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Message: <blockquote data-quote="mutantlast" data-source="post: 2941418" data-attributes="member: 115180">I did not tell you that big bang machine is not a reality. I know about it.. I tolled you about being fast than light..You can travel in light speed, Only if you have 0 mass. It is the theory.. PLS study more about time and space theories like this..then you will understand about this.. eference frames, coordinates and the Lorentz transformation   <img src="http://upload.wikimedia.org/wikipedia/commons/e/e4/Lorentz_transform_of_world_line.gif" alt="" class="fr-fic fr-dii fr-draggable " style="" /> Diagram 1. Changing views of spacetime along the world line of a rapidly accelerating observer. In this animation, the vertical direction indicates time and the horizontal direction indicates distance, the dashed line is the spacetime trajectory ("world line") of the observer. The lower quarter of the diagram shows the events that are visible to the observer, and the upper quarter shows the light cone- those that will be able to see the observer. The small dots are arbitrary events in spacetime. The slope of the world line (deviation from being vertical) gives the relative velocity to the observer. Note how the view of spacetime changes when the observer accelerates.   Relativity theory depends on "reference frames". A reference frame is an observational perspective in space at rest, or in uniform motion, from which a position can be measured along 3 spatial axes. In addition, a reference frame has the ability to determine measurements of the time of events using a 'clock' (any reference device with uniform periodicity). An event is an occurrence that can be assigned a single unique time and location in space relative to a reference frame: it is a "point" in space-time. Since the speed of light is constant in relativity in each and every reference frame, pulses of light can be used to unambiguously measure distances and refer back the times that events occurred to the clock, even though light takes time to reach the clock after the event has transpired. For example, the explosion of a firecracker may be considered to be an "event". We can completely specify an event by its four space-time coordinates: The time of occurrence and its 3-dimensional spatial location define a reference point. Let's call this reference frame S. In relativity theory we often want to calculate the position of a point from a different reference point. Suppose we have a second reference frame S', whose spatial axes and clock exactly coincide with that of S at time zero, but it is moving at a constant velocity <img src="http://upload.wikimedia.org/math/2/d/3/2d3fdc651d296cf7a5bde9d58fa58c47.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> with respect to S along the <img src="http://upload.wikimedia.org/math/6/b/2/6b206a28e60f665e235f89f460448467.png" alt="" class="fr-fic fr-dii fr-draggable " style="" />-axis. Since there is no absolute reference frame in relativity theory, a concept of 'moving' doesn't strictly exist, as everything is always moving with respect to some other reference frame. Instead, any two frames that move at the same speed in the same direction are said to be comoving. Therefore S and S' are not comoving. Let's define the event to have space-time coordinates <img src="http://upload.wikimedia.org/math/0/d/8/0d871653a78a18c3218d0d8b87d03fc9.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> in system S and <img src="http://upload.wikimedia.org/math/b/1/0/b100279dfc8b3561ac2e3b52e9373ce7.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> in S'. Then the Lorentz transformation specifies that these coordinates are related in the following way: <img src="http://upload.wikimedia.org/math/3/d/1/3d19435a89f6266f75ba4428624a1bc2.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> where <img src="http://upload.wikimedia.org/math/3/d/d/3ddd7a11a3c82d824dc8204b3c740d49.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> is called the Lorentz factor and <img src="http://upload.wikimedia.org/math/0/8/1/08163b03d3a58471d7f88fc4e581a282.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> is the speed of light in a vacuum. The <img src="http://upload.wikimedia.org/math/e/c/9/ec9ff0a12771e750c2685d3b89a37c79.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> and <img src="http://upload.wikimedia.org/math/7/7/6/77698ae92ac0435f8da1e266eeb528e3.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> coordinates are unaffected, but the <img src="http://upload.wikimedia.org/math/6/b/2/6b206a28e60f665e235f89f460448467.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> and <img src="http://upload.wikimedia.org/math/0/c/6/0c68620ee2ea4f1286fcd672a47ea080.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> axes are mixed up by the transformation. In a way this transformation can be understood as a hyperbolic rotation. A quantity invariant under Lorentz transformations is known as a Lorentz scalar.  [edit] Simultaneity  <img src="http://upload.wikimedia.org/wikipedia/en/thumb/e/e4/Relativity_of_simultaneity_%28color%29.png/180px-Relativity_of_simultaneity_%28color%29.png" alt="" class="fr-fic fr-dii fr-draggable " style="" />  <img src="http://en.wikipedia.org/skins-1.5/common/images/magnify-clip.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> Event B is simultaneous with A in the green reference frame, but it occurred before in the blue frame, and will occur later in the red frame.    Main article: Relativity of simultaneity  From the first equation of the Lorentz transformation in terms of coordinate differences <img src="http://upload.wikimedia.org/math/5/3/2/532fc767d8b4fac5b36c40cf4faa9215.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> it is clear that two events that are simultaneous in frame S (satisfying <img src="http://upload.wikimedia.org/math/7/6/9/769fb77b3f855bce076350ec36de1fde.png" alt="" class="fr-fic fr-dii fr-draggable " style="" />), are not necessarily simultaneous in another inertial frame S' (satisfying <img src="http://upload.wikimedia.org/math/9/7/7/977a5928a0c3b56941099eb8f2e3903d.png" alt="" class="fr-fic fr-dii fr-draggable " style="" />). Only if these events are colocal in frame S (satisfying <img src="http://upload.wikimedia.org/math/1/1/0/110e15ea845293c80fd86b2ecded98d7.png" alt="" class="fr-fic fr-dii fr-draggable " style="" />), will they be simultaneous in another frame S'.  [edit] Time dilation and length contraction Writing the Lorentz transformation and its inverse in terms of coordinate differences we get <img src="http://upload.wikimedia.org/math/3/4/9/3491a6c9567162e3c7b087b89afb1cfd.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> and <img src="http://upload.wikimedia.org/math/2/e/b/2eb931bf3d165b17113d841d8c0ccd33.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> Suppose we have a clock at rest in the unprimed system S. Two consecutive ticks of this clock are then characterized by Δx = 0. If we want to know the relation between the times between these ticks as measured in both systems, we can use the first equation and find: <img src="http://upload.wikimedia.org/math/9/1/7/9171bfb675e35af3bc928c31f8d8a9be.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> for events satisfying <img src="http://upload.wikimedia.org/math/1/e/7/1e72d4936ea0c297c0e3c0dd3d07a5ea.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> This shows that the time Δt' between the two ticks as seen in the 'moving' frame S' is larger than the time Δt between these ticks as measured in the rest frame of the clock. This phenomenon is called time dilation. Similarly, suppose we have a measuring rod at rest in the unprimed system. In this system, the length of this rod is written as Δx. If we want to find the length of this rod as measured in the 'moving' system S', we must make sure to measure the distances x' to the end points of the rod simultaneously in the primed frame S'. In other words, the measurement is characterized by Δt' = 0, which we can combine with the fourth equation to find the relation between the lengths Δx and Δx': <img src="http://upload.wikimedia.org/math/2/b/c/2bc787848ed680ebda1c3cfbe2d90e50.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> for events satisfying <img src="http://upload.wikimedia.org/math/3/6/6/3669eefd79bd0397b462f2bdc31737ac.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> This shows that the length Δx' of the rod as measured in the 'moving' frame S' is shorter than the length Δx in its own rest frame. This phenomenon is called length contraction or Lorentz contraction. These effects are not merely appearances; they are explicitly related to our way of measuring time intervals between events which occur at the same place in a given coordinate system (called "co-local" events). These time intervals will be different in another coordinate system moving with respect to the first, unless the events are also simultaneous. Similarly, these effects also relate to our measured distances between separated but simultaneous events in a given coordinate system of choice. If these events are not co-local, but are separated by distance (space), they will not occur at the same spacial distance from each other when seen from another moving coordinate system. See also the twin paradox.  [edit] Causality and prohibition of motion faster than light See also: Causality  <img src="http://upload.wikimedia.org/wikipedia/commons/thumb/2/27/Light_cone.svg/180px-Light_cone.svg.png" alt="" class="fr-fic fr-dii fr-draggable " style="" />  <img src="http://en.wikipedia.org/skins-1.5/common/images/magnify-clip.