**Scientists Believed** **Time Made Of Discrete Quantas** **Called** **Chronons**

**Scientists Believed**

**Time Made Of Discrete Quantas**

**Called**

**Chronons**

One of the implications of * quantum physics* is that certain aspects and properties of the

*are*

**universe****. They are composed of**

*quantized***.**

*discrete indivisible packets or quanta*As an example, the* electrons orbiting* an atom are found in specific fixed orbits and don’t slide nearer or beyond the nucleus as their energy levels change, but jump from one discrete

**quantum stat****to a different .**

*e*Even light, which we all know to be a kind of ** electromagnetic wave** which moves in waves, is additionally composed of

**of sunshine called**

*quantas***. In order that light has aspects of both**

*photons**and sometimes it behaves sort of a wave and sometimes it behaved sort of a*

**waves and particles**

*particle***.**

*(wave particle duality)*An obvious question:* is time divided into discrete quanta?* Consistent with quantum physics, the solution appears to be

*and*

**“no”***appears to be actually smooth and continuous.*

**time**Tests are administered using sophisticated timing equipment and * pulsating laser beams* to watch chemical changes happening at very small fractions of a second (

*) and at that level*

**femto second, or 10**^{-15}sec*certainly appears to be smooth and continuous.*

**time**However, if * time* actually is

**, it is likely to be at the extent of**

*quantized**(about 10*

**Planck time**^{-43}seconds). The littlest possible length of your

*consistent with*

**time***, and doubtless forever beyond our practical measurement abilities.*

**theoretical physics**It should be noted that our ** current knowledge of physics** remains incomplete and consistent with some theories that look to mix quantum. Physics and gravity into one

*(mentioned as*

**“Theory of Everything”***). There is an opportunity that point could actually be*

**quantum gravity***.*

**quantized**A * hypothetical chronon* unit for a

*of your*

**discrete quantum***has been proposed, although it is not clear just how long a*

**time***should be.*

**chronon***Introduction*

*Introduction*

The idea of a * discrete temporal evolution* isn’t a replacement one and, as most the

*, has from*

**physical ideas***to*

**time***been recovered from oblivion. For instance in classical Greece this concept came to light as a part of the atomistic thought. In*

**time****, belief with in the discontinuous character of your time was at the idea of the**

*Middle Age**held by the*

**“theistic atomism“***of the*

**Arabic thinkers***.*

**Kalam**In ** Europe**, discussions about the discreteness of space and

*are often found for instance within the writings of*

**time***and*

**Isidore of Sevilla**,**Nicolaus Boneti***, who discussed the character of continuum.*

**Henry of Harday**The idea of the existence of fundamental interval of your * time* was rejected by

**. Since it had been incompatible together with his rationalistic**

*Leibniz**.*

**philosophy**Within modern physics, however, ** Planck’s** famous work on

*inspired a replacement view of the topic.*

**black body radiation**In fact, the introduction of the quanta opened a good range of latest scientific possibilities regarding the way the physical world are often conceived. Including considerations, like those within the present paper, on the ** “discretization“** of your

*within the*

**time***.*

**framework of quantum physics (QM)**Early years of our century, Mach regarded the concept of continuum to be a consequence of our physiological limitations

Also Poincare took into consideration the possible existence of what he called an * “atom of your time“*. The minimum amount of

*which allows to distinguish between two states of a system. Finally*

**time***suggested the electrical force to act during a discontinuous way, producing finite increments of momentum separated by finite intervals of your time .*

**J.J.Thomson**Such a seminal work has ever since inspired a series of papers on the existence of a fundamental interval of your time, named * chronon*; though the outcome of all that work was small, at that point .

A further seminal article was the one by * Ambarzumian and Ivanenko*, appeared in

*1930*. Which assumed

*as being discrete and also stimulated an outsized number of subsequent papers.*

**space time**It is important to worry that in theory * Time Discretization* are often introduced in two distinct ways:

** 1.** By attributing to

*a discrete structure, i.e., by regarding*

**time***not as a continuum, but as a one-dimensional*

**time****.**

*“Lattice“*** 2.** By considering

*as a continuum, during which events can happen (discontinuously) only at discrete instants of your time .*

**time**Almost all the attempts to introduce a discretization of your time followed the primary way, generally as a part of a more extended procedure during which the *space*** time** as an entire is considered as intrinsically discrete

