68 research outputs found
On the Possibility and Consequences of Negative Mass
We investigate the possibility and consequences of the existence of particles having negative relativistic masses, and show that their existence implies the existence of faster- than-light particles (tachyons). Our proof requires only two postulates concerning such particles: that it is possible for particles of any (positive, negative or zero) relativistic mass to collide inelastically with 'normal' (i.e. positive relativistic mass) particles, and that four-momentum is conserved in such collisions
Vienna Circle and Logical Analysis of Relativity Theory
In this paper we present some of our school's results in the area of building
up relativity theory (RT) as a hierarchy of theories in the sense of logic. We
use plain first-order logic (FOL) as in the foundation of mathematics (FOM) and
we build on experience gained in FOM.
The main aims of our school are the following: We want to base the theory on
simple, unambiguous axioms with clear meanings. It should be absolutely
understandable for any reader what the axioms say and the reader can decide
about each axiom whether he likes it. The theory should be built up from these
axioms in a straightforward, logical manner. We want to provide an analysis of
the logical structure of the theory. We investigate which axioms are needed for
which predictions of RT. We want to make RT more transparent logically, easier
to understand, easier to change, modular, and easier to teach. We want to
obtain deeper understanding of RT.
Our work can be considered as a case-study showing that the Vienna Circle's
(VC) approach to doing science is workable and fruitful when performed with
using the insights and tools of mathematical logic acquired since its formation
years at the very time of the VC activity. We think that logical positivism was
based on the insight and anticipation of what mathematical logic is capable
when elaborated to some depth. Logical positivism, in great part represented by
VC, influenced and took part in the birth of modern mathematical logic. The
members of VC were brave forerunners and pioneers.Comment: 25 pages, 1 firgure
The existence of superluminal particles is consistent with the kinematics of Einstein's special theory of relativity
Within an axiomatic framework of kinematics, we prove that the existence of
faster than light particles is logically independent of Einstein's special
theory of relativity. Consequently, it is consistent with the kinematics of
special relativity that there might be faster than light particles.Comment: 19 pages, 3 figure
Three Different Formalisations of Einsteinâs Relativity Principle
We present three natural but distinct formalisations of Einsteinâs special principle of relativity, and demonstrate the relationships between them. In particular, we prove that they are logically distinct, but that they can be made equivalent by introducing a small number of additional, intuitively acceptable axioms
Is "the theory of everything'' merely the ultimate ensemble theory?
We discuss some physical consequences of what might be called ``the ultimate
ensemble theory'', where not only worlds corresponding to say different sets of
initial data or different physical constants are considered equally real, but
also worlds ruled by altogether different equations. The only postulate in this
theory is that all structures that exist mathematically exist also physically,
by which we mean that in those complex enough to contain self-aware
substructures (SASs), these SASs will subjectively perceive themselves as
existing in a physically ``real'' world. We find that it is far from clear that
this simple theory, which has no free parameters whatsoever, is observationally
ruled out. The predictions of the theory take the form of probability
distributions for the outcome of experiments, which makes it testable. In
addition, it may be possible to rule it out by comparing its a priori
predictions for the observable attributes of nature (the particle masses, the
dimensionality of spacetime, etc) with what is observed.Comment: 29 pages, revised to match version published in Annals of Physics.
The New Scientist article and color figures are available at
http://www.sns.ias.edu/~max/toe_frames.html or from [email protected]
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