C O N T E N T S:

- Special Relativity considers the laws of nature from the point of view of frames of reference upon which no forces are acting, and describes the way time, distance, mass, and energy must be perceived by observers who are in uniform motion relative to each other if the speed of light must always turn out the same for all observers.(More…)
- The mass of object changes when its speed approaches zero because according to Einstein postulates of theory of relativity all the laws are same in all inertial frames and speed of light remains constant in inertial frame in vacuum.(More…)
- Rod Kawecki’s theory on faster than light possibilities is based on whether or not a limited particle mass can be physically and separately using a propulsion force be accelerated to a velocity faster than light is the hypothesis not whether a material particle can exceed its natural velocity.(More…)

- To avoid the need to study the transformation laws of force, we shall analyze a collision, where we need know nothing about the laws of force, except that we shall assume the conservation of momentum and energy.(More…)
- Another argument sometimes put forward for dropping the use of relativistic mass is that since e.g. all electrons have the same rest mass (whereas their relativistic masses depend on their speeds), then their rest mass is the only quantity able to be tabulated, and so we should discard the very idea of relativistic mass.(More…)
- This tiny “weight” of heat energy, however, represents about a million times as much energy as an equivalent weight of coal could produce, partly due to the prodigious strength of the strong nuclear force which holds the nucleus of an atom together.(More…)

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link: https://readingfeynman.org/tag/relativistic-mass/

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**KEY TOPICS **

**[1] In addition to the formulas for length and time, relativity changes everything else associated with motion, including mass, energy, momentum, and force. [2]**

*Special Relativity considers the laws of nature from the point of view of frames of reference upon which no forces are acting, and describes the way time, distance, mass, and energy must be perceived by observers who are in uniform motion relative to each other if the speed of light must always turn out the same for all observers.*Between 1905 and 1909, the relativistic theory of force, momentum, and energy was developed by Planck, Lewis, and Tolman. [3] If two particles come together and produce potential or any other form of energy; if the pieces are slowed down by climbing hills, doing work against internal forces, or whatever; then it is still true that the mass is the total energy that has been put in. [4] Because einstein made a blind choice and assumed mass increased, instead of the force becoming less effective, he sent the entire investigation into a blind alley where speeds in excess of light are artificially impossible. (Which greatly benefits the owners of the means of contemporary energy production, otherwise known as energy barons and the current handlers of the greatly hated shrub administration). [5]

E mc 2 The famous equation E mc 2 is what comes out of relativity when you look at what has to happen to energy, momentum, and force for objects moving near the speed of light. [2] If you could just lop-off parts of an equation and claim whatever is left is equal i.e. “energy equals mass” then you could also say that “power equals mass” and so does momentum and force. [6]

The derivative of kinetic energy becomes mass times acceleration which works in harmony with Newton’s force of F ma. [7]

You’ve heard all the fancy terms like Einstein’s theory of relativity, matter, mass, energy, speed of light, time, dimension, gravity, black hole, quantum mechanics, string theory, the big bang, the creation of the universe, the expanding universe, time travel, event horizon, quantum singularity, Newtonian space, the expanding universe, the uncertainty principle and many others. [8] Note, though, that while relativistic mass γ m is not a body’s total energy in general relativity, it’s also not simply the source of gravity within the same theory. [3] The definition m p/v now also neatly defines a relativistic mass for a photon: this moves with speed c and has energy E, and electromagnetic theory gives it a momentum of magnitude p E/c, so it has relativistic mass p/v E/c 2. [3]

Necessarily, the conservation of energy must go along with the conservation of momentum in the theory of relativity. [4]

The first difficulty with this line of reasoning is that it is quite selective; after all, it should surely rule out the use of rest mass as well, since within special relativity, rest mass is proportional to a body’s rest energy. [3]

Action is, however, defined in terms of a certain physical quantities that are mentioned as efficient causes (such as spatial relations, mass, force, velocity, acceleration, momentum, and energy). [9] In the equation we have visualized mc and its kinetic energy for motion to be a limit but now we review the facts and discover that in E part of the equation we find the (F) the same value that is used in Newton?s law is not part of the objects rest mass but is an extension for acceleration and force so it retains attributes by itself. [10] He accelerates with a rest mass energy conservation measuring zero but having the potential of c energy already enabling him to travel close to the speed of light racing with the force gravity is traveling before any kinetic energy over exceeds him balancing with his ship?s center of mass. [10]

