Talk:Time dilation
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Two clocks experiment
When I do the two clocks experiment as a thought experiment using the consequences of relativity I get that both clocks have slowed down relative to a midpoint, and that gravity accounts for the discrepancy. The midpoint is where you'd stand to get the same result. at two quater points the further away one would appear slower than the near one. So under time dilation they both appear slow to each other, but should become roughly the same time once they are together, the discrepancy, being due to distances moved in the gravity well.
determining Newtonian gravitational constant G
When equal gravitational time dilation factors are applied, first to blue shift a photon to a maximum energy density (limit wavelength), and then to convert photon energy into gravitational field energy, each of the two factors is equal to the square root of [(3/2) exponent 1/2, times Planck time divided by two pi seconds]. (Note that when Planck time is expressed in seconds and divided by two pi seconds a dimensionless ratio is obtained.) This is a required condition if the electron is a gravitationally confined particle. When the Planck time is 5.391 times 10 exponent-44 seconds, the blue shift time dilation factor is 1.025 times 10 exponent-22 seconds per second. The critical or limit wavelength photon that has the energy density to materialize a pair of gravitationally confined particles, has energy equal to (2/3) exponent 1/2 times the Planck mass energy. This mass is 1.7775 times 10 exponent-8 kg. The limit wavelength is (3/2) exponent 1/2 times two pi times Planck length in meters. The quantized electron mass is equal to 1/2 of the mass energy of the limit wavelength photon when this energy is reduced by the gravitational time dilation factor 1.025 times 10 exponent-22 seconds per second. The product of 1.7775 times 10 exponent-8 kg and 1.025 times 10 exponent-22 seconds per second is 1.8219 times 10 exponent-30 kg. This mass times 1/2 is the electron mass, 9.1095 times 10 exponent-31 kg. The electron mass may then be defined as (h/4 pi c) times (c/3 pi h G) exponent 1/4 kg. From this equation and the known electron mass (9.1093819 times 10 exponent-31 kg) a hypothetical value for the gravitational constant (G) may be determined. This value is 6.6717456 times 10 exponent-11 m exponent 3,kg exponent-1, second exponent-2. This could be useful because the gravitational constant is the least precisely determined fundamental constant.
Author B.G.Sidharth has modeled the electron as a Kerr-Newman type black hole. This is consistant with the electron being described as a gravitationally confined particle. User: DonJStevens
See Black hole electron, See also Micro black hole
- Can you please not reference this talk page in the article unless it's absolutely necessary? Many thanks. -- Graham :) | Talk 01:05, 12 Mar 2004 (UTC)
question about relativity of time
This is just a question and I apologize if this is the wrong forum, I am trying to understand how time can be relative? Shouldn't time be constant, for example just because the Solar System is separated by millions of miles, it is the same time there as it is here. The distance in between should not affect the time, my point being on the previous page, "When one accelerates towards the speed of light, time slows down with respect to the rest of the Universe. That is, a stationary observer would see the traveling objects slowing down their activity (while still traveling fast). For them, time passes slower." So my point is time may seem to be passing slower but we are in fact all in the same instant or moment of time? No matter how fast one is traveling, is it not still "now"?
- No. It turns out that two events that happen at different points in space can't be observed by two or more observers that move in relation to each other as happenning at "the same time" (and so the same goes for "now"). "The same time" has no physical meaning. It turned out to be only a human concept not having a counterpart in the nature.
- The reason for it is a physical fact that the speed of light is the same for all observers regardless of their velocities and the information from any event can reach the observer only with speed of light at the best. It creates a situation that if one observer establishes that some two events happened "now" (in his time i.e. in the time measured by his clock) an obsever that moves in relation to the first one sees those events as happening at different times in his time. So "now" as related to certain events has meaning only for one observer in the universe and so it is only a subjective idea, valid only for this particular observer and therefore "relative". It can't be something "absolute" that would be valid for everyone. Jim 17:04, 2004 Jul 3 (UTC)
No matter how fast one is traveling, is it not still "now"?
- Yes I do believe you are correct. I think the same myself and have yet to see a satisfactory explanation otherwise. To think time slows down or speeds up just because you are moving very fast is preposterous to me.
- Hi, you bring up a very good point, one of the stranger predictions of relativity. I am just an amateur, and much of relativity is beyond my grasp, but I believe I can explain at least part of this. First of all, I agree that the notion of time slowing or speeding based on one's velocity does seem preposterous. This is because even at our top speeds, we travel so slowly compared to the speed of light that the time dilation is negligible. If one were to graph the amount of time dilation versus the speed, it would appear as a curve stretching up to infinity as one's speed approached c, the speed of light. However, if one just looks at the section of the graph that shows velocities we can currently attain, it would appear horizontal. The notion seems preposterous because our species evolved only achieving speeds on the beginning almost-flat part of the curve, and because we grow up and all of our experiences are at extremely low speeds (relatively speaking; no pun intended). In a similar manner, the idea that the Earth might be (approximately) spherical and not flat seemed preposterous to many people in its time; if you grew up in a small area and never traveled far enough to see the curvature, it would seem flat to you. In fact, the Earth still seems flat to us; however, we grow up learning that it is round, and we can take airplanes and such around the world which helps solidify the concept. Furthermore, globes, and now photographs of the Earth from space further help us to visualize this.
