Summary of test conditions for esterification experiments.
--\x3e\n
Due to the nature of the multiphase reaction, the efficiency or rate of biodiesel production relies heavily on two primary factors: (i) the kinetics of catalyzed transesterification or esterification reactions and (ii) the hydrodynamics of liquid-liquid mixing promoted by reactor design and operation. In order to arrive at a high-efficiency and optimized biodiesel reactor, these two fundamental features must be understood. To date, a large quantity of biodiesel research works has been carried out in many different aspects, such as production rate and the quality of biodiesel products derived from different feedstocks, kinetic studies to find optimal reaction conditions for achieving higher yields, and use of enzyme and heterogeneous catalysts as an alternative to the conventional homogeneous catalysts [6–11]. Most kinetic works reported biodiesel conversion profiles as a function of reaction time under specific reaction conditions and for specific types of reactor design and operation. As such, the reported kinetic data essentially reflect the combined performance of both reaction kinetics and hydrodynamics of liquid-liquid reaction systems.
\nDespite its importance to the development of high-performance reactors, the knowledge of hydrodynamics or mass-transfer interfacial area (ae) between the two immiscible reactants during biodiesel reaction is very limited. Only one study by Stamenkovic et al. [12] relates to the interfacial area in the biodiesel production process. In their work, the effect of agitation intensity during the base-catalyzed transesterification of sunflower oil was investigated under a specific reaction condition, that is, 20°C and alcohol-to-oil ratio of 6:1. There are no other studies reporting the interfacial area for the acid-catalyzed reaction system.
\nTherefore, the objectives of this work are: (i) to extend knowledge of interfacial area formed between immiscible reactants during the acid-catalyzed esterification reaction which can be used for the design of a high-efficiency reactor, (ii) to investigate the role of process parameters on interfacial area in the esterification process, and (iii) to develop an empirical correlation for interfacial area estimation as a function of process parameters. To achieve these objectives, a series of esterification experiments were performed using a stirred reactor operated under variable ranges of reaction conditions (Table 1). The experimental results were obtained in forms of free fatty acid (FFA) conversion profiles which were subsequently used for determining the interfacial area values.
Process parameter | \nRange | \n
---|---|
Reaction temperature (°C) | \n45–65 | \n
Agitation speed (rpm) | \n200–400 | \n
Methanol-to-oil ratio (mol:mol) | \n3:1–9:1 | \n
Catalyst concentration (wt%) | \n0.5–2.0 | \n
Free fatty acid concentration (%) | \n5–30 | \n
Type of free fatty acid | \nOleic acid | \n
Type of catalyst | \nSulfuric acid | \n
Summary of test conditions for esterification experiments.
Two sets of chemicals were used in the experiments: (i) reactants and an acid catalyst for the esterification reaction and (ii) supporting chemicals for liquid sample analysis. For esterification experiments, canola oil was used as the base ingredient of oil feedstock. Oleic acid (90%) from Sigma-Aldrich (Oakville, Ontario) was used as the representative of free fatty acids (FFAs) commonly found in the feedstock. A predetermined amount of oleic acid was added to the base canola oil in order to simulate low-quality feedstock. Sulfuric acid (98%) was used as the acid catalyst, and methanol (99.98%) was chosen to represent the alcohol reactant. Both sulfuric acid and methanol were purchased from Fisher Scientific (Ottawa, Ontario). For liquid sample analysis, toluene (99.9%), isopropyl alcohol (99.9%), and potassium hydroxide (0.1 N) were used for titrations to determine the acid number or FFA content of the oil phase.
\nThe mass-transfer interfacial area (ae) and reaction kinetics between oil feedstock and methanol were determined by carrying out esterification experiments in a bench-scale reaction system. As shown in Figure 1, the reaction system consists of a 500-mL glass reactor that is jacketed for heating/cooling (Ace Glass Inc., USA), a mechanical agitator powered by a variable-speed drive (Cole-Parmer, Canada), and a water bath with a temperature controller/circulator (Cole-Parmer, Canada). The reactor was designed for operating pressures and temperatures of up to 35 psig and 100°C, respectively. The reactor head has three connecting ports: one for the mechanical agitator, one for sampling collection, and one for temperature measurement. A glass bearing with PTFE coupling was connected to the reactor head to accommodate the agitator. The sampling port was equipped with a silicone rubber septum, thus making possible the collection of liquid samples without interrupting the reaction progress. A K-type thermocouple connected to a handheld meter was used for monitoring reaction temperature. During the experiments, a heating medium (i.e., water from the temperature-controlled water bath) was circulated through the reactor jacket in order to keep reaction temperature constant.
A schematic diagram of the bench-scale reaction system for esterification experiments.
The experiments were conducted in two different modes: (i) esterification tests with a well-defined interfacial area between oil feedstock and methanol, and (ii) esterification tests with the complete mixing between the two reactants. The first mode of experiments provided the true kinetic features of the esterification reaction, while the second gave the reaction performance that integrates both kinetic and hydrodynamic effects of the reaction system.
\nFor the experiments with a fixed interfacial area (first mode), the canola oil was mixed with oleic acid to simulate a low-quality feedstock containing different levels of FFA. A 250 mL of the prepared feedstock was then transferred into the 500-mL glass reactor and maintained at a desired reaction temperature. An impeller or agitator was placed in the middle of this oil phase and set at a particular mixing speed in order to keep the oil phase homogenized but yet the oil-surface undisturbed. Meanwhile, a predetermined amount of H2SO4 (catalyst) was mixed with methanol to form a catalyst/methanol mixture with a desired catalyst concentration. For each experimental run, a 93 mL of catalyst/methanol mixture was used to ensure an excessive amount of methanol (more than 40 mol/mol ratio) available for reacting with FFA in the oil phase. Prior to the reaction, the catalyst/methanol mixture was heated to the desired reaction temperature in a water bath. Once the reaction temperature was reached, the methanol mixture was transferred into the glass reactor to start the esterification reaction. In order to keep the interface between the oil phase and the methanol phase undisturbed, a separating funnel was used to smoothly transfer the preheated catalyst/methanol mixture into the reactor. For each experiment, the reaction temperature was controlled by the water bath. The reaction was timed until it reached its equilibrium. During the experiment, a series of samples were collected from the oil phase at different time intervals. Each sample was transferred into a test tube and then immersed in cold water at 4°C to quench the reaction immediately. For better separation of the final mixture, the samples were centrifuged for 5 min at 3000 rpm, and then, the top layer sample was collected and sent for analysis.