** The mass of object changes when its speed approaches zero because according to Einstein postulates of theory of relativity all the laws are same in all inertial frames and speed of light remains constant in inertial frame in vacuum.** [11] One of the consequences of Einstein’s special theory of relativity (1905) is that the mass of an object increases with its velocity relative to the observer. [12]

While we usually think of mass as being constant for an object, Relativity tells us that energy and mass are interchangeable. [12] The previously separate ideas of space, time, energy and mass were linked by special relativity, although without a clear understanding of how they were linked. [13] In special relativity the actual invariant is the magnitude of the covariant energy momentum 4-vector $(E_0/c_0, p_x,p_y,p_z)$, not the apparent mass itself. [11]

The special theory of relativity also leads to the Einstein mass-energy relation, E mc 2, where E is the energy, and m and c are the (relativistic) mass and the speed of light, respectively. [14] “It followed from the Special Theory of Relativity that mass and energy are both but different manifestations of the same thing – a somewhat unfamiliar conception for the average mind. [15]

In the holistic viewpoint of relativity theory, concepts such as length, mass and time take on a much more nebulous aspect than they do in the apparently rigid reality of our everyday world. [13]

What has this to do with the Theory of Everything, let alone a way to quantify Gravity? Since Einstein came up with “Energy equals Mass times the speed of light squared”, it has been accepted that for Mass to reach the speed of light it would have to increase to infinite size, which would guarantee to be impossible. [6]

I assumed that the nature of matter coincides with space in all the forms that are counted by physics in its principle of the conservation of mass and energy: rest mass, kinetic energy, two kinds of force-field matter (electric charges and gravitational fields), and two kinds of waves of forces (electromagnetic waves and gravitational waves). [9] In popular culture that relation between energy and mass is virtually synonymous with relativity, and Einstein, its originator, has become a symbol of modern physics. [16] [xyz-ihs snippet=”Amazon-Affiliate-Native-Ads”] In relativity, the definitions of the different species of energy are a bit different and, most importantly, there is a completely new type of energy: even if a particle is neither moving nor part of a bound system, it has an associated energy, simply because of its mass. [17] General relativity says that energy (in the form of mass, light, and whatever other forms it comes in) tells spacetime how to bend, and the bending of spacetime tells that energy how to move. [18] Perhaps the best-known implication of Special Relativity is the equation Emc 2, which expresses a close relation between energy and mass. [1]

Relativity tells us that the Universe does have a speed limit, the speed of light, because in order for a particle with mass to get there, it would have to acquire all the energy in the Universe. [2] We use the phrase “rest-mass”, because Einstein’s Special Theory of Relativity tells us that the mass of an object is not actually constant, but actually increases with an object’s velocity (a strange and wonderful implication of this theory). [19] Tesla interviewed on his birthday, was quoted in the following: “The theory of relativity, he described as a mass of error and deceptive ideas violently opposed to the teachings of great men of science of the past and even to common sense. [5] If we are correct, physical theory need no longer suppose that there is something called mass having an innate property, inertia, that resists acceleration; what is really happening, instead, is that an electromagnetic force acts on the charge inside matter to create the effect of inertia. [16] Einstein’s general theory of relativity is based on the assumption that inertial and gravitational mass are equivalent and indistinguishable-the so-called principle of equivalence. [16] Einstein’s General Theory of relativity extended his Special Theory to include non-inertial reference frames, frames acted on by forces and undergoing acceleration, as in cases involving gravity. [1]

** Rod Kawecki’s theory on faster than light possibilities is based on whether or not a limited particle mass can be physically and separately using a propulsion force be accelerated to a velocity faster than light is the hypothesis not whether a material particle can exceed its natural velocity.** [10] Since this condition does include time travel as maintained in relativity faster than light speed space travel is said to be instantaneous to its mobility nor is the infinite mass theory need to be enclose time is measured as the period of the distance traveled and is not considered a dimension of its own. [10] According to the special theory of relativity, mass is not strictly constant but increases with the speed according to the formula m m 0 /1- v 2 / c 2, where m 0 is the rest mass of the body, v is its speed, and c is the speed of light in vacuum. [14]

In relativity, mass and energy are equivalent and when you say that something has gained energy (of the potential variety or otherwise), you also mean that it has gained mass. [2] In general relativity, given the distribution of mass and energy, spacetime bends to minimize its curvature, denoted R. But in so-called f(R) (pronounced “eff-of-are”) theories, spacetime contorts to minimize the curvature plus some extra function of the curvature. [20]

