Time and Energy, Inertia and Gravity The Relationship between Time, Aeleration, and Veloity and its Affet on Energy, and the Relationship between Inertia and Gravity Copyright 00 Joseph A. Rybzyk Abstrat Presented is a theory in fundamental theoretial physis that establishes the relationship between time and energy, and also the relationship between inertia and gravity. This theory abandons the onept that mass inreases as a result of relativisti motion and shows instead that the extra energy related to an objet undergoing suh motion is a diret result of the affet that the slowing of time has on veloity. In support of this premise, new formulas are introdued for aeleration and used in onjuntion with a relativisti time transformation fator to develop new equations for both kineti and total energy that replae those of speial relativity. These and subsequently derived equations for momentum, distane, aeleration, inertia, gravity, and others, establish a diret relationship between the presented theory and the priniples of an earlier theory, the millennium theory of relativity. A final onsequene of this theoretial analysis is the disovery of two new laws of physis involving aeleration, and the realization that a unified theory of physis is now possible.
Time and Energy, Inertia and Gravity The Relationship between Time, Aeleration, and Veloity and its Affet on Energy, and the Relationship between Inertia and Gravity Copyright 00 Joseph A. Rybzyk. Introdution This paper introdues a new physial siene that bridges the gap between lassial and relativisti physis. It provides the final piee of the puzzle started by Newton with his Prinipia in 687, and expanded by Einstein with his Speial Theory of Relativity in 905. What will be shown is the true relationship between aeleration, time, and veloity, and the affet this relationship has on energy and thus our pereption of other physial phenomena. We will see that time expansion is real and its affets on veloity and energy are real, but the affets on mass (see appendix A) and distane are only pereptual. We will aomplish this by evaluating and orreting the lassial formula for aeleration, and employ the new formula together with a relativisti transformation fator to diretly derive a orret equation for kineti energy. This new equation replaes both the Newtonian and Einsteinian equations for kineti energy and is subsequently used in the formulation of a new total energy equation that replaes Einstein s famous E = MC equation. In the proess, the limitations of the former formulas and equations will be learly demonstrated and their replaements validated. The final results of this work are new equations for aeleration, momentum, kineti and total energy, and transformation fators not diretly dependent on veloity. With these new equations it is no longer neessary to distinguish between lassial physis and relativisti physis. In their plae is the beginning of a new physis from whih future disoveries may be antiipated.. The Millennium Transformation Fator and Time Transformation In relativisti physis it is widely aepted and supported by evidene that time slows down in a moving frame of referene. The relationship of moving frame time relative to stationary frame time an be expressed by the time transformation formulas, t` t v () and, t t` () v Time Transformation where v is the relative veloity, is the speed of light, t` is moving frame time relative to stationary frame time, and t is time in the stationary frame. In the given equations t and t` an be used to represent a unit of time, or an interval of time. Also of note is the fat that the more familiar Lorentz transformation fators,
v (3) and, (4) v Lorentz Transformation Fators have been replaed by their respetive millennium theory of relativity equivalents 3 (see appendix B), v (5) and,. (6) v Millennium Transformation Fators In the past, these fators were normally assoiated with time and distane transformation. In the present work their use will be expanded to inlude modifiation of veloity and a numerial onstant assoiated with aeleration. 3. Constant Time and Relative Time Defined There is often onfusion about time transformation and the terms used to define stationary frame time vs. moving frame time. It should be understood that time in the moving frame is idential to time in the stationary frame. That is, time in both frames may be represented by the variable t. Thus time t is atually onstant time, or time that inreases at a onstant rate. Time t` then is atually relative time, or time whose rate of inrease is affeted by relative motion. It is used to show that time t in the moving frame is slower than time t in the stationary frame. Or stated another way, that onstant time in either frame has a redued rate relative to onstant time in the other frame as defined by the transformation formulas. From this point forward, it should be understood that when we say stationary frame time, we atually mean onstant time t, and when we say moving frame time, we atually mean relative time t`. 4. The New Kineti Energy Equation Although the lassial equation for kineti energy seems to be supported by the evidene for low values of veloity, it is refuted by the evidene for high values of veloity in the area that represents a signifiant fration of the speed of light. At the other end of the spetrum is the relativisti equation that seems to be supported by the evidene for veloities that are a signifiant fration of light speed, but as will be shown later, is not representative of very low veloities in the area of lassial physis. In fat, in both the real and theoretial sense, neither equation is truly orret at any veloity. The auses by whih this happened are as follows:. Relativisti effets were unknown during the development period of lassial physis. The problem is then ompounded by the manner in whih the lassial kineti energy equation is normally derived that in turn obsures its true meaning.. The relativisti effets, when disovered, were then used in an indiret derivation for the new kineti energy equation that in turn obsured the true meaning that equation. 3