- Of course, none of this establishes relativity as being accurate. However, this a good deal of evidence supporting time dilation. One comes from muons produced from cosmic rays. The half-life of muons is well-known and unchangeable by any known process. One can calculate that all the muons should decay well before they reach Earth's surface; yet we detect many of these high-speed particles hitting Earth. This is in perfect accord with special relativity; the muons are travelling close to the speed of light and for them, time is travelling more slowly relative to us. From their "point of view", they are surving the proper amount of time, but from our point of view it is taking them a lot longer to decay. A second confirmation has been multiple experiments where two atomic clocks are synchronized, then one is flown at high speeds on a jet while the other one remains on Earth. When they are reunited, the one on the jet is slow by exactly the amount predicted by relativity. The third example is the most tangible, it concerns the operation of the Global Positioning Satellite system launched by the United States. These satellites all carry atomic clocks on board which continually broadcast signals including the current time. Commercial and military receivers on Earth receive these signals; it takes a fraction of a second for the signal to reach them. They subtract the signal time from the current time to determine how long the signal took to travel and using the known positions of the satellite, can calculate their distance and therefore their position. However, this does not take relativity into account; a system implemented in this manner would not work. See, there are two influences occuring here. One is that according to general relativity, time proceeds more slowly in a stronger gravitational field; this would predict that the clocks on the satellites would run faster. But special relativity predicts that faster objects experience time more slowly, and therefore the satellite clocks would run slower. The precise variance can be calculated and these two influences do not exactly cancel out; the clocks on the satellites should run slower than Earth-based clocks. The satellites' programming takes this time dilation into account and adjusts the clocks accordingly. Incidentally, not everyone was sure if relativity was really "correct" when the satellites were being constructed, so they were built in with both normal and relativity-corrected programming that could be switched remotely. They originally were launched in "normal" mode but it was soon obvious that the clocks were all getting out of sync, and the relativity programming was activated. — Knowledge Seeker দ (talk) 08:17, 20 Feb 2005 (UTC)
(William M. Connolley 15:31, 20 Feb 2005 (UTC)) The best way of thinking about this (IMHO) is to realise that things that are in principle unobservable have no place in science (this links relativity to quantum mechanics). When you think, "how exactly would I determine if two events are simultaneous" (which is the essence of defining time) you realise that there is no absolute way of doing this, in most circumstances. If you then decide that the best way of doing this is synchronising clocks via light beams, you end up with (special) relativity. If the speed of light were infinite, it would in principle be possible to sychronise all clocks, and (philosophically) we would be back to absolute time. And as it happens, the same happens in the mathematical formalism.
modifying "time dilation" description
I removed remarks that time dilation is relevant only in extreme conditions, since of course it is relevant always (the same as its results as "magnetic field" or "gravitational field"), and I removed the remark that velocity time dilation in satellites is negligible when compared with gravitational time dilation which is not true. Jim 17:04, 2004 Jul 3 (UTC)
symmetrical?
The effect is of course symmetrical: an observer fixed on the "moving" object sees the "stationary observer" slowing down.
This sentence is entirely contrary to logic, and also contradicts the last paragraph of the "Gravitational time dilation" section. -- 66.32.110.58 21:38, 18 Sep 2004 (UTC)
- (William M. Connolley 22:31, 18 Sep 2004 (UTC)) You're wrong. I've added a link to twin paradox which I think explains it better. Grav TD is a bit different - the symmetry is missing.
it's still contrary to logic.
- I suppose it seems that way. In fact, starting with a few basic assumptions (for instance, the speed of light is measured the same for observers in all intertial reference frames), and using just the laws of logic/math, one will arrive at this result. So it's really not contrary to logic; in fact, it is quite logical. It is, however, contrary to intuition. In an analagous manner, the ancients were able to use logic to surmise that the Earth was round, not flat. Others might object "Why don't people on the bottom of the Earth fall off?" and the answer would be that for them, they are upside up and we are upside down, hanging off the bottom of the Earth. Now this is perfectly straightforward to us today in an age where we can travel around the globe and view photographs from space. Doubtless if our great-grandchildren grow up in an era where relativistic speeds are commonplace, they will find it perfectly natural and will politely smile at our ignorance. — Knowledge Seeker দ 01:53, 8 Mar 2005 (UTC)
But if one person sees time slowing down for another person, they might watch them, say, standing still while the other person goes on to live their life, comes back and sees they've only managed to move one inch in that time.. the other person watching the first person would -have- to see that person living their life in fast motion, or the two events aren't simultaneous.. and aren't existing in the same continuity. For both to see the other slowing down while they themselves moved at normal speed means events between the two aren't synching up, and that's simply illogical, right? Everything has to synch up!
- I'm not sure I understand your scenario, but one of the concepts we must give up in relativity is that of absolute simultaneity. That is, observers in different reference frames will disagree about simultaneous events. Observer 1 might measure A and B as occurring at the same time, while Observer 2 measures A to occur before B, and Observer 3 measures B occurring before A. In some ways, this is analogous to what Newton proposed: in classical (Newtonian) physics, the concept of a preferred reference frame or "absolute rest" was discarded. That is, you cannot say "absolutely" that two events occurred in the same place, but at different times. To one observer it may appear so, but to another observer they will appear to occur in different places. That's absolute location. Absolute time means that you could say that two events occured at the same time, but in different places. We normally take this for granted, like that of absolute location. We can do this because we move at very low speeds relative to the speed of light (so we can use absolute time) and at low speeds relative to each other and the planet (so we can use absolute location). However, according to physics, neither model is accurate, and will break down at higher speeds. Of course, I find it extremely difficult to grasp a universe without absolute simultaneity. So does almost everyone. That's what makes Einstein a genius. Of course, anyone can come out with imaganitive theories. But that his theories provide testable hypotheses which have so far always been borne out provides evidence that his model is more accurate than our classical model. Hope this helps, and if you can elaborate on the scenario I can try to help you with that. — Knowledge Seeker দ 21:10, 11 May 2005 (UTC)
Thank you. THAT makes sense.