Einstein’s Relativity requires both an Electromagnetic Force Field to explain Charge, and a Gravitational Field to explain Mass. He tried and failed throughout his life to unite these two fields into one (and to remove the ‘particle’ concept from them). [21] Einstein knew that his General Theory of Relativity described Space as a fabric that moves and is affected by mass. [6]

Albert Einstein became famous for the theory of relativity, which laid the basis for the release of atomic energy. [22]

Later in 1905 came an extension of special relativity in which Einstein proved that energy and matter are linked in the most famous relationship in physics: Emc 2. (The energy content of a body is equal to the mass of the body times the speed of light squared). [23] In the special theory of relativity, length, time, velocity and mass is relative. [24] This is not quite true, because according to the special theory of relativity, mass increases with velocity. [9] For decades the theory of relativity taught that as a body moves with increasing velocity its mass also increases. [25] The theory of relativity have discontinuities whereby the limit of a physical quantity as a variable (such as mass or velocity) approaches a fixed value is not the same as the physical quantity at the fixed value. [25] To Tesla, the Theory of Relativity was just “a mass of error and deceptive ideas violently opposed to the teachings of great men of science of the past and even to common sense. [26]

The articles claiming that the slower GPS satellite clocks confirm relativity do not address the effect, if any, of the weaker gravitational force under Newton’s theory on the GPS satellite clocks, likely because in Newtonian Mechanics every clock in the universe keeps time at the same rate regardless of velocity, acceleration, or the presence or absence of force. [25] This assumption about the motion of electromagnetic waves (or photons) is crucial to the spatiomaterialist explanation of relativity theory, because it is the motion of objects with rest mass relative to the inherent motion that gives rise to the Lorentz distortions which explain the phenomena of special relativity. [9]

**POSSIBLY USEFUL **

**[4] We “shift the origin” of energy by adding a constant $m_0c^2$ to everything, and say that the total energy of a particle is the mass in motion times $c^2$, and when the object is standing still, the energy is the mass at rest times $c^2$. [4] E mc 2 becomes an expression that tells us how much energy a given mass has; it also tells us how much a body will resist being accelerated depending on its energy content. [3] For instance, if we were to weigh the carbon dioxide molecule and compare its mass with that of the carbon and the oxygen, we could find out how much energy would be liberated when carbon and oxygen form carbon dioxide. [4]**

*To avoid the need to study the transformation laws of force, we shall analyze a collision, where we need know nothing about the laws of force, except that we shall assume the conservation of momentum and energy.*With these he could write the equations of motion for an electron in an electromagnetic field in the newtonian form, provided the electron’s mass was allowed to increase with its speed. [3] After the collision we have the mass $M$ moving upward with velocity $u$, considered very small compared with the speed of light, and also small compared with $w$. [4] If we assume the conservation of momentum and the principle of relativity, we can demonstrate an interesting fact about the mass of the new object which has been formed. [4] We can show that, as a consequence of relativity plus a few other reasonable assumptions, the mass must vary in this way. (We have to say “a few other assumptions” because we cannot prove anything unless we have some laws which we assume to be true, if we expect to make meaningful deductions.) [4]

When a body’s mass is constant (as it usually is, except when we are analysing the motion of e.g. a rocket), the force law becomes F m d v / d t m a, where a is the body’s acceleration. [3] The relativistic version of F m a turns out to be F ( 1 + γ 2 v v t ) γ m a and a ( 1 – v v t ) F γ m So defining mass via force and acceleration isn’t as simple as it was for Newton (although it is simple, in principle, to define the mass as relating impulse and momentum increase, as mentioned a few lines up). [3] Newton used mass to define momentum and force vectors: he defined a body’s momentum as p m v (where v is its velocity), and he defined force to be the rate of increase of the body’s momentum: F d p / d t. [3]

We learned in the last chapter that the mass of an object increases with velocity, but no demonstration of this was given, in the sense that we made no arguments analogous to those about the way clocks have to behave. [4] If two objects with relativistic masses m 1 and m 2 collide and stick together in such a way that the resulting object is at rest, then its (relativistic rest) mass will be m 1 + m 2. [3] Since $2m_w$ is what is put in, but $2m_0$ are the rest masses of the things inside, the excess mass of the composite object is equal to the kinetic energy brought in. [4] Lastly, the energy E of an object, whether moving or at rest, is given by Einstein’s famous relation E mc 2, where m is its relativistic mass. [3]