To avoid suh problems we must derive the lassial equation in a manner that makes its true meaning unambiguous. Then with our knowledge of relativity it beomes possible to orret the equation in suh a manner as to make it properly represent the physial laws of nature along the entire range of valid veloities. In lassial physis the following formulas are given for momentum, and onstant aeleration: Where p is momentum, m is mass, and v is veloity, we are given, p mv (7) Where a is the rate of onstant aeleration, and t is the time interval, we are given, v at (8) and therefore, v a (9) t And lastly, where d is the distane traveled by an objet under onstant aeleration we are given, at d (0) Although these equations provide satisfatory results for Newtonian levels of veloity, none of them are truly orret at any veloity. For the moment we will defer treatment of the momentum equation and proeed with the equations for onstant aeleration. That is, if relativisti physis is a orret model for physial phenomena, then all of these equations and others to follow, inluding the lassial equation for kineti energy will have to be modified. Until now, however, no one has been suessful in figuring out how it ould be aomplished. The problems are many, and involve a very diffiult analysis due to irular relationships that involve many interdependent variables. To proeed we must first deide the order in whih the variables will be used. Additionally, we will need to make ertain assumptions that appear to be 4
reasonable and in agreement with the evidene. And finally, we must assure that the resulting irular arguments are self-enforing throughout the analysis and lead to orret final results. The first assumptions to be made involve the lassial formulas for onstant aeleration. The evidene shows that relative veloity inreases asymptotially and therefore equations, 8 and 9, annot be orret for onstant aeleration. If the rate of aeleration, a is onstant, and time t inreases at a onstant rate, then the instantaneous veloity v, given by equation 8, will also inrease at a onstant rate. Suh a result is of ourse inonsistent with the evidene and therefore in disagreement with the priniples of relativisti physis. On the other hand, where v is the instantaneous veloity, a is the rate of aeleration, and t` is the time interval, our analysis will show that, v a t` () and, v a () t` Constant Aeleration are the orret formulas for onstant aeleration. That is, sine t` inreases asymptotially at the same rate as v, the rate of aeleration will remain onstant as the veloity inreases toward. To verify this, in a omputer math program for example, we will first need to derive different forms of equations and, those that do not depend on the variable t`. This is beause, as seen in equation, time interval t` is itself dependent on the value of v. Suh treatment, however, must be deferred to a later point in the analysis. The forgoing is an example of the irular dependeny ommented on earlier. The subsript in the preeding equations is needed to distinguish between onstant aeleration and relative aeleration, whih ours simultaneously and is defined by, v a t (3) and, r v a r (4) t Relative Aeleration where a r is the rate of relative aeleration. These are nothing more than orret versions of equations 8 and 9 respetively, rewritten to show their true meanings. Thus, if t inreases at a onstant rate, and if v is asymptoti, a r the rate of aeleration relative to the stationary frame will derease as the veloity inreases toward. For onsisteny with the modifiations used in equations and, we must also modify the assoiated distane formula given in equation 0. This gives us, d t a ` (5) where the travel distane is denoted by the variable d. This hange, however, is insuffiient for arriving at a orret formula for the distane traveled by an objet or partile under onstant 5
aeleration. One of the problems involves the onstant, ½. This onstant is also affeted by the asymptotial nature of veloity. That is, as is approahed, further inreases in veloity approah 0. Thus, the distane traveled approahes vt`, and not ½ vt`. If this were the only onsideration, we would modify the onstant ½ so that its value approahes at a rate that is onsistent with the rate that v approahes. But there is another fator to onsider. One involving the energy required for the aeleration, and this too affets the required modifiation. In the interest of larity, this modifiation is best deferred to a later part of our analysis where suh modifiation an be more easily understood. Now, by using the right sides of equation 7 (p = mv) and equation 5 we an formulate a new formula where the temporary variable k a = momentum over distane traveled by an objet under onstant aeleration. Thus we have, ka ( mv) at` (6) By substituting v/t` from equation (a = v/t`) for a in the above equation, we obtain, v t t` k a mv ` (7) whih simplifies to, k a mv t` (8) Now, sine the lassial formula for kineti energy is, mv k (9) we an state, 6
ka k (0) t` and by substitution get, mv t` k () t` The reason for deriving the kineti energy equation in this manner is to make it lear what the various variables and onstant represent. This last version of the equation an now be evaluated from a relativisti perspetive and orreted to properly represent all values of veloity, v. At this point it is neessary to all upon the millennium transformation fator, previously introdued as expression 6. Referring now to figure, we an ompare the relativisti motion of a partile to the Newtonian motion when a onstant fore is applied. Whereas in Newtonian motion the veloity inreases without limit, in relativisti motion the veloity inreases asymptotially as the objet approahes the speed of light, and of ourse the speed of light is never exeeded. From what we understand about relativisti effets, the transformation fators 3 through 6, are mathematial definitions of the behavior. If time slows down in the moving frame of referene, it is not unreasonable to assume that this slowing of time diretly affets the veloity of the moving objet. Thus, as veloity inreases, time slows down ausing further inreases