time slowing down
The whole idea of time dilation is preposterous! How is it possible? A light-year is the distance light travels in one year! That definition contradicts the idea of time dilation! Light travels a certain distance in one year! If you were travelling at, say, 186,000 miles per second, you would cover about 11,160,000 miles per minute, at which you would cover about 667,600,000 miles per hour. Now if you travelled that far per hour, you would cover about 2,670,400,000 miles per day, at which you would cover approximately 18,692,800,000 miles per week. At that rate you would cover about 972,025,600,000 miles in one year. That's how much distance is covered in one light year. Of course, I needn't go into all that. Time is not something that can slow down! Time is always going at the same rate! You can't slow it down! There is absolutely no way! What evidence do they have for this crazy theory anyway? There's another thing. They say that if you travelled in one second the distance it would take 100 years to travel, and then you travelled back to Earth at the same rate, 200 years would have passed on Earth. Ha! What kind of nonsense is that? That would be saying that time actually sped up! It contradicts time dilation! I don't see why there would be any evidence for this theory at all! And don't give me a bunch of mumbo-jumbo about us only being able to go at certain speeds. It doesn't really matter how fast you are going! Time isn't going to slow down! And no nonsense about people-used-to-think-that-the-earth-is-flat-but-it's-really-round-therefore-just-because-we-think-that-time-dilation-doesn't-exist-doesn't-mean-it-doesn't! It sure DOES mean that! There's a world of difference between the earth being round and time dilation existing! One could easily see that when you leave the land, it dissappears over a horizon rather than dissappearing into a point! Time dilation ISN'T LIKE THAT! It's not as obvious! Think about it. What is time? Time is the space between two events. Let's say your birthday is next week. Well, let's say that something happens and so you move your birthday party to today. Well, that's not speeding up time. That's just moving the party to today. You can't make next week happen today! Simple as that! Scorpionman 20:08, 19 May 2005 (UTC)
- There is evidence. To name a couple examples:
- clocks at the tops of buildings (gravitational dilation) and in airplanes and spacecraft (both gravitational and velocity)
- fast-moving muons (particles of cosmic radiation that decay rapidly) are observed to last longer than slow-moving ones
- I really don't see what the speed of light or the birthday-party example has to do with anything.
- Nickptar 21:10, 19 May 2005 (UTC)
- Okay, explain those examples. How does that happen? Scorpionman 01:57, 20 May 2005 (UTC)
- Hello, Scorpionman; thanks for your questions. You're right, it is a crazy theory (but like they say, truth is stranger than fiction). If you haven't already, take a look at the discussions above with a couple other users who also had difficulty grasping relativity (don't worry, we all do). I agree with Nickptar's comments above, and I'm just an amateur, but I'll add a few more comments. Your conversion of light years to miles looks accurate, although I haven't checked the calculations and I'm not certain what relevance it has. It is true that relativity predicts that if one were to fly away from Earth at high speeds and then return, one would find that a great deal of time had passed on Earth while perhaps only a few days passed for the traveler. This is because according to relativity, an observer would measure time travelling more slowly for a clock (or person) moving at high speeds relative to the observer. So two centuries later, the ship returns to Earth, but since time was travelling more slowly for it, the traveler has only aged a few days. Of course, all of this would be speculation, but General and Special Relativity make specific predictions which are different than those of classical physics. Since we are currently unable to achieve high speeds, the effects are virtually unnoticeable. However, there are several situations where there would be a measurable difference, and so far every one tested is consistent with relativity and not with classical physics. A practical example is the very accurate atomic clocks in the satellites of the Global Positioning System. Under classical physics, they should keep time at the same rate as their counterparts on Earth. However, general relativity predicts that time goes more slowly in stronger gravitational fields (slowing down Earth-based clocks) and special relativity goes more slowly for faster-moving clocks (slowing down the satellite clocks). These effects don't quite cancel out; it is predicted that the satellite clocks should go slower than terrestrial ones. Sure enough, the GPS clocks have software that adjusts their time to account for relativity. It is a tiny difference at those slow speeds, but enough to affect the precision needed for GPS. The only matter that we observe or can accelerate to near the speed of light are atomic and subatomic particles. As Nickptar mentions, some of these are unstable and decay at a predicatable rate. It has been observed that these unstable particles last longer when travelling at very high speeds in particle accelerators, or when produced in our atmosphere by fast-moving cosmic rays. Does this answer your questions? — Knowledge Seeker দ 22:11, 19 May 2005 (UTC)
Somewhat, although I still don't understand how time can be warped. And how it can be warped by speed! How would travelling at the speed of light make time pass more slowly? Exactly how does this happen? And how, how would gravity affect time? Scorpionman 01:54, 20 May 2005 (UTC)