\nFor the experiments with the complete mixing (second mode), each esterification experiment also began with the preparation of low-quality feedstock by mixing canola oil and oleic acid at a specific ratio. The FFA content of the prepared feedstock was analyzed in terms of acid number in accordance with the ASTM D974-04 standard, the details of which are provided in the next subsection. Following the preparation, a known amount of feedstock was charged to the reactor and heated to the desired reaction temperature with an accuracy of ±1°C. The feedstock was also stirred by the agitator at a fixed speed. Once the reaction temperature was reached, a predetermined amount of methanol/sulfuric acid mixture (with a given catalyst concentration) was rapidly injected into the reactor to start the esterification reaction. Prior to injection, this alcohol/catalyst mixture was preheated to the reaction temperature in order to avoid unwanted fluctuation in reaction temperature, especially at the beginning of the test. Each experimental run was carried out for at least 70 min at the desired temperature and agitation speed. A series of liquid samples (3 mL) were collected from the reactor at a regular time interval during the experiment. These liquid samples were then analyzed for their acid number so as to determine the depletion of FFA as a function of time.
\nA 3-mL liquid sample collected from the reactor was transferred to a test tube where 6 mL of de-ionized water was added. The tube was then capped and shaken vigorously to promote complete contact between water and the sample. This allowed the methanol and catalyst to combine with water, thus separating them from the sample. After being shaken, the test tube was placed in a centrifuge operating at 4000 rpm for 10 min. The centrifugal force helped develop two liquid layers, that is, the top layer for oil and the bottom layer for a mixture of water, methanol, and catalyst. The top layer was then withdrawn from the test tube for FFA content analysis by ASTM D974-04. A 2-mL sample was taken from the oil phase, weighed for its mass, and then dissolved in a 100-mL titration solvent (a mixture of toluene, water, and isopropyl alcohol with a volumetric mixing ratio of 100:1:99). Then, p-naphtholbenzein (the titration indicator) was added into the sample which was eventually titrated with 0.1 N potassium hydroxide (KOH) solution. Results from titration were then used for calculating the acid number (in mg KOH/g oil) based on the following equation:
\nwhere A is the volume of KOH solution required for the titration of the sample in mL, B is the volume of KOH solution required for the titration of 100 mL of titration solvent in mL, M is the molarity of the KOH solution, and W is the weight of the sample in grams. The acid number was then converted to a FFA content value.
\nData obtained from each esterification experiment were composed of a set of FFA content values (or acid numbers) taken at different reaction times. These data were subsequently used for determining mass-transfer interfacial area (ae) formed during esterification reaction. The following demonstrates how kinetic and mass-flux equations were used for the analysis of ae.
\nThe rate of esterification reaction is essentially the rate of FFA conversion into fatty acid methyl ester (FAME). With the stoichiometric ratio of 1:1, the conversion rate can be expressed as a function of reactant concentrations (i.e., CFFA for free fatty acid and CAlc for alcohol):
\nwhere k is the reaction rate constant varying with reaction temperature. Because an excess amount of alcohol for reaction was used in this experimental study, the conversion rate can be rewritten in the pseudo–first-order form:
\nwhere
where ae is the interfacial area per unit volume of the reaction system. By combining Eqs. (3) and (4), the mass-transfer flux can be written as a function of FFA concentration:
\nBecause the magnitude of constant
where
Integrating the above equation results in the following equation:
\nwhere CFFA,0 is the initial FFA concentration. To determine ae under a given reaction condition, a plot between
The effect of reaction temperature was observed from the experiments carried out at three different temperatures: 45°C, 55°C, and 65°C and for oil feedstock containing 5%, 15%, and 30% FFA. Other experimental conditions were fixed at 0.5 wt% H2SO4 catalyst, 6:1 methanol-to-oil ratio, and 300 rpm agitation speed. Results in Figure 2a, b show that the conversion of FFA proceeded rapidly at the beginning of the reaction period. As much as 80% conversion (based on initial FFA concentration) was observed within the first 20 min. Then, the conversion rate diminished significantly when FFA conversion approached the plateau. Both figures also show that the FFA conversion rate (or slope of FFA conversion profiles at the first reaction period) increased with reaction temperature regardless of the initial FFA concentration. The increasing conversion rate was quantified and presented in terms of percent improvement compared to the conversion rate at 45°C, as shown in Figure 3. It appears that the conversion rate could be enhanced as much as 160% when the reaction temperature was raised from 45 to 65°C. Both kinetic and hydrodynamic factors (ae) contribute to the rate improvement. Between the two factors, the kinetics plays the major role in controlling the conversion of FFA.
\nAs for the role of temperature on ae, results in Figure 2c show that ae increases with temperature. The ae could increase approximately 30 - 60% when the temperature increases from 45°C to 65°C. This is due to the decrease in liquid density and viscosity with increasing temperature. The dependence of density and viscosity of oil on temperature was previously reported by [14, 15]. According to [16], the rate of any reactions in an immiscible liquid-liquid system is controlled by the mass transfer of chemical species across the interface between the two liquids. For the FFA esterification, mass-transfer interfacial area is dependent upon the dispersion level of methanol in the oil feedstock, which is usually controlled by mixing characteristics (e.g., flow, shear, and turbulence). Such mixing characteristics are ultimately dependent upon physical properties, especially the density and viscosity of liquids. This is supported by the fact that Reynolds number (Re) is a function of density and viscosity [17]. Therefore, an increase in reaction temperature causes the density and viscosity of liquids to drop, thus allowing methanol to easily disperse in oil.
\nEffect of temperature on esterification performance: (a) FFA conversion profiles for initial FFA concentration of 5%; (b) FFA conversion profiles for initial FFA concentration of 30%; and (c) interfacial area at different temperatures (300 rpm agitation speed, 0.5 wt% of catalyst, 6:1 methanol-to-oil ratio).
Hydrodynamic and kinetic contributions for effect of reaction temperature on FFA conversion rate (300 rpm agitation speed, 0.5 wt% of H2SO4, and 6:1 mol/mol methanol-to-oil ratio).
The effect of methanol-to-oil ratio was investigated under 0.5 wt% H2SO4, 300 rpm agitation speed, 45°C and 65°C reaction temperature, for three different FFA concentrations (5%, 15%, and 30%). It was found that methanol-to-oil ratio has a significant impact on FFA conversion performance. An increase in methanol-to-oil ratio enhances the conversion rate for all test conditions. From Figure 4a, b FFA conversion rate could be improved by as much as 30 - 35% when methanol-to-oil ratio increases from 3:1 to 9:1. The increasing conversion rate is due to a significant increase in interfacial area ae. As shown in Figure 4c, d, the area ae increases by 2.1 5.3 times when methanol-to-oil ratio increases from 3:1 to 9:1. This is due to the greater amount of methanol available for dispersion in the oil phase.
\n\nBased on the analysis shown in Figure 5, the improvement in FFA conversion rate due to increasing methanol-to-oil ratio is primarily caused by ae, not reaction kinetics. This is because the increasing methanol-to-oil ratio leads to more dispersion of methanol, which in turn provides a greater interfacial area for esterification reaction. On the contrary, increasing the amount of methanol in oil does not result in any changes in concentration of methanol at the reaction interface; thus, the reaction kinetics is unaffected.