in veloity to require inreasingly greater amounts of energy. With respet to kineti energy this is a paradoxial ontradition of Newton s seond and third Laws of motion. Sine kineti energy is a diret funtion of veloity it would inrease at a slower rate along with the veloity inreases when at the same time it must inrease at an inreasingly greater rate along with the energy ausing the aeleration. Obviously it annot do both. Of the two hoies, reason and experiene support the view that the kineti energy must always equal the input energy. If we now refer to the lassial kineti energy equation 9, we an see there are only two variables to hoose from should we wish to modify the formula to bring it into onformane with the evidene. The hoies are, mass and, veloity. Einstein made what appeared to be a reasonable hoie at the time and seleted mass. If mass inreases with veloity, it would explain the observed behavior. This, it will be shown, appears to have been the wrong hoie and at very least results in an anomaly that is well hidden in the E = M equation, but is very apparent in the resulting relativisti kineti energy equation, K = M - M o. But even more than this, as the analysis ontinues the evidene builds in favor of the new theory thus hallenging the very premises upon whih Einstein s equations are founded. It will be shown now, that neither variable should be modified. This is not to say that the kineti energy equation itself should not be modified. 7
v Newtonian motion v = relativisti motion t FIGURE The veloity of a partile starting at rest when a onstant fore is applied. Referring bak to figure, and also to equations, 5, and, (repeated below) it an be seen that equation must be modified in suh a manner as to offset the relativisti effet that the motion has on veloity. v a () t` d t a ` (5) mv t` k () t` That is, if equation is to produe the orret result for kineti energy, the experiened relativisti effet on veloity must in the mathematial sense, be reversed. The obvious onlusion is that we must fator the veloity by the reiproal millennium fator, expression 6. If we are right, however, we must also fator the frational onstant, ½, in equations 5 and. This onlusion is supported as follows: We an assume from equation 5 that the distane, d, traveled by an objet under onstant aeleration should = ½ a t`. Referring to equation, we an see that this is the same as saying distane ½ vt`. In other words, the distane traveled by an objet under onstant aeleration should = ½ times the veloity, v, ahieved for the interval, t`, during whih the aeleration takes plae. However, when we study the relativisti motion urve in figure, we an see that as veloity inreases toward, there is less and less hange in veloity over an interval of time. Stated another way, as veloity inreases toward, the distane traveled by the objet approahes vt`, and not ½ vt`. This implies that the onstant ½ should inrease toward a value of. But sine at this point, v, is not only near the value of but, with our first hange, its value is being dramatially inreased by the millennium fator, the onstant 8
½ must atually be modified to derease rather than inrease in order to ompensate and bring the final result into agreement with the evidene that supports relativity. When these hanges are properly implemented, the distane will progress toward vt` as orretly assumed while at the same time the resulting kineti energy equation is a orret equation for all values of v. Proeeding now with the neessary modifiations to equation, we derive, m v t` v k v, () t` whih redues to, m v k. (3) Kineti Energy v v This equation replaes both, the Newtonian and Einstein s equations for kineti energy. (see appendix C) With it, and other equations presented in this work, there is no longer a need to differentiate between lassial and relativisti physis. For onveniene purposes, this new physis will be referred to as millennium physis from this point forward. 5. The New Total Energy Equation If we now add the internal energy term, m to equation 3, we arrive at the millennium equation for total energy that replaes Einstein s E = M equation. Thus, where E is the total energy for an objet or partile in motion, m v E m, (4) Total Energy v v produes a orret result for all values of v. In view of these findings, it is no longer appropriate to refer to mass, m, as a rest mass, or for that matter the term, m as the rest energy of an objet. As an be seen, mass appears to be unaffeted by veloity. (This assumption will be explored further in setion.) Nonetheless, the present theory is in agreement with the relativisti onept that matter does ontain internal energy as defined by the expression, m. 9
6. Comparison of the Millennium Equations with the Relativity Equations Under lose evaluation it will be seen that the relativity equation for kineti energy beomes errati at low values of v. This behavior is apparent at veloities as high as 00,000 km/hr and beomes very notieable as the veloity drops below 000 km/hr. It ontinues to intensify as the veloity drops below 00 km/hr, and at approximately 6-0 km/hr, the equation produes a result of zero. Obviously then, this equation is not reliable at those veloities where most of our experiene resides. There we have to rely on the Newtonian equation for aurate results. The Newtonian equation, however, is non-relativisti and therefore losses auray as the veloity inreases. Subsequently, neither equation provides a good program for analyzing the entire range of veloities. To make matters worse, it is unlear where reliane on the Newtonian equation should end and reliane on the relativity equation should begin. Comparison of Energy Equations 400 00 000 Kineti Energy 800 600 Rybzyk Einstein 400 00 0 0 5 0 5 0 5 30 35 40 45 50 Km per hour Figure Comparison of the millennium kineti energy equation to the speial relativity equation. 0