Suppose that we have an object whose mass $M$ is measured, and suppose something happens so that it flies into two equal pieces moving with speed $w$, so that they each have a mass $m_w$. [4] In Newton’s mechanics, this equation relates vectors F and a via the mass m of the object being accelerated, which is invariant in Newton’s theory. [3] A rest-mass-only analysis describes the interaction by saying that the objects have (rest) masses of M 1 and M 2, with a combined (rest) mass of γ 1 M 1 + γ 2 M 2. [3] According to Newtonian mechanics it is all right for two things to collide and so form an object of mass $2m_0$ which is in no way distinct from the one that would result from putting them together slowly. [4] If we define mass in such a way that the object’s mass does not increase as it heats up, then we will have to give up the idea that mass is proportional to weight. [3] When we put the objects together gently they make something whose mass is $2m_0$; when we put them together forcefully, they make something whose mass is greater. [4] Now, let us accept that momentum is conserved and that the mass depends upon the velocity according to ( 16.10 ) and go on to find what else we can conclude. [4] It turned out that a single mass dependence could be used for any acceleration, thus enabling mass to retain its independence of the body’s direction of acceleration, if a speed-dependent “relativistic mass” m was understood as present in Newton’s original expression p m v. [3] Mass is a property of a body that we have an intuitive feel for; its definition as a resistance to acceleration is very fundamental. [3] In fact the argument is completely general, and our discussion of the inelastic collision shows that the mass is there whether or not it is kinetic energy. [4] We know from the law of conservation of energy that there is more kinetic energy inside, but that does not affect the mass, according to Newton?s laws. [4]

The above argument that E mc 2 demotes mass in favour of energy–or rather, that it selectively demotes relativistic mass, but not rest mass–also neglects the very definitions of mass and energy. [3]

They must have the same speeds, since they are exactly similar objects; in fact, they must have the same speed they started with, since we suppose that the energy is conserved in these collisions. [4] Energy, on the other hand, is defined in physics in a technical way that involves the concept of a system’s time evolution; this is not something that bears any obvious similarity to the concept of an object’s resistance to being accelerated. [3] Therefore we have a new idea : we do not have to know what things are made of inside; we cannot and need not identify, inside a particle, which of the energy is rest energy of the parts into which it is going to disintegrate. [4] Of course, all that meant was that he could tell us ahead of time how much energy would be released if we told him what process would occur. [4]

When we discussed the theory of vectors, we noted that the fundamental laws of motion are not changed when we rotate the coordinate system, and now we learn that they are not changed when we change the space and time variables in a particular way, given by the Lorentz transformation. [4] Because m is just a number, in Newton’s theory the force on an object is always parallel to the resulting acceleration. [3] When the body is moving we find that its force-acceleration relationship now depends on two quantities: the body’s speed, and the angle between its direction of motion and the applied force. [3]

The quantities that a moving observer measures as scaled by γ in special relativity are not confined to mass. [3] Another mass concept that everyone agrees on is the idea of reduced mass in non-relativistic mechanics. [3] If we prefer to maintain the usual idea that mass is proportional to weight–assuming we don’t step onto an elevator or change our home planet midway through the experiment–then it follows that the object’s mass has increased. [3] Some historical details can be found in Concepts of Mass by Max Jammer and Einstein’s Revolution by Elie Zahar. [3] Everyone knows the realm of applicability of the concept of reduced mass and how useful it is. [3] Of course, when the velocity is small, it is the same mass that we would measure in the slow-moving experiments that we are used to. [4] As far as the maths goes, it’s as if we are replacing the two original bodies by two new ones: the first new body has infinite mass, and the second new body has a mass equal to the system’s reduced mass, which has this name because it’s smaller than either of the two original masses that gave rise to it. [3] Yet, strangely, many of the same physicists who insist that a moving train’s mass does not scale by γ are quite happy to say that its length does scale by γ. [3] When the mechanics of e.g. a sun-satellite system or a mass oscillating on a spring is analysed, a mass term appears that combines the two masses in a particular way. [3] This definition of mass was applied in a straightforward way for almost two centuries. [3] The reason rest mass, rest length, and proper time find their way into the tensor language of relativity is that all observers agree on their values. (These invariants then join with other quantities in relativity: thus, for example, the four-force acting on a body equals its rest mass times its four-acceleration.) [3] The main difference between the relativity of Einstein and the relativity of Newton is that the laws of transformation connecting the coordinates and times between relatively moving systems are different. [4]

