Definitions of risk.
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For example, if an elementary particle has proven not a temporal (t > 0) or a timeless (t = 0) particle, it has no reason to spend that big a budget for experimentally searching a timeless (t = 0) particle since timeless particle does not exist within our universe. Similarly, a mathematician discovers a 10-dimensional subspace, would not you want to prove that his 10-dimensional subspace is a temporal (t > 0) subspace, before experimentally search for it since mathematical solution is virtual.
Nevertheless at the dawn of science, scientists have been using a piece or pieces of papers; drawn models and paradigms in it and using mathematics as a tool analyzing for possible solution. But never occurs to them the back ground of that piece of paper represented a mathematical subspace that is “not” existed within our universe, for which practically all the laws, principles, and theories were developed from a piece or pieces of papers, which are timeless (t = 0) and strictly speaking are virtual.
Since science is mathematics but mathematics is “not” equaled to science, it is vitally important for us to understand what science really is. In order to understand science, firstly we have to understand what supported the science? For which the supporter must be the subspace within our universe. In other words, any scientific solution has to be proven existed within our universe; otherwise, it may be fictitious and virtual as mathematics is, since science is mathematics. In which we see that, our universe is a physical subspace that supports every physical realizable aspect within her space, “if and only if” the scientific postulation complies within the existent condition of our universe; dimensionality and causality or temporal (t > 0).
The essence of our temporal (t > 0) universe is that; if a mathematical solution is “not” complied within the temporal (t > 0) condition of our universe, it cannot exist within our universe. Since quantum mechanics is one of the pillars in modern science, I will start with one of the most intriguing principles in quantum mechanics; uncertainty principle. I will carry on the principle onto a newly found “certainty” principle. In which I will show Heisenberg’s principle was based on diffraction limited observation, instead upon on “nature” of time, developing his principle. I will also show the mystery of coherence theory can be understood with principle of certainty. In which I will show that; certainty subspace can be created within our temporal (t > 0) universe. Samples as applied to synthetic aperture imaging and wave front reconstruction will be included.
There is a profound relationship between science and mathematics, in which we have seen that without mathematics there would be no science. In other words, science needs mathematics but mathematics does not need science. Although science is mathematics but mathematics is not science. For example, any mathematical solution if it cannot be proven it exists within our universe, then her solution is “not” a “physical realizable” solution that can be “directly” implemented within our temporal (t > 0) universe.
But this is by no means to say that; the solutions are not temporal (t > 0) or timeless (t = 0) solutions there are not science. In fact practically all the fundamental laws, principles, and theories are timeless (t = 0) or time-independent. And these timeless (t = 0) laws, principles, and theories were and “still” are the corner stone and foundation of our science, as I will call them timeless (t = 0) or time-independent science; a topic I will elaborate in a different occasion. For simplicity, let me take one of the simplest examples; Einstein’s energy Eq. (1) as given by;
where E is the energy, m is the mass and c is the velocity of light. This equation is one of the most famous equations in science, yet it is timeless (t = 0). Although this equation has been repeatedly used and applied in practice, but strictly speaking; it cannot be directly implemented within our temporal (t > 0) universe, since it is not a time variable function. Let us transform Einstein’s equation into a time variable equation as given by [1].
where 𝜕E(t)/𝜕t is the rate of increasing energy conversion, −𝜕m/𝜕t is the corresponding rate of mass reduction, c is the speed of light, and t > 0 denotes a forward time-variable equation. In which we see Eq. (2) is a time-dependent equation exists at time t > 0, which represents a forwarded time variable function that only occurs after time excitation at t = 0. Incidentally, this is the well-known “causality” constraint (i.e., t > 0) [2] as imposed by our temporal (t > 0) universe.
Nevertheless in mathematical, a postulation is first needed to proof that there is solution existed before we search for the solution, although it is not guarantee that we can find it. But it seems to me it does not have a criterion to proof that a hypothetical science is existed within our universe, before we search for the science. For example, an analytically solution indicates that it exists an “angle particle” from a complicated mathematical analyses, will not you want to find out first is the solution existed within our temporal (t > 0) universe before experimentally to search for it. And this is precisely that we shall know first before experimentation is taken place, since it is a very costly in time and in revenue to find a physical particle.
Although science needs mathematics, but without simplicity mathematically approximation, science would be very difficult to learn and to facilitate. And this is precisely the reason practically all the fundamental laws are point-singularity approximated. In which we see precisely, science is a “law of approximation” and mathematics is “an axiom of certainty”. Again we take Einstein’s energy equation of Eq. (1) as an example, no dimension and size and it is a typical point-singularity approximated equation. It is discernible; if we include all the negligibly terms, “physical significances” of this equation would be over whelmed by the terms of mathematics. For which we see that an ounce of good approximation worth more than tons of mathematical calculation!
Let me stress that the essence of simplicity in science is that without the symbolic substitution and approximation, it will be extremely difficult or even impossible to develop science since science itself is already very complicated. Yet simplicity representation of science has also been misinterpreted as referred them as “classical and deterministic (i.e., classical physics).” The implication of deterministic or classical is a totally misled by our part, since our predecessors who developed those fundamental laws and principles were “precisely” understood the deficiency of approximation. Yet without the approximated presentation, how can we develop science? Instead of ignoring our predecessors’ wisdom, turns around we had treated them “deterministic” or classical, which were “never” been our predecessors intention. Again without the point-singularity approximated science, please tell me how we can develop those simple and elegant laws, principles, and theories. Although those laws, principles, and theories were timeless (t = 0), most of them were and “still” are the foundation and corner stone of our science. Nevertheless, mathematics is a “symbolic” langue of science, but mathematics is not science.
Since all laws, principles, and theories were made to be broken or revised or even to replace, as science advances into sub-subatomic scale regime and moving closer to near real time processing, those timeless (t = 0) laws, principles, and theories could produce incomprehensible consequences; particularly as applied them directly confronting the temporal (t > 0) constraint of our universe. For example, as applying superposition principle to quantum computing and communication, since superposition is a timeless (t = 0) principle [3].
In this section, I will show several subspaces that have been used by the scientists, in the past as depicted in Figure 1. It is reasonable to stress that why subspace of a scientific model embedded is crucially important is that any analytical solution produced follows the “limitation” of the subspace, because it is the subspace dictates the science but “not” the mathematics changes the subspace.
(a) Shows an absolute-empty space, (b) a virtual mathematical space, (c) a Newtonian space, and (d) a temporal (t > 0) space, respectively.
For example, when you are designing a submarine, the subspace that the submarine is supposed to be situated within is vitally important; otherwise, your submarine will very “likely” not to survive thousands of feet underwater pressure. Therefore, it is necessary to know the subspace that a postulated science to be implementing into it; otherwise, the postulated science is very likely “cannot” be existed within the subspace.
In view of Figure 1, we see that; there is an absolute-empty space, a mathematical virtual space, a Newtonian’s space [4], and a temporal (t > 0) space. An absolute-empty space or just empty space has no substance and has no time. A mathematical virtual space is an empty space which has no substance in it, but mathematicians and theoretical scientists can implant coordinate system in it, since mathematics is virtual and theoretical scientists are also mathematicians.
We note that mathematical virtual space has been used over centuries by scientists at the dawn of science, but this is a virtual space that does “not” exist within our temporal (i.e., t > 0) universe. The next subspace is known as Newtonian space [4]; it has substance and coordinates in it, but treated time as an “independent” variable, for which Newtonian and mathematical spaces are virtual the “same.” Since Newtonian space is time independent, it “cannot” be exist within our temporal (t > 0) space since time and substance has to be “mutually coexisted” within our temporal (t > 0) universe. Yet scientists have been using Newtonian space for their analyses over centuries and not knowingly it is a virtual space.
The last subspace is known as temporal (t > 0) space [5], where time and substance are interdependently “coexisted” and time is a forward “dependent variable” runs at a “constant speed”. We stress that this temporal (t > 0) subspace is currently “only” physical realizable space, where the space was created by Einstein energy Eq. (2).
Physical reality is that any scientific hypothesis that deviates “away” the boundary condition that imposed by our temporal (t > 0) universe is “not” a physically realizable solution. But this is by no means that the virtual mathematical empty space and Newtonian space are useless. The fact is that all the physical sciences were developed within timeless (t = 0) or Newtonian subspaces “inadvertently,” at the dawn of science. Practically all the fundamental laws, principles, and theories were derived from a timeless (t = 0) subspace, which was from the background subspace of a piece of paper although not intentionally [6]. In which we see that practically all the laws, principle, and theories are timeless (t = 0).