Figure is an atual graph omparing the millennium kineti energy equation to the relativity equation for veloities below 50 km/hr. At these veloities, and with the 5 deimal plae preision used, the millennium urve is indistinguishable from, and therefore synonymous with, the Newtonian urve. Very evident in the graph is the errati behavior of the relativity equation as previously disussed. Interestingly, analysis of the two total energy equations shows the millennium results to be idential to the relativity results throughout their entire range. The reason for this is simple. At the lower end of the sale, the kineti energy is insignifiant in omparison to the internal energy, m aounted for in the equations. Thus the relativity equation for total energy obsures the fat that the kineti energy result is errati at low veloities. Sine the internal energy is also a omponent of the millennium equation, and sine it is very signifiant at low veloities, both, equations will produe the same values for the level of preision used. On the other hand, at the upper end of the sale, the kineti energy omponent is the most signifiant omponent of both equations. And, as was alluded to earlier, at the higher levels of veloity, the relativity kineti energy equation beomes inreasingly less errati. Therefore, it is not surprising that both total energy equations produe idential results. 7. The New Momentum and Distane Equations Referring bak to equations 6, 0 and, (repeated below) it should be remembered that the top of the right side of equation represents momentum over distane traveled. ka ( mv) at` (6) ka k (0) t` m v t` v k v () t` Therefore we an plae the top of right side of equation = to pd, where p is momentum and d is the distane traveled by an objet or partile under onstant aeleration. pd v m v v t` (5) Now we an rearrange the right side of the resulting equation and separate the momentum omponent from the distane omponent as follows:
pd mv v t` (6) v v v By removing the left omponent on the right side of the equation and plaing it equal to p, we obtain the equation for momentum. mv p (7) Momentum v Here Einstein was only partially orret. Although the most apparent differene between the new millennium equation and the older relativity equation is the use of the millennium fator in plae of the Lorenz fator, there is a more important differene. In the millennium equation it is the veloity that is operated on by the fator. In Einstein s equation it is the rest mass that is operated on. This of ourse is a profound distintion between the two theories and will be disussed further in setion. If we now take the remaining omponent from the right side of equation 6 and plae it = to d, we have one form of the distane equation for an objet under onstant aeleration, d v t` (8) v v whih simplifies to, d vt`. (9) v Distane based on v and t` Sine, v = a t`, for an objet under onstant aeleration, by way of substitution in equation 9, we obtain,
d a t` ( a t`). (30) Distane based on a and t` This gives us an alternate form of the equation for distane traveled by an objet under onstant aeleration. To arrive at an equation that uses onstant time t instead of relative time t` we need only to substitute the right side of equation for t` in equation 9. After simplifiation we arrive at, d vt v (3) v Distane based on v and t This gives us our final form of the millennium equation for the distane traveled by an objet under onstant aeleration. 8. The New Constant Aeleration Equations Now that we understand how the veloity of an objet under onstant aeleration is affeted by the millennium fator, we an formulate new equations for onstant aeleration that do not rely on moving frame time. As stated earlier in setion 4, equations suh as equations and have limited pratial appliation beause of the interdependeny between veloity and moving frame time. What we need are equations that use stationary frame time, suh as will be developed now. Given the relationships of equations and, (repeated below) v t` t () and, v a t` () we an substitute the right side of equation for t` in equation to obtain, v v at. (3) If we now solve for the variable v, we obtain, 3
at v (33) a t Instantaneous Veloity based on a and t where, v, is the instantaneous veloity of an objet or partile under onstant aeleration. This is an important equation. By breaking the diret link between v and t` it allows for the type of analysis given in the addendum. Suh analysis not only allows us to verify the many assumptions of the presented theory, but also permits a diret omparison of the new kineti and total energy equations to those of speial relativity over an unlimited range of masses, veloities, and aeleration rates. Many suh analyses were used to verify the validity of all of the assumptions presented in this work. If we now solve equation 33 for the variable a we arrive at its variation for finding onstant aeleration that also does not rely on moving frame time. a v (34) t v Constant Aeleration based on v and t It should be noted that equations 33 and 34 do not invalidate equations and. They are simply the respetive onstant time equivalents of those two equations. It should also be noted that in regard to the millennium transformation fator it should normally not matter how veloity v is arrived at. That is, it is not normally neessary to make a distintion between the veloity of uniform motion and the instantaneous veloity arrived at through onstant or relative aeleration. Uniform motion is after all, the final result of aeleration. 9. Consisteny with Newton s Seond Law of Motion Aording to Newton s seond law of motion, where F is the applied fore, the relationship between fore and the aeleration of an objet or partile is given by, F ma, (35) while aording to the present theory, a taken from equation, and a r taken from equation 4, are expressed as, v a () t` v a r (4) t 4