- If you're asking for a mechanism, I'm afraid I don't know. It seems to be a property of spacetime itself. It's not so much that time is warped; it's that humans intuitively have an erroneous conception of space and time as separate, non-interchangeable dimensions. Here's a very bad example: Suppose there is someone who lives in a universe (make it two-dimensional, for clarity), where nothing can move around. He can look around, though, so he A little distance away is a stick five feet long, lying at an angle to him. You ask him to measure the stick. He surveys it and says: there is a stick which 4 feet side-to-side. He can also tell that one end is closer to him than another, and reports that it is 9 "distances" far (equivalent to our 3 feet, but he doesn't realize that). Those are both fixed as far as he knows. Now he develops a machine that gives him the ability to move a little. He moves to his left and the stick remains the same, but now it is at a different angle. He looks at it, and to his horror, the stick is now only 1 foot side-to-side! He measures its "farness" and finds it to be about 14.7 "distances" (4.9 feet)! He calls his friend to tell him; his friend does not believe him. How can farness be changed? Just by moving around? It's completely illogical! Our first guy can't explain it either. But he notices that if he uses the conversion factor 3 "distances" = 1 foot, then he can calculate a "true-length" parameter of the stick, by using the Pythagorean theorem, adding their squares and then taking the square root. Even though the side-to-side decreased, the farness increased, and they offset each other perfectly. In both cases the stick has a "true length" of 5 feet. I admit this example is highly contrived but I hope you can see the parallels. The ends of the stick are equivalent to two points in spacetime (for instance, a spaceship now, right in front of me and a 10 minutes later, 9 light-minutes from me). We measure the distance between the two points (9 light minutes) and the time between the two points (10 minutes) as completely separate quantities. Relativity says they are both dimensions in spacetime, and are related. If we use the speed of light, c, as a conversion factor, we can convert time into units of distance as well. For a reference frame moving at high speed relative to me, I would measure time as going slower (so the time dimension increase) while the distance was less (length contraction, so the space dimension increases). Using the Pythagorean theroem (and converting time to distance as mentioned before), we can calculate a "space-time interval". One will find that although time is increased, length has decreased, and the space-time interval is the same from all reference frames. Just as we can easily move around to see that "side-to-sideness" and "farness" are different aspects of the same thing, if we could easily move fast enough to directly observe the shifts between time and space, we would intuitively realize that the space-time interval was the true, constant, measure—but different reference frames would measure the time and distance dimensions differently. In simplifying I've left out some details; also, as I am an amateur, any physicist or someone well-versed in relativity is welcome to correct/expand on what I've said. Scorpionman, I also suggest you take a look at Special relativity for beginners—I found it quite interesting. If you have more questions, let me know. — Knowledge Seeker দ 08:12, 20 May 2005 (UTC)
- Some simple answers:
- Space is not warped by speed. Instead what happens in the space and time get exchanged as one moved from one inertial frame of reference to another. So of what we perceived as being space becomes time and vice versa.
- Time is not slowed down per se. Instead how your clock ticks is slower in the frame of reference of another observer. Your time is just as valid as his. However, if you travel away from another observer and then accelerate and return you will find that you experienced less time. See the proper time and twin paradox pages for an explanation of this.
- Gravity affects time through acceleration. To stay at the same distance from the center of the Earth, you are always being accelerated upwards in the viewpoint of relativity. (This acceleration is due to massive objects such as the Earth warping spacetime. BTW - You can choose not to be accelerated: The result is freefall.) In any case, since being accelerated means constantly switching inertial frames of reference, your view of "at the same time" keeps being changed and so you find that clocks at higher potentials are ticking faster and clocks at lower potentials are ticking slower. (My apologies if I lost you on this, but GR is just plain wierd even in comparison to SR.)
- --EMS | Talk 04:43, 26 May 2005 (UTC)
- Some simple answers:
Faster than light travel
Lets say you use a constant 1g to travel to a star that is 100 light years away. The star will appear one light year away when your length contraction reaches 100:1. First of all, how long does it take for length contraction to reach 100:1 at constant 1g? But more importantly, where did the 99 light years go? How is it that a star that was 100 light years away is now only one light year away? From your frame, you have observed faster than light travel toward this star.
- I'm just an amateur, so anyone more knowledgeable please correct me. By my calculations (solving <math>\sqrt{1-\frac{v^2}{c^2}}={1 \over 100}<math>) gives a velocity of 299,777,468 m/s, or 0.99995c. Dividing this by g (9.80665 m/s²) gives a time of 3.06×107 seconds or about 354 days. Of course, for an engine to maintain a constant acceleration of 1g, it would have to massively increase its force as higher velocities were reached; the acceleration produced by an engine that outputs a constant force would drop as higher velocities were attained. While we have engines that could produce a constant 1-g acceleration at conventional speeds, none of ours could keep up the acceleration at high speeds. The 99 light years don't really go anywhere; space would appear compressed from your point of view. It would be as if I placed a rod in front of you, parallel to your line of sight. Then I turned it so it was almost on end, and you asked "where did 90% of its length go?" It didn't go anywhere; the actual length was always the same, but the dimension parallel to you decreased while the dimension perpendicular to you increased. In the same way, while the distance of the star has decreased, when you arrive you would find that a great deal of time had passed in that star system. The distance dimension decreased but the time dimension increased. (This part of the explanation is slightly inaccurate; it glosses over a few details). I understand your point about exceeding the speed of light, but you really haven't. From your point of view, the distance to the star has decreased; you would measure your speed as 0.99995c. Or, more importantly, forget the acceleration; suppose I steal a spaceship that could instantly attain 0.99995c. I take off in the ship and at the exact second I engage the high-speed drive, the people on my planet send a warning signal to the other star system. To my delight, I reach in only 16 years and I'm thrilled because I think I've somehow passed the speed of light; signals from my home system will take another 84 (100-16) years to arrive! Yet I'll be doubly dismayed; not only did the light signal arrive almost 44 hours earlier, but a century has passed for them while I've been travelling, and their technology easily captures my ship. It doesn't matter if it's time dilation or if I underwent hibernation for a century on a slow ship and thought I was going very fast—a light signal will still beat me. Make sense? — Knowledge Seeker দ 07:12, 25 May 2005 (UTC)