Nevertheless what temporal (t > 0) space means is that any subspace is coexisted with time, where time is a forward dependent variable with respect to its subspace and its speed has been well settled when our universe was created. This means that before the creation of our temporal universe, there is a “larger” temporal space that our universe is embedded in; otherwise, our universe will “not” be existed. Nevertheless every subspace within our universe is a time varying stochastic [7] subspace, in which every substance or subspace changes with time. Strictly speaking our universe is a “temporal (t > 0) stochastic expanding subspace.” For which we see that; any postulated law, principle, and theory has to comply with the temporal (t > 0) condition within our universe; otherwise, it is virtual as mathematics.
Let me show what mathematicians can do within a virtual subspace as depicted in Figure 2. Since quantum mechanists are also mathematicians, they can implant coordinate system within an empty space as they wishes, regardless whether the model is physically realizable or not.
A set of atomic models embedded within virtual empty subspaces. (a) shows a singularity approximated atomic model is situated within an empty space, which has no coordinate system. (b) shows an atomic model is embedded within empty space that has a coordinate system drawn into it.
The basic difference between Figure 2(a) and (b) is that there is a virtual coordinate system that has been added in Figure 2(b) by quantum mechanists. Once the coordinate system is implanted, dimensionality of the sub-atomic particles cannot be ignored. The reason is that for the atomic model to be existed within the subspace, the atomic model has to “comply” with the existence conditions within the subspace, since it is the subspace affects the solution and not the solution changes the subspace. In which we see that neither Figure 2(a) nor Figure 2(b) are “not” physical realizable paradigms. For which solutions obtained from these empty subspace models will be timeless (t = 0).
Aside the non-physical realizable paradigms of Figure 2, I will show what a timeless (t = 0) subspace can do for substances within the subspace. Let me assume we have three particles situated within an empty space, as normally do on a “piece of paper”, shown in Figure 3.
A hypothetical scenario shows three particles are embedded within an empty subspace.
Since empty subspace has “no time,” all particles within the subspace collapse or “superimposing” instantly all together at t = 0, because time is distance and distance is time. This is precisely the “simultaneous and instantaneous” superposition principle does in quantum mechanics [3]. The reason particles collapsed at t = 0, it is because the subspace has “no time.” And the other reason that particles superimposed together, since within a timeless (t = 0) space, it has “no distance” or no space.
By virtue of energy conservation, we see that superimposed particles has a mass equals to the sum of entire superimposed particles, but it has “no size.” In view of timelessness space, we see that the superimposed particles can be found everywhere within the entire timeless (t = 0) subspace, since timeless (t = 0) subspace has “no” distance, as depicted hypothetically in Figure 4. In which we see that Schrödinger’s fundamental principle of superposition is existed within a virtual timeless (t = 0) subspace, and it cannot be existed within our temporal (t > 0) universe, since timeless and temporal are “mutually exclusive.”
Superimposed particle existed “simultaneously and instantaneously” all over the entire timeless (t = 0) subspace.
By the way, this is precisely the superposition principle that Einstein was objecting to, which he called it spooky. As I quote from a 1935 The New York Times’ article (i.e., Figure 5), “Einstein and two scientists found quantum theory is incomplete even though correct” [8]. In view of preceding illustration, we see that Schrödinger’s superposition principle is “correct” but only within a timeless (t = 0) subspace and it is “incorrect” within our temporal (t > 0) space,” since timeless space cannot exist within our temporal universe.
A 1935 New York times’ article.
As we accepted subspace and time are coexisted within our temporal (t > 0) universe, time has to be real and it cannot be virtual, since we are physically real. And every physical existence within our universe is real. The reason some scientists believed time is virtual or illusion is that; it has no mass, no weight, no coordinate, no origin, and it cannot be detected or even be seen. Yet time is an everlasting existed real variable within our known universe. Without time there would be no physical matter, no physical space, and no life. The fact is that every physical matter is associated with time which including our universe. Therefore, when one is dealing with science, time is one of the most enigmatic variables that ever presence and cannot be simply ignored. Strictly speaking, all the laws of science as well every physical substance cannot be existed without the existence of time. For which we see that time “cannot” be a dimension or an illusion. In other words, if time is an illusion, then time will be “independent” from physical reality or from our universe. And this is precisely that many scientists have treated time as an “independent” variable such as Murkowski’s space [9], for which the space can be “curved” or time-space can be changed by gravity [10]. If time-space can be curved, then we can change the “speed” of time. In other words, is our universe exists with time, or time exists with universe? The answer is our universe exists with time, although space and time are interdependent but is not time exists with our universe.
As time is coexisted with subspace, we see that any subspace within our temporal (t > 0) universe cannot be empty and speed of time is the same everywhere within our universe. This means that the speed of time within a subspace is “relatively” with respect to the different subspaces, as based on Einstein’s special theory of relativity [9]. For example, subspaces closer to the edge of our universe, their time runs faster “relative” to ours, but the speed of time within the subspaces near the edge as well within our subspace are the “same,” which has been determined by the speed of light as our universe was created by a big bang theory using Einstein equation as given by [5];
where 𝜕E/𝜕t is the rate of increasing energy conversion, −𝜕m/𝜕t is the corresponding rate of mass reduction, c is the speed of light and t > 0 represents a forward time-variable. In which we see that it a “time-dependent” equation exists at time t > 0; a well-known causality constraint (i.e., t > 0) [2] as imposed by our universe. Similarly preceding equation can be written as:
where 𝜀 and 𝜇 are the permittivity and the permeability of the deep space, respectively, 𝜐 is the radian frequency variable, E2(𝜐) and H2(𝜐) are the respective electric and magnetic field intensities, the negative sign represents the “out-flow” energy per unit time from an unit volume,
In view of this equation, we see how our universe was created as depicted by a composited diagram in Figure 6, in which we see that radian energy (i.e., radiation) diverges from the mass, as mass reduces with time. In which we see that our universe enlarges and her boundary expands at speed of speed of light.
Composite temporal (t > 0) universe diagrams. r = ct, r is the radius of our universe, t is time, c is the velocity of light, and 𝜀0 and 𝜇0 are the permittivity and permeability of the space.
Figure 7 shows a schematic diagram of our temporal (t > 0) universe, which depicts approximately the behavior of subspace changes as her boundary expands with speed of light. In which we see that, subspace enlarges faster closer toward the boundary, but solid substance m (t) changes little within the subspace. We also see that the out-ward speed of particle (or subspace) increases “linearly” as boundary increases with light speed. For example; out-ward speed of particle 2 is somewhat faster than particle 1 (i.e., v2 > v1). For which we see that our universe is a dynamic temporal (t > 0) “stochastic” universe that simple geometrical equation or mathematical abstract space can describe. One of the important aspects of our universe is that every subspace, no matter how small it is, “cannot” be empty and it has time.
A schematic diagram of our temporal (t > 0) universe. c is the speed of light, m(t) is the temporal mass, and v is the radial velocity.
For instance, in order for us to be existed within our planet, we must be temporal (t > 0): that is we have time and must change with time; otherwise, we cannot exist within our universe. In other words, our time is the same as our planet and the universe but the velocity of our planet is different from other subspaces. For example, subspaces near the edge of our universe are moving faster than us, for which it has “relative” speed of time between us and a subspace closer to the edge of our universe. On the other hand, if we assume that we are timeless (t = 0), we could “not” have existed within our universe, since time and timelessness are mutually exclusive.
I further note that any subspace within our universe cannot empty, since subspace is coexisted with time. Although subspace is coexisted with time, but time is neither equaled to subspace. Yet, space is time and time is space since time and space are mutually inclusive. For example, substance has dimension (or space), but time has no dimension and no mass. In which we see that time is “not” a dimension but it is “dependently” existed with respect to subspace. In which we stress that it is our universe governs the science and it is not the science changes our universe.
Once again, we have shown that time is “not “an illusion or virtual, time is physically real because everything existed within our living space is physical real; otherwise, it will not be existed within our temporal universe. In other words, everything within our universe is temporal (t > 0), of which I have discovered that practically all the laws, principles, theories, and paradoxes of science were developed from a timeless (t = 0) platform (i.e., a pieces or pieces of papers) for centuries, at the dawn of science “inadvertently” [6].
Nevertheless, one of the important aspects within our universe is that every subspace has a price, an amount of energy 𝛥E, and a section of time 𝛥t to create (i.e., 𝛥E and 𝛥t), and it is “not free.” For example, a simple facial tissue takes a huge amount of energy 𝛥E and a section of time 𝛥t to create. It is, however, a “necessary” but not sufficient condition, because it also needs an amount of information 𝛥I to make it happen (i.e., 𝛥E, 𝛥t, and 𝛥I) [12].
In short, I would stress that if there is a beginning then there is an end. Since time and space are coexisted, then time and space have no beginning and no end. In which we see that time-space [or temporal (t > 0) space] is ever existed, since existence and non-existence are mutually exclusive. In other words, emptiness and non-emptiness are mutually excluded, then time “always” exists with space. Thus, time is real because the space is real, for which time-space has no beginning and has no end. And this must be the art of temporal (t > 0) universe.
