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K. Urbanowski

Publications and source records attributed to K. Urbanowski.

At least 19 recordsLinked to original sources
arXiv2025

On the Weak Point of the Stronger Uncertainty Relation

We analyze the uncertainty relation for the sum of variances, which is called in some papers, the stronger uncertainty relation for all incompatible observables. We show that this uncertainty relation for the sum of variances of the observables $A$ and $B$ calculated for the eigenstate of one of these observables, (say of $B$), contrary to the suggestions presented in some papers, leads to the same results as the Heisenberg--Robertson uncertainty relation, that it does not give any bounds on the variance of $A$.

quant-ph↗
arXiv2023

Multiverse as an ensemble of stable and unstable Universes

Estimates of the Higgs and top quark masses, $m_{H} \simeq 125.10 \pm 0.14$ [GeV] and $m_{t} \simeq 172.76 \pm 0.30$ [GeV] based on the experimental results place the Standard Model in the region of the metastable vacuum. A consequence of the metastability of the Higgs vacuum is that it should induce the decay of the electroweak vacuum in the early Universe with catastrophic consequences. It may happen that certain universes were lucky enough to survive the time of canonical decay, that is the exponential decay, and live longer. This means that it is reasonable to analyze conditions allowing for that. We analyze properties of an ensemble of Universes with unstable vacua considered as an ensemble of unstable systems from the point of view of the quantum theory of unstable states. We found some symmetry relations for quantities characterizing the metastable state. We also found a relation linking the decay rate, ${\itΓ}$ of the metastable vacuum state with the Hubble parameter $H(t)$, which may help to explain why a universe with an unstable vacuum that lives longer then the canonical decay times need not decay.

gr-qc↗
arXiv2023

A universe born in a metastable false vacuum state needs not die

We try to find conditions, the fulfillment of which allows a universe born in a metastable false vacuum state to survive and not to collapse. The conditions found are in the form of inequalities linking the depending on time $t$ instantaneous decay rate ${\itΓ}(t)$ of the false vacuum state and the Hubble parameter $H(t)$. Properties of the decay rate of a quantum metastable states are discussed and then the possible solutions of the conditions found are analyzed and discussed. Within the model considered it is shown that a universe born in the metastable vacuum state has a very high chance of surviving until very late times if the lifetime, $τ_{0}^{F}$, of the metastable false vacuum state is much shorter, than the duration of the inflation process. Our analysis shows that the instability of the electroweak vacuum does not have to result in the tragic fate of our Universe leading to its death.

gr-qc↗
arXiv2020

Remarks on the uncertainty relations

We analyze general uncertainty relations and we show that there can exist such pairs of non--commuting observables $A$ and $B$ and such vectors that the lower bound for the product of standard deviations $ΔA$ and $ΔB$ calculated for these vectors is zero: $ΔA\,\cdot\,ΔB \geq 0$. We show also that for some pairs of non--commuting observables the sets of vectors for which $ΔA\,\cdot\,ΔB \geq 0$ can be complete (total). The Heisenberg, $Δt \,\cdot\, ΔE \geq \hbar/2$, and Mandelstam--Tamm (MT), $ τ_{A}\,\cdot \,ΔE \geq \hbar/2$, time--energy uncertainty relations ($τ_{A}$ is the characteristic time for the observable $A$) are analyzed too. We show that the interpretation $τ_{A} = \infty$ for eigenvectors of a Hamiltonian $H$ does not follow from the rigorous analysis of MT relation. We show also that contrary to the position--momentum uncertainty relation, the validity of the MT relation is limited: It does not hold on complete sets of eigenvectors of $A$ and $H$.

quant-ph↗
arXiv2019

Critical look at the time-energy uncertainty relations

The Heisenberg and Mandelstam-Tamm time-energy uncertainty relations are analyzed. The conlusion resulting from this analysis is that within the Quantum Mechanics of Schrödinger and von Neumann, the status of these relations can not be considered as the same as the status of the position-momentum uncertainty relations, which are rigorous. The conclusion is that the time--energy uncertainty relations can not be considered as universally valid.

quant-ph↗
arXiv2018

Survival amplitude, instantaneous energy and decay rate of an unstable system: Analytical results