There is another school of philosophers who feel very uncomfortable about the theory of relativity, which asserts that we cannot determine our absolute velocity without looking at something outside, and who would say, “It is obvious that one cannot measure his velocity without looking outside. [4] What, then, are the philosophic influences of the theory of relativity? If we limit ourselves to influences in the sense of what kind of new ideas and suggestions are made to the physicist by the principle of relativity, we could describe some of them as follows. [4] The old story about the elephant that several blind men describe in different ways is another example, perhaps, of the theory of relativity from the philosopher?s point of view. [4] Of course, Paul notices nothing unusual, but if he travels around and about for a while and then comes back, he will be younger than Peter, the man on the ground! That is actually right; it is one of the consequences of the theory of relativity which has been clearly demonstrated. [4] Certainly there must be deeper things in the theory of relativity than just this simple remark that “A person looks different from the front than from the back.” [4] Probably the frames of reference that were originally referred to were the coordinate systems which we use in the analysis of the theory of relativity. [4] Then Einstein arrived on the scene and, in his theory of motion known as special relativity, the situation became more complicated. [3]

In this chapter we shall continue to discuss the principle of relativity of Einstein and Poincar as it affects our ideas of physics and other branches of human thought. [4] In the final analysis, the history of relativity, with its quotations from those in favour of relativistic mass and those against, has no real bearing on whether the idea itself has value. [3] On that note, a second difficulty of the line of reasoning is more technical: equating energy and relativistic mass cannot be done more generally. [3] A body moving with speed v and whose momentum has magnitude p has a relativistic mass given by m p/v, and (it turns out) a total energy of mc 2. [3] A commonly heard argument against the use of relativistic mass runs as follows: “The equation E mc 2 says that a body’s relativistic mass is proportional to its total energy, so why should we use two terms for what is essentially the same quantity? We should just stay with energy, and use the word ‘mass’ to refer only to rest mass.” [3]

It is not convenient and often not possible to separate the total $mc^2$ energy of an object into rest energy of the inside pieces, kinetic energy of the pieces, and potential energy of the pieces; instead, we simply speak of the total energy of the particle. [4]

In the last chapter we discussed the heating of a gas, and showed that because the gas molecules are moving and moving things are heavier, when we put energy into the gas its molecules move faster and so the gas gets heavier. [4] This equation was used to estimate how much energy would be liberated under fission in the atomic bomb, for example. (Although the fragments are not exactly equal, they are nearly equal.) [4] How much energy will they have given to the material when they have stopped? Each will give an amount $(m_w – m_0)c^2$, by the theorem that we proved before. [4]

An infinite amount of energy would have to be expended, via the accelerating force, to reach the speed of light. [12] If we keep applying a constant force to a body, the body will keep gaining energy and momentum and its velocity will rise accordingly. [27]

As an object approaches the speed of light, Einstein predicts that the objects mass will increase as energy is turned into matter so as to prevent an object from traveling faster than light. [8] As it gets closer to the light barrier, the rate the mass increases is such that at the speed of light the mass would increase to infinity, which would take an infinite amount of energy to make the object go faster than light. [8]

** Another argument sometimes put forward for dropping the use of relativistic mass is that since e.g. all electrons have the same rest mass (whereas their relativistic masses depend on their speeds), then their rest mass is the only quantity able to be tabulated, and so we should discard the very idea of relativistic mass.** [3] Because, for example, the photon has no rest mass but does have relativistic mass, the use of relativistic mass makes it much easier to describe the mass changes that happen when light interacts with matter. [3] An optimistic view would hold that it’s a measure of the richness of physics that focussing on different aspects of concepts like mass produces different insights: intuition in the case of relativistic mass in special relativity, and the also-intuitive notion of invariance and geometrical quantities in the case of rest mass within the tensor language of special and general relativity. [3] While contracted length and time intervals are used–or not–insofar as they simplify special relativity analyses, relativistic mass has found itself at the centre of much debate in recent years about whether it is necessary in a physics curriculum. [3] Whereas rest mass is routinely used in many areas of physics, relativistic mass is mostly restricted to the dynamics of special relativity. [3]

Relativistic mass came into common usage in the relativity texts of the early 1920s written by Pauli, Eddington, and Born. [3]