When using the origin frame of reference a close enough approximation is c/g. But the only useful frame of reference for 1g acceleration is that of the traveller. A 100:1 length contraction from the perspective of the traveller to the destination should take more than one, but less than 100 years. I understand the compression of space as a function of relative velocity. This is the symmetry: the traveller see a length contraction while the destination sees a proportional time dilation happening to the traveller. And this is the crux of the question. If the traveller observes the destination continuously while in transit, he initially observes the destination to be 100 light years distant. But the distance to the destination decreases as his velocity increases relative to the destination. Lets assume for simplicity since I have no idea how to do the math, that it does only take one year in the travellers frame to achieve 100:1 time dilation (length contraction) at 1g. Between the beginning of the trip and now, the traveller has observed that his destination which was 100 light years away is now less than one light year away. I can do this math: 100-1=99. The observer has travelled 99 times the speed of light, from his reference. --JackN 02:58, 26 May 2005 (UTC)
- Those are some excellent points you bring up. Unfortunately, I no longer possess the mathematical abilities (nor have I ever understood the details of relativity in enough detail) to deal with continuously changing functions like this. Offhand, I can point out two difficulties with your argument. One, as I understand it, the reference frames described in relativity are inertial reference frames; your accelerating traveller is continuously jumping to different reference frames. My grasp of relativity is shaky for single reference frames, and tenuous at best when observers (instantaneously) jump reference frames. I lack the ability to properly calculate continuous changes like this, so hopefully someone else can answer. The other problem I see is that the traveller is using an improper technique to measure his speed. Picking a single object like that may work well at low speeds, but not at relativistic speeds. Had he chosen a farther star, he would observe it to move even faster. Had he chosen a closer to star, it would move more slowly. The speed of light principle applies to objects moving through spacetime, not the fabric of spacetime itself moving. In any case, a beam of light would beat our traveller by a considerable margin in this case. Anyone else care to correct my explanation or flesh it out some more? — Knowledge Seeker দ 04:37, 26 May 2005 (UTC)
- For the case of an object undergoing a continuous proper acceleration of g (with "proper" meaning "locally perceived"), the speed of that object v with respect to an inertial observer given that v=0 at t=0 is
- <math>v = cgt/\sqrt{c^2 + g^2t^2}<math>.
- For <math>gt \gg c<math>, this approaches v=c. One way to look at this is that the Lorentz Transformations also action on acceleartion, reducing it as v approaches c.
- Thank you, EMS. JackN, I was thinking about this issue today, and I think I realized the more fundamental problem here. I think the problem statement is "The observer has travelled 99 times the speed of light, from his reference." This is not true; the observer has travelled zero times the speed of light, from his reference. All speeds must specify a reference frame against which they are measured (except for the speed of light); if I say that an object travels at 100 km/s I must also state (or imply) the frame of reference measuring that speed. Measured from the traveller's reference frame (which is not an inertial frame, actually), he is travelling at exactly 0 m/s. Is there any reference frame in which he is travelling at 99c? Not that I can see. From the reference frame of the star? No, observers in that frame would measure his maximum speed as 0.99995c. The traveller was in error when he tried to measure his speed by comparing his changing distance to an object. This works fine at low speeds: I can measure the speed of my airplane by calculating the rate of change of distance to that mountain ahead, because at my low speeds, there is very little difference in the distance I'd measure to the mountain and the distance the mountain would measure to me. Therefore, I can assume that from the reference frame of the mountain/Earth, the same distance change is observed, so they would calculate the same speed. However, the interstellar traveller cannot make the same approximation. He measures different lengths to the star than the star would measure to him. He cannot assume that the distances he measures will be the same distances those reference frames will measure. Travelling at 99c? Relative to what? Even in Newtonian mechanics you must specify the reference frame. If he had picked a further star, perhaps he'd have measured a speed of 200c. A closer one, 20c. Even closer, 0.4c. His method of calculating speed is flawed—an approximation that works well at low speeds to which we are accustomed but breaks down at higher speeds when those very concepts no longer apply. Does that make sense? I hope I've been able to explain what I'm thinking. — Knowledge Seeker দ 06:11, 27 May 2005 (UTC)
- Knowledge Seeker - I think that you have missed a more fundamental issue here: JackN is saying "I have gone 100 ly in 1 year", and therefore sees himself as having travelled at a rate 99c greater that c. However, the 100 ly is as measured in the pre-acceleration frame of reference, while the 1 year is in the accelerating frame of reference. A velocity must be as described using time and distance values in a single frame of reference. (There is something in relativity called "rapidity" which is distance travelled divided by proper time, and which is used to construct the relativistic velocity tensor. However, it is not be confused with an observed velocity.) So in the final accelerated frame of reference, the accelerated observer will find the place he started from to be less than 1 ly away due to the Lorentz Contraction. Then the proper time of the accelerated observer having only progressed by 1 year is fine, as his average speed as determined by himself with respect to the starting point remains <c.
- This is one of the nuances of relativity: There is no absolute time, and therefore there is also no absolute instantaneous distance. The observers disagree on the distance covered by the time of flight of the accelerated observer, and on the spatial separation the flight created between the observers. These views can be reconciled throught he Lorentz Equations, however. Also, the observers will agree on the proper time of the accelerated observer's flight.