The question is, whih form of aeleration, a or a r is intended by Newton s fore equation? Most, if not all, textbooks, even those of a higher level intended for sientists and engineers do not make a distintion here. The pratie has been to use the lassial version of equation 4 even when onstant aeleration is expliitly stated. This is beause at Newtonian levels of veloity, t and t` have essentially the same value. On the other hand in disiplines suh as partile physis or theoretial physis where suh distintion is neessary, an appropriate swith is made to relativisti physis. In millennium physis it is reommended that the appropriate form be used at all times. This permits the investigation of physial phenomena throughout the entire spetrum of veloities and aeleration rates without onern about whih branh of physis is appropriate. Continuing now, for onstant aeleration, by way of substitution we an then state that, v F ma (36) and, F m. (37) Constant Fore t` Sine it is found through mathematial modeling on a omputer that v/t` is indeed a onstant, this relationship between fore, mass, and aeleration is onsistent with the present theory. In aordane with the present theory, an objet under onstant aeleration does not experiene an inrease in mass. Thus, if the aeleration is onstant, and the mass is onstant, the applied fore is onstant. Beause of time expansion, however, it does require greater amounts of energy than an be attributed to veloity alone to maintain a onstant fore on an objet undergoing signifiant aeleration. In other words, a small amount of energy, in a frame of referene that is moving at a signifiant fration of the speed of light, is equal to a large amount of energy, as defined by the energy equations, in the stationary frame of referene. This is a phenomenon of whih there are ountless analogies in everyday life, involving only Newtonian physis. Consider for example a bullet fired from a gun. If you are in the frame of referene in whih the gun was fired and tried to stop the bullet with your hand, you ouldn t beause of its large amount of kineti energy. Yet, if you were moving ahead of the bullet at, say, one kilometer per hour faster than the bullet, you would have no trouble at all of stopping it. That is, in your frame of referene the bullet has very little kineti energy. Relativisti effets on energy are nothing more than an extension of this priniple. The only thing that makes it appear strange is that we are approahing light speed, the standard of measure by whih time itself is gauged. This auses time to slow down, whih in turn auses required energy inreases, to maintain a onstant rate of aeleration, to be greater than that predited by the lassial priniples of Newtonian physis. In view of these findings, it is not unreasonable to suggest that the new aeleration equations through 4 are worthy of elevation to the status, laws of aeleration. This reommendation was the subjet of a paper subsequent to the original version of this revised work. 0. The Connetion Between Inertia and Gravity In aordane with Newton s first law of motion: An objet at rest tends to remain at rest, and an objet in motion tends to ontinue in motion in a straight line unless ated upon by an outside fore. This property of matter that auses it to resist any hange of its motion in either 5
diretion or speed is referred to as inertia, whih is in turn used to define mass. It will now be shown that suh property an be expressed mathematially. Thus, where I r is the rest inertia of an objet or partile and m is its mass we an state, I r m. (38) Rest Inertia This simple aknowledgement that Newton s first law atual refers to the rest inertia of the objet or partile in question allows us to establish the relationship between inertia and gravity, or inertial fore and gravitational fore. If we now ombine this formula for rest inertia with one that defines motion inertia, we will have a omplete formula for inertia. As it is, formulas for motion inertia already exist. They are the momentum formulas 7 and 7. Suh formulas express Newton s first law with respet only to the ontribution that motion has on inertia. Whereas the rest inertia is always a fator regarding total inertia, momentum is a fator only when motion is involved, but it is by far the most prominent fator even at relatively low veloities. Thus where I is the total inertia, the omplete formula for inertia is, I I p. (39) Total Inertia r By substituting the right sides of equations 38 and 7 for I r and p respetively, we obtain, I m mv (40) giving, I m( v ) (4) for what ould be alled the lassial version of the formula. We an derive the relativisti form of the formula by using equation 7 instead of equation 7 for p in the above substitution. Thus we obtain, I mv v I m m v (4) giving, v (43) Total Inertia for the relativisti form of the formula. Now we are ready to establish the relationship between inertia and gravity. Where g is the aeleration of gravity, G is the gravitational onstant 6.670 0 -, and r is the distane to the enter of gravity, the Newtonian formula for gravity is, 6
m g G. (44) r If we now solve the two inertia equations, 4 and 43, and the above gravity equation for the variable m, we get respetively, I m (45) v I m (46) v v gr m (47) G If we then plae the right side of the inertia equation, 45 equal to the right side of the gravity equation, 47 and solve the resulting equation, first for g and then for I, we obtain, I g G (48) r v I v. r g (49) G This gives us the lassial formulas that relate inertia to gravity. To gain onfidene in the orretness of these two formulas we need simply to substitute the right side of equation 4, in plae of I in equation 48. Sine equation 4 is, I = m(v + ) it should be obvious that the terms, (v + ) will anel and we will end up with the equation for gravity (44) originally given. Doing similar, using the right side of the relativisti inertia equation, 46 with the right side of the gravity equation 47 and solving first for g and then for I, we obtain, I g G (50) v r v I g r v v G. (5) Gravity and Inertia for the relativisti form of the equations that relate inertia to gravity. Sine we know that lassial formulas are not ompletely valid it is the relativisti formulas, 43, 50, and 5 that we are most onerned with. As before, if we substitute the right side of equation 43 in plae of I in equation 50, the terms enlosed in brakets will anel and we will again end up with the equation (44) originally given for gravity. This proves that the values we initially assigned to inertia are not only onsistent with Newton s laws of motion, but are also onsistent with his universal law of gravitation. 7
