Janus

Now your twin brother could not travel at c, but he could travel at .866c. In which case, you would would see him age at half speed and only age 4 min during the trip. He on the other hand, would measure the distance between Sun and Earth as only half that that you did (length contraction) and for him the trip would then take only 4 min. Thus both of you agree that he aged only 4 min during the trip.

Yes, people do get muddled up, A part of the reason is that the "force" being experinced by each twin is only a part of the picture. The real difference in time dilation is more related to the difference in potential. (or the Amount of work that it would take to move a mass form point to point.) For a person standing on the Earth, the time differential between himself and a object in space would be related to the amount of work it would take to lift an object to that distance against Earth's gravity. Since the Earth's gravity falls off with distance this energy does not increase very much once you get past the distance of the moon's orbit. In the case of the person accelerating towards the Earth, the case is different. He could consider himself at rest within a gravity field (his engines are firng in order to keep him from falling.) if he looks out his window, he sees the whole universe falling by. If he looks "above" him, he sees the Earth falling towards him. If the Earth is falling, then it must be in response to the same gravity field he himself is stationary in. If he measures the Earth's rate of fall, he will note that it matches that as if the gravity field strength is the same for the Earth as it is for him. This indicates that the gravity field is uniform (does not decrease with distance) This means that to "lift" a mass to the Earth "height" at any given moment, you would have to fight the same force of gravity the whole way (as opposed to from on the Earth, where the field strength weakens with distance). Thus from his veiwpoint,there is a greater difference in gravitational potential between himself and the Earth, then what a person on the Earth would measure between them. This also means that he will see a different time differential, then the Earth observer would.

If you place the path of light along the path of travel, it makes no difference which direction the mirror is from the light source, the return time is the same in both cases. In the case where the mirror is placed in front of the light, the time it takes to reach the mirror is equal to : [math]T_1 = \frac{x_1}{c-V}[/math] the time it takes for the light to return from the mirror is [math]T_2 = \frac{x_1}{c+V}[/math] In the case where the mirror is placed behind the light source, these two times are reversed. (both of these cases are as measured by someone that the mirror and light are moving with resepect to. In both cases, the total time for the light to travel to and back from the mirror is: [math]T_t = \frac{x_1}{c-V}+\frac{x_1}{c+V} = x_1 \left(\frac{1}{c-V}+\frac{1}{c+V}\right)[/math] [math]= \frac{2x_1c}{c^2-v^2} = \frac{2x_1}{c\left(1-\frac{v^2}{c^2}\right)}[/math] x1 is the distance from the from light to mirror as measured by this same observer. But this distance is length contracted from the distance as measured by the frame of the light source and mirror, which we will call x0 The tranformation between these two measurements is [math]x_1 = x_0\sqrt{1-\frac{v^2}{c^2}}[/math] Thus [math]T_t =\frac{2x_0\sqrt{1-\frac{v^2}{c^2}}}{c\left(1-\frac{v^2}{c^2}\right)}[/math] [math]=\frac{2x_0}{c\sqrt{1-\frac{v^2}{c^2}}}[/math] If t0 is the time time it takes in the mirror/ lightsource frame for the light to return, then [math]t_0 = \frac{2x_0}{c}[/math] and [math]T_t=\frac{t_0}{\sqrt{1-\frac{v^2}{c^2}}}[/math] Which is the time dilation formula. So time dilation holds no matter what the orientation of the light and mirror.

Watts in of themselves are not measures of energy, but measures of power. To get energy use must measure wattage against time. For example, the amount of energy a light bulb uses depends on its wattage and how long it is on, or wattage x time. Ten 100 watt bulb use 1000 watts, if you had the bulbs on for an hour, the total energy used would equal 1000 x 1 = 1 kilowatt-hour. (kilowatt-hrs are also the measure your electric company uses to tell how much electricity you use in a month.)

I there are at least 20 moons that orbit in retrograde (opposite of the rotation of their planet), including most of Uranus' moons and Triton, the largest moon of Neptune.

Wrong. The sound "barrier" was never a barrier in any real sense of the word. No one ever said' date=' "It is not possible to exceed the speed of sound". In fact, we were propelling objects faster than sound for decades before the "sound barrier" was "broken". All the sound barrier consisted of was the problem involved with designing a plane that could acheive [i']controlled[/i] flight at super-sonic speeds. The speed of light barrier is another animal all together, it is a consequence of how the universe, and reality itself, works at its most fundamental levels. No, it is not. The light speed limit is a consequence of the postulates of Relativity, not a base starting point. There are a number of consequences of Relativity's postulates, and these are tested and shown to be correct everyday in high energy particle labs around the world. The postulates are shown to hold, and thus the light speed barrier holds, because it is an unescapable result of those very postulates. The very fact that you would make such a statement shows that you have not thoroughly studied the subject.

Yep, I did. I'll go back and edit. Thanks.

Then there's no problem the gamma factor at .25c is 1.03, which means that Picard would have to travel at full impulse for 100 yrs in order for his Earth superiors to age 3 more years than him. Not a real noticeabe effect. However it does mean that The Enterprise most likely had to readjust its clocks everytime it traveled at impulse for any length of time.

I get a rough estimate of 1.5 ly for the radius of the Sun's gravitational sphere of influence. At this distance, the tendancy for an object to travel in an independant orbit around the center of the galaxy will over ride the Sun's ability to hold the object in orbit around itself.