- The bottom line is that any exercise of this sort must be done using the Lorentz Transformation and it derivative relationships (such as the relativistic addition of velocities formula). For instance, the speed needed to obtain a Loretnz factor of 1/100 can be computed, and views in the frames of reference for both observers determined assuming linear, inertial travel at that speed. This may help JackN to better see what is going on. (This can also be done assuming continuous acceleration, but the math is a lot messier and would be difficult for a relativity novice to follow.) --EMS | Talk 14:49, 27 May 2005 (UTC)
EMS - Thank you so much for the time you have taken to answer my questions. I am somewhat rusty with the Lorentz Equations since I have not had to use them since the late 70s, and math is not my strength. And thanks for providing an application of the Lorentz Transformation to acceleration, but the paradox still remains. At the beginning of the trip the destination is 100 ly. While travelling at continous acceleration toward the destination there is a Lorentz Contraction of 100:1. It seems to me that if I were to observe the destination during continous acceleration I would seem to be observing faster than light travel. I hope I am not sounding dense, but is there a good way to explain the actual mechanism? --JackN 03:09, 30 May 2005 (UTC)
- You are using the Lorentz Contraction is exactly the wrong way. The distance to your destination at the end of your trip to it is zero. You have arrived, and the issue is now one of how far away the Earth is as you pass that place which in the inertial frame of reference of the Earth is 100 ly away from the Earth. The trick is that you are not in the inertial frame of reference of the Earth. To have reached this place after 1 year, your average inverse Lorentz factor must be 100, but your current inverse Lorentz factor should be greater! So you would look back at the Earth as you pass this star, and find that it is less than 1 ly away.
- You could "hit the brakes" so that you are back at rest with respect to the Earth at this star, and now it would be 100 ly away, but so what? Throughout your trip, light signals from the Earth were passing you. They may have been red-shifted more and more (before you fired the retro-rockets), but they could still be received. Given that, you never went faster than the light with respect to the Earth. In fact, in the frame of reference of the Earth, you took over 100 years to get to the star. Your proper time is not Earth time.
- It is known that time dilation can be used to get to distant stars in a reasonable amount of proper time. The issue is the energy needed to pull it off. BTW - If you turned around at this star and came back in another year of your time, you would find that over 200 years have passed on the Earth. (This stunt in known as the twin paradox.) So you have traveled 200 light years in over 200 years. Just how fast did you think that you were going again?
EMS - Thanks a million! I am familiar with the twin paradox, but this is the first real explanation I've heard. I'll have to think about what you have said a few days to become comfortable with it, but I've got the gist. If I understand you correctly, the "proper distance" of a trip is dependent on the acceleration of the traveller.
- You are getting there. How a distance is perceived is a function of the relative velocities of the observers. In the context of SR an acceleration is merely a change of velocity. So to be technical, you cannot say by what factor things have been time dilated and Lorentz contracted for your accelerating observer without specifying when the observation is made. Of course since time is relative in GR, you also need to specify by whose clock the time was determined. "C'est la vie."
- I think that it may help you to get ahold of a good book on SR and refamiliarize yourself with it. Issues like how coordinates are defined in SR and how that behave under the Lorentz transformations will be very helpful to you. As for Wikipedia, I do not advise it as a good source on information on relativity. It is getting better step by step, but it still has a ways to go. Even this page needs more work.
BTW: Na22 is a natural emmitter of e+ which could be magnetically bottled in a good vacuum. The last time I looked at it, permitting the collision of e+ and e- produces 2 γ particles at right angles to the path of the original e+ and e-. The development of a proper γ reflector would provide enough thrust to enable a constant acceleration of 1g, to the stars. We would also need to develop a method to create Na22 since it does not exist in nature. --JackN 04:20, 31 May 2005 (UTC)
Problems with Intro
After staring at it for some time, I decided that I had to revert the introduction. While I could work with the changes to the velocity section, the new introduction made imporper claims:
- It implied that time dilation is peculiar to clocks that are separated and later reunited. That is the twin paradox. Time dilation itself occurs with respect to the coordinate system defined by a given clock whether or not the other clock has ever or will ever be next to the clock defining the coordinate system.
- It called proper time a "perceived" measurement, placing it on the same level as the coordinate times. Proper time is not just perceived, it is the physical passage of time for that observer. Proper time also is not relative. Instead it is an invariant that all observers will agree on. (They may disagree over the parameters of a clock's worldline, but not on how much time that clock ticked off as it traveled that worldline.)
- "The faster one travels ..., the greater the time dilation relative to their origin": This is nonsense. An observer cannot travel with respect to himself, and therefore is never time dilated with respect to himself or with respect to his own temporal coordinate system. The effect occurs with respect to other observers and their temporal coordinate systems.
I am happy to work with others, and with edits that improve on my own work. However, the new intorduction was a solid step backwards for the reasons listed above. I regret the need to revert it.
--EMS | Talk 04:24, 26 May 2005 (UTC)
Special relativity, time dilation, and synchronization procedures
Synchronization procedures according to special relativity
Let there be a formation of three spaceships, A, B and C. The formation is in the shape of a line, and the distance AB is the same as the distance BC. The formation as a whole is moving inertially.
The ships of the formation are constantly monitoring their spatial separation by transmittng radio-signals (or they exchange lightpulses, or any other pulse that travels at lightspeed). As long as the transit times of consecutive relays stays the same they know their mutual distances are unchanging. The ships of the fleet maintain a standard fleet time. Since the ships do not move relative to each other the ratio's of proper time for the onboard clocks of A:B:C is 1:1:1, so maintaining standard fleet time is straightforward, only the transit time of the radio-signals needs to be taken into account.