The analysis just ompleted will be used in the following setion as one of the proofs that mass does not inrease as a result of motion.. The Mathematial Proofs Proof. Where k is kineti energy, p is momentum, d is the distane through whih a ats, and t` is the time interval, the formula for kineti energy an be expressed as, pd k. (5) Kineti Energy t` For analysis purposes this equation an be expressed in its expanded form as, mv v t` v v v k (53) t` Sine this equation produes the same results as Einstein s equation for kineti energy it is not unreasonable to laim that it is supported by the same evidene that supports the latter equation. For similar reasons, it an be further laimed that the momentum omponent of this equation is also supported by the evidene. With this in mind, if we now examine the omposition of this equation we an draw ertain onlusions from it.. If the momentum omponent is valid and the overall equation is valid, it is then reasonable to assume that the distane omponent is also valid.. Sine there is no mass element m in the distane omponent, and sine the interval t` element disappears when the equation is simplified, there an be no question as to the fat that the millennium fator operates on the veloity element v in this omponent of the equation. 3. In view of the above observations one is then left to explain by what rationale do we wish to laim that the millennium fator in the momentum omponent is operating on the mass m element and not the veloity v element in that omponent? In plain words, why should veloity be treated differently in one omponent as opposed to the other? 8
4. It ould be argued that sine t` remains an element of the distane formula when it is used separately, it is atual t` that is operated on in this omponent of the kineti energy equation. That is, it is only an illusion that it is the veloity operated on when t` anels out of this omponent in the kineti energy equation. However, if that is the ase then the distane formula is onverted to a onstant time formula as shown in equation 54 below: d vt (54) v That is, t` ated upon in suh manner is onverted to t as shown by equation (repeated below): t t` () v However, although equation 54 is orret in the mathematial sense, it is exatly that, a onversion. Equation 54 does not truly represent the physial laws of Nature any more than Newton s laws do when onstant time is used in plae of relative time. It is simply a onversion for purposes of mathematial onveniene like all of the other onversions given here. Although, unlike Newton s laws, the onversion given here is orret for all veloities, like Newton s laws it misleads us, and thus does not aurately portray the physial laws of Nature. It has been shown throughout this work that only relative time t` is truly orret whenever relative motion and its assoiated relationships are defined. Proof. In the analysis on inertia and gravity in setion 0, it was shown that the results fundamentally agree with Newton s laws of motion and his law of universal gravitation. Yet the analysis learly shows that gravity is unaffeted by relative motion. It is reasonable to onlude therefore that Einstein s theory involving the effet veloity has on mass is invalid. In Einstein s relativity, mass and energy are seen to be interhangeable in reognition of the apparent effet veloity has on mass. But if mass represents a given quantity of matter then suh assumption means that matter inreases as a result of relative motion. And if matter inreases, so must its gravity. The validity of suh assumption was found to be false in the inertia, gravity analysis. Perhaps one of the reasons the effet motion has on veloity was overlooked in favor of an effet on mass is beause of the apparent interdependeny veloity has on itself when the transformation fator is applied to veloity instead of mass. That is, veloity is represented within the transformation fator. This is another of the problemati irular dependenies disussed earlier in this paper. In this ase the 9
problem is not so muh one involving the funtionality of the math, but rather one involving omprehension. As it turns out, this problem is easily remedied. For that matter, the transformation fators used to this point appear to be nothing more than a misleading form of the true transformation fators involved. This problem is further disussed and resolved in the next setion.. Aeleration Based Time Transformation Formulas One the fundamentals of relativisti behavior are suffiiently understood, the following order of simultaneously ourring phenomena seems to be self-evident:. Energy is required in appliation of fore.. Fore auses aeleration. 3. Aeleration auses time to slow down. 4. The slowing of time redues the rise in veloity, and thus the rate of aeleration. 5. A redution in the rate of aeleration implies a redution in the magnitude of the fore. 6. An inrease in energy is therefore needed to maintain the fore and thus the aeleration. Apparent in the above analysis is the fat that aeleration and not veloity auses time to slow down. It is also apparent then, and rather obvious, that the slowing of time requires the use of energy whereas, in the absene of an outside fore, uniform motion does not. Sine any veloity, however, is atually the instantaneous veloity resulting from aeleration, its use in the transformation fator though possibly misleading is nonetheless orret. Nevertheless, it ould be of benefit to develop transformation fators that use the rate of aeleration over an interval of time instead of the veloity ahieved during the interval. Suh development may be aomplished as follows: By taking the right sides of the veloity equations and 3 and plaing them equal to eah other we obtain, v at` at. (55) Sine v = a t`, (equation ) we an substitute the right side of this equation for v in the above equation to arrive at, ( at`) at` at. (56) If we solve equation 56, first for t` and then for t we obtain the following two equations for time transformation: 0