We consider a model of a unstable state defined by the truncated Breit-Wigner energy density distribution function. An analytical form of the survival amplitude $a(t)$ of the state considered is found. Our attention is focused on the late time properties of $a(t)$ and on effects generated by the non--exponential behavior of this amplitude in the late time region: In 1957 Khalfin proved that this amplitude tends to zero as $t$ goes to the infinity more slowly than any exponential function of $t$. This effect can be described using a time-dependent decay rate $γ(t)$ and then the Khalfin result means that this $γ(t)$ is not a constant but at late times it tends to zero as $t$ goes to the infinity. It appears that the energy $E(t)$ of the unstable state behaves similarly: It tends to the minimal energy $E_{min}$ of the system as $t \to \infty$. Within the model considered we find two first leading time dependent elements of late time asymptotic expansions of $E(t)$ and $γ(t)$. We discuss also possible implications of such a late time asymptotic properties of $E(t)$ and $γ(t)$ and cases where these properties may manifest themselves.

quant-ph↗
arXiv2017

Nonclassical behavior of moving relativistic unstable particles

We study the survival probability of moving relativistic unstable particles with definite momentum $\vec{p} \neq 0$. The amplitude of the survival probability of these particles is calculated using its integral representation. We found decay curves of such particles for the quantum mechanical models considered. These model studies show that late time deviations of the survival probability of these particles from the exponential form of the decay law, that is the transition times region between exponential and non-expo\-nen\-tial form of the survival probability, should occur much earlier than it follows from the classical standard approach resolving itself into replacing time $t$ by $t/γ$ (where $γ$ is the relativistic Lorentz factor) in the formula for the survival probability and that the survival probabilities should tend to zero as $t\rightarrow \infty$ much slower than one would expect using classical time dilation relation. Here we show also that for some physically admissible models of unstable states the computed decay curves of the moving particles have fluctuating form at relatively short times including times of order of the lifetime.

hep-ph↗
arXiv2016

Properties of the false vacuum as the quantum unstable state

We analyze properties of unstable vacuum states from the point of view of the quantum theory. In the literature one can find some suggestions that some of false (unstable) vacuum states may survive up to times when their survival probability has a non-exponential form. At asymptotically late times the survival probability as a function of time $t$ has an inverse power--like form. We show that at this time region the energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t \to \infty$. This means that the energy density in the unstable vacuum state should have analogous properties and hence the cosmological constant $Λ= Λ(t)$ too. The conclusion is that $Λ$ in the Universe with the unstable vacuum should have a form of the sum of the "bare" cosmological constant and of the term of a type $1/t^{2}$: $Λ(t) \equiv Λ_{bare} + d/ t^{2}$ (where $Λ_{bare}$ is the cosmological constant for the Universe with the true vacuum).

hep-th↗
arXiv2016

The true quantum face of the "exponential" decay law

Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature od the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, "exponential" (or "canonical") described by the decay law of the exponential form, and late time characterized by the decay law having inverse--power law form. Based on the fundamental principles of the quantum theory we give the proof that there is no time interval in which the survival probability (decay law) could be a decreasing function of time of the purely exponential form but even at the "exponential" regime the decay curve is oscillatory modulated with a smaller or a large amplitude of oscillations depending on parameters of the model considered.

quant-ph↗
arXiv2015

On the velocity of moving relativistic unstable quantum systems

We study properties of moving relativistic quantum unstable systems. We show that in contrast to the properties of classical particles and quantum stable objects the velocity of moving freely relativistic quantum unstable systems can not be constant in time. We show that this new quantum effect results from the fundamental principles of the quantum theory and physics: It is a consequence of the principle of conservation of energy and of the fact that the mass of the quantum unstable system is not defined. This effect can affect the form of the decay law of moving relativistic quantum unstable systems.

physics.gen-ph↗
arXiv2015

Comments on "Which is the Quantum Decay Law of Relativistic Particles?"

Results presented in a recent paper "Which is the Quantum Decay Law of Relativistic particles?", arXiv: 1412.3346v2 [quant--ph]], are analyzed. We show that approximations used therein to derive the main final formula for the survival probability of finding a moving unstable particle to be undecayed at time $t$ force this particle to almost stop moving, that is that, in fact, the derived formula is approximately valid only for $γ\cong 1$, where $γ= 1/\sqrt{1-β^{2}}$ and $β= v/c$, or in other words, for the velocity $v \simeq 0$.

quant-ph↗
arXiv2015

Emission of Cosmic Radio-waves, $X$- or $γ$-rays by Moving Unstable Particles at Late Times