Each radio-signal carries a time-stamp of the moment of sending. In a sense, the time-stamp is frozen in time. The receiver takes the time-stamp, adds the transit time of the radio-signal, and so reconstructs the standard fleet time of the fleet.
Now what if instead of photons muons are used? Suppose that beams of muons are used, and the muons are given a velocity of 0.866 of the speed of light with respect to the ships of the fleet. Suppose that the separation of the ships is such that out of a 100 muons 50 reach the receiver.
In that synchronization procedure the receiver needs to take more than just the transit time into account. For the bunch of muons some proper time has elapsed, but not as much as for the sender and reciever. In fact, the velocity of 0.866 of the speed of light with respect to the fleet corresponds to half as much proper time over the length of the transit as the amount of proper time of the fleet. In this example the decay rate of a large amount of muons serves as a clock.
Special relativity describes that the two procedures: using the decaying muons or lightspeed signals yields mutually consistent results. Special relativity also describes that if there is a second fleet of spaceships, D, E, F, that has a velocity v with respect to the A, B, C fleet, and both fleets use the muon beams procedure to maintain synchronized fleet time, then both fleets see in the other fleet the same ratio of muons beamed to muons received.
Time_dilation01.gif
Graphical representation
In the graphical representation the blue lines represent the timelines of the pulses of light in spacetime, the grey lines represent the timelines of the muons. The green lines represent fleet A, B, C, at five consecutive points in time. The red lines represent fleet D, E, F, at five consecutive points in time.
The observers onboard the green fleet can choose to interpret the physics of the moving muons of the red fleet either from the perspective of their own fleet, or from the perspective of the other fleet: in both cases the distances and velocities come out such that the amount of proper time of the muons in transit is the same, so as seen from either perspective the expected percentage of muons that is lost to decay during the transit is the same.
In this particular example all the relevant motion is on the same line, which is represented as the horizontal axis in the graphical representation. The two fleets of ships have a particular velocity relative to each other, and that is represented as a rotation of their timelines with respect to each other.
This is somewhat like a rotation of a cartesian coordinate system, but the difference is that when a cartesian coordinate system is rotated the axes remain perpendicular. When the axes of a spacetime diagram are rotated, then the only consistent way to represent that is to have the axes move in a scissor-like way.
The motion of the green fleet is represented with a perpendicular grid and the motion of the red fleet is represented with a rotated grid. That is an arbitrary choice, it does not represent a measurable physical difference. All the observations from both the perspective of the green fleet and from the perspective of the red fleet are consistent with both the perpendicular representation and the rotated representation; there is nothing to measure a difference. (Notice that without relativistic time dilation there would be a measurable difference.)
Formula
The structure that relates all these phenomena is mathematically represented by the following formula:
- <math>c^2(\Delta t_g)^2 - (\Delta x_g)^2 = c^2(\Delta t_r)^2 - (\Delta x_r)^2 <math>
As seen from the green perspective the formula can be applied as follows: <math>\Delta t_g<math> (delta t) stands for a period of time of the Green fleet, and <math>\Delta t_r<math> stands for the how much red-fleet-time elapses during <math>\Delta t_g<math> (as seen from the green perspective). <math>\Delta x_g<math> stands for distance traveled by green during <math>\Delta t_g<math>. <math>\Delta x_r<math> stands for distance traveled by red during <math>\Delta t_g<math>. In this example, time is measured in seconds, and distance is measured in kilometers.
If you take the frame of reference that is stationary with respect to the green fleet, then in that frame of reference <math>\Delta x_g<math>, (the distance traveled by the greens), is zero. As seen from the green-stationary frame of reference the reds do cover distance, which corresponds to less proper time for the reds as seen from the green perspective. What is invariant from frame to frame is the spacetime interval: the square of coordinate time minus the square of coordinate distance travelled. ('Coordinate time' is the amount of time as seen from the frame of reference of the observer; coordinate distance is the amount of distance traveled as seen from the frame of reference of the observer.)
The spacetime geometry that is described by this formula is called 'Minkowski spacetime geometry'. The amount of proper time of one object/observer with respect to another depends of their relative velocity. In a sense two observers who have a relative velocity are cutting dissimilar slices through spacetime, and thes cuts, these slices, are in a sense rotated with respect to each other. (There is no upper limit to this. In special relativity, the following scenario is self-consistent: a spaceship accelerates to a velocity that is close to lightspeed with respect to the home-planet, then it releases a probe that itself accelerates to close to the speed of light with respect to the spaceship; the probe itself releases a sub-probe, etc etc.)
Why time dilation
Why there is such a thing as relativistic time dilation anyway? It is not clear whether it is possible at all to find an answer to that question. For a start: what would a universe without relativistic time dilation (have to) look like?
The speed of light can in a more general sense be seen as the maximum speed of information: the maximum speed of causality. In our universe the speed of causality is very high indeed: 300.000 kilometers per second. Because of the extremely hich velocity of causality, the relativistic time dilation was completely unnoticable until the high technology of the 20th century was developed. What if the speed of light would be trillions of kilometers a second? If the speed of causality would be even higher, then our universe would resemble a universe without time dilation much, much closer than our actual universe. A universe with infinite speed of causality would be a universe with total separation of time and space, a universe without time dilation. But can a universe with infinite speed of causality exist at all? If every location of the universe is instantaneously connected to every other location, then how can such a thing as distance even exist?
Mayby finite speed of causality is a price to pay for the very existance of spatial distance. And maybe the only self-consistent universe with a finite speed of causality is a universe with Minkowski space-time geometry.