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> Diagram 2. Light cone   In diagram 2 the interval AB is 'time-like'; i.e., there is a frame of reference in which event A and event B occur at the same location in space, separated only by occurring at different times. If A precedes B in that frame, then A precedes B in all frames. It is hypothetically possible for matter (or information) to travel from A to B, so there can be a causal relationship (with A the cause and B the effect). The interval AC in the diagram is 'space-like'; i.e., there is a frame of reference in which event A and event C occur simultaneously, separated only in space. However there are also frames in which A precedes C (as shown) and frames in which C precedes A. If it were possible for a cause-and-effect relationship to exist between events A and C, then paradoxes of causality would result. For example, if A was the cause, and C the effect, then there would be frames of reference in which the effect preceded the cause. Although this in itself won't give rise to a paradox, one can show[19][20] that faster than light signals can be sent back into one's own past. A causal paradox can then be constructed by sending the signal if and only if no signal was received previously. Therefore, one of the consequences of special relativity is that (assuming causality is to be preserved), no information or material object can travel faster than light. On the other hand, the logical situation is not as clear in the case of general relativity, so it is an open question whether there is some fundamental principle that preserves causality (and therefore prevents motion faster than light) in general relativity. Even without considerations of causality, there are other strong reasons why faster-than-light travel is forbidden by special relativity. For example, if a constant force is applied to an object for a limitless amount of time, then integrating F = dp/dt gives a momentum that grows without bound, but this is simply because p = mγv approaches infinity as v approaches c. To an observer who is not accelerating, it appears as though the object's inertia is increasing, so as to produce a smaller acceleration in response to the same force. This behavior is in fact observed in particle accelerators. See also the Tachyonic Antitelephone.  [edit] Composition of velocities  Main article: Velocity-addition formula  If the observer in S sees an object moving along the x axis at velocity w, then the observer in the S' system, a frame of reference moving at velocity v in the x direction with respect to S, will see the object moving with velocity w' where <img src="http://upload.wikimedia.org/math/2/9/1/291bfd8042576ef4c34fb191693e72c0.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> This equation can be derived from the space and time transformations above. Notice that if the object were moving at the speed of light in the S system (i.e. w = c), then it would also be moving at the speed of light in the S' system. Also, if both w and v are small with respect to the speed of light, we will recover the intuitive Galilean transformation of velocities: <img src="http://upload.wikimedia.org/math/0/1/0/01024237ce4b4758264717bfc5226ef7.png" alt="" class="fr-fic fr-dii fr-draggable " style="" />.  [edit] Mass, momentum, and energy  Main article: Mass in special relativity  Main article: Conservation of energy  In addition to modifying notions of space and time, special relativity forces one to reconsider the concepts of mass, momentum, and energy, all of which are important constructs in Newtonian mechanics. Special relativity shows, in fact, that these concepts are all different aspects of the same physical quantity in much the same way that it shows space and time to be interrelated. There are a couple of (equivalent) ways to define momentum and energy in SR. One method uses conservation laws. If these laws are to remain valid in SR they must be true in every possible reference frame. However, if one does some simple thought experiments using the Newtonian definitions of momentum and energy one sees that these quantities are not conserved in SR. One can rescue the idea of conservation by making some small modifications to the definitions to account for relativistic velocities. It is these new definitions which are taken as the correct ones for momentum and energy in SR. Given an object of invariant mass m traveling at velocity v the energy and momentum are given (and even defined) by <img src="http://upload.wikimedia.org/math/0/e/4/0e419401477937951f338ef318c3d020.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> <img src="http://upload.wikimedia.org/math/0/d/e/0de7c35654c4a75d1799c03b4a5c9376.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> where γ (the Lorentz factor) is given by <img src="http://upload.wikimedia.org/math/9/c/9/9c9326e31375f7b1414ba44625f82617.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> where <img src="http://upload.wikimedia.org/math/4/b/7/4b7d8a868a6b40d0acedc244a1492e25.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> is the ratio of the velocity and the speed of light. The term γ occurs frequently in relativity, and comes from the Lorentz transformation equations. Relativistic energy and momentum can be related through the formula <img src="http://upload.wikimedia.org/math/f/6/5/f653e9c4c421742eebeca629813279d0.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> which is referred to as the relativistic energy-momentum equation. It is interesting to observe that while the energy <img src="http://upload.wikimedia.org/math/4/b/8/4b88f47f80273fd5788e1e20aa81c38a.