t` t (57) and, ( a t) t t` (58) ( a t`) Aeleration Based Time Transformation Thus, for finding relative time t` we have equation 57, and for finding onstant time t we have equation 58. (Note the hange of signs.) These of ourse ould also have been arrived at by substituting a t` for v in equation at the beginning of this paper. From equations 57 and 58 above we an dedue the following new transformation fators that do not diretly rely on veloity: (I.e., the two fators used above and their reiproals) ( a t) (59) and, ( at`) (60) Stationary Frame to Moving Frame Transformations ( a t`) (6) and, ( at) (6) Moving Frame to Stationary Frame Transformations It should be noted that beause the time variables t and t` are inluded in these four fators, only two, 59 and 60, are useful for time transformation. 3. The Contraditions of Speial Relativity It is well known that the ontroversy over speial relativity has never ended. Although many of the arguments against it may be flawed in the sientifi sense they are often orret in the logial sense. The problem with speial relativity is that ontrary to sientifi laims there are no true ornerstones in it. Everything is dependent on everything else. From the purely sientifi line of reasoning this may appear to make sense beause after all, all things are relative. But this line of reasoning is atually in itself sientifially unreasonable. With it we are led down a road of endless ontraditions. It appears that there are absolutes in the universe after all. It is just that these absolutes are different than we originally assumed. The existene of matter, for example is absolute, and if mass is a true measure of a quantity of matter, then the true mass is also absolute. Whereas all things do appear to have a relative value they also have an absolute, or onstant value. For example, if a seond of onstant time in one frame of referene is the measure of a ertain amount of atomi ativity in that frame, then under idential onditions, that same amount of idential atomi ativity represents a seond of onstant time in any other frame of referene. This is the absolute value of time. Relative time, on the other hand, is simply the relative value of absolute time in one referene frame to the absolute time in another referene frame. The same is true of mass. If mass represents a given quantity of matter in one referene frame, then under idential onditions it represents the exat same quantity of matter in any other referene frame. This then is the absolute value of mass.
In the presented theory the ontraditions of speial relativity do not arise beause there is an aeptane of absolutes. Matter and energy are absolutes and are not interhangeable with eah other. Suh are the ases with the momentum and kineti energy assoiated with matter. Matter has physial existene and energy does not. Sine energy has no physial existene, it an only be measured indiretly by its effets on matter. If energy had physial existene it should be measurable diretly. For example, we should be able to measure potential and kineti energy without regard for the matter that is ausing it. The opposite is atually true. We an determine energy only by measuring the effets it has on matter. Fore as treated in general relativity is yet another enigma we have to deal with. In the ase of inertia, it is regarded as a fititious fore, or fititious representation of gravitational fore. But then at the same time, gravitational fore is shown not to be a real fore at all. Spae urves around massive objets or bodies of matter. So we are left with a fititious representation of something that does not truly exist. While it is true that fore does not exist in the physial sense, it does indeed exist. Like energy it is atually a measured of an effet on mass and is not diretly measurable independent of those effets. Gravitational fore, for example, is a measure of the effet gravity has on matter. And gravity, although we little understand it, does in fat exist. The evidene to that effet is overwhelming, yet for some reason we feel ompelled to disprove it. Objets enter into orbit, naturally only by hane, or when aomplished by man, only with a great deal of effort. It also takes effort to remove an objet from orbit. But it takes no intervention on our part whatsoever for an objet to fall to earth. Does this sound like urve spae influening the outome? No, it is gravity doing exatly what it does, and whether we understand it or not, it does in one manner or another exist. 4. Conlusion The evidene presented here strongly supports the view that mass is not affeted by aeleration. The evidene shows onviningly that only those things that are a funtion of time are affeted by the slowing of time. This inludes veloity and aeleration. Mass is a funtion of the quantity of matter ontained in an objet, and this quantity is not a funtion of time. These onlusions are not only sensible and logial, but they appear to be self-evident. Time and distane (spae), however, have no physial presene and it appears equally self-evident that their quantitative values are interdependent on the ativity (motion) of the matter upon whih they are referened to. Even here, it appears that only the variane of time is a real fat of Nature. It was pointed out in the millennium theory of relativity that the shrinking of distane is not a real effet but rather a perspetive effet related to the slowing of time. Thus it appears that even distanes have onstant, or absolute values in addition to relative values. Whereas gravity appears to be unaffeted by inertia it is itself a fore that auses aeleration. And sine aeleration auses time to slow down it is equally apparent that gravity indiretly affets the relative nature of time. This relationship between gravity, aeleration and relative time are worthy of further exploration in a future work. Of equal importane here, is the diret link established between the present theory and the millennium theory of relativity. This onnetion was established throughout the analysis and provides strong supporting evidene as to the validity of both theories. Also of importane here is unifying role that time variane plays in both theories. This suggests that time may be the unifying element of all physial siene.