\nEffect of methanol-to-oil ratio on esterification performance: (a) FFA conversion profiles at 45°C for initial FFA concentration of 30%; (b) FFA conversion profiles at 65°C for initial FFA concentration of 30%; (c) interfacial area plotted against methanol-to-oil ratio at 45°C; and (d) interfacial area plotted against methanol-to-oil ratio at 65°C (300 rpm agitation speed, 0.5 wt% of catalyst).
The effect of agitation speed on FFA conversion was investigated by varying the agitation speed from 200 to 300 rpm and further to 400 rpm. The investigation was done for three different FFA concentrations (5%, 15%, and 30%) at 0.5 wt% H2SO4, 6:1 methanol-to-oil ratio, and 45°C and 65°C. Results show that agitation speed has an impact on FFA conversion performance. As shown in Figure 6a, b, increasing agitation speed from 200 to 300 rpm leads to a significant increase in the conversion rate. For instance, the rate could be improved by 150% at the reaction temperature of 45°C for oil feedstock containing 5% FFA (Figure 7). However, it should be noted that raising agitation speed further from 300 to 400 rpm leads to only a small increase in the rate of FFA conversion. It is apparent that the improvement under fixed reaction conditions (excluding agitation speed) was solely caused by an increase in ae, not reaction kinetics. Raising agitation speed induces more turbulence, thereby creating smaller size methanol droplets in oil and in turn providing a greater ae for esterification reaction. The increase in ae is evidenced in Figure 6c, d.
\nHydrodynamic and kinetic contributions for the effect of methanol-to-oil ratio on FFA conversion rate: (a) reaction temperature of 45°C; (b) reaction temperature of 65°C (test conditions = 300 rpm agitation speed and 0.5 wt% of H2SO4).
It should be noted that the degree of rate improvement also depends on reaction temperature. This exhibits an interaction effect between agitation speed and temperature. The effect of agitation speed at a lower reaction temperature (45°C) is much greater than the effect at the higher temperature (65°C). This behavior can be explained by comparing the magnitude of interfacial area formed at these two temperatures. From Figure 6c, d it can be seen that the higher temperature (65°C) tends to offer a greater area, ae, than the lower temperature (45°C) does. This is due to the reduction in density and viscosity of liquid mixtures with an increase in temperature. Therefore, increasing agitation speed at 65°C, where the higher ae is already established, does not yield a much greater improvement in conversion rate.
\nEffect of agitation speed on esterification performance: (a) FFA conversion profiles at 45°C for initial FFA concentration of 5%; (b) FFA conversion profiles at 65°C for initial FFA concentration of 30%; (c) interfacial area plotted against agitation speed at 45°C; and (d) interfacial area plotted against agitation speed at 65°C (6:1 methanol-to-oil ratio, 0.5 wt% of catalyst).
As mentioned previously, raising agitation speed beyond 300 rpm does not have much impact on the conversion rate of FFA. This can be explained by considering the conventional power correlation for agitated reaction. According to McCabe et al. [18], the power number, NP, for the typical stirred reactor (i.e., an index that reflects friction preventing the impeller rotation) tends to decrease with the Reynolds number (Re), especially at low and moderate turbulence regions, while it remains virtually unaffected by the Reynolds number under highly turbulent conditions. This suggests that the effect of agitation speed should be gradually diminished with the increasing level of system turbulence. This behavior was observed in this work. The ae increases considerably due to the significant reduction in friction on the impeller when agitation speed increases from 200 to 300 rpm. However, when agitation speed increases from 300 to 400 rpm, despite the increase in turbulence, the friction on the impeller does not diminish much further. This indicates that the friction may reach its minimum for a given system geometry that accounts for the design and dimensions of the reaction system as well as the type of fluid in the reactor. As such, the degree of mixing does not improve, causing the interfacial area, ae, to remain unchanged. This in turn results in the stabilization of the FFA conversion rate.
\nHydrodynamic and kinetic contributions for the effect of agitation speed on FFA conversion rate (0.5 wt% of H2SO4 and 6:1 methanol-to-oil ratio).
The effect of catalyst concentration was studied by varying H2SO4 concentration from 0.5 to 2.0 wt%. The effect was examined for three FFA concentrations (5%, 15%, and 30%) and two reaction temperatures (45°C and 65°C) at 6:1 methanol-to-oil ratio and 300 rpm agitation speed. Results in Figure 8a, b show that an increase in H2SO4 concentration leads to an enhancement of FFA conversion performance for all test conditions. For instance, the conversion rate can be improved by 70% when H2SO4 concentration increases from 0.5 to 2.0 wt% at 45°C. Both hydrodynamics and kinetics were found to contribute to such improvement as shown in Figure 9. The hydrodynamic contribution (or an increase in ae) results from the reduction in liquid viscosity. Note that the hydrodynamic contribution is not as significant as the kinetic contribution at a higher temperature (i.e., 65°C). This is supported by the results in Figure 8c, d which show that the change in ae with H2SO4 concentration is relatively small at the higher temperature.
Effect of catalyst concentration on esterification performance: (a) FFA conversion profiles at 45°C for initial FFA concentration of 30%; (b) FFA conversion profiles at 65°C for initial FFA concentration of 30%; (c) interfacial area plotted against catalyst concentration at 45°C; and (d) interfacial area plotted against catalyst concentration at 65°C (300 rpm agitation speed, 6:1 methanol-to-oil ratio).
The effect of FFA concentration was examined over ranges of operating conditions, that is, 45 - 65°C reaction temperature, 200 - 400 rpm agitation speed, 3:1 - 6:1 methanol-to-oil ratio, and 0.5 - 2.0 wt% catalyst concentration. The results in Figure 10 show that FFA concentration plays an important role in the FFA conversion performance. An increase in FFA concentration causes the conversion rate to decrease. However, it should be noted that the hydrodynamics of the reaction system in this case does not contribute to the changes in FFA conversion rate since the interfacial area, ae, does not vary with FFA concentration in oil (Figure 11). It seems that the unaffected ae is a result of the invariable physical properties of oil feedstock. According to Kulkarni et al. [19] and Zhou et al. [20], the viscosity and density of canola oil (base ingredient of oil feedstock) and oleic acid (FFA) are in similar ranges. The density of canola oil and oleic acid is 0.912 and 0.90 g/mL, while the viscosity of canola oil and oleic acid is 33.4 and 34.8 cP, respectively. Due to the similar properties of the two ingredients, increasing FFA concentration from 5 to 30% does not considerably alter the viscosity and density of the oil mixture. The unchanged oil properties help establish the stable turbulence level within the reaction system, thus keeping the interfacial area, ae, relatively unchanged.