One of the most intriguing principles in quantum mechanics [13] must be the Heisenberg’s Uncertainty Principle [14], as shown by the following equation:
where 𝛥p and 𝛥x are the momentum and position errors, respectively, and h is the Planck’s constant. As reference to “wave-particle dynamics,” the momentum p of a “photonic particle” is presented by a “quanta” of energy h𝜐 as given by:
where h is the Planck’s constant, λ is the wavelength, 𝜐 is the frequency, and c is the velocity of light.
In which we see that Heisenberg’s principle was based on “wave-particle duality” existed within an “empty space.” The essence of the Heisenberg’s uncertainty principle is that one cannot precisely determine the position x and the momentum p of a particle “simultaneously under observation”, as illustrated in Figure 8. In which we see that; it is “independent” of time, since Heisenberg’s principle was based on “observation” stand point which has nothing to do with changing naturally with time. Yet we know that if there is “no” time there is “no” uncertainty.
A particle in motion within an “empty” subspace. v is the velocity. Note that background paper has been treated as an “empty” subspace for centuries.
In view of Figure 8, Heisenberg principle was derived on an empty timeless (t = 0) subspace and it has “nothing to do or independent” with the “underneath subspace” that the particle is situated. Strictly speaking, it is “not” a physical realizable paradigm should be used in the first place, since particle and empty subspace are “mutual exclusive.” Secondly, the position error 𝛥x of Heisenberg was based on a “diffraction limited” microscopic observation, where the “spatial” ambiguity of 𝛥x is given by [15]:
where λ is the observation wavelength, 2(sin α) is the “numerical aperture” of the microscope and α is subtended half-angle of observation aperture. In which we see that the position error 𝛥x is “not” due to particle in motion, but based on the diffraction limited aperture. This is precisely why Heisenberg’s position error 𝛥x has been interpreted as an “observation error” which is independent with time. But uncertainty changes naturally with time, since without time it has no uncertainty.
Secondly, the momentum error 𝛥p as I quote [15]: after collision the particle being observed, the photon’s path is only to lie within a cone having semi-vertical angle α in which momentum of the particle is uncertain by the amount as given by:
where λ is the wavelength of the quantum leap of h𝜐. In which we see that; momentum error 𝛥p is “not” due to band width 𝛥𝜐 of quantum leap since any physical radiator has to be band limited. In other words, the momentum error 𝛥p of preceding Eq. (8) is a singularity approximated λ, which is “not” a band limited 𝛥λ of physical reality.
As we look back at the subspace that Heisenberg’s principle developed from, it was an “inadvertently” timeless (t = 0) subspace as shown in Figure 8. Aside the timeless (t = 0) subspace, it is the uncertainty mainly due to diffraction limited observation, which is a “secondary cause” by human intervention, but not due to naturally change with time. This is similar to entropy theory of Boltzmann [16]: entropy increases naturally with time within an enclosed subspace. In which we see that uncertainty should be increasing with time, without human intervention. As I have noted, without time, there would be no entropy and no uncertainty.
Nevertheless, momentum error 𝛥p and position error 𝛥x are mutually “coexisted.” In principle they can be traded. But the trading cannot without constraint, since time is a dependent forward variable. But Heisenberg uncertainty; 𝛥p and 𝛥x are “not” mutually dependent, since his position error 𝛥x is due to diffraction limited observation, which is nothing to do with time. For which it poses a physical “inconsistency” within our universe, although Heisenberg principle has been widely used without any abnormality. But it is from the “physical consistency” standpoint, Heisenberg’s position error 𝛥x was based on diffraction limited observation has “nothing” to do with time. And also added and his momentum error 𝛥p was based on singularity wavelength λ which is “not” a band limited reality.
Yet, uncertainty principle can be made temporal (t > 0), similar to entropy theory of Boltzmann. For which we have a “law of uncertainty” as stated: uncertainty of an isolated particle increases naturally with time. Or more specific: uncertainty of an isolated particle within an isolated subspace, increases with time and eventually reaches to a maximum amount within the isolated subspace. For which we see that there it exists a profound connection between uncertainty and entropy.
Since it is our universe governs the science and it is not the science governs our universe. Therefore, every principle within our universe has to comply with the temporal (t > 0) condition within our universe; otherwise, the principle cannot be existed within our universe. Which includes all the laws, principles and theories; such as Maxwell’s Electro-Magnetic theory, Boltzmann’s entropy theory, Einstein’s relativity theory, Bohr’s atomic model, Schrödinger’s superposition principle, and others. Of which uncertainty principle cannot be the exception?
Let us now assumed a temporal (t > 0) particle m(t) is situated within a temporal (t > 0) subspace as depicted in Figure 9. Strictly speaking any particle existed within a temporal subspace must be a temporal (t > 0) particle; otherwise, the particle cannot be existed within our temporal (t > 0) universe.
A temporal (t > 0) particle m(t) within a temporal (t > 0) subspace. r is the radial direction. Note: it is a “physical realizable” paradigm, since a temporal particle m(t) is embedded within a temporal subspace.
For simplicity, we further assume m(t) has no time or “pseudo-timeless,” after all science is a law of approximation. The same as Heisenberg’s assumption, the particle is a photonic particle (i.e., a photon), as from wave particle-duality standpoint [17] momentum of a photon is given by:
where h is the Planck’s constant, λ is the wavelength and 𝜐 is the frequency of the photonic particle. As I have mentioned earlier, within our universe any radiator has to be band limited. Thus the momentum error is naturally due changes of bandwidth 𝛥𝜐, as given by;
Instead of using a cone of light as Heisenberg had postulated. By virtue of time-bandwidth product 𝛥𝜐 𝛥t = 1, 𝛥𝜐 “decreases” with time. For which position error can be written as:
where r is the radial distance, we have the following uncertainty relationship;
In which we see that; 𝛥𝜐 · 𝛥t is the “time-bandwidth” product. As we imposed the optimum energy transfer criterion on time-bandwidth product [12], as given by:
Since lower bound for a photonic particle is limited by Planck’s constant, we have the following equivalent form as given by:
Nevertheless, in view of Eq. (13), momentum uncertainty principle can be shown as:
where (t > 0) denotes that uncertainty principle is complied with the temporal (t > 0) condition within our universe. In view of either conservation of momentum or energy conservation, we see that position error 𝛥r increases naturally with time. Which shows that momentum error 𝛥p “decreases” naturally with bandwidth 𝛥𝜐, as in contrast with Heisenberg’s assumption; momentum error 𝛥p has “nothing” to do with the changes of 𝛥𝜐. This is precisely the “law of uncertainty” as I have described earlier, uncertainty of an isolated particle increases naturally with time.
Since the increase in position error 𝛥r is due to time, it must be due to the dynamic expansion of our universe [5]. For example, as the boundary of our universe constantly expanding at the speed of light, by virtue of energy conservation, it changes every dynamic aspect within our universe. As time moves on naturally, the larger the position error 𝛥r increases with respect to that starting point, as illustrated in Figure 10.
Position error 𝛥r (i.e., sphere of 𝛥r) enlarges naturally with time within a temporal (t > 0) subspace: 𝛥r represents a position error of the particle, at various locations as time moves constantly.
Therefore we see that uncertainty is “not” a static process it is a temporal (t > 0) dynamic principle, as in contrast with Heisenberg’s position error 𝛥r is “independent” with time and his momentum error 𝛥p is “independent” with 𝛥𝜐. In which we see that if there is no time, there is no uncertainty and no probability. Nevertheless, each of the uncertainty unit or cell, such as (𝛥p, 𝛥x), (𝛥E, 𝛥t) and (𝛥𝜐, 𝛥t) is self-contained. In other words, 𝛥E and 𝛥t are coexisted which they can be bilateral traded, but under the constraint of time as a forward moving dependent variable. In other words, if a section of 𝛥t has been used, we cannot get the “same” section back, but can exchange for a different section of 𝛥t. In which we see that we can trade for a narrower 𝛥t with a wider 𝛥E or wider 𝛥t with a narrower 𝛥E. But we “cannot” trade 𝛥t for 𝛥E, since 𝛥t is a real dependent variable has “no” substance to manipulate.
One of the important aspects of “temporal uncertainty” is that subspace within our universe is a temporal (t > 0) uncertain “subspace.” In other words, any subspace is a temporal (t > 0) stochastic subspace, such that the dynamic behavior of the subspace changes “dependently” with time. In which any change within our universe has a profound connection with the constant expanding universe. In which we have shown that uncertainty increases naturally with time, even though without any other perturbation or human intervention. Similar to the myth of Boltzmann’s entropy theory [16], entropy increases naturally with time within an enclosed subspace, which has been shown is related to the expanding universe [5].