Appendix A. For the purpose of this paper mass is defined as an absolute quantitative measure of matter. Mass is detetable through either its gravitational, or inertial fore whih have been onveniently set equal to eah other at the earth s surfae by use of the gravitational onstant G. To be useful as a quantitative measure, however, it is reognized that apparent hanges of mass due to hanges in veloity or gravitational field must be taken into aount. Thus it is reognized that even on earth, varianes of the gravitational field or the experiene of g fores imposed by aeleration ause only an apparent hange of mass, and not a real hange. True mass in the sense meant here is that whih is experiened in an isolated system outside of any gravitational field. In suh a system it is the inertial resistane suh mass offers to aeleration. B. In the millennium theory of relativity it is shown that the millennium fator is diretly derived from the evidene. By use of the same evidene the Lorentz fator an also be arrive at but requires more mathematial steps. Thus, the Lorentz fator and its reiproal are simply another form of the millennium fator and its respetive reiproal. If one wishes to go through the exerise, the Lorentz fators an be used in plae of the millennium fators throughout the analysis inluding in equation. After simplifiation, the resulting equation will be unhanged from that given as equation 3. C. Although equation 3 may appear a bit more ompliated then the speial relativity ounterpart, one is reminded that K = M - M o is really an abbreviated form of, K M o v M o. Similar is true for the speial relativity total energy equation, E = M whih in the unabbreviated form is, E M o v. Note: This is an MSWord Offie 000 doument. MSWord must be in the print layout view to view equations, figures and, and the addendum. The addendum was opied over from a Mathad file to show the method used in verifying mathematial results. 3
Addendum Addendum - Time and Energy, Inertia and Gravity - J. Rybzyk - February 4, 00 9979458 a..000000000073 t 00000000000 m o 000 m m o v a.. t. a t kineti energy v = 0.866090568739 t. t v. 60 = 93465359.6646437 km/hr 000 n = Newton, r = Rybzyk, e = Einstein v k.. n m o v k n = 3.37084865535 0 9 m.. v k r =. v v m. o k e Total energy v m.. v E r Momentum. v v mv.. p r v = Distane from aeleration k r 8.9875633073946 0 9 k r = t = 5 0 0 m. o k e = 8.9875633073946 0 9 k r = k e m. m. o E e v Note: t used in plae of t` due to s/w program unreliability in handling variables with prime designators. k n.66658844377394 k e =.66658844377394 k n E r =.797470880764 0 0 E r = E e E e =.797470880764 0 0 p r 5.9 0 p e m. o v p e = 5.9 0 p r v = p e vt.. d v d a.. t a. t v. t. v d 3 d = 8.654 0 8 v d = 8.654 0 8 Distane from uniform motion. d. u v t d u =.596 0 9 d 3 = 8.654 0 8 Constant aeleration a = 0.005 v. a t v =.596 0 8 v a t a = 0.005 a.. t v. a t v =.596 0 8 v. a a = 0.005 t. v 4
Relative aeleration a r v t v r a. r t v r =.596 0 8 a r = 0.003 m = 0 3 Constant fore F. ma F = 5.9 F. m v F F = 5.9 = t F Inertia and Gravity I r m I I r p r I. m G. 6.670 0 r 000. v v I = 5.9 0 I = I I = 5.9 0 g. G m g = 6.67 0 4 I g. G r r.. v v I 3. g r.. v v G Transformation fators g = 6.67 0 4 I 3 = 5.9 0 I g = = I 3 g e r 3 v e r v r v v. a t r 4 a. t. a t r 5 a. t r 6 e = 0.5 r = 0.5 r 3 = 0.5 r 5 = 0.5 e = r = r 4 = r 6 = e e e = = =.00000000000000 r r 3 r 5 e e e = = 0.999999999999999 = r r 4 r 6 5
REFERENCES Isaa Newton, The Prinipia, (687) as presented in Physis for Sientists and Engineers, seond addition, (Ginn Press, MA, 990) and Exploration of the Universe, third edition, (Holt, Rinehart and Winston, NY, 975) Albert Einstein, Speial Theory of Relativity, (905) as presented in Physis for Sientists and Engineers, seond addition, (Ginn Press, MA, 990) and Exploration of the Universe, third edition, (Holt, Rinehart and Winston, NY, 975) 3 Joseph Rybzyk, Millennium Theory of Relativity, Unpublished Work, (00) Time and Energy, Inertia and Gravity Copyright 00 Joseph A. Rybzyk All rights reserved inluding the right of reprodution in whole or in part in any form without permission. Note: If this doument was aessed diretly during a searh, you an visit the Millennium Relativity web site by liking on the Home link below: Home 6