Hydrodynamic and kinetic contributions for the effect of catalyst concentration on FFA conversion rate: (a) reaction temperature of 45°C; (b) reaction temperature of 65°C (test conditions = 300 rpm agitation speed and 6:1 methanol-to-oil ratio).
Effect of FFA concentration on esterification performance: (a) based on temperature data series; (b) based on agitation speed data series; (c) based on catalyst concentration data series; and (d) based on methanol-to-oil ratio data series.
The effects of process parameters on the interfacial area reported earlier were correlated in the form of an empirical equation that would facilitate the design of a biodiesel reactor. Development of the correlation was focused primarily on four important parameters controlling the interfacial area between methanol and oil feedstock, that is, reaction temperature, agitation speed, methanol-to-oil ratio, and catalyst concentration. Firstly, the effect of each process parameter was regressed individually to arrive at the best mathematical expression offering simplicity and the lowest data deviation. Four types of mathematical expressions were considered in this screening step: linear, exponential, logarithmic, and power forms. It was found that most parametric effects can be described by linear expressions, except for the effect of agitation speed, the nonlinear behavior of which can be expressed well by the logarithmic equation. Values of average absolute deviation (%AAD) and R2 derived from individual regressions are summarized in Table 2.
\nBased on the selected equations in the screening step, an overall empirical correlation that combines all four parametric effects was formulated and expressed in the following form:
\nwhere k1 to k6 are correlation constants, T is reaction temperature in K, n is agitation speed in rpm, R is methanol-to-oil ratio in mol/mol, and c is catalyst concentration in wt%. The calculated interfacial area (ae) is presented in m2/m3 units. Based on all experimental data obtained in this study, a computer-software package called “NLREG” was used for regression to arrive at values of correlation constants (k1 to k6) as listed in Table 3. It should be noted that this empirical correlation is capable of predicting methanol-oil interfacial area with an average absolute deviation (AAD) of 12%. A good agreement between the calculated ae values and experimental data can be observed from a parity plot in Figure 12, which shows a R2 value of 0.88.
\nEffect of FFA concentration on mass-transfer interfacial area: (a) based on temperature data series; (b) based on agitation speed data series; (c) based on catalyst concentration data series; and (d) based on methanol-to-oil ratio data series.
Process parameter | \nMathematical expression | \n%AAD | \nR2 | \n
---|---|---|---|
Temperature (T) | \n4.06 | \n0.91 | \n|
Methanol-to-oil ratio (R) | \n13.34 (45°C) 14.68 (65°C) | \n0.89 (45°C) 0.82 (65°C) | \n|
Agitation speed (n) | \n16.81 (45°C) 3.64 (65°C) | \n0.83 (45°C) 0.96 (65°C) | \n|
Catalyst concentration (c) | \n11.09 (45°C) 11.09 (65°C) | \n0.69 (45°C) 0.48 (65°C) | \n
Results of individual regressions for parametric effects.
Correlation constant | \nValue | \n
---|---|
k1 | \n3.85 | \n
k2 | \n32.50 | \n
k3 | \n198.04 | \n
k4 | \n51.98 | \n
k5 | \n53.01 | \n
k6 | \n−1465.72 | \n
Correlation constants for Eq. (9).
Parity plot between experimental data and calculated interfacial area.
Mass-transfer interfacial area plays an important role in the performance of acid-catalyzed esterification-based biodiesel production. Increasing the interfacial area enhances rate of biodiesel production (or rate of free fatty acid conversion). The magnitude of the interfacial area varies with process parameters, except free fatty acid content in oil feedstock. The interfacial area increases with increasing reaction temperature, agitation speed, methanol-to-oil ratio, and catalyst concentration, thus resulting in the increase in biodiesel production rate.
\nThe increase in the biodiesel production rate may or may not be solely attributed to the available interfacial area. It can be attributed to both reaction kinetics and interfacial area. The interfacial area is the exclusive contributor to the increase in the biodiesel production rate when the agitation speed or the methanol-to-oil ratio increases. Both interfacial area and kinetics contribute to the enhancement of biodiesel production rate when the reaction temperature or the catalyst concentration increases.
\nThe authors would like to thank the Natural Sciences and Engineering Research Council of Canada (NSERC) and the City of Regina for their financial support and collaboration.
\nOne of the most intriguing variables in science must be time. Without time, there would be no physical substances, no space, and no life. In other words, time and substance have to coexist. In the chapter, I will start with Einstein’s relativity theory to show his famous energy equation, derived from in which we will show that energy and mass can be traded. Since mass is equivalent to energy and energy is equivalent to mass, we see that mass can be treated as an energy reservoir. We will show any physical space cannot be embedded in an absolute empty space and it cannot have any absolute empty subspace in it and empty space is a timeless (i.e., t = 0) space. We will show that every physical space has to be fully packed with substances (i.e., energy and mass), and we will show that our universe is a subspace within a more complex space. We see that our universe could have been one of the many universes outside our universal boundary. We will also show that it takes time to create a subspace, and it cannot bring back the time that has been used for the creation. Since all physical substances exist with time, all subspaces are created by time and substances (i.e., energy and mass). This means that our cosmos was created by time with a gigantic energy explosion, for which every subspace coexists with time. This means that without time the creation of substances would not have happened. We see that our universe is in a temporal (i.e., t > 0) space, and it is still expanding based on current observation. This shows that our universe has not reached its half-life yet, as we have accepted the big bang creation. We are not alone with almost absolute certainty. Someday, we may find a planet that once upon a time had harbored a civilization for a period of light-years. In short, the burden of a scientific postulation is to prove a solution exists within our temporal universe; otherwise it is not real or virtual as mathematics is.
Professor Hawking was a world renowned astrophysicist, a respected cosmic scientist, and a genius who passed away last year on March 14, 2018. As you will see, our creation of universe was started with the same root of the big bang explosion, but it is not a sub-universe of Hawking’s. You may see from this chapter that the creation of temporal universe is somewhat different from Hawking’s creation.
The essence of Einstein’s special theory of relativity [1] is that time is a relative quantity with respect to velocity as given by
where
We see that the time window
Equivalently, Einstein’s relativity equation can be shown in terms of relative mass as given by
where m is the effective mass (or mass in motion) of a particle, mo is the rest mass of the particle, v is the velocity of the moving particle, and c is the speed of light. In other words, the effective mass (or mass in motion) of a particle increases at the same amount with respect to when the relative time window increases.
With reference to the binomial expansion, Eq. (2) can be written as
By multiplying the preceding equation with the velocity of light c2 and noting that the terms with the orders of v4/c2 are negligibly small, the above equation can be approximated by
which can be written as
The significance of the preceding equation is that m − mo represents an increase in mass due to motion, which is the kinetic energy of the rest mass mo. And (m − mo)c2 is the extra energy gain due to motion.
