatment. Rather, some elements of this structure emerge from the analysis.

quant-ph↗

arXiv2019

Evolution equations from an epistemic treatment of time

Relativistically, time $t$ is an observable just like position $r$. In quantum theory, $t$ is a parameter, in contrast to the observable $r$. This discrepancy suggests that there exists a more elaborate formalization of time, which encapsulates both perspectives. Such a formalization is proposed in this paper. The evolution is described in terms of sequential time $n\in \mathbf{\mathbb{N}}$, which is updated each time an event occurs. Sequential time $n$ is separated from relational time $t$, which describes distances between events in space-time. There is a space-time associated with each $n$, in which $t$ represents the knowledge at time $n$ about temporal relations. The evolution of the wave function is described in terms of the parameter $σ$ that interpolates between sequential times $n$. For a free object we obtain a Stueckelberg equation $\frac{d}{dσ}Ψ(r_{4},σ)=\frac{ic^{2}\hbar}{2\langle ε\rangle}\BoxΨ(r_{4},σ)$, where $r_{4}=(r,ict)$. Here $σ$ describes the time $m$ passed between the start of the experiment at time $n$ and the observation at time $n+m$. The parametrization is assumed to be natural, meaning that $\frac{d}{dσ}\langle t\rangle=1$, where $\langle t\rangle$ is the expected temporal distance between the events that define $n$ and $n+m$. The squared rest energy $ε_{0}^{2}$ is proportional to the eigenvalue $\tildeσ$ that describes a 'stationary state' $Ψ(r_{4},σ)=ψ(r_{4},\tildeσ)e^{i\tildeσσ}$. The Dirac equation follows as a `square root' of the stationary state equation from the condition that $\tildeσ>0$, which follows from the directed nature of $n$. The formalism thus implies that all observable objects have non-zero rest mass, including elementary fermions. The introduction of $n$ releases $t$, so that it can be treated as an observable with uncertainty $Δt$.

quant-ph↗

arXiv2018

Quantum mechanics from an epistemic state space

We derive the Hilbert space formalism of quantum mechanics from epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. An epistemic formalism is developed, where concepts like individual and collective knowledge are used, and knowledge may be actual or potential. The physical state $S$ corresponds to the collective potential knowledge. The state $S$ is a subset of a state space $\mathcal{S}=\{Z\}$, such that $S$ always contains several elements $Z$, which correspond to unattainable states of complete potential knowledge of the world. The evolution of $S$ cannot be determined in terms of the individual evolution of the elements $Z$, unlike the evolution of an ensemble in classical phase space. The evolution of $S$ is described in terms of sequential time $n\in \mathbf{\mathbb{N}}$, which is updated according to $n\rightarrow n+1$ each time potential knowledge changes. In certain experimental contexts $C$, there is initial knowledge at time $n$ that a given series of properties $P,P',\ldots$ will be observed within a given time frame, meaning that a series of values $p,p',\ldots$ of these properties will become known. At time $n$, it is just known that these values belong to predefined, finite sets $\{p\},\{p'\},\ldots$. In such a context $C$, it is possible to define a complex Hilbert space $\mathcal{H}_{C}$ on top of $\mathcal{S}$, in which the elements are contextual state vectors $\bar{S}_{C}$. Born's rule to calculate the probabilities to find the values $p,p',\ldots$ is derived as the only generally applicable such rule. Also, we can associate a self-adjoint operator $\bar{P}$ with eigenvalues $\{p\}$ to each property $P$ observed within $C$. These operators obey $[\bar{P},\bar{P}']=0$ if and only if the precise values of $P$ and $P'$ are simultaneoulsy knowable.

quant-ph↗

arXiv2017

A strict epistemic approach to physics

The general view is that all fundamental physical laws should be formulated within the framework given by quantum mechanics (QM). In a sense, QM therefore has the character of a metaphysical theory. Consequently, if it is possible to derive QM from more basic principles, these principles should be of general, philosophical nature. Here, we derive the formalism of QM from well-motivated epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. First, an epistemic formalism is developed, using concepts like knowledge and potential knowledge, identifying a physical state $S$ with the potential knowledge of the physical world. It is demonstrated that QM emerges from this formalism. However, Hilbert spaces, wave functions and probabilities are defined in certain well-defined observational contexts only. This means that the epistemic formalism is broader than QM. In the fundamental layer of description, the physical state $S$ is a subset of a state space $\mathcal{S}=\{Z\}$, such that $S$ always contains many elements $Z$. These elements correspond to unattainable states of complete knowledge of the world. The evolution of $S$ cannot be determined in terms of the individual evolution of the elements $Z$, unlike the evolution of an ensemble in classical phase space. The evolution of $S$ is described in terms of sequential time $n\in \mathbf{\mathbb{N}}$, which is updated according to $n\rightarrow n+1$ each time an event occurs, each time potential knowledge changes. Sequential time $n$ can be separated from relational time $t$, which describes distances between events in space-time. There is an entire space-time associated with each $n$, in which $t$ represents the knowledge at sequential time $n$ about the temporal relations between present and past events.

quant-ph↗