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Everything posted by Janus

  1. How do you get that from the second analogy? Both men end up next to each other at the end. Each man just took a different route to get there, with one of them taking a longer path. In the analogy, the "time" it takes to get to that final point as measured by each man is equal to the number of steps he had to take. They start at the same point and end at the same point, but each take a different number of steps(time) to get there. There is no need for either to "jump forward or back". Again, time is not the absolute progression you keep wanting to make it.
  2. The problem is in how you are visualizing time. Maybe an analogy will help. Here's the analogy of how you are looking at time. You have two men starting at the same point and walking in the same direction at different speeds (the two twins aging at different rates.) In this scenerio, one man is always ahead of the other, and if "the future" lies in the direction they are walking, then the other man is always in his "past". (thus your confusion of how they could meet again.) In this view "Time" is a absolute reference and everyones movement through time is measured with respect to this reference. But this is not how "Time" works. Instead it works more like this: The two men start off at the same point, but don't walk in the same direction, but at an angle to each other. Again, one man walks faster than the other. At some point, the faster walking man changes direction so that he will now intercept the slower man. After the two men meet again they will have walked different distances, with the faster man having traveled the longer distance. (This is like one twin being older when they meet up again.) In this case, "Time" is not a universal absolute measurement, but a relative one. Just as as the two men can walk different distances starting from the same point and still meet up, The two twins can age differently and not end up in each other's past or future.
  3. Janus

    Relativity Q

    No, this is after the Doppler effect is factored out. at any given point this depends on which ship you are making the determination from. More time has elasped for ship 2. But why this is so depends on which ship is made to make the detemination. From ships 2's perspective, the following sequence of the events takes place. 1.Ship 1 speeds off at .99c and thus its clock runs slow by a factor of 7. 2.Ship 2 instantly turns around when it is .99 light hours distant and comes back at .99c, its clock still running slow. 3. Ship 1 returns to Ship 2 after 2 hrs Ship 2 time, having aged only 2/7 of an hr by Ship 1's clock. From Ship 1's perspective. 1. Ship 1 undergoes an instantaneous acceleration and the Relative velocity between ship 1 and 2 becomes .99c, at this point clock 2's clock runs slow by a factor of 7. 2. After 1/7 of an hour has passed on its own clock, Ship 2 undegoes a second instantanous acceleration, after which it has a .99c velocity towards ship 2. At the instant of acceleration ship 1 will determine that ship 2's clock has jumped forward in time by 1 47/49 hours, then runs slow by a factor of 7 thereafter. 3. Ship 1 and ship 2 meet up again in another 1/7 of an hour by Ship 1's clock. total time elasped on Ship 1's clock = 1/7hr + 1/7hr = 2/7hr. Total time elasped on Ship 2's clock = 1/49hr + 1 27/49hr + 1/49hr = 2 hrs. This jump forward that Ship1 sees in ship 2's clock is due to the fact that when Ship 1 goes from .99c away from ship 2 to .99c towards ship 2, it changes interial frames of reference.
  4. No. Relativity says that "Time" is a relative measurement. Or put another way, time is "what clocks measure" and clocks in relative motion to each other measure time differently. They will not even agree whether given events are simultaneous or not. The problem you are having is that you are still stuck on the idea of time as an universal absolute concept rather than the relative one that it is. Absolute time behaves something like the directions of North and South. Put two people in a room and no matter how they are facing, they both agree which direction North is. Relative time behaves like the directions left and right. Two people standing in the same room can disagree on which direction "right" is, depending on how they are facing relative to each other. One's left may be the other's right. It is this second example that is closer to how real time behaves.
  5. As a star collapses to zero size, its surface gravity approaches infinity. This is due to the fact that the Newtonian gravitation equation is: [math]A_g = \frac{M}{r^2}[/math] Where Ag is the acceleration due to gravity. As the star collapses r approaches 0 and thus Ag approaches infinity. However, the total energy of the gravitational field, nor the acceleration due to gravity at a fixed distance does not change as the star collaspes. There is no difference in the force of gravity felt by an object a given distance from the star from before the collapse and after the collapse. Thus there is no need to involve density in calculating the gravity. As far as the thermodynamics go, In the case of the collapsing star, the increase in temperature comes from the the gravitational potential of the stars mass as it collapses. As the material of the star falls inward, it gives up potential energy for kinetic energy and the star gets hotter. But, the total energy of the star does not increase, there has just been a transfer from one kind of energy to another. Since the total energy of the Star was not infinite before the collapse, it will not be so after the collapse.