Poincarmade the following statement of the principle of relativity: “According to the principle of relativity, the laws of physical phenomena must be the same for a fixed observer as for an observer who has a uniform motion of translation relative to him, so that we have not, nor can we possibly have, any means of discerning whether or not we are carried along in such a motion.” [4] This is called a “paradox” only by the people who believe that the principle of relativity means that all motion is relative; they say, “Heh, heh, heh, from the point of view of Paul, can?t we say that Peter was moving and should therefore appear to age more slowly? By symmetry, the only possible result is that both should be the same age when they meet.” [4] This is how relativity reproduces Lorentz’s original concepts of longitudinal and transverse masses; they are actually contained in these equations. [3] We shall continue to use this simpler form, since it contains all the essential features of relativity. [4] Because there are multiple ways of describing scenarios in relativity depending on which frame we are in, it is useful to focus on whatever invariances we can find. [3]

Why then did the philosophers not make all this fuss about “all is relative,” or whatever, in Newton?s time? Because it was not until Maxwell?s theory of electrodynamics was developed that there were physical laws that suggested that one could measure his velocity without looking outside; soon it was found experimentally that one could not. [4]

Another many-particle example occurs in pre-relativistic physics, in which the centre of mass of an object is calculated by “weighting” the position vector r i of each of its particles by their mass m i : ∑ i m i r i Centre of mass ∑ i m i The same expression will hold relativistically if each of the above masses is now a particle’s relativistic mass. [3] Another place where the idea of relativistic mass surfaces is when describing the cyclotron, a device that accelerates charged particles in circles within a constant magnetic field. [3] When particles are moving, relativistic mass provides a very economical description that absorbs the particles’ motion naturally. [3]

Let m be the rest mass, and v be the velocity as a column vector, whose entries are expressed as fractions of c and whose magnitude v is the speed as a fraction of c. [3] When it moves, its acceleration is determined by both its relativistic mass (or its rest mass, of course) and its velocity. [3] Lastly, an object has a rest mass, being the mass it “came off the production line with”, and a relativistic mass, being defined as above. [3] While relativistic mass is useful in the context of special relativity, it is rest mass that appears most often in the modern language of relativity, which centres on “invariant quantities” to build a geometrical description of relativity. [3]

When we relate the force to the resulting acceleration along each of three mutually perpendicular spatial axes, we find that in each of the three expressions a factor of γ m 0 appears, where the gamma factor γ (1-v 2 /c 2 ) -1/2 occurs frequently in special relativity. [3] Now, for all we know, that is true; we have no way, at the present time, of telling whether there would have been centrifugal force if there were no stars and nebulae around. [4] It turns out that the force F is not always parallel to the acceleration a. [3]

Now let us turn to the question of whether we should add $m_0c^2$ to the kinetic energy and say from now on that the total energy of an object is $mc^2$. [4] This much energy is left in the material in some form, as heat, potential energy, or whatever. [4]

A body with rest mass m 0 turns out to have relativistic mass γm 0. [3] The question to ask is not whether relativistic mass is fashionable or not, or who likes the idea and who doesn’t; rather, as in any area of physics notation and language, we should always ask “Is it useful ?”. [3] In 1991 Tom Sandin wrote an article in the American Journal of Physics that argued in favour of relativistic mass. [3] A debate of the subject surfaced in Physics Today in 1989 when Lev Okun wrote an article urging that relativistic mass should no longer be taught. [3]

All physicists use rest mass, but not all physicists would have relativistic mass appear in textbooks, preferring instead always to write it in terms of rest mass when it is used (although this can’t be done for photons). [3] When at rest, the object’s rest mass equals its relativistic mass. [3] Selecting one of the other of relativistic versus rest mass will never lead to problems for practitioners of the subject. [3] The above definition of mass still holds for a body at rest, and so has come to be called the body’s rest mass, denoted m 0 if we wish to stress that we’re dealing with rest mass. [3] Everyone agrees that a moving train’s rest mass is a fixed property inherent to it, just as its rest length is a fixed property inherent to it. [3] Some physicists cite this view to maintain that rest mass is the only way in which mass should be understood. [3] It’s okay to say that the mass of an electron is about 10 -30 kg without having to specify that we are referring to the rest mass; everyone knows we mean rest mass when we tabulate a particle’s mass. [3]

Besides this definition and use of relativistic mass, we wish here to write down the relativistic version of Newton’s second law, F m a. [3] The concept of relativistic mass is neatly encapsulated in the expression F d (m v )/ d t, where m is relativistic mass. [3] That’s purely a useful linguistic convention, and it does not imply that we have discarded the idea of relativistic mass, or that it should be discarded at all. [3] It’s not clear just why there should be this perennial confusion about preferences, and why some of those who dislike the idea of relativistic mass show such fundamentalist opposition to a choice of formalism that can never produce wrong results. [3]