What Einstein postulated, as I remembered, is that there must be energy associated with the mass even at rest. And this was exactly what he had proposed:
where ε represents the total energy of the mass and
the energy of the mass at rest, where v = 0 and m ≈ mo.
We see that Eq. (6) or equivalently Eq. (7) is the well-known Einstein energy equation.
One of the most enigmatic variables in the laws of science must be “time.” So what is time? Time is a variable and not a substance. It has no mass, no weight, no coordinate, and no origin, and it cannot be detected or even be seen. Yet time is an everlasting existing 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 includes our universe. Therefore, when one is dealing with science, time is one of the most enigmatic variables that are ever present and cannot be simply ignored. Strictly speaking, all the laws of science as well every physical substance cannot exist without the existence of time.
On the other hand, energy is a physical quantity that governs every existence of substance which includes the entire universe. In other words without the existence of energy, there would be no substance and no universe! Nonetheless based on our current laws of science, all the substances were created by energy, and every substance can also be converted back to energy. Thus energy and substance are exchangeable, but it requires some physical conditions (e.g., nuclei and chemical interactions and others) to make the conversion start. Since energy can be derived from mass, mass is equivalent to energy. Hence every mass can be treated as an energy reservoir. The fact is that our universe is compactly filled with mass and energy. Without the existence of time, the trading (or conversion) between mass and energy could not have happened.
Let us now start with Einstein’s energy equation which was derived by his special theory of relativity [1] as given by
where m is the rest mass and c is the velocity of light.
Since all the laws in science are approximations, for which we have intentionally used an approximated sign. Strictly speaking the energy equation should be more appropriately presented with an inequality sign as described by
This means that in practice, the total energy should be smaller or at most approaching to the rest mass m times square of light speed (i.e.,
In view of Einstein’s energy equation of Eq. (8), we see that it is a singularity-point approximation and timeless equation (i.e., t = 0). In other words, the equation needs to convert into a temporal (i.e., t > 0) representation or time-dependent equation for the conversion to take place from mass into energy. We see that, without the inclusion of time variable, the conversion would not have taken place. Nonetheless, Einstein’s energy equation represents the total amount of energy that can be converted from a rest mass m. Every mass can be viewed as an energy reservoir. Thus by incorporating with the time variable, the Einstein’s energy equation can be represented by a partial differential equation as given by [2]
where
One of the important aspects in Eq. (10) must be that energy and mass can be traded, for which the rate of energy conversion from a mass can be written in terms of electromagnetic (EM) radiation or Radian Energy as given by [4]
where
Similarly the conversion from energy to mass can also be presented as
The major difference of this equation, as compared with Eq. (11), must be the energy convergent operator −∇·S(v), where we see that the rate of energy as in the form of EM radiation converges into a small volume for the mass creation, instead of diverging from the mass. Since mass creation is inversely proportional to
Incidentally, black hole [5, 6] can be considered as one of the energy convergent operators. Instead the convergent force is relied more on the black hole’s intense gravitational field. The black hole still remains an intriguing physical substance to be known. Its gravitational field is so intense even light cannot be escaped.
By the constraints of the current laws of science, the observation is limited by the speed of light. If light is totally absorbed by the black hole, it is by no means that the black hole is an infinite energy sink [6]. Nonetheless, every black hole can actually be treated as an energy convergent operator, which is responsible for the eventuality in part of energy to mass conversion, where an answer remained to be found.
In our physical world, every matter is a substance which includes all the elemental particles; electric, magnetic, and gravitation fields; and energy. The reason is that they were all created by means of energy or mass. Our physical space (e.g., our universe) is fully compacted with substances (i.e., mass and energy) and left no absolute empty subspace within it. As a matter of fact, all physical substances exist with time, and no physical substance can exist forever or without time, which includes our universe. Thus, without time there would be no substance and no universe. Since every physical substance described itself as a physical space and it is constantly changing with respect to time. The fact is that every physical substance is itself a temporal space (or a physical subspace), as will be discussed in the subsequent sections.
In view of physical reality, every physical substance cannot exist without time; thus if there is no time, all the substances which include all the building blocks in our universe and the universe itself cannot exist. On the other hand, time cannot exist without the existence of substance or substances. Therefore, time and substance must mutually coexist or inclusively exist. In other words, substance and time have to be simultaneously existing (i.e., one cannot exist without the other). Nonetheless, if our universe has to exist with time, then our universe will eventually get old and die. So the aspects of time would not be as simple as we have known. For example, for the species living in a far distant galaxy moving closer to the speed of light, their time goes somewhat slower relatively to ours [1]. Thus, we see that the relativistic aspects of time may not be the same at different subspaces in our universe (e.g., at the edge of our universe).
Since substances (i.e., mass) were created by energy, energy and time have to simultaneously exist. As we know every conversion, either from mass to energy or from energy to mass, cannot get started without the inclusion of time. Therefore, time and substance (i.e., energy and mass) have to simultaneously exist. Thus we see that all the physical substances, including our universe and us, are coexisting with time (or function of time).
Let us define various subspaces in the following, as they will be used in the subsequence sections:
An absolute empty space has no time, no substance, and no coordinate and is not event bounded or unbounded. It is a virtual space and timeless space (i.e., t = 0), and it does not exist in practice.
A physical space is a space described by dimensional coordinates, which existed in practice, compactly filled with substances, supported by the current laws of science and the rule of time (i.e., time can only move forward and cannot move backward; t > 0). Physical space and absolute empty space are mutually exclusive. In other words, a physical space cannot be embedded in an absolute empty space, and it cannot have absolute empty subspace in it. In other words, physical space is a temporal space in which time is a forward variable (i.e., t > 0), while absolute empty space is a timeless space (i.e., t = 0) in which nothing is in it.
A temporal space is a time-variable physical space supported by the laws of science and rule of time (i.e., t > 0). In fact, all physical spaces are temporal spaces (i.e., t > 0).
A spatial space is a space described by dimensional coordinates and may not be supported by the laws of science and the rule of time (e.g., a mathematical virtual space).
A virtual space is an imaginary space, and it is generally not supported by the laws of science and the rule of time. Only mathematicians can make it happen.
As we have noted, absolutely empty space cannot exist in physical reality. Since every physical space needs to be completely filled with substances and left no absolutely empty subspace within it, every physical space is created by substances. For example, our universe is a gigantic physical space created by mass and energy (i.e., substances) and has no empty subspaces in it. Yet, in physical reality all the masses (and energy) existed with time. Without the existence of time, then there would be no mass, no energy, and no universe. Thus, we see that every physical substance coexists with time. As a matter of fact, every physical subspace is a temporal subspace (i.e., t > 0), which includes us and our universe.