Similarly, there is a profound “connection” between coherence theory [18] and “certainty” principle as I shall address. Nevertheless, it is always a myth of coherence, as refer to Figure 11, where coherence theory can be easily understood by Young’s experiment. In which degree of coherence can be determined by the “visibility” equation as given by:
Young’s experiment. 𝜮 represents an extended monochromatic source, Q1 and Q2 are the pinholes, and “I” represents the irradiance distribution.
where Imax and Imin are the maximum and minimum intensities of the fringes. But the theory does not tell us where the physics comes from. For which, it can be understood from “certainty principle,” as I shall address.
It is trivial that if there is an uncertainty principle, it is inevitable not to have a certainty principle. This means that, as photonic particle we are looking for is “likely” to be found within a “certainty” subspace. Since “perfect certainty” (or absolute uncertainty) occurs at t = 0, which is a timeless (t = 0) virtual subspace not exist within our universe. Nevertheless, “certainty principle” can be written in the following equivalent forms;
where (t > 0) denotes that equation is subjected to temporal (t > 0) constrain. In view of the position error 𝛥r in Eq. (17), it means that it is “likely” the photonic particle can be found within the certainty subspace. Since the size of the subspace is limited by Planck constant h, it is normally used as limited boundary “not” to be violated. Yet within this limited boundary, certainty subspace had been exploited by Dennis Gabor for his discovery of wave front reconstruction in 1948 [19] and as well it was applied to synthetic aperture radar imaging in 1950s [20].
Since the size of certainty subspace is exponentially enlarging as the position error 𝛥r increases, for which the “radius” of the certainty sub-sphere is given by:
where c is the speed of light, 𝛥t is the time error, and 𝛥𝜐 is the bandwidth of a light source or a quantum leap h𝜐. Thus we see that position error 𝛥r is inversely proportional to bandwidth 𝛥𝜐, as plotted in Figure 12.
A plot of position error 𝛥r versus bandwidth 𝛥𝜐.
In view of this plot, we see that when bandwidth 𝛥𝜐 decreases, a larger certainty subspace enlarges “exponentially” since the volume of the subspace is given by:
In which we see that, a very “large” certainty subspace can be realized within our universe which is within limited Planck’s constant h as depicted in Figure 13, where we see a steady state radiator A emits a continuous band limited 𝛥𝜐 electro-magnetic wave as illustrated. A “certainty subspace” with respect to an assumed “photonic particle” A for a give 𝛥t can be defined as illustrated within r = c 𝛥t, where 𝛥t = 1/𝛥𝜐. In other words, it has a high degree of certainty to relocate particle A within the certainty subspace. Nevertheless, from electro-magnetic disturbance standpoint; within the certainty subspace provides a high “degree of certainty” (i.e., degree of coherence) as with respect to point A.
A certainty subspace is embedded within uncertainty subspace. A is assumed a steady state photonic particle emits a band limited 𝛥𝜐 radiation, r is the radius with respect to the emitter A; and B represents the boundary of certainty subspace of A.
As from coherence theory stand point, any other disturbances away from point A but within the certainty subspace (i.e., within r < c 𝛥t) are mutual coherence (i.e., certainty) with respect A; where r = c 𝛥t is the radius of the “certainty subspace” of A. In other words, any point-pair within d < c 𝛥t, where 𝛥t = 1/𝛥𝜐, are “mutual coherence” within a radiation subspace. On the other hand, distance greater than r > c 𝛥t from point A is a mutual “uncertainty” subspace with respect to A. In other words, any point-pair distance is larger than d > c 𝛥t within the radiation space are mutually “incoherent.” In which we see that; it is more “unlikely” to relocate a photonic particle, after it has been seen at point A, within a “certainty subspace.”
Since certainty subspace represents a “global” probabilistic distribution of a particle’s location as from particle physicists stand point, which means that it is “very likely” the particle can be found within the certainty subspace. In which we see that a postulated particle firstly is temporal (t > 0) or has time; otherwise, there is no reason to search for it. Then after it has been proven it is a temporal (i.e., m(t)) particle, it is more favorable to search the particle, within a certainty subspace.
The essence of “wave-particle duality” is a mathematical simplistic assumption to equivalence a package of wavelet energy as a particle in motion from statistical mechanics stand point, in which the momentum p = h/λ is conserved. However one should “not” treated wave as particle or particle as wave. It is the package of wavelet energy “equivalent” to a particle dynamics (i.e., photon), but they are “not” equaled. Similar to Einstein’s energy equation, mass is equivalent to energy and energy is equivalent to mass, but they are not equaled. Therefore as from energy conservation, bandwidth 𝛥𝜐 “decreases” with time is the physical reality instead of treating a package of wavelet as a particle (i.e., photon), which was due to the classical mechanics standpoint, treats quantum leap momentum p = h/λ. In which we see that photon is a “virtual” particle although many quantum scientists have been regarded photon as a physical particle?
We further note that any point-pair within the certainty subspace exhibits some degree of certainty or coherence, which has been known as “mutual coherence” [18]. And the mutual coherence can be easily understood as depicted in Figure 14, in which a steady state band limited 𝛥𝜐 electro-magnetic wave is assumed existed within a temporal (t > 0) subspace. As we pick an arbitrary disturbance at point B, a certainty subspace of B can be determined within r ≤ c 𝛥t, as shown in the figure. This means that any point disturbance within in the certainty subspace has a strong certainty (or coherence) with respect to point B disturbance. Similarly if we pick an arbitrary point A, then a certainty subspace of A can be defined as illustrated in the figure, of which we see that a portion is overlapped with certainty subspace of B. Any other disturbances outside the corresponding subspaces of certainty A, B, and C are the uncertainty subspace. It is trivial to see that a number of configurations of certainty subspaces can be designed for application. In which we see that multi wavelengths, such as 𝛥𝜐1, 𝛥𝜐2, and 𝛥𝜐3, can also be simultaneously implemented to create various certainty subspace configurations, such as for multi spectral imaging or information processing application.
Various certainty subspace configurations, as with respect to various disturbances within a steady state band limited 𝛥𝜐 electro-magnetic environment within a temporal (t > 0) subspace.
One of the commonly used for producing certainty subspaces for complex wave front reconstruction is depicted in Figure 15 [21]. In which we see that a band limited 𝛥𝜐 laser is employed, where a beam of light is split-up by a splitter BS. One beam B2 is directly impinging on a photographic plate at plane P and other beam B1 diverted by a mirror and then is combined with beam B2 at the same spot on the photographic plate P. It is trivial to know that if the difference in distances between these two beams is within the certainty subspace, then B1 and B2 are “mutually” coherence (or certainty); otherwise, they are mutually incoherence (or uncertain). In which we see that the distance between B1 and B2 is required as given by:
An example of exploiting certainty subspace for wave front reconstruction. BS, beam splitter; P, photographic plate.
where d1 and d2 are the distances of bean B2 and B2, respectively, from the splitter BS. In which we see that radius of certainty subspace of BS is written by;
where |d1 – d2 | = c/𝛥𝜐 is the “coherent length” of the laser. In which we see that by simply reducing the bandwidth 𝛥𝜐, a lager certainty subspace can be created within a temporal (t > 0) subspace.
Since every substance or subspace within our universe was created by an amount of energy 𝛥E and a section of time 𝛥t [i.e., (𝛥E, 𝛥t)], any changes of 𝛥E changes the size of certainty subspace 𝛥r. This is a topic that astrophysicists may be interested. Similarly to particle physicists, subatomic particle has to be temporal (t > 0); otherwise, the particle must be a virtual particle cannot exist within our universe. Secondly, it is more “likely” a temporal (t > 0) particle to be found within its certainty subspace; otherwise, it will be searching a timeless (t = 0) particle “forever” within our temporal (t > 0) universe. In view of the certainty unit: 𝛥E and 𝛥t are mutually coexisted in which time is a forward dependent variable. Any changes of 𝛥E can “only” happen with an expenditure of a section time 𝛥t, but it “cannot” change the speed of time. Since the energy is “conserved,” 𝛥t is a section of time required to have the amount of 𝛥E within a certainty unit of (𝛥E, 𝛥t). In other words, 𝛥E and 𝛥t can be traded; for example, a wider variance of 𝛥E is traded for a narrower 𝛥t.
Nevertheless, time has been treated as an “independent” variable for decades, as normally assumed by scientists. But whenever a section of time 𝛥t has been used, it is not possible to bring back the “original” moment of 𝛥t, even though it is possible to reproduce the same section of 𝛥t. This similar as we reconstructed a damaged car, but we cannot bring back the “original” car that has been crashed. And this is precisely the “price of time” to pay for everything within our universe. Then my question is that if time is a forward dependent variable with respect to its subspace, how can we “curve” the space with time? Similarly, we are coexisted with time, how can we get back the moment of time that has passed by?