--Cleon Teunissen | Talk 22:40, 31 May 2005 (UTC)
Responses to the synchronization description
Nice try, but you seem to have goofed. The tilted red lines should be in the upper diagram. The red lines instead should be straight across in the lower diagram. Also, in the lower diagram it is the green line that should be moving (albeit in the opposite direction as that of the red line).
Beyond that, I find this illustration to be overly complex. Time dilation arises from a very simple and illustratable mechanism: Let observer A send a light beam down a 1-light-second path. By his clock it takes that light beam 1 second to travel the path. Now let there be an observer B who is traveling in a direction perpendicular to the path of the light (as seen by observer A). For observer B, observer A and the place the light beam is going to are offset during the time of flight of the light due to their relative motion. Since observer B must see that light also travel at c, its time of flight must be <math>1/\sqrt{1 - v^2/c^2}<math> seconds. For the times of flight for the observers to be consistent, the clock for observer A must be running at a rate of <math>\sqrt{1 - v^2/c^2}<math> in the frame of reference of observer B.
Also, this page is about time dilation, not the relativity of simultaneity. (That one does need an article, but once again any illustration needs to be kept simple.)
--EMS | Talk 15:03, 1 Jun 2005 (UTC)
- The way you describe it makes it sound as if the proper time of observer B is the absolute time, and that time-keeping of observer A is distorted with respect to the absolute time. I am looking for a way to present that the perspective of A and the perspective of B are symmetrical and reciprocal in all respects.
- Also, you make it sound as if it only has to do with the propagation of light. I see as the essence of relativity that all procedures that involve keeping track of how much time has elapsed yield mutually consistent outcomes. There is:
- Coordinate distance; the amount of distance to be travelled in a transit is different as seen from different frames of reference.
- Coordinate time: the amount of time that the transit takes is different as seen from different frames of reference.
- Coordinate time dilation: the amount of time dilation that is involved is different as seen from different frames of reference.
- In the middle of all of that is the constancy of the speed of light. That is the most fundamental reason for time dilation. The goal of my little exercise is
- to illustrate that connection, and
- to create as simple as description as possible.
- In the middle of all of that is the constancy of the speed of light. That is the most fundamental reason for time dilation. The goal of my little exercise is
- The relative qualities: distance, time, time dilation, relate to each other in such a way that as seen from all frames of reference the physics taking place is the same physics. In the case of muons in transit: as seen from all perspectives, the expected amount of loss to decay during transit is the same.
- So yes, the diagram/animation is quite complex, in order to represent the interconnectedness that is so typical of relativistic physics.
- If you are going to teach people about relativity, then your article needs to be understandable. Hitting them in the face with the full interconnectedness of relativity is not that way to do that. Instead you need to feed someone digestable pieces. Also, while I know that the interconnectedness is there, but the relativity of simultaneity is not the subject to the time dilation article. There is no way for a novice to look at that diagram and gain an understanding of time dilation, much less relativity. Besides, your diagram has blatant errors in it:
- In the lower diagram, the tilted red lines should be green. You are now in the red frame of reference, where the red simultaneity lines by convention are vertical. The lines that you colored red are actually connected events that are simultaneous in the green frame, and so should be green.
- The dots on your red line moving change direction at the same time. That is not the view in the red frame. (Perhaps you are showing the green viewpoint on the red line?)
- The sub-diagram with the moving red line is below the diagram for the red frame, in which it is the green frame that is in relative motion.
- --EMS | Talk 16:08, 2 Jun 2005 (UTC)
- In the case of the moving red line I had made the decision to depict the motion of the muons as seen from the red perspective. As seen from the green perspective the reds timing signals do not reach the ends simultaneously, as represented in the tilted (stationary) diagram. The moving red line is inconsistent with that, as it displays the motion of the muons as seen from the red perspective.
- This mixing of perspectives has disadvantages, so I will change that. --Cleon Teunissen | Talk 11:58, 2 Jun 2005 (UTC)
- I think that you have done a wonderful job of confusing as to which frame of reference in which and what is being viewed in each. You also have done a wonderful job of losing track of the scope of this article, which is time dilation. Also please note that even corrected that diagram is so complex that it is uninformative. Only someone very adept at relativity would understand it, and that is not (or at least should not be) the intended audience.
- Don't try to be cute. Don't deal with metaphysics. Also, don't worry about any part of relativity here other than time dilation. If you want to contribute, then get down to brass tacks here, and help me by creating an illustration of how the constancy of c requires the existance of time dilation.
The self-consistency of time
- Let observer A send a light beam down a 1-light-second path. By his clock it takes that light beam 1 second to travel the path. Now let there be an observer B who is traveling in a direction perpendicular to the path of the light (as seen by observer A). For observer B, observer A and the place the light beam is going to are offset during the time of flight of the light due to their relative motion. Since observer B must see that light also travel at c, its time of flight must be <math>1/\sqrt{1 - v^2/c^2}<math> seconds. For the times of flight for the observers to be consistent, the clock for observer A must be running at a rate of <math>\sqrt{1 - v^2/c^2}<math> in the frame of reference of observer B. --EMS | Talk 15:03, 1 Jun 2005 (UTC)
I have made a GIF-animation that illustrates what you describe.
Time_dilation02.gif
The green dots in the animation represent spaceships. The ships of the green fleet have no relative motion, so for the clocks onboard the individual ships the same amount of time elapses, and they can set up a procedure to maintain a synchronized standard fleet time. The ships of the "red fleet" are moving with a velocity of 0.866 of the speed