Since a physical space cannot be embedded within an absolute empty space and it cannot have any absolute empty subspace in it [7], our universe must be embedded in a more complex physical space. If we accepted our universe is embedded in a more complex space, then our universe must be a bounded subspace.
How about time? Since our universe is embedded in a more complex space, the complex space may share the same rule of time (i.e., t > 0). However, the complex space that embeds our universe may not have the same laws of science as ours but may have the same rule of time (i.e., t > 0); otherwise our universe would not be bounded. Nevertheless, whether our universe is bounded or not bounded is not the major issue of our current interest, since it takes a deeper understanding of our current universe before we can move on to the next level of complex space revelation. It is however our aim, abiding within our current laws of science, to investigate the essence of time as the enigma origin of our universe.
One of the most intriguing questions in our life must be the existence of time. So far, we know that time comes from nowhere, and it can only move forward, not backward, not even stand still (i.e., t = 0). Although time may somewhat relatively slow down, based on Einstein’s special theory of relativity [1], so far time cannot move backward and cannot even stand still. As a matter of fact, time is moving at a constant rate within our subspace, and it cannot move faster or slower. We stress that time moves at the same rate within any subspace within the universe even closer the boundary of our universe, but the difference is the relativistic time. Since time is ever existing, then how do we know there is a physical space? One answer is that there is a profound connection between time and physical space. In other words, if there is no time, then there would be no physical space. A physical space is in fact a temporal (i.e., t > 0) space, in contrast to a virtual space. Temporal space can be described by time, while virtual space is an imaginary space without the constraint of time. Temporal space is supported by the laws of science, while virtual space is not.
A television video image is a typical example of trading time for space. For instance, each TV displayed an image of (dx, dy) which takes an amount of time to be displayed. Since time is a forward-moving variable, it cannot be traded back at the expense of a displayed image (dx, dy). In other words, it is time that determines the physical space, and it is not the physical space that can bring back the time that has been expended. And it is the size (or dimension) of space that determines the amount of time required to create the space (dx, dy). Time is distance and distance is time within a temporal space. Based on our current constraints of science, the speed of light is the limit. Since every physical space is created by substances, a physical space must be described by the speed of light. In other words, the dimension of a physical space is determined by the velocity of light, where the space is filled with substances (i.e., mass and energy). And this is also the reason that speed of time (e.g., 1 s, 2 s, etc.) is determined by the speed of light.
Another issue is why the speed of light is limited. It is limited because our universe is a gigantic physical space that is filled with substances that cause a time delay on an EM wave’s propagation. Nevertheless, if there were physical substances that travel beyond the speed of light (which remains to be found), their velocities would also be limited, since our physical space is fully compacted with physical substances and it is a temporal (i.e., t > 0) space. Let me further note that a substance can travel in space without a time delay if and only if the space is absolutely empty (i.e., timeless; t = 0), since distance is time (i.e., d = ct, t = 0). However, absolute empty space cannot exist in practice, since every physical space (including our universe) has to be fully filled with substances (i.e., energy and mass), with no empty subspace left within it. Since every physical subspace is temporal (i.e., t > 0), in which we see that timeless and temporal spaces are mutually exclusive.
Strictly speaking, all our laws of physics are evolved within the regime of EM science. Besides, all physical substances are part of EM-based science, and all the living species on Earth are primarily dependent on the source of energy provided by the sun. About 78% of the sunlight that reaches the surface of our planet is well concentrated within a narrow band of visible spectrum. In response to our species’ existence, which includes all living species on Earth, a pair of visible eyes (i.e., antennas) evolved in us humans, which help us for our survival. And this narrow band of visible light led us to the discovery of an even wider band of EM spectral distribution in nature. It is also the major impetus allowing us to discover all the physical substances that are part of EM-based physics. In principle, all physical substances can be observed or detected with EM interaction, and the speed of light is the current limit.
Then there is question to be asked, why is the speed of light limited? A simple answer is that our universe is filled with substances that limit the speed of light. The energy velocity of an electromagnetic wave is given by [3]
where (μ, ε) are the permeability and the permittivity of the medium. We see that the velocity of light is shown by
where (μ0,ε0) are the permeability and the permittivity of the space.
In view of Eq. (13), it is apparent that the velocity of electromagnetic wave (i.e., speed of light) within an empty subspace (i.e., timeless space) is instant (or infinitely large) since distance is time (i.e., d = ct, t = 0).
A picture that is worth more than a thousand words [8] is a trivial example to show that EM observation is one of the most efficient aspects in information transmission. Yet, the ultimate physical limitation is also imposed by limitation of the EM regime, unless new laws of science emerge. The essence of Einstein’s energy equation shows that mass and energy are exchangeable. It shows that energy and mass are equivalent and energy is a form of EM radiation in view of Einstein’s equation. We further note that all physical substances within our universe were created from energy and mass, which include the dark energies [9] and dark matter [10]. Although the dark substances may not be observed directly using EM interaction, we may indirectly detect their existence, since they are basically energy-based substances (i.e., EM-based science). It may be interesting to note that our current universe is composed of 72% dark energy, 23% dark matter, and 5% other physical substances. Although dark matter contributes about 23% of our universe, it represents a total of 23% of gravitational fields. With reference to Einstein’s energy equation (Eq. (8)), dark energy and dark matter dominate the entire universal energy reservation, well over 95%. Furthermore, if we accept the big bang theory for our universe creation [11], then creation could have been started with Einstein’s time-dependent energy formula of Eq. (11) as given by
where [∇·S(v)] represents a divergent energy operation. In this equation, we see that a broad spectral band intense radian energy diverges (i.e., explodes) at the speed of light from a compacted matter M, where M represents a gigantic mass of energy reservoir. It is apparent that the creation is ignited by time and the exploded debris (i.e., matter and energy) starts to spread out in all directions, similar to an expanding air balloon. The boundary (i.e., radius of the sphere) of the universe expands at the speed of light, as the created debris is disbursed. It took about 15 billion chaotic light-years [12, 13, 14] to come up with the present state of constellation, in which the boundary is still expanding at the speed of light beyond the current observation. With reference to a recent report using the Hubble Space Telescope, we can see galaxies about 15 billion light-years away from us. This means that the creation process is not stopping yet and at the same time the universe might have started to de-create itself, since the big bang started, due to intense convergent gravitational forces from all the newly created debris of matter (e.g., galaxies and dark matter). To wrap up this section, we would stress that one of the viable aspects of Eq. (15) is the transformation from a spatially dimensionless equation to a space-time function (i.e., ∇·S); it describes how our universe was created with a huge explosion. Furthermore, the essence of Eq. (15) is not just a piece of mathematical formula; it is a symbolic representation, a description, a language, a picture, or even a video as may be seen from its presentation. We can visualize how our universe was created, from the theory of relativity to Einstein’s energy equation and then to temporal space creation.