Since certainty subspace changes with bandwidth 𝛥𝜐 as illustrated in Figure 16, in which we see that as bandwidth 𝛥𝜐 decreases a very large certainty subspace can be created within our universe as depicted in Figure 16(a)–(c).
Size of certainty subspace enlarges rapidly as band width 𝛥𝜐 narrows. (a) shows a very small size of certainty subspace as the result of 𝛥𝜐 approaching to very wide. (b) shows the size of certainty subspace reduces as 𝛥𝜐 continues to reduce. And (c) shows a huge size certainty subspace can be created as band width 𝛥𝜐 narrows.
High resolution observation requires shorter wavelength but shorter wavelength inherently has broader bandwidth 𝛥𝜐 that creates a smaller certainty subspace, which can be used for high resolution wave front reconstruction [21]. On the other hand, for a larger certainty subspace, it required a narrower bandwidth of 𝛥𝜐 which has a larger certainty subspace for exploitation, such as applied to side looking radar imaging [20]. In which we see that the size of the certainty subspace can be manipulated by the bandwidth 𝛥𝜐 as will be shown in the following:
Since narrower bandwidth 𝛥𝜐 offers a huge certainty subspace that can be exploited for long distance communication, in which I have found that the certainty subspace is “in fact” the coherence subspace as I have discussed in the preceding. In other words, within a certainty subspace it exhibits a “point-pair certainty” or coherent property among them as illustrated in Figure 17. In other words, it has a high degree of certainty within a certainty subspace between points. This means that, if a photonic particle as it has been started at point u1, then it has a high degree of certainty that the particle to be found at the next instantly 𝛥t at u2, since distance is time within a temporal (t > 0) subspace.
Mutual certainty within a certainty subspace. u1(r1; t) and u2(r2; t) represent two arbitrary disturbances separated at distance d.
For example, given any two arbitrary complex disturbances u1(r1; t) and \tu2(r2; t), as long the separation between them is shorter than the radius 𝛥r of the certainty subspace as given by:
the disturbances between u1(r1; t) and u2(r2; t) are “certainly” related (or mutually coherence). For which the “degree of certainty” (i.e., degree of coherence) between u1 and u2 can be determined by the following equation:
where, “mutual certainty” (or mutual coherence) function between u1 and u2 can be written as:
Similarly, the respective “self certainty” (or self coherence) functions are, respectively, given by:
One of the interesting applications for certainty principle must be to synthetic aperture radar imaging as I have mentioned earlier is shown in Figure 18. In which we see an aircraft carried a side looking synthetic radar system shown in Figure 18(a), emitting a sequence of radar pulses scanned across the flight path of the terrain. The returned pulses are combined with local radar pulses, which are “mutual coherence” (i.e., high degree of certainty), to construct a recording format that can be used for imaging the terrain, for which a synthetic imagery is shown in Figure 18(b). In which we see a variety of scatters, including city streets, wooded areas, and farmlands and lake with some broken ice floes can also be identified on the right of this image. Since microwave antenna has a very narrow carrier bandwidth (i.e., 𝛥𝜐) and its certainty radius (i.e., d = c·𝛥t) or the coherence length can be easily reached to hundreds of thousand feet. In other words, a very large certainty subspace for complex-amplitude imaging (or for communication) can be realized.
Side-looking radar imaging within certainty subspace: (a) shows a side-looking radar scanning flight path; (b) shows an example of synthetic aperture radar imagery.
Finally I would address again within the certainty unite (𝛥p, 𝛥r) [i.e., equivalently for (𝛥E, 𝛥t) and (𝛥𝜐, t) unit] can be mutually traded. But it is the trading of 𝛥p for 𝛥r (or 𝛥E for 𝛥t and 𝛥𝜐 for 𝛥t) is physically visible, since time is not a physical substance but a forward constant dependent “variable” that we “cannot” manipulate. For which we see that the “section” of 𝛥t that has been “used” cannot get it back. In other words, we can get back the same amount 𝛥t, but “not” the same moment of 𝛥t, that has been expensed. As I have shown earlier, everything within our universe has a price, an amount of energy 𝛥E, and a section of time 𝛥t. Aside 𝛥E we can physically change, it is the moment of time 𝛥t which has been expensed that is “preventing” us to get it back, because that moment of 𝛥t is the “same moment” of time of our temporal (t > 0) universe that has been passed. And this is the “moment of time” 𝛥t within our temporal (t > 0) universe, once the “moment” passes by and we can never able to get it back.
In conclusion, I would point out that quantum scientists used amazing mathematical analyses added with their fantastic computer simulations provide very convincing results. But mathematical analyses and computer animations are virtual and fictitious, and many of their animations are “not” physically real; for example such as the “instantaneous and simultaneous” superimposing principle for quantum computing is “not” actually existed within our universe. One of the important aspects within our universe is that, one cannot get something from nothing there is always a price to pay, an amount of energy 𝛥E and a section of time 𝛥t. The important is that they are not free!
Since any science existed within our universe has time or temporal (t > 0), in which we see that any scientific law, principle, theory, and paradox has to comply with temporal (t > 0) aspect within our universe; otherwise, it may not be science. As we know that science is mathematics but mathematics is not equaled to science. In which we have shown that any analytic solution has to be temporal (t > 0); otherwise, it cannot be implemented within our universe. Which includes all the laws, principles, and theories have to be temporal (t > 0)?
Since it is our universe governs our science and it is not our science changes our universe. In which we have shown every hypothetical science, law, principle, and theory has be temporal (t > 0); otherwise, they are virtual and fictitious which cannot exist within our universe. Since time is a dependent variable coexisted with space, we have concluded that time is not an illusion but real, since we are real. As in contrast with most of the scientists, they believe that time is an independent variable and some of them even believe that time is an illusion?
Uncertainty principle is one of the most fascinating principles in quantum mechanics, yet Heisenberg principle was based on diffraction limited observation, it is not due to the nature of time or temporal (t > 0) nature of our universe. We have shown uncertainty increases with time, as in contrast with Heisenberg’s principle. We have also introduced a certainty principle, in which we have shown high degree of certainty within a certainty subspace can be exploited. For which we have shown that certainty subspace can be created within our temporal subspace for complex amplitude communication and imaging. Yet the important aspect of this chapter is that it is not how rigorous the mathematics is, but it is the physical realizably of science is, since mathematics is not science.
Risk is defined in terms of uncertain events which may have positive or negative effect on the project objectives. Risks include circumstances or situations, the existence or occurrence of which, in all reasonable foresight, results in an adverse impact on any aspect of the implementation of the project. Various definitions of risks are presented in Table 1.
Sl. no | Source | Definition |
---|---|---|
1 | Project Management Institute [10] | An uncertain event or a condition that if it occurs has a positive or negative effect on project objectives |
2 | Institute of Risk Management [7] | The combination of a probability of an event and its consequences |
3 | Association of Project Management Body of Knowledge [1] | Project Risk is an uncertain event or condition, that, if it occurs, has a positive/negative effect on project objectives. A risk has a cause and if it occurs, a consequence. |
4 | British Standard BS IEC 62198:2001 | Combination of probability of an event occurring and its consequences on project objectives |
5 | A probability or threat of damage, injury, liability, loss, or any other negative occurrence that is caused by external or internal vulnerabilities and that may be avoided through preemptive action. | |
6 | Fundamentals of Risk Management [9] | “A chance or possibility of danger, loss, injury or other adverse consequences” and the definition of risk is “exposed to danger.” However, taking risk can also result in positive outcome. A third possibility is risk related to uncertainty of outcome. |
7 | Adams [8] | Risk is the probability “that a particular adverse event occurs during a stated period of time, or results from a particular challenge.” |
8 | Philosophy of Risk [3] | Risk has been interpreted as Risk = hazard × exposure where Hazard is defined as the way in which a thing or situation can cause harm and exposure as the extent to which the likely recipient of the harm can be influenced by the hazard |
Definitions of risk.
Classification and definition of risks is furnished in Table 2.
Risk | Definitions |
---|---|
Pure risk | A risk which has chance of loss or no loss. Example. A building may get affected by fire or not. These are best covered by insurance |
Speculative risk | Involves chance of gain/loss. Example. A builder may take a risk by promoting a new venture depending upon the prevailing conditions in the vicinity of proposed project, but it may bring him gain/loss. |
Fundamental risk | These are external to a project and which, if they materialise, would be on a large scale and cannot be prevented. These risks are associated with major natural, economic, political or social changes and generate large scale losses. Examples are: Floods, earthquakes, fluctuation of exchange rates, etc. This risk may or may not be insurable. |
Particular risk | These are project specific risks and are identified within the parameters of a project and can be controlled during the implementation of a project, e.g. quality risks, safety risks, legal risks, etc. |
Classification of risks and their definitions.