A new quantum effect connected with the late time behavior of decaying states is described and its possible observational consequences are analyzed: It is shown that charged unstable particles as well as neutral unstable particles with non--zero magnetic moment which live sufficiently long may emit electromagnetic radiation. This mechanism is due to the nonclassical behavior of unstable particles at late times (at the post exponential time region). Analyzing the transition times region between exponential and non-exponential form of the survival amplitude it is found that the instantaneous energy of the unstable particle can take very large values, much larger than the energy of this state at times from the exponential time region. Based on the results obtained for the model considered, it is shown that this new purely quantum mechanical effect may be responsible for causing unstable particles produced by astrophysical sources and moving with relativistic velocities to emit electromagnetic--, $X$-- or $γ$--rays at some time intervals from the transition time regions.

astro-ph.HE↗
arXiv2014

Decay Law of Relativistic Particles: Quantum Theory Meets Special Relativity

Late time properties of moving relativistic particles are studied. Within the proper relativistic treatment of the problem we find decay curves of such particles and we show that late time deviations of the survival probability of these particles from the exponential form of the decay law, that is the transition times region between exponential and non-expo\-nen\-tial form of the survival amplitude, occur much earlier than it follows from the classical standard approach boiled down to replace time $t$ by $t/γ_{L}$ (where $γ_{L}$ is the relativistic Lorentz factor) in the formula for the survival probability. The consequence is that fluctuations of the corresponding decay curves can appear much earlier and much more unstable particles have a chance to survive up to these times or later. It is also shown that fluctuations of the instantaneous energy of the moving unstable particles has a similar form as the fluctuations in the particle rest frame but they are seen by the observer in his rest system much earlier than one could expect replacing $t$ by $t/γ_{L}$ in the corresponding expressions for this energy and that the amplitude of these fluctuations can be even larger than it follows from the standard approach. All these effects seems to be important when interpreting some accelerator experiments with high energy unstable particles and the like (possible connections of these effects with GSI anomaly are analyzed) and some results of astrophysical observations.

hep-ph↗
arXiv2014

Effective Hamiltonians for Complexes of Unstable Particles

Effective Hamiltonians governing the time evolution in a subspace of unstable states can be found using more or less accurate approximations. A convenient tool for deriving them is the evolution equation for a subspace of state space sometime called the Krolikowski-Rzewuski (KR) equation. KR equation results from the Schrödinger equation for the total system under considerations. We will discuss properties of approximate effective Hamiltonians derived using KR equation for $n$--particle, two particle and for one particle subspaces. In a general case these affective Hamiltonians depend on time $t$. We show that at times much longer than times at which the exponential decay take place the real part of the exact effective Hamiltonian for the one particle subsystem (that is the instantaneous energy) tends to the minimal energy of the total system when $t \rightarrow \infty$ whereas the imaginary part of this effective Hamiltonian tends to the zero as $t\rightarrow \infty$.

quant-ph↗
arXiv2014

Possible Emission of Cosmic $X$-- and $γ$--rays by Unstable Particles at Late Times

Not all astrophysical mechanisms of the emission of electromagnetic radiation including $X$-- and $γ$-- rays coming from the space are clear. We find that charged unstable particles as well as neutral unstable particles with non--zero magnetic moment which live sufficiently long may emit electromagnetic radiation. This new mechanism is connected with the properties of unstable particles at the post exponential time region. Analyzing the transition time region between exponential and non-exponential form of the survival amplitude it is found that the instantaneous energy of the unstable particle can take very large values, much larger than the energy of this state for times from the exponential time region. Basing on the results obtained for the model considered, it is shown that this purely quantum mechanical effect may be responsible for causing unstable particles to emit electromagnetic--, $X$-- or $γ$--rays at some time intervals from the transition time regions.

astro-ph.HE↗
arXiv2013

False vacuum as an unstable state: possible cosmological implications

Recent LHC results concerning the mass of the Higgs boson indicate that the vacuum in our Universe may be unstable. We analyze properties of unstable vacuum states from the point of view of the quantum theory of unstable states. From the literature it is known that some of false vacuum states may survive up to times when their survival probability has a non-exponential form. At times much latter than the transition time, when contributions to the survival probability of its exponential and non-exponential parts are comparable, the survival probability as a function of time $t$ has an inverse power-like form. We show that at this time region the instantaneous energy of the false vacuum states tends to the energy of the true vacuum state as $1/t^{2}$ for $t \to \infty$. Properties of the instantaneous energy at transition times are also analyzed for a given model. It is shown that at this time region large and rapid fluctuations of the instantaneous energy take place. This suggests analogous behavior of the cosmological constant at these time regions.

physics.gen-ph↗