Let us now take one of the simplest connections between physical subspace and time [15]:
where d is the distance, v is the velocity, and t is the time variable. Notice that this equation may be one of the most profound connections between time and physical space (or temporal space). Therefore, a three-dimensional (Euclidean) physical (or temporal) subspace can be described by
where (vx, vy, vz) are the velocities’ vectors and t is the time variable. Under the current laws of science, the speed of light is the limit. Then, by replacing the velocity vectors equal to the speed of light c, a temporal space can be written as
Thus, we see that time can be traded for space and space cannot be traded for time, since time is a forward variable (i.e., t > 0). In other words, once a section of time Δt is expended, we cannot get it back. Needless to say, a spherical temporal space can be described by
where radius r increases at the speed of light. Thus, we see that the boundary (i.e., edge) of our universe is determined by radius r, which is limited by the light speed, as illustrated in a composite temporal space diagram of Figure 1. In view of this figure, we see that our universe is expanding at the speed of light well beyond the current observable galaxies. Figure 2 shows a discrete temporal space diagram, in which we see that the size of our universe is continuously expanding as time moves forward (i.e., t > 0). Assuming that we have already accepted the big bang creation, sometime in the future (i.e., billions of light-years later), our universe will eventually stop expanding and then start to shrink back, preparing for the next cycle of the big bang explosion. The forces for the collapsing universe are mainly due to the intense gravitational field, mostly from giant black holes and matter that were derived from merging (or swallowing) with smaller black holes and other debris (i.e., physical substances). Since a black hole’s gravitational field is so intense, even light cannot escape; however, a black hole is by no means an infinite energy reservoir. Eventually, the storage capacity of a black hole will reach a limit for explosion, as started for the mass to energy and debris creation.
Composite temporal space universe diagram. 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.
Discrete temporal universe diagrams; t is time.
In other words, there will be one dominant giant black hole within the shrinking universe, to initiate the next cycle of universe creation. Therefore, every black hole can be treated as a convergent energy sink, which relies on its intense gravitation field to collect all the debris of matter and energies. Referring to the big bang creation, a gigantic energy explosion was the major reason for the universe’s creation. In fact, it can be easily discerned that the creating process has never slowed down since the birth of our universe, as we see that our universe is still continuingly expanding even today. This is by no means an indication that all the debris created came from the big bang’s energy (e.g., mc2); there might have been some leftover debris from a preceding universe. Therefore, the overall energy within our universe cannot be restricted to just the amount that came from the big bang creation. In fact, the conversion processes between mass and energy have never been totally absent since the birth of our universe, but they are on a much smaller scale. In fact, right after birth, our universe started to slow down the divergent process due to the gravitational forces produced by the created matter. In other words, the universe will eventually reach a point when overall divergent forces will be weaker than the convergent forces, which are mostly due to gravitational fields coming from the newly created matter, including black holes. As we had mentioned earlier, our universe currently has about 23% dark matter, which represents about 23% of the gravitational fields within the current universe. The intense localized gravitational field could have been produced from a group or a giant black hole, derived from merging with (or swallowing up) some smaller black holes, nearby dark matter, and debris. Since a giant black hole is not an infinite energy sink, eventually it will explode for the next cycle of universal creation. And it is almost certain that the next big bang creation will not occur at the same center of our present universe. One can easily discern that our universe will never shrink to a few inches in size, as commonly speculated. It will, however, shrink to a smaller size until one of the giant black holes (e.g., swallowed-up sufficient physical debris) reaches the big bang explosive condition to release its gigantic energy for the next cycle of universal creation. The speculation of a possible collapsing universe remains to be observed. Nonetheless, we have found that our universe is still expanding, as observed by the Doppler shifts of the distant galaxies at the edge of our universe, about 15 billion light-years away [12, 13, 14]. This tells us that our universe has not reached its half-life yet. In fact, the expansion has never stopped since the birth of our universe, and our universe has also been started to de-create since the big bang started, which is primarily due to convergent gravitational forces from the newly created debris (e.g., galaxies, black holes, and dark matter).
Relativistic time at a different subspace within a vast universal space may not be the same as that based on Einstein’s special theory of relativity [1]. Let us start with the relativistic time dilation as given by
where Δt′ is the relativistic time window, compared with a standstill subspace, Δt is the time window of a standstill subspace, v is the velocity of a moving subspace, and c is the velocity of light. We see that time dilation Δt′ of the moving subspace, relative to the time window of the standstill subspace Δt, appears to be wider as velocity increases. For example, a 1-s time window Δt is equivalent to the 10-s relative time window Δt’. This means that a 1-s time expenditure within the moving subspace is relative to about a 10-s time expenditure within the standstill subspace. Therefore, for the species living in an environment that travels closer to the speed of light (e.g., at the edge of the universe), their time appears to be slower than ours, as illustrated in Figure 3. In this figure, we see an old man traveling at a speed closer to the velocity of light; his relative observation time window appears to be wider as he is looking at us, and the laws of science within his subspace may not be the same as ours.
Effects on relativistic time.
Two of the most important pillars in modern physics must be Einstein’s relativity theory and Schrödinger’s quantum mechanics [15]. One is dealing with very large objects (e.g., universe), and the other is dealing with very small particles (e. g., atoms). Yet, there exists a profound connection between them, by means of the Heisenberg’s uncertainty principle [16]. In view of the uncertainty relation, we see that every temporal subspace takes a section of time Δt and an amount of energy ΔE to create. Since we cannot create something from nothing, everything needs an amount of energy ΔE and a section of time Δt to make it happen. By referring to the Heisenberg uncertainty relation as given by
where h is the Planck’s constant. We see that every subspace is limited by ΔE and Δt. In other words, it is the h region, but not the shape, that determines the boundary condition. For example, the shape can be either elongated or compressed, as long as it is larger than the h region.
Incidentally, the uncertainty relationship of Eq. (21) is also the limit of reliable bit information transmission as pointed out by Gabor in [17]. Nonetheless, the connection with the special theory of relativity is that the creation of a subspace near the edge of our universe will take a short relative time with respect to our planet earth, since Δt’ > Δt. The “relativistic” uncertainty relationship within the moving subspace, as with respect to a standstill subspace, can be shown as
where we see ΔE energy is conserved. Thus a narrower time-width can be achieved as with respect to standstill subspace. It is precisely possible that one can exploit for time-domain digital communication, as from ground station to satellite information transmission.
On the other hand, as from satellite to ground station information transmission, we might want to use digital bandwidth (i.e., Δv) instead. This is a frequency-domain information transmission strategy, as in contrast with time domain, which has not been exploited yet. The “relativistic” uncertainty relationship within the standstill subspace as with respect to the moving subspace can be written as
Or equivalently we have
in which we see that a narrower bandwidth Δv can be in principle use for frequency-domain communication.