Source: Project Risk Management, D Van Well-Stam et al., Kogan Page Publications, 2003.
Risk management is a planned and a structured process aimed at helping the project team make the right decision at the right time to identify, classify, quantify the risks and then to manage and control them. The aim is to ensure the best value for the project in terms of cost, time and quality by balancing the input to manage the risks with the benefits from such act. It is just a cost benefit analysis.
Risk management is a continuous process which is to be implemented in any project from inception to completion. However, in order to realise its full potential, risk management should be implemented at the earliest stage of a project, i.e. feasibility design and construction. Risk is an uncertain event or condition that, if occurs, has a positive or negative effect on a project’s objectives. Components of risk are the probability of the occurrence of an event and the impact of the occurrence of that event. There are many sources of uncertainty in construction projects, which include the performance of construction parties, resources availability, contractual relations, etc. because of which, construction projects face problems that cause delay in the project completion time. Success of a project is measured by its ability to get completed within the budgeted cost and time. These goals are interrelated where each parameter has an impact when other parameters get affected. An accurate cost estimating and scheduling should be performed in order to meet the overall budget and time deadline of a project. As such, risk management becomes an integral part of construction management which intends to identify and manage potential and unforeseen risks during the period of implementation of the project; hence, the necessity of risk management [5].
Definitions of risk management are presented in Table 3.
Sl. no | Definition of risk management |
---|---|
1 | https://en.wikipedia.org/wiki/Risk_management Risk Management is the identification, evaluation, and prioritization of risks followed by coordinated and an economical application of resources to minimise, monitor, and control the probability or impact of unfortunate events [6] or to maximize the realization of opportunities. |
2 | Nadeem Ehsan et al., 2012 Risk Management in a project involves the identification of influencing factors which could have negative impact on the the cost, schedule and quality objectives of the project and quantification of impact of potential risk and implementation of mitigation measures to minimise the potential impact of risk |
3 | Bahamid et al., 2017 Risk Management is defined as organized and comprehensive method tailored towards “ organizing”, “identifying” and “responding” to risk factors in order to achieve project goals. |
4 | www.stakeholdermap.com/risk/risk-management-construction Risk Management in construction consists of planning, monitoring and implemeting the measures needed to prevent exposure to risk. To do this, it is necessary to identify the hazards, assess the extent of risks, provision of measures to control the risks and to manage residual risk |
5 | www.vp-projects.kau.edu.sa Risk management is a systematic method of identifying, analysing, treating and monitoring the risks that are all involved in any activity/ process and is a systematic method that minimises the risks which may be an impediment to attainment of objectives |
6 | Cleden [4] Risk is exposure to the consequences of uncertainty. In a project context, it is the chance of something happening that will have an impact upon objectives. It includes the possibility of loss or gain, or variation from a desired or planned outcome, as a consequence of the uncertainty associated with following a particular course of action. Risk thus has two elements: the likelihood or probability of something happening, and the consequences or impacts if it does. |
7 | Project Risk Management, D Vanwell-Stam, Kogan Page India publications, 2004 The entire set of activities and measures that are aimed at dealing with risks in order to maintain control over a project |
8 | www.gpmfirst.com/risk.management-construction Risk Management is a means of dealing with uncertainty – identifying sources of uncertainty and the risks associated with them, and then managing those risks such that negative outcomes are minimized (or avoided altogether), and any positive outcomes are capitalised upon. |
9 | Risk Management in Construction Projects by NICMAR [2] Risk Management is the planned and structured process of bringing the project team make the right decisions at the right time by identifying, classifying and quantifying the risks and then for managing and controlling them, |
10 | Dr Patrick et al., 2006 retrieved from feaweb.aub.edu.lb Risk Management is “a systematic way of looking at areas of risk and consciously determining how each should be treated. It is a management tool that aims at identifying sources of risk and uncertainty, determining their impact, and developing appropriate management responses” |
11 | http://economictimes.indiatimes.com/definition/risk-management Risk Management refers to the practice of identifying potential risks in advance, analysing them and taking precautionary steps to reduce/curb the risk. |
Definitions of risk management.
Construction projects are extremely complex and fraught with uncertainty. Risk and uncertainty can potentially have damaging consequences for the construction projects. Hence, risk analysis and risk management has come to be a major feature of the project management in construction projects. Construction projects are unique, inherently complex, dynamic and risks emanate from multiple sources. The interests of individuals and organisations who are actively involved in a construction project may be positively or negatively affected depending upon the course which a project takes from concept to completion. Multiple stakeholders with varied experience and skills have different expectations and interests in the project which creates problems for smooth execution of the project. Risk management is a concept which many construction companies have never thought of, despite the fact that, the risks can be better controlled if they are identified in the first instance and a well-structured mitigation mechanism is in place. Risk management helps the key project participants namely the client, contractor/developer, consultant and supplier to meet their commitments and to minimise negative impacts on construction project performance in relation to cost, time and quality objectives. Success of a construction project is associated with three aspects of time, cost and quality outcomes.
Successful commissioning of any project, necessarily calls for sound planning on various fronts and getting the project executed in a competent manner. An organisation executing a project would have to reckon with the various risks to which the project may be exposed to and these have to be managed effectively. The construction industry, being vulnerable is potentially more prone to risks and uncertainties than any other industry. The process of taking a project from the conceptual stage to its final completion and putting into operation is quite complex and entails painstaking process at every stage. Construction industry is highly fragmented in that each of its participants—designers, constructors, planners, suppliers, etc. can be highly skilled in their own area and yet there is no clear perspective as to how all the players can come on the same platform for achieving the objectives.
Construction industry is also dependent on quality of its people rather than technology. The increasing technological complexity and more complex interdependencies and perpetual shortage of resources namely materials, equipment, technical/supervisory staff, finance, etc. calls for a comprehensive risk management framework which will insulate the risks of the participants to a great extent.
Given the nature of the construction sector, risk management is an extremely important process. It is most widely used in such of those projects where susceptibility to risks is very high and is characterised by planning, monitoring and controlling the risks in a more structured and formal manner. The most efficient method of identifying the risks is to study a project of similar size which was executed in the recent past which gives an insight into the failure/success of the project. In order to be sure that the project objectives are met, the portfolio of risks associated with all stakeholders should be considered across the project life cycle (PLC). In later stages, risk management when applied systemically helps to control those critical elements which can negatively impact project performance. Keeping track of identified threats will result in early warnings to the project manager if any of the objectives, time, cost or quality, are not being met. There are a plethora of risks which are to be identified in the construction industry and which can be faced in each construction project at any point of time regardless of its size and scope. Frequent change in scope is one of the major risks in any construction project. If revised scope or design is implemented, it can have effect in the form of additional resources of time and cost. Early project completion may be as troublesome as delays in a schedule. Completing too early which may be a result of insufficient planning or design problems can lead to a low quality of final product and increased overall cost. Thus it is important to keep a balance in the concept of time–cost-quality trade-off, which more widely is becoming an important issue for the construction sector. Risks may vary depending on the project scope, types and are to be treated accordingly.
Risk management process is shown in Figure 1.
Risk management process.
Risk identification, the first step in the risk management process is usually informal and is performed in various ways, depending on the organisation and the project team. Identification of risks relies mostly on past experience and study of similar executed projects. This being a preliminary stage, a combination of tools and techniques may be used to identify the risks in any project. Here are many methods that fit specific types of challenges and projects especially at identification stage. Risks and threats may be difficult to eliminate, but when they have been identified, it becomes easy to take actions and have control over them. Risk management will be more effective if the source of the risks have been identified and allocated before any problems occur. The main purpose of risk management is that the stakeholders should prepare for potential problems that can occur unexpectedly during the course of a project. Risk management will not only facilitate anticipating problems in advance, but also preparing oneself for the potential problems that may occur unexpectedly. Handling potential threats is not only a way to minimise the losses within a project, but also a way to transform risks into opportunities which can lead to economic and financial profitability. The purpose of identifying risks is to obtain a list of risks which has got the potential to have a cascading effect on the progress of project and different techniques are applied for managing/mitigating the same. In order to find all potential risks which might impact a specific project, different techniques are applied. The project team should use a method they are familiar with so that the exercise will be effective. Effective identification of risks is the first step to a successful risk management.
Parameter | Methodology |
---|---|
Documentation reviews | A structured review of project documentation, study of history of execution of similar projects and quality of plans as well as the consistency between those plans and project requirements/ assumptions would be an indicator of risks in the project |
Information gathering techniques |
|
Identification of risks: tools and techniques.
Tools and techniques for risk identification are presented in Table 4.