Escape velocity is usually figured as from the point of departure, in this case, the surface of the Earth, even if the rocket never quite reaches that velocity. For instance, assuming a rocket fires its engines until it reaches an altitude of 300 km (About Leo) . At the Surface of the Earth, Escape velocity is 11.205km/s. At 300km its is 10.950km/s. So the rocket would only have to attain 10.950km/s to escape. But the total amount of energy the rocket had to expend to do this is the same as it would have been to give the rocket a velocity of 11.205km/s at ground level. It is actually more advantagous to reach escape velocity as soon and as low as possible. When you burn most of your fuel close to the ground, you use less fuel to get the same effect because you are using less fuel to lift fuel. (If you burn your engines until you get to 300km, you have to lift at least some of the fuel to 300km, and that takes extra fuel as opposed to burning all your fuel before you reach 10km, where you only have to lift fuel a maximum of 10km.)

Imagine you are throwing a ball up in the air. As it leaves your hand it starts with an upward velocity, but immediately starts to lose it due to gravity as it climbs. Eventually it loses all its velocity, comes to a stop and then begins to fall back down. The greater the velocity it has when it leaves your hand, the higher it will travel before falling back. If Earth's gravity reached to infinity and maintained the same strength the whole way, there would be no speed at which you could throw the ball that it wouldn't fall back. But Earth's gravity doesn't do both. It does reach to infinity, but it gets weaker the further from the center of the Earth you get. (By the square of the distance; at twice the distance of the Earth's surface, it has fallen to 1/4 strength) Thus, when you throw the ball upwards, as it climbs, the force of gravity pulling it back weakens as it gets further from the Earth. As long as you throw it at less than 11km/sec, the Earth will win out and eventually slow the ball to a stop and pull it back. But at 11km/sec, something happens, the ball gains height and the pull of gravity weakens faster than the ball loses speed. As the ball climbs, it still loses speed, but at a smaller and smaller rate. No matter how high it has climbed it still has some speed left and it will never fall back to the Earth. Another way of looking at Escape velocity is that it is the speed that an object dropped from an infinite distance would be traveling when it hits the surface of the Earth. (neglecting resistance)

Yes, you are wrong here. The planets weren't created by an explosion from the sun. They were created from material left over from when the sun intially condensed from a nebula. Since this nebula was spinning in one direction, the planets and the sun all ended up revolving more or less along the same axis. I think you might being confused by the fact that the much of the material that formed our Solar system was created in an explosion of another star when it went supernova.

What happens here is not any increase in the sensitivity of hearing, merely that the brain devotes more of its sensory processing power to the sense of hearing. The ears constantly detect sounds that we are not consciously aware of. The same is true with the other senses. All this sensory input would drive us to distraction if it weren't for the fact that most of it is filtered out by a subconscious mechanism. When a person loses their sight, the brain slowly redistributes the sensory processing for sight to the other senses. The filters start letting more information from those senses through . The senses don't become more acute, just more attention is paid to them.

Actually, the idea of explosive decompression as shown in many movies doesn't happen. There will be some swelling of tissue, but nothing to that extent. A person would even stay conscious for about 10 sec, and if repressurized within 90 sec, would survive with no permanent ill effects. There is actually evidence to support this. In 1966, a technician testing a pressure suit was accidentally exposed to hard vacuum for 30 sec. He came out of it just fine.

Check out the following attachment. It shows the light clock arrangement as seen by both the person next to the clock and by the person for which the clock is moving. For the first person, the distance between emitter and mirror is ct0 (the speed of light times the time it takes to traverse the distance as measured by him. For the second person (who sees the light clock as moving) the light follows the diagonal path shown, and this distance is ct1. The distance the clock travels is vt1, where v is the velocity the clock is seen as moving. The distance between the emitter and mirror at any instant (x) can be found by x² = (ct1)²-(vt1)² Now x is the same distance the first person got by ct0, so x=ct0 and therefore: (ct1)²-(vt1)² = (ct0)² c²t1²-v²t1² = c²t0² c²t1²/c²-v²t1²/c² = t0² t1²- v²t1²/c² = t0² t1²(1-v²/c²) = t0² t1 sqrt(1-v²/c²) = t0 ( Usually this is written with t0 and t1 reversed, but I intially got them switched around when I drew the diagram, and was too lazy to go back and change it later. It doesn't effect the math any.)

The Doppler effect is a completely different effect from time dilation. Usually iin Relativity, we assume for simplicites sake that the doppler effect has been factored out, and we are just dealing with time dialtion.

Okay, you have two people and two light clocks. each prson is standing next to his light clock. For each person, the light clock next to him takes one second for the beam to travel to the mirror and back. This is true no matter what manner he uses to measure the time. (stop watch, his own pulse etc. ) Now these two people are moving relative to each other, and each watches the other. By their measurement, the other light clock takes more than one second to "tick". By extension, they have to see the timepiece used by the other person run slow by the same amount. (If he didn't, then all kinds of paradoxes would arise.) Each sees the other's clock as running slow. So this answers your first question; what happens is not that high veloctiy causes one to age more slowly, but that high relative velocity causes each to measure the other as aging more slowly. Now in the twin paradox, at the end, one twin has aged less than the other. This will be the twin that experienced an acceleration. This is because experinced acceleration also effects how you measure things. At one point of the trip he will see the other twin age much more rapidly than he does. (but only for part of the trip, for the rest of the time he sees his brother age more slowly. ) The twin who doesn't accelerate, merely sees his brother age more slowy during the trip. At the end of the trip both brother's will agree as to their relative ages, but they won't agree as to how that age diffence came about. And neither twin is more correct as to what happened. As far as each is concerned, they are the ones who measured "real" time and their brother experienced "altered time". And they are both right. This what is meant by "time is Relative".

Okay, the first thing you probably need to do is re-think the concept of "real time". Time is merely a measurement used to separate events, it is no more "real" than that. As far as the clocks go: Remember, as each observer is concerned, the light clock next to him and any other method of time measuring are in perfect sync. And, each observer also has to see that the other set of light clock and time measuring device are in sync with each other. (even though they won't be in sync with his.)