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We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
In this paper we show that in systems where the probability distribution of the the overlap is non trivial in the infinity volume limit, the property of ultrametricity can be proved in general starting from two very simple and natural…
We provide a consistency relation between cosmological observables in general relativity without relying on the equation of state of dark energy. The consistency relation should be satisfied if general relativity is the correct theory of…
There are no limits for the speeds of light and particles in general relativity (GR). Four examples illustrate this basic result, which is too often neglected.
In some recent theories including Quantum SuperString theory we encounter duality - it arises due to a non commutative geometry which in effect adds an extra term to the Heiserberg Uncertainity Principle. The result is that the micro world…
The fine-tuning of the universe for life, the idea that the constants of nature (or ratios between them) must belong to very small intervals in order for life to exist, has been debated by scientists for several decades. Several criticisms…
The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients…
In this paper within the scope of FRW cosmology for k = 0, \pm1 we study the dynamics of the universe for a cosmological model with a scalar field nonminimally coupled to matter. By best- fitting the model parameters with the observational…
We show the absence of continuous symmetry breaking in 2D lattice systems without any smoothness assumptions on the interaction. We treat certain cases of interactions with integrable singularities. We also present cases of singular…
We present the interesting coincidence of cosmology and astrophysics that points toward a dimensionless age of the universe H_0*t_0 that is close to one. Despite cosmic deceleration for 9 Gyr and acceleration since then, we find H_0t*_0 =…
Special relativity is no longer a new revolutionary theory but a firmly established cornerstone of modern physics. The teaching of special relativity, however, still follows its presentation as it unfolded historically, trying to convince…
Phantom dark energy models, with w < -1, are characterized by a future singularity and therefore a finite lifetime for the universe. Because the future singularity is triggered by the onset of dark-energy domination, the universe spends a…
It is shown that certain structures in classical General Relativity can give rise to non-classical logic, normally associated with Quantum Mechanics. A 4-geon model of an elementary particle is proposed which is asymptotically flat,…
Broad arguments indicate that quantum gravity should have a minimal length scale. In this essay we construct a minimum length model by generalizing the time-position and energy-momentum operators while keeping much of the structure of…
The determination of the most straightforward evidence for the existence of the Superworld requires a guide for non-experts (especially experimental physicists) for them to make their own judgement on the value of such predictions. For this…
The uncertainty relation and the probability interpretation of quantum mechanics are intrinsically connected, as is evidenced by the evaluation of standard deviations. It is thus natural to ask if one can associate a very small uncertainty…
The Standard Model plus gravitation is derived from general relativity with three dimensions of time. I claim that when the Lagrangian for general relativity is calculated using three dimensions of time, the unified field theory results. I…
These lectures contain an introduction to supersymmetric theories and the minimal supersymmetric standard model. Phenomenological and cosmological consequences of supersymmetry are also discussed.
I discuss some central issues in particle physics which are potentially relevant to cosmology. I first briefly review the present (glorious) experimental status of the Standard Model, emphasizing that it provides a firm foundation both for…
We introduce a simple quantum mechanical model in which time and space are discrete and periodic. These features avoid the complications related to continuous-spectrum operators and infinite-norm states. The model provides a tool for…