The corresponding equation in special relativity is a little more complicated. [3] In general relativity, it’s natural to consider quantities that are conserved for a system moving on a geodesic. [3]

** This tiny “weight” of heat energy, however, represents about a million times as much energy as an equivalent weight of coal could produce, partly due to the prodigious strength of the strong nuclear force which holds the nucleus of an atom together.** [28] They both employ the concepts of energy, momentum and force and they both respect the two relations stated below that obtain between them. [27] It turns out that the relation can be derived in this case with very little more fuss merely by combining the two relations we saw above for energy, momentum and force. [27] Force: When two bodies interact, the force measures the rate of transfer of momentum and energy, such as through the two relations below. [27] The most important is force and two quantities derived from it, energy and momentum. [27]

It follows, then, that if the energy pushing the body is being converted into additional mass, then mass itself is just another form of energy, and, vice versa, energy ( energy of any sort, not just light, including sound energy, electrical energy, energy of motion, etc) therefore has an effective mass. [28] Einstein contradicts himself here because based on EMC^2, the increase in mass of an object moving near the speed of light would create a measurable gravitational change that could be used to calculate speed through absolute space, which doesn’t exist. [8] I contend that this law not only applies to speed and position in space, but also to the rate of time passage, to the measurement of mass, and to the relative effects of gravity between objects moving at the same speed. [8] And, if both mass and gravity are relative to quantum time, that would preserve the laws of physics at all speeds so that no one could calculate their own speed through absolute space by measuring their own change in mass and gravity. [8]

The energy has to go somewhere, so it is added to the mass of the object, as observed from the rest frame. [13] A black hole spinning at its maximum possible rate is much more efficient, though, and as matter swirls into a black hole, it liberates energy (as heat and light ) equivalent to 43% of the mass of the matter. [28] As the Sun pumps out energy and light, it actually also loses some of its mass, although very slowly (less than 0.1% since its birth). [28] With higher mass the speed is less and the energy level still works the same. [8] When a body loses or gains energy of motion, it loses or gains mass according to E mc 2. [27] Whenever a body gains or loses mass or energy it gains or loses a corresponding amount of energy or mass according to the conversion formula E mc 2. [27] The prodigious amounts of energy required to cause particles to literally pop out of thin air in this way is an indication of just how much energy is encapsulated within mass. [28] The equivalence of mass and energy allowed Einstein to predict that the photon has momentum, even though its mass is zero. [13] Basically, when einstein put forward the very famous equation, $E M.C^2$, he meant very clearly that mass IS energy, and energy IS mass. [11] Put most briefly, Einstein’s equation says that energy and mass are really just two different names for the same thing. [27] The flywheel has considerable energy of motion and thus a corresponding mass. [27] The only process that converts mass into energy with 100% efficiency is the meeting of matter and antimatter. [28] Because c 2 is so large, the result of converting even a small part of the mass into another form is the release of a huge amount of energy. [27] What about other forms of energy ? What about heat energy, chemical energy, electrical energy, etc. Do bodies also lose and gain mass according to E mc 2 when they lose or gain these forms of energy? Yes they do, but it takes a little bit more argumentation to establish the result. [27] To me, devolving honest perception into theoretical soup does not make you any more informed on the true nature of mass vis a vis energy and velocity. [11] The conversion of energy into mass leads to the concept that mass and energy are somewhat equivalent, and that it is actually the total which is conserved. [29] This famous equation asserts an equivalence of energy and mass. [27] The same principle applies to nuclear reactors and nuclear weapons, and even to the energy liberated in chemical reactions (where the change in mass is too small to be measured). [29] The production of energy in nuclear reactions (i.e. fission and fusion) was shown to be the conversion of a small amount of atomic mass into energy. [13] Because of this there became an equivalence where a certain amount of mass is equal to a certain amount of energy. [8] A small amount of mass under conversion yields a huge amount of energy. [27] When a piece of coal is burned, mass – energy is converted to heat energy, and the total products of burning (ash, gases, etc) would in fact weigh slightly less than the original coal. [28] Both of these examples suggest that the energy ( photons ) leaving the Sun actually weighs something, actually has mass, even if very little. [28] The products of this reaction have slightly less mass than the original hydrogen and this difference in mass (Dm) accounts for the radiant energy (E Dm c^2 4.0E16 J/s) liberated. [29] The reverse process, conversion of mass into energy, is also possible. [29]

The equation breaks down when the electron velocity approaches the speed of light as mass increases. [11] The increase in mass limits and object from exceeding the speed of light. [8] Theoretically, the mass would become infinite if the object could be accelerated all the way to the speed of light. [12]