  6. First off, in Relativity material objects like trains can not travel at the speed of light, 99.999...9% percent of the speed of light, yes, but not the speed of light itself. The other thing is that, due to length contraction, the people in the train will not measure the distance between you and the sensor as being 100m. Nor will they measure the distance between the point at which the train turns on its lights and you as being 1 lightsecond in distance. The distance will contract by an amount dependant on how close to the speed of light the relative velocity is. At very nearly the speed of light, these distances drop to nearly zero in length. So while form your perspective you would see the light strike the sensor just split seconds before the train reaches it, the people on the train see the light strike the sensor just split seconds before the train reaches its also, becuase by their measurement the train was almost on top of the sensor already when the lights were turned on.
  7. Janus

    earth and moon

    First off, the Moon has 1/81 the mass of the Earth, not 1/6. The 1/6 is the surface gravity of the Moon. Secondly, the force acting between the Earth and the Moon is equal to [math]F = \frac{GM_1M_2}{d^2}[/math] M1 and M2 are the masses of the Earth and Moon respectively. But you get the same answer for force if M1 is the mass of the Moon and M2 is the mass of the Earth. They exert equal force on each other, the Moon just has a greater response to this force because of its smaller mass.
  8. You seem to be confused over different type of energies. The energy that is relative is the kinetic energy. Forget about living organisms and the energy they get from food. Kinetic energy depends on the object's relative motion. A hunk of dead rock moving at 20 ft per sec relaitve to you has kineitc energy. A dead you moving relative to me has a kinetic energy, and has a different kinetic energy as measured by someone moving relative to me. All you have to know to catch a football is its relative motion with respect to you. You don't have to know that the surface of the Earth is turning at about 1670 kph at the Equator, or that the Earth is orbitng the Sun at 30 kph, or that the Solar system is moving at some 200 kph. Try this experiment: Have someone drive you in a car down a straight stretch of road maintaining a constant speed. Toss a ball straight up into the air and catch it. Did you have to take the car's speed down the road into account? No. When it is said that there is no absolute motion, it means that there is no special "prefered" reference that motion can be measured by. Animals that hunt track their prey's relative motion to themselves not by some universal Absolute motion.
  9. Put both you and the runner on a giant treadmill, and add a third observer sitting in chair beside the treadmill. From his point of view the treadmill runs in the opposite direction of and at the same speed as the runner. (the runner doesn't move relative to this observer. ) Thus we have three observers: two sitting and burning no calories, and one running and burning calories. From the positon of one seated observer, neither he or the runner are moving, yet the runner is burning calories and he himself isn't. Also, the other seated observer is moving and not burning calories either. The problem is that the calories the runner burns has nothing to do with his motion, it has to do the inefficiencies of muscles and the act of running itself. He burns just as many calories staying in one place against a treadmill as he does running on a track. It also has nothing to do with his kinetic energy, which is the energy associated with motion. And it is this kinetic energy that accounts for "relativistic" mass. And kinetic energy is frame dependant, it depends on relative motion. Thus the runner, by the measure of the person seated by the tread mill, is burning calories like mad, but is motionless, and thus has zero kinetic energy and zero "relativistic mass". OTOH, the according to the other observer, the runner is in motion, has a kinetic energy and a "relativistic mass". The thing is, that while energy is conserved within any single frame, it is not conserved between frames. The same object can have different amounts of energy when measured by different observers. So no, there isn't any absolute way to measure motion.
  10. The ping pong ball runs out of energy because it loses it to the friction between it and the bed. The Earth orbits in the vaccuum of space where friction doesn't come into play. If your bed sheets were made of a fricitionless material and you sucked all the air out of the room to remove air friction, the ping pong ball would also continually orbit the the bowling ball.