Every physical (or temporal) subspace is created by substances (i.e., energy and mass), and substances coexist with time. In this context, we see that our universe was essentially created by time and energy and the universe is continuously evolving (i.e., changing) with time. Although relativistic time may not be the same at the different subspaces within our universe, the rule of time may remain the same. As for the species living closer to the speed of light, relativistic time may not be noticeable to them, but their laws of science within their subspace may be different from ours. Nonetheless, our universe was simultaneously created by time with a gigantic energy explosion. Since our universe cannot be embedded in an empty space, it must be embedded in a more complex space that remains to be found. From an inclusive point of view, mass is energy or energy is mass, which was discovered by Einstein almost a century ago [1]. And it is this basic fundamental law of physics that we have used for investigating the origin of time. Together with a huge energy explosion (i.e., big bang theory [11]), time is the igniter for the creation of our universe. As we know, without the existence of time, the creation of our universe would not have happened. As we have shown, time can be traded for space, but space cannot be traded for time. Our universe is in fact a temporal physical subspace, and it is continuously evolving or changing with time (i.e., t > 0). Although every temporal subspace is created by time (and substances), it is not possible for us to trade any temporal subspace for time. Since every physical substance has a life, our universe (a gigantic substance) cannot be excluded. With reference to the report from a recent Hubble Space Telescope observation [12, 13, 14], we are capable of viewing galaxies about 15 billion light-years away and have also learned that our universe is still by no means slowing down in expansion. In other words, our universe has still not reached its half-life, based on our estimation. As we have shown, time ignited the creation of our universe, yet the created physical substances presented to us the existence of time.
In view of the preceding discussion, we see that our universe is a time-invariant system (i.e., from system theory stand point); as in contrast with an empty space, it is a not a time-invariant system and it is a timeless or no-time space. We see that timeless solution cannot be directly implemented within our universe. Since science is a law of approximation and mathematics is an axiom of absolute certainty, using exact math to evaluate inexact science cannot guarantee its solution to exist within our temporal (i.e., t > 0) universe. One important aspect of temporal universe is that one cannot get something from nothing: There is always a price to pay; every piece of temporal subspace (or every bit of information [7]) takes an amount of energy (i.e., ΔE) and a section of time (i.e., Δt) to create. And the subspace [i.e., f(x, y, z; t), t > 0] is a forward time-variable function. In other words, time and subspace coexist or are mutually inclusive. This is the boundary condition and constrain of our temporal universe [i.e., f(x, y, z; t), t > 0], in which every existence within our universe has to comply with this condition. Otherwise it is not existing within our universe, unless new law emerges since laws are made to be broken. Thus we see that any emerging science has to be proven to exist within our temporal universe [i.e., f(x, y, z; t), t > 0]. Otherwise it is a fictitious science, unless it can be validated by repeated experiments.
In mathematics, we see that the burden of a postulation is first to prove if there exists a solution and then search for a solution. Although we hardly have had, there is an existent burden in science. Yet, we need to prove that a scientific postulation is existing within our temporal universe [i.e., f(x, y, z; t), t > 0]; otherwise it is not real or virtual as mathematics is. For example such as the superposition principle in quantum mechanics, in which we have proven [18] it is not existed within our temporal universe (i.e., t > 0), since Schrödinger’s quantum mechanics is timeless as mathematics is.
There is however an additional constrain as imposed by our temporal universe which is the affordability. As we have shown that everything (e.g., any physical subspace) existed within our universe has a price tag, in terms of an amount of energy ΔE and a section of time Δt (i.e., ΔE, Δt). To be precise, the price tag also includes an amount of “intelligent” information ΔI or an equivalent amount of entropy ΔS (i.e., ΔE, Δt, ΔI) [7]. For example, creation of a piece of simple facial tissue will take a huge amount of energy ΔE, a section of time Δt, and an amount of information ΔI (i.e., equivalent amount of entropy ΔS). We note that on this planet Earth, only humans can make it happen. Thus we see that every physical subspace (or equivalently substance) within our universe has a price tag (i.e., ΔE, Δt, ΔS), and the question is that can we afford it?
Within our universe, we can easily estimate there were billions and billions of civilizations that had emerged and faded away in the past 15 billion light-years. Our civilization is one of the billions and billions of current consequences within our universe, and it will eventually disappear. We are here, and will be here, for just a very short moment. Hopefully, we will be able to discover substances that travel well beyond the limit of light before the end of our existence, so that a better observational instrument can be built. If we point the new instrument at the right place, we may see the edge of our universe beyond the limit of light. We are not alone with almost absolute certainty. By using the new observational equipment, we may find a planet that once upon a time had harbored a civilization for a period of twinkle thousands of (Earth) years.
We have shown that time is one of the most intriguing variables in the universe. Without time, there would be no physical substances, no space, and no life. With reference to Einstein’s energy equation, we have shown that energy and mass can be traded. In other words, mass is equivalent to energy, and energy is equivalent to mass, for which all mass can be treated as an energy reservoir. We have also shown that a physical space cannot be embedded in an absolute empty space or a timeless (i.e., t = 0) space, and it cannot even have any absolute empty subspace in it. In reality, every physical space has to be fully packed with physical substances (i.e., energy and mass). Since no physical space can be embedded in an absolute empty space, it is reasonable to assume that our universe is a subspace within a more complex space, which remains to be found. In other words, our universe could have been one of the many universes outside our universal boundary, which comes and goes like bubbles. We have also shown that it takes time to create a physical space and the time that has been used for the creation cannot be brought back. Since all physical substances exist with time, all physical spaces are created by time and substances (i.e., energy and mass). This means that our cosmos was created by time and a gigantic energy explosion, in which we see that every substance coexists with time. That is, without time, the creation of physical substances would not have happened. We have further noted that our universe is in a temporal space and it is still expanding based on current observation. This shows that our universe has not reached its half-life yet, as we have accepted the big bang creation. And it is noted that we are not alone with almost absolute certainty. Someday, we may find a planet that once upon a time had harbored a civilization for a period of light-years. We have further shown that the burden of a scientific postulation is to prove it exists within our temporal universe [i.e., f(x, y, z; t), t > 0]; otherwise it is not real or virtual as mathematics is.
Finally, I would like to take this opportunity to say a few words on behalf of Professor Stephen Hawking, who passed away last year on March 14, 2018. Professor Hawking was a world-renowned astrophysicist, a respected cosmic scientist, and a genius. Although the creation of temporal universe started with the same root of the big bang explosion, it is not a subspace of Professor Hawking’s universe. You may see from the preceding presentation that the creation of temporal universe is somewhat different from Hawking’s creation. One of the major differences may be at the origin of big bang creation. My temporal universe was started with a big bang creation within a “non-empty” space, instead within of an empty space which was normally assumed.
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