How to be causal: time, spacetime and spectra

  title={How to be causal: time, spacetime and spectra},
  author={Paul Kinsler},
  journal={European Journal of Physics},
  pages={1687 - 1700}
  • P. Kinsler
  • Published 9 June 2011
  • Philosophy
  • European Journal of Physics
I explain a simple definition of causality in widespread use, and indicate how it links to the Kramers–Kronig relations. The specification of causality in terms of temporal differential equations then shows us the way to write down dynamical models so that their causal nature in the sense used here should be obvious to all. To extend existing treatments of causality that work only in the frequency domain, I derive a reformulation of the long-standing Kramers–Kronig relations applicable not only… 

Linear response laws and causality in electrodynamics

Linear response laws and causality (the effect cannot precede the cause) are of fundamental importance in physics. In the context of classical electrodynamics, students often have a difficult time

Causal wave propagation for relativistic massive particles: physical asymptotics in action

Wavepackets representing relativistic quantum particles injected into a half-space, from a source that is switched on at a definite time, are represented by superpositions of plane waves that must

Electromagnetism, axions, and topology: A first-order operator approach to constitutive responses provides greater freedom

We show how the standard constitutive assumptions for the macroscopic Maxwell equations can be relaxed. This is done by arguing that the Maxwellian excitation fields (D, H) should be dispensed with,

Faraday’s Law and Magnetic Induction: Cause and Effect, Experiment and Theory

Faraday’s Law of induction is often stated as “a change in magnetic flux causes an electro-motive force (EMF)”; or, more cautiously, “a change in magnetic flux is associated with an EMF”. It is as

A comparison of the factorization approach to temporal and spatial propagation in the case of some acoustic waves

The evolution of acoustic waves can be evaluated in two ways: either as a temporal, or a spatial propagation. Propagating in space provides the considerable advantage of being able to handle

Born's Rule, EPR, and the Free Will Theorem

Many physicists believe that the EPR experiment exhibits instantaneous non-local effects. I argue below that an application of Born's Rule to EPR shows no such instantaneous effects and that EPR is

Criterion of Existence of Power-Law Memory for Economic Processes

The use of the proposed criteria allows apply the fractional calculus to construct dynamic models of economic processes and can be also used to identify the linear integro-differential operators that can be considered as fractional derivatives and integrals of non-integer orders.

Uni-directional optical pulses, temporal propagation, and spatial and temporal dispersion

I derive a temporally propagated uni-directional optical pulse equation valid in the few cycle limit. Temporal propagation is advantageous because it naturally preserves causality, unlike the

Superluminal speeds for relativistic random waves

For Klein–Gordon and Dirac waves representing massive quantum particles, the local group velocity v (weak value of the velocity operator) can exceed c. If the waves consist of superpositions of many

On spacetime transformation optics: temporal and spatial dispersion

The electromagnetic implementation of cloaking, the hiding of objects from sight by diverting and reassembling illuminating electromagnetic fields has now been with us ten years, while the notion of



Causality and the Dispersion Relation: Logical Foundations

A rigorous proof is given of the logical equivalence of strict causality ("no output before the input") and the validity of a dispersion relation, e.g., the relation expressing the real part of a generalized scattering amplitude as an integral involving the imaginary part.

Is There an Independent Principle of Causality in Physics?

  • J. Norton
  • Philosophy
    The British Journal for the Philosophy of Science
  • 2009
Mathias Frisch has argued that the requirement that electromagnetic dispersion processes are causal adds empirical content not found in electrodynamic theory. I urge that this attempt to reconstitute

What did Kramers and Kronig do and how did they do it?

Over time the account of how the Kramers–Kronig (dispersion) relations between the real and imaginary parts of response functions were derived in 1926 and 1927 has been transmogrified into anecdotes

Nature of time and causality in Physics

The conceptual definition and understanding of the nature of time, both qualitatively and quantitatively is of the utmost difficulty and importance, and plays a fundamental role in physics. Physical

Electromagnetism and time-asymmetry

It is a commonplace to note that in a world governed by special or general relativity, an observer has access only to data within her past lightcone (if that). The significance of this for

Causality-based criteria for a negative refractive index must be used with care.

Using the principle of causality as expressed in the Kramers-Kronig relations, we derive a generalized criterion for a negative refractive index that admits imperfect transparency at an observation

Causality: Models, Reasoning and Inference

1. Introduction to probabilities, graphs, and causal models 2. A theory of inferred causation 3. Causal diagrams and the identification of causal effects 4. Actions, plans, and direct effects 5.

Presenting electromagnetic theory in accordance with the principle of causality

A method of presenting electromagnetic theory in accordance with the principle of causality is described. Two 'causal' equations expressing time-dependent electric and magnetic fields in terms of

Space, Time, and Causality: An Essay in Natural Philosophy

If looking for the book by J. R. Lucas Space, Time, and Causality: An Essay in Natural Philosophy in pdf format, then you've come to the faithful website. We furnish full option of this ebook in doc,

A formal interpretation of the displacement current and the instantaneous formulation of Maxwell’s equations

Maxwell’s displacement current has been the subject of controversy for more than a century. Questions on whether the displacement current represents a true current like the conduction current and