  11. Another example was the water injection systems used on some WWII aircraft. In order to get more power, they would use a turbocharger. The problem was that this could lead to pre-detonation of the fuel mixture, which, in turn, could damage the engine. The water was injected to prevent this pre-detonation.
  12. But this would be a arbitrary choice for "absolute location and absolute speed." I could choose a completely different point in space, one that has a motion relative to yours, and claim it to be the origin of Absolute space and motion, and my choice would be just as valid as yours. There is no way to make a definite choice between the two. Neither can be prefered over the other. IOW, there is no objective test that can be performed that shows that my point is really moving and yours motionless or that mine is motionless and yours is really moving. This is what is meant by there being no absolute motion; that any assignment of such is purely subjective and not objective.
  13. Why not just use the ones already in existance: http://en.wikipedia.org/wiki/Relativistic_rocket Unless it just a exercise in deriving them yourself. In which case, isn't asking for help cheating?
  14. Actually your equation is quite bad. While it gives a fairly close answer for this particular situation, this not the case for all possible variations. For instance, if you make one velocity 0.5c and the other -0.5c, the correct formula gives [math] \frac{0.5c+(-0.5)c}{1+\frac{0.5c(-0.5c)}{c^2}}= 0c[/math] While yours gives [math] 0.5c +(1-0.5)(-.05c) = .25c[/math] Secondly, the proper equation is derived from the postulates of the theory, while yours was merely an attempt at a "curve fit".
  15. Actually [math]\frac{0.99c+0.5c}{1+ \frac{0.99c(0.5c)}{c^2} }= .9967c[/math]
  16. Not for the occupants of the ship, they feel a constant 20m/sec² acceleration the whole time.
  17. Taking Relativity into account: [math]t_{ship time} = \frac{c}{a} \cosh^{-1}\left ( \frac{ad}{c^2}+1 \right ) = 2.24 yr[/math] Earth time would be 26.39 yr
  18. Atmospheres can get thicker or thinner or change composition, but they don't "rupture".
  19. Well, that can depend on who you ask. Some have the position that SR only holds in intertial reference frames, and since it deals with acceleration, it is GR Other would say that it is a result The Realtivity of Simultaneity and thus an SR effect. At the moment of the first passing the distance between the two twins is small so the acceleration effect will be small. The velocity difference will be large, so each twin would see the other's clock running slow. As time goes by, the distance will increase, and the velocity difference will decrease, each twin sees the other's clock as running fast. When the two twins reach the turnaround point (that instant when their velocities stasrt to change direction) The total time each twin will have seen the other's clock gain and lose due to running fast and slow will cancel out, and the accumulated time on both of their clocks will be the same. The two twins start to come back together and the reverse of the outbound leg happens. At the instant they pass each other, their clocks will once again agree. (but only for that instant, for each twin will see the other's as runing slow at this point.)
  20. Acceleration has an effect on what each twin sees. After factoring out time dilation due to velocity: If your accelerate away from a clock, you see it running slower. If you accelerate towards a clock, you see it running faster. How fast or how slow depends on the magnitude of the acceleration, and the distance to the clock as measured along the line of acceleration. (Note, the actual distance between the observer and the clock does not have to be increasing or decreasing. If you have two clocks accelerating in the same direction at the same rate, the leading clock will run faster than the trailing clock, according to both clocks.) If you factor in this effect, it turns out, that each twin will see the other's clock as running fast during a portion of the trip, and this will cancel out that portion when he saw it running slow, so that, at the end, each twin will have aged the same.
  21. Don't count on FTL to save us from population growth. Even if we had it right now, in order to maintain a fixed population on the Earth, we would have to load people on ships at a rate of 91 million per day.
  22. The Great Bear, aka the Big Dipper, more properly known as Ursa Major, is a Northernly constellation of 7 stars. The front two stars of the dipper are called the pointers, because if you extend the line joining them it will point to the last star in the handle of the Little Dipper, aka the Small Bear, or Ursa Minor (another 7 star constellation). This star, named Polaris, is the North star.