Various risks that confront a construction industry are not limited to and include financial, economical, political, legal environmental, technical, contractual, planning/scheduling, design, quality operational labour, stakeholder safety and security, logistics and construction.
Risk assessment is the second stage in the risk management process where collated data is analysed for potential risks. Risk assessment is described as short listing of risks starting from low impact highest impact on the project, out of all threats mentioned in the identification phase. Risk assessment consists of qualitative risk assessment and qualitative risk assessment.
This involves registration of identified risks in a formal manner. A risk register is used for formalising this process which is not limited to the following
Classification and reference
Description of the risk
Relationship of the risk to other risks
Potential impact
Likelihood of occurrence
Risk response/mitigation strategy
Allocation of risks to stakeholders.
Classification is an aid to identifying the source of risk. Examples are furnished below (Table 5).
Risk | Classification |
---|---|
Environmental | Site conditions, health and safety issues at site |
Contractual | Client, contractor, sub-contractor, etc. |
Design | Planning permission, preliminary and detailed design, etc. |
Classification of risk and its reference.
Referencing refers to unique reference number given for each of the identified risks.
This involves giving a brief description of the risk. The description must be unique in order to avoid confusion with similar risks in the risk management process.
In any project, it is extremely rare that any activity is independent of activities which occurs concurrently or consequentially and this will always be the case for risks also for successful implementation of risk management,
Impact of risk on a project is measured in terms of cost and quality. Since this assessment is done at an early stage of the project, information may not be available to accurately predict the impact of risk on the project. At this stage, the risk is classified suitably and accordingly high impact risks are to be given more fundamental consideration than that of medium/low/negligible risks by ranking the impact of risks on a scale of 1 (low) to 10 (high).
Based on intuition and experience, the likelihood of occurrence (P) of risks and its impact (I) is to be given on a suitable scale ex. 1–10 (1 refers to low probability and 10 refers to high probability). The risk factor for each of the identified risks is calculated by the formula RF = P + I – (P*I) (where the values of P and I are brought on a scale of 0–1 by dividing the values with 10).
This action is taken to reduce, eradicate or to avoid the identified risks. The most common among the risk mitigation methods are risk avoidance, risk transfer, risk reduction and risk sharing. Based on the competency in handling the risks, the identified risks are allocated to respective stakeholders who will be responsible for addressing those risks.
This risk assessment is normally taken for such of those risks which are classified are high/critical/unmanageable as per the qualitative risk assessment. The purpose of this assessment is to find the amount of contingency to be inserted in the estimate for the risks undergoing this assessment so that in case the risks occur, there would be sufficient budgeted amount to overcome the extra expenditure.
Quantitative methods need a lot of analysis to be performed. This analysis should be weighed against the effort and outcomes from the chosen method. Complex and larger projects require more in depth analysis as compared to projects which are small in size. The purpose of carrying out quantitative analysis is to estimate the impact of a risk in a project in terms of scope, time, cost and quality. The suitability of this analysis is more for medium and large projects as these projects have more complex risks as compared to smaller projects.
The detailed quantitative assessment of risk is the one which is identified as risk analysis. In undertaking quantitative assessment, the potential impact of risks in terms of time, cost and quality is quantified. While preparing the estimate, it is generally split into two distinct elements, namely (1) base estimate of those items which are known and a degree of certainty exists and (2) contingency allowance for all uncertain elements of a project. Historically, contingencies have been calculated on a rule of thumb basis varying from 5 to 10% on risk-free base estimate. By adopting risk management approach, contingencies are set up to reflect realistically the risks that are inherent in the project. When used correctly, contingency allowances ensure that expenditure against risks is controlled. The methods for quantitative risk assessment are described below.
The Monte Carlo method is based on statistics which are used in a simulation to assess the risks. This is a statistical technique whereby randomly generated data is used within predetermined parameters and produce realistic project outcomes. The overall project outcome is predicted by randomly simulating a combination of values for each risk and repeating the calculation a number of times and all outcomes are recorded. After completing the simulations required, the average is drawn from all of the outcomes, which will constitute the forecast for the risk. It is important to realise that parameters and appropriate distribution within which the random data is simulated is itself a series of subjective inputs. Accurate and realistic project outcomes will not be generated if inaccurate parameters are set. Different scenarios are generated by simulation are used for forecasting, estimations and risk analysis. Data from already executed projects is normally collected for simulation purpose. The data for variables is presented in terms of pessimistic, most likely and optimistic scenarios depending upon the risks encountered, i.e. pessimistic value means lot of risks and optimistic value means least risks. The result from this method is a probability of a risk to occur is often expressed as percentage. The most common way of performing the Monte Carlo simulation is to use the program Risk Simulator Palisade Software, where more efficient simulations can be performed.
This is a method used to demonstrate the variable impact on the whole caused by a change in one or more element or risk. It is used to test the robustness of choices made where rankings have been established, particularly when those rankings are considered to be marginal. It can identify the point where variation in one parameter will affect decision making. A typical method for carrying out sensitivity analysis is by use of a spider diagram which shows the areas in the project which are the most critical and sensitive The higher the level of uncertainty a specific risk has, the more sensitive it is concerning the objectives. In other words, the risk events which are the most critical to the project are the most sensitive and appropriate action needs to be taken (Heldman, 2005). Disadvantage with this analysis is that the variables are considered separately, which means that there is no connection between them (Perry, 1986 and Smith et al.. 2006). The method requires a project model in order to be analysed with computer software. According to Smith et al. (2006), the project stands to be benefited if the analysis is carried out in the initial phases of a project in order to focus on critical areas during the execution of the project.
Decision tree analysis is commonly used when there is sequence of interrelated possible courses of action and future outcomes in terms of time and cost. This method of analysis is commonly used when certain risks have an exceptionally high impact on the two main project objectives, i.e. time and cost. Where probabilities and values of potential outcomes are known or can be estimated, they are used for quantification to provide a more informed basis for decision making. Each decision process expected value (EV) which forms the basis for decision making process. A sample problem on decision tree is given in Table 6.
Method | Design time (months) | Construction period in months and probabilities | Total time (construction period + design time) (months) |
---|---|---|---|
Construction management | 2 | 15 (0.6) = 9 18(0.4) = 7.2 Total 16.2 months | 18.2 |
Design and construct | 3 | 12(0.3) = 3.6 Total = 13.8 months 14(0.5) = 7 16(0.2) = 3.2 | 16.8 |
Traditional method | 8 | 10(0.3) = 3 12(0.7) = 8.4 Total 11.4 months | 19.4 |
Problem on decision tree.
This can be depicted in the form of decision trees and the expected value (EV) in terms of time for each of the three scenarios is furnished. The least of this i.e. construction management will be preferred since it consumes less time.
Multiple estimating using risk analysis (MERA) attempts to provide a range of estimates. These are presented as risk free base estimate, average risk estimate (ARE) and maximum likely risk estimate (MLRE). ARE is the sum of risk free base estimate and average risk allowance and MLRE is the sum of ARE and maximum risk allowance.
MERA attempts to finds a level i.e. the estimate that has a 50% chance of being successful. This is known as average risk estimate (ARE) which is found out by multiplying the average allowance with average probability of occurrence. Maximum risk allowance is found out by multiplying the maximum allowance with maximum probability of occurrence of that risk. This is added to ARE to get MLRE which is the estimate that has 90% chance of not being exceeded.
The output of quantitative risk assessment is presented in Table 7.
Parameter | Outputs |
---|---|
Probabilistic Analysis of project | Estimates are made of potential project schedule and cost outcomes listing the possible completion dates and costs with their confidence levels. This output is described as cumulative distribution and also risk tolerances for permitting quantification of cost and time contingency reserves. Contingency reserves bring the risk of overshooting stated project objectives to acceptable levels to the organisation |
Prioritised list of quantified risks | This list includes risks that pose the greatest threat or present the greatest opportunity in a project. These risks also have the greatest impact on cost contingency |
Trends in quantitative risk analysis results | As the risk analysis is repeated, a trend becomes apparent that leads to conclusions affecting risk responses, Historical information on project’s schedule, cost, quality and performance reflects new insights gained through quantitative process. This takes the form of quantitative risk analysis report. |
Quantitative risk assessment: outputs.
The risk response will be in the form of mitigation by adopting necessary strategies in respect of positive and negative risks which is furnished below (Tables 8–10).