This theory describes how physical properties with which we are familiar (mass, length, period of oscillation of a physical system, etc) would appear if viewed by an observer who is in uniform motion (constant velocity) relative to the observed object. [29] Gravity is not a force that keeps objects in orbit, but that space itself is bent by objects with mass and that an object orbits because it is really following a straight line through bent space. [8] When an object is at rest (relative to the observer), it has the usual (inertial tendency to resist an applied force) mass that we are all familiar with. [12] I therefore predict that a particle accelerated to nearly light speed will appear to increase in mass as Einstein predicts and will have an increased gravitational force proportional to the increase on mass as measured by a stationary observer as it passes. [8]

“The relativistic increase of mass happens in a way that makes it impossible to accelerate an object to light speed: The faster the object already is, the more difficult any further acceleration becomes. [11] This equation describes the increase in mass that limits an object from crossing the light barrier. [8] As one can not add any speed in speed of light, the Lorentz transformation equations are derived and using these variation of mass with velocity relation. [11] If this is so, then observers moving at different speeds will measure mass and gravity differently based on their quantum time thickness. [8] Their rate of motion through time cancels out their increase in mass and gravity due to the increase in quantum time thickness. [8] If mass is really a thickness in quantum time, then the faster an object moves, and the more apparent mass it has because of that motion, the stronger the gravitational field. [8]

From that point of view there is obviously no dependence of the (rest) mass on the speed of an object. [11] And, therefore, the mass of an object does not increase when its speed increases. [11] For speeds significantly less than the speed of light, the increase in mass is nearly imperceptible, but as the speed of light is approached, the mass starts to increase very rapidly toward infinity. [12] According to classical physics, this arrangement is quite able to accelerate the mass past the speed of light, as long as the blocks are massive enough and the materials strong enough not to break in the violent collisions. [27] By extension, if a material body were ever to reach the speed of light it would effectively have to have acquired an infinite mass. [28] If a body with mass is pushed ever closer to the speed of light, the body would have to become harder and harder to push, so that its speed never actually reached or exceeded the speed of light, which we know to be the de facto maximum speed. [28] The closer the body gets to the speed of light, the greater its mass becomes and the harder it gets to accelerate. [27]

The higher mass times the slower speed will come to the same amount of kinetic energy. [8] When he calculates his kinetic energy, he multiplies his unchanged mass times his near infinite speed. [8]

Conservation of momentum requires that the rest mass of the original configuration consist not just of the rest masses of the two particles, but also a contribution equal to the energy necessary to propel them apart at the speed v. We suggested an ideal massless spring to represent this energy, but the above argument applies to any form of energy (e.g., a small amount of gunpowder, accounting for the chemical energy). [30]

As can perhaps be reasonably easily deduced from these equations, as the velocity ( v ) approaches the speed of light ( c ), energy ( E ) approaches infinity, indicating that the body would in fact require an infinite amount of energy to accelerate to the speed of light. [28] As a body approaches the speed of light, then, the energy put into pushing the body clearly can not be used to increase its velocity and must therefore go somewhere else. [28]

Another way of expressing the fact that a massive object cannot be accelerated to the speed of light is through the concept of energy. [12] Adding more energy to an object will not make it go faster since the speed of light is the limit. [13] Since it takes an infinite amount of energy to be at the speed of light, and we don’t have infinite energy, then we never actually get there. [8]

What actually changes at relativistic speeds is the dynamical law that relates momentum and energy depend with the velocity (which was already written). [11] Gravitational waves carry energy and momentum, travel at the speed of light, and are characterized by frequency and wavelength. [31] At high speeds instead of more energy resulting in more motion through space, it causes more motion in time. [8] As more and more energy is added the increase in speed through space becomes very small and the increase in speed through time become near infinite. [8] The correct (from that point of view) way to talk about the phenomenon is to say that with increase of the speed of an object you need more and more energy in order to make it move faster. [11] If an object became more massive as it’s speed increased, then it would take more energy to increase the speed of the object. [8]

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10. (46) Relativity

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15. (38) Einstein’s Relativity

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29. (14) Albert Einstein

30. (13) Does Relativistic Mass Imply Special Relativity?

31. (13) Dynamic Energy in Physics

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33. (12) What is theory of relativity? – Definition from WhatIs.com

34. (11) Attempt to explain away “dark energy? takes a hit | Science | AAAS

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37. (5) TR-2-15.ppt

38. (3) Relativistic Momentum