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> and the momentum <img src="http://upload.wikimedia.org/math/5/a/3/5a34bb082daf037b3c4b14c13af6855b.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> are observer dependent (vary from frame to frame) the quantity <img src="http://upload.wikimedia.org/math/f/6/5/f653e9c4c421742eebeca629813279d0.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> is observer independent. For velocities much smaller than those of light, γ can be approximated using a Taylor series expansion and one finds that <img src="http://upload.wikimedia.org/math/0/2/7/027310ccc3a42491d3f9fc1b802ffb28.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> <img src="http://upload.wikimedia.org/math/7/d/8/7d80e8d905402dac56a5d950fd9eea3b.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> Barring the first term in the energy expression (discussed below), these formulas agree exactly with the standard definitions of Newtonian kinetic energy and momentum. This is as it should be, for special relativity must agree with Newtonian mechanics at low velocities. Looking at the above formulas for energy, one sees that when an object is at rest (v = 0 and γ = 1) there is a non-zero energy remaining: <img src="http://upload.wikimedia.org/math/f/5/7/f57148ca06805f12698851acbfafdbaf.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> This energy is referred to as rest energy. The rest energy does not cause any conflict with the Newtonian theory because it is a constant and, as far as kinetic energy is concerned, it is only differences in energy which are meaningful. Taking this formula at face value, we see that in relativity, mass is simply another form of energy. In 1927 Einstein remarked about special relativity: Under this theory mass is not an unalterable magnitude, but a magnitude dependent on (and, indeed, identical with) the amount of energy.[21] This formula becomes important when one measures the masses of different atomic nuclei. By looking at the difference in masses, one can predict which nuclei have extra stored energy that can be released by nuclear reactions, providing important information which was useful in the development of nuclear energy and, consequently, the nuclear bomb. The implications of this formula on 20th-century life have made it one of the most famous equations in all of science.  [edit] Relativistic mass Introductory physics courses and some older textbooks on special relativity sometimes define a relativistic mass which increases as the velocity of a body increases. According to the geometric interpretation of special relativity, this is often deprecated and the term 'mass' is reserved to mean invariant mass and is thus independent of the inertial frame, i.e., invariant. Using the relativistic mass definition, the mass of an object may vary depending on the observer's inertial frame in the same way that other properties such as its length may do so. Defining such a quantity may sometimes be useful in that doing so simplifies a calculation by restricting it to a specific frame. For example, consider a body with an invariant mass m moving at some velocity relative to an observer's reference system. That observer defines the relativistic mass of that body as: <img src="http://upload.wikimedia.org/math/b/1/4/b14f7fe6981082bc7c748bace9149e70.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> "Relativistic mass" should not be confused with the "longitudinal" and "transverse mass" definitions that were used around 1900 and that were based on an inconsistent application of the laws of Newton: those used f=ma for a variable mass, while relativistic mass corresponds to Newton's dynamic mass in which <img src="http://upload.wikimedia.org/math/6/c/8/6c800c98064d48e822ad3db5a2ddb534.png" alt="" class="fr-fic fr-dii fr-draggable " style="" /> and <img src="http://upload.wikimedia.org/math/5/d/9/5d9efdf6aa0fb7a612740d2a786ac583.png" alt="" class="fr-fic fr-dii fr-draggable " style="" />. Note also that the body does not actually become more massive in its proper frame, since the relativistic mass is only different for an observer in a different frame. The only mass that is frame independent is the invariant mass. When using the relativistic mass, the applicable reference frame should be specified if it isn't already obvious or implied. It also goes almost without saying that the increase in relativistic mass does not come from an increased number of atoms in the object. Instead, the relativistic mass of each atom and subatomic particle has increased. Physics textbooks sometimes use the relativistic mass as it allows the students to utilize their knowledge of Newtonian physics to gain some intuitive grasp of relativity in their frame of choice (usually their own!). "Relativistic mass" is also consistent with the concepts "time dilation" and "length contraction".</blockquote>

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