Risk mitigation strategy | Description |
---|---|
Risk avoidance | Risk avoidance involves changing the project management plan to eliminate the threat entirely. The project manager may isolate the project objectives that are in jeopardy. Examples: (a) Extending the schedule of an activity; (b) Changing the strategy or reducing the scope of work; (c) Changes in clauses of contract regarding abnormal price rise of any material or dealing with extra quantum of work. |
Risk transfer | Risk transfer requires shifting some or all of the negative impact of a threat along with ownership of the response to a third party. Examples are
|
Risk reduction | Risk reduction implies reduction in the probability and consequence of an adverse risk event to be within acceptable threshold limits. Conducting detailed tests or choosing a more stable supplier are some examples. Risk reduction is adopted where the resultant increase in costs is less than the potential loss that could be caused by the risk being mitigated. Examples are:
|
Risk acceptance | This strategy is adopted when it is not possible to eliminate all risks from a project. This strategy indicated that the project team had decided not to change the project management plan or is unable to identify any other suitable response strategy. This requires no action except to document the strategy leaving the project team to deal with risks as they occur |
Strategies for mitigating negative risks.
Risk mitigation strategy | Description |
---|---|
Exploit | This strategy is selected for risks with positive impacts where the organisation wishes to ensure that the opportunity is realised. This strategy seeks to eliminate the uncertainty associated with a particular risk by ensuring that the opportunity is exploited. Examples are assigning the most talented resources of the organisation to the project to reduce the time for completion or providing at a lower cost than originally planned |
Share | Sharing a positive risk involves allocating some or all of the ownership of the opportunity to a third party capable of capturing the opportunity for the benefit of the project. Risk sharing, joint ventures, etc. are examples of this strategy |
Enhance | This strategy is used to enhance the positive impact of an opportunity. Identifying and maximising key drivers of risks may increase their probability of occurrence. Examples are adding more resources to an activity for completing it before scheduled time |
Accept | Accepting an opportunity means willing to take advantage if it comes along, but not pursuing it actively. |
Contingent response strategies | Some responses are designed for implementation only if certain events occur. It is appropriate for the project team to prepare a contingency response plan that will be executed under certain predefined conditions if there will be sufficient warning to implement the plan |
Expert judgement | Expert judgement is from knowledgeable individuals pertaining to the actions to be taken on a specific and a defined risk. |
Risk mitigation strategies for positive risks/opportunities.
Source: Project Risk Management, Van Well Stam et al. 2008.
Sl. No | Contents |
---|---|
1 | Identified risk. Their descriptions, areas of project affected, their causes and how they affect project objectives |
2 | Risk owners and assigned responsibilities |
3 | Prioritised list of project risks based on the outputs from quantitative analysis reports |
4 | Agreed upon response strategies and specific actions taken to implement the strategy |
5 | Triggers, symptoms and warning signs of risks occurrence |
6 | Fallback plans as a reaction to a risk that has occurred and primary response proved to be inadequate |
7 | Contingency reserves to be calculated based on quantitative risk analysis of the project and the threshold risk of the organisation. |
Contents of risk response: outputs.
Inputs to monitoring and controlling of risks are presented in Table 11.
Tools and Techniques for monitoring and controlling risks are furnished in Table 12.
Parameter | Inputs |
---|---|
Risk register | The key inputs to risk register includes identified risks and owners of risk, agreed upon risk responses, specific actions to be implemented, symptoms/warning signs of any risk, residual/secondary risks, list of low priority risks and contingency measures in terms of time/cost |
Risk management plan | The risk management plan should contain risk tolerances, assignment of manpower including bearer of risk, time and other resources to project risk management |
Work performance information | Work performance information related to various performance results is to be quantified in terms of deliverable status, schedule progress and costs incurred. |
Performance reports | Performance reports will be analysed for variance analysis, earned value data and forecasting the likely date of completion of project |
Parameter | Explanation |
---|---|
Risk reassessment | Monitoring and controlling of risks will result in identification of new risks, reassessment of current risks and closing of risks that are not a threat to project. Project risk assessment is to be performed regularly. The frequency and depth of assessment depends on how the project progresses relative to the objectives. |
Risk audits | The purpose of risk audits is to examine and document the effectiveness of risk responses in dealing with identified risks and their root causes as well as effectiveness of the risk management process meetings. A separate risk audit meeting may be held or it may be included in routine project review meetings. |
Earned value analysis | Variance analysis is done by comparing the planned results with actual. Trends in execution of a project are reviewed using performance information and based on earned value analysis, deviation from cost and schedule targets is determined which may indicate potential impact of threat/opportunities. |
Technical performance measurement | This measures technical accomplishments during project execution and will help in forecasting degree of success in achieving the project scope and it may expose the degree of technical risk faced by the project |
Reserve analysis | This compares the amount of contingency reserves available at any time to the amount of risk remaining in the project to determine whether the reserves are adequate |
Status meetings | Project risk management should be an agenda item at all status review meetings. The amount of time for any item will depend on risks that have been identified, their priority and difficulty of response. Frequent discussions about risk make it more likely that concerned stakeholders will identify risks and opportunities. |
To maximise the efficiency of risk management, the risk management process should be continuously developed during the entire project.
The benefits from risk management finally go to the stakeholders involved. A clear understanding and awareness of potential risks in the project contributes to better management of risks by suitable mitigation techniques. Another benefit of working with risk management is increased level of control over the whole project and more efficient problem solving processes which can be supported on a more genuine basis
Risk management when conducted effectively, reduce sudden surprises. The advantage with risk management is that the stakeholders are aware as to the risk that they have to bear among all the risks that have been identified in a project and can prepare themselves accordingly, should any eventuality occur. No doubt, this formal exercise may translate into extra cost for an activity, but if taken in holistic manner, the benefits will far outweigh the costs. This has another advantage in that there is no passing of buck as risks are either shared/retained or transferred depending upon the ability of the stakeholder to handle the risk. The three approaches to risk management are normally risk natural firm which does not invest much in risk management but is still aware of important risk, risk averse firm where no investments are made and the last one is risk seeker wherein the organisation is prepared to face all risks and is often called gambler. The outcome of the objectives of project naturally depends upon the path adopted by the firms in their approach to risk management.
The fact that there are manifold risks which can be identified in any construction project is explained by their size and complexity. Bigger the project is, the larger the number of potential risks that may be faced.
Occurrence of risk is stimulated by several factors. Most often the risks faced in any project are financial, environmental (surrounding location of project and overall regulations), time, design and quality. The technology used for construction and the internal environment also contributes to risk which can have substantial bearing on the outcome of a project.
Risks are directly proportional to complexity of a project. Bigger and more complex a project is, the more resources are required to complete it. In spite of identifying all potential risks, there might be more potential threats. Therefore, the project team should not solely focus on management of those identified risks but also be alert for any new potential risks which may arise during execution.
Risk management is a tool for managing risks in a project and a project manager should be prepared for managing uncertainties not included in a risk management plan.
Effective management of risky project demands rapid and realistic predictions of alternative courses of action and positive decision making and requires flexible attitudes and procedures.
Perception of severity and frequency of occurrence of risk is to be done in tandem between the stakeholders. This will eliminate lot of unnecessary correspondence as well as misunderstanding and friction between the stakeholders
Insurance is just one aspect of risk mitigation and it cannot absorb all the risks. Insurance is project specific and it should be taken as per the needs of client/contractor. Other ways of risk mitigation needs to be explored.
Adoption of good project management practices like proper planning and implementation, willingness of stake holders to share the risks in the project is essential for success of a project
Executing a complex project requires meticulous planning, i.e. planning to the smallest details, and this can be achieved through concerted dedication from the concerned stakeholders.
Risks are to be thoroughly studied and understood before bidding for the project.
Special care should be taken regarding the seasonal variation of labourers, so that the construction activities does not get delayed due to shortfall in manpower resources during execution, which can have adverse effects on cost and time
Proper risk allocation techniques should be framed between the stakeholders so that in the event of occurrence of a risk, this will eliminate doubts as to which stakeholder should address the risk
Given its complexity, risk management is a very important process in construction projects. It is most widely used in those projects which exhibits high level of uncertainty. Formal planning, assessment and monitoring/control process characterises risk management in such projects.
Risk management procedures should be initiated in the early stages of the project where planning and contracting of work, together with the preliminary capital budget are being chalked out. In later stages, Risk management applied systemically, helps to control those critical elements which can have negative impact on project performance.
Keeping track of identified threats, will result in early warnings to the project manager if any of the objectives, time, cost or quality, is being met or not.
Risks in complex construction projects can be mitigated by entering into various agreements like execution, operation/maintenance, etc.
Proper risk strategy formulation and research is necessary based on real life experiences so that identification of potential risks and providing solutions can produce effective and efficient risk strategies to overcome impacts of risk events.
Risk identification is the first step in the risk management process. It means that the identification of risks which is informal relies mostly on past experience of similar executed projects and that of advice from experts. There are a good number of methods for identifying the risks in a project and a combination of methods may be used for identification of risks in a project.
Handling potential threats is not only a way to minimise losses within the project, but also a way to transform risks into opportunities, which can lead to economical profitability and finally, .it is suggested that if risks are given due care at all stages of the project, stakeholders will be showered with manifold benefits subsequent to commissioning of project
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