  23. Okay, now that I understand where you are coming from, let's attack this from a different direction. Start with a a given mass (M) that can be converted to energy, either in whole or in part. If we covert it all to energy in the form of photons this energy will be: [math]E=Mc^2[/math] (The total energy equivalence of M) and the momentum: [math]P_p= \frac{E}{c} = \frac{Mc^2}{c} = Mc[/math] If we convert all but a part (m) to energy and that energy is in the form of the kinetic energy of m, the total energy is: [math]E= \gamma mc^2 [/math] Since the total energy involved is conserved, it must stay the same both before and after conversion, thus. [math]E=Mc^2[/math] and [math]E= \gamma mc^2 [/math] are the same and so, [math]Mc^2= \gamma mc^2 [/math] [math]M= \gamma m [/math] Solving for gamma: [math] \gamma = \frac{M}{m} [/math] The momentum will be [math]P_m = \gamma mv[/math] substituting from above: [math]P_m =\frac{M}{m} mv[/math] [math]P_m =Mv[/math] Comparing Pm to Pp: [math]\frac{P_p}{P_m} = \frac{Mc}{Mv} = \frac{c}{v}[/math] Which is the same relationship you arrived at from a different direction. Here, however we can see why the gamma factor doesn't come into play in the final analysis: If we go back to the equation: [math]M= \gamma m [/math] and re-arrange: [math]m= \frac{M}{\gamma} [/math] We see that as you convert more and more of M to energy to increase the velocity of m(the rest mass of the remaining matter), m decreases such that that amount of mass that gamma has to work on in [math]P_m = \gamma mv[/math] decreases at the same rate as gamma increases. As a result, the momentum increases in a steady fashion until it reaches a maximum when all the matter is converted to photons.
  24. You mean that you have x amount of energy that you can either release as photons, or partially convert to matter while using the rest to provide the velocity? This second choice seems a little silly, as it would be easier to store the mass that you are ejecting as matter rather than trying to store it as energy and then converting. Also, in this case, the momentum you will get will depend on how much of the energy is converted to matter. From 0 if you converted all of it to matter (leaving none for kinetic energy and giving it 0 velocity) to approaching that of the photons as the amount of matter approaches 0 and its velocity approaches c.
  25. [math] \gamma mc^2[/math] is the total energy equivalence of the matter, which includes the energy equivalence of the rest mass of the matter (The energy released if you convert this matter into energy) But you are not converting this matter into energy, you are just shootiing it out the back as reaction mass. What you want here is the kinetic energy of the matter alone, which is found by [math]c^2( \gamma m -m)[/math] [math] p = \frac{c^2( \gamma m -m)}{c}[/math] [math] p = c( \gamma m -m)[/math] Now we have [math] c( \gamma m -m)[/math] compared to [math]\gamma mv[/math] let's assume that v = .866 c, which gives a gamma of 2. Then for photons: [math]p= c( 2m -m) = cm[/math] and and for matter [math]p= 2 m (.866c) = 1.732cm [/math] matter has more momentum at the same energy. at .1c we would get for photons [math]p = .005cm[/math] and matter [math]p= .1005cm[/math] at .99c we would get for photons [math]p = 6cm[/math] and matter [math]p= 6.93cm[/math] Actually, it has more to do with the relationship between energy and momentum. You get the same type of effect in non-relativistic physics. consider [math]p=mv[/math] and [math]E= \frac{mv^2}{2}[/math] Now, lets take two masses m1 and m2, with equal kinetic energy. so that [math]\frac{m_1 v_1^2}{2} = \frac{m_2 v_2^2}{2}[/math] [math]m_1 v_1^2 = m_2 v_2^2[/math] [math]\frac{m_1}{m_2}=\frac{v_2^2}{v_1^2}[/math] [math]\frac{m_1}{m_2}=\left (\frac{v_2}{v_1}\right )^2[/math] Thus the ratio of the masses is equal to the inverse of the square of the ratio of the velocities. If m1 is twice the mass of m2 then v1 is .707 that of v2 if v1 is 1 m/s and m1 = 1kg then v2 is 1.414 m/s and m2 =.5kg comparing momentums [math]1kg(1\frac{m}{s}) = 1\frac{kgm}{s}[/math] and [math].5kg(1.414\frac{m}{s}) = .707\frac{kgm}{s}[/math] The larger mass (m1) has a greater momentum than the smaller mass (m2) when both are at the same energy. No relativistic effects involved.
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