**(four***.*

**dimensional lattice)**Also * T.D.Lee* introduced

*discretization on the idea of the finite number of experimental measurements performable in any finite interval of your time .*

**time**This approach was first adopted within the twenties by ** Pokrowski**, after

*work, and resulted within the first real example of a theory supported the existence of a fundamental interval of*

**Thomson***: the one set forth by*

**time***, within the fifties.*

**Caldirola**Namely, * Caldirola formulated a theory* for the classical electron, with the aim of providing a classical theory for its motion in an

*. In the late seventies,*

**electromagnetic field***extended its procedure to non-relativistic*

**Caldirola***.*

**quantum physics**It is known that classical theory of the electron in an electromagnetic field (efforts by * Abraham, Lorentz, Poincare and Dirac*, among others) actually presents many serious problems; except of course when the sector of the particle is neglected.

By replacing Dirac’s equation by two finite difference equations. * Caldirola *developed a theory during which the most difficulties of

**Dirac’s***were overcome.*

**theory**As we shall see, in his relativistically invariant formalism the * chronon* characterizes the changes suffered by the dynamical state of the electron when it’s submitted to

**. In order that the electron are going to be considered an object, which is point like only at discrete positions**

*external forces***xn**(along its trajectory) such that the electron takes a quantum of proper

*to travel from one position to the following one or rather*

**time****.**

*two chronons*It is tempting to look at extensively the generalization of such a theory to the quantum domain; and this may be performed within the present work.

Let us recall that one among the foremost interesting aspects of the discretized* Schrodinger equations *is that the mass of the

*and of the*

**muon****taulepton**followed as like the 2 levels of the primary

*excited state of the electron.*

**(degenerate)**In conventional QM there’s an ideal equivalence among its various pictures: * Schrodinger’s, Heisenberg’s*, density matrix’s .

When * discretizing* the evolution equations, we shall achieve writing down those pictures during a form such they result to be still equivalent. However, so as to be compatible with the

**, our**

*Schrodinger representation**cannot generally be obtained by an immediate discretization of the continual*

**Heisenberg equations****.**

*Heisenberg equation***The Introduction of the Chronon within the Classical Theory of the Electron**

**The Introduction of the Chronon within the Classical Theory of the Electron**

Almost a century after its discovery, the electron continues to be an object waiting for a convincing description , both in classical and QED. As * Schroedinger* put it, the electron remains a stranger in

*.*

**electrodynamics***may be a field theoretical approach during which no reference is formed to the existence of fabric corpuscles.*

**Maxwell’s electromagnetism**Thus, one may say that one among the foremost controversial questions of the **20th century physics****“the wave particle paradox”**,is not characteristic of QM only. In the * electron classical theory*, matching the outline of the electromagnetic fields (obeying Maxwell equations) with the existence of charge carriers just like the electron remains a challenging task.

The hypothesis that * electric currents* might be related to charge carriers was already present with in the early

**“particle electrodynamics“**formulated in 1846 by

*and*

**Fechner***. But such a thought was taken into considerations again only a couple of decades. Later, in 1881, by*

**Weber****Helmholtz**. Up there to

*,*

**time***had been developed on the hypothesis of an electromagnetic continum and of an ether.*

**electrodynamics**In that same year, ** J.J.Thomson** wrote his seminal paper during which the electron mass was considered purely

*. Namely, the energy and momentum related to the electromagnetic fields produced by an electron were held entirely liable for the energy and momentum of the electron itself.*

**electromagnetic in nature*** Lorentz’s electrodynamics*, which described the particle particle interact via

*by the famous*

**electromagnetic fields***, p being the charge density of the particle on which the fields act, dates back to the beginning of the*

**force law +ivAB^***.*

**1890 decade**The electron was finally discovered by * Thomson* in

**and with in the following years various theories appeared. The famous (pre-relativistic) theories by**

*1897***regarded it as an extended-type object, endowed again with a**

*Abraham, Lorentz and Poincare**.*

**purely electromagnetic mass**As well known, in ** 1903 Abraham** proposed the simple-minded (and questionable)

**, with a consistent electric charge density on its surface. The idea of**

*Model of a Rigid Sphere***Lorentz (1904)**was quite similar, trying to enhance things with the mere introduction of the consequences resulting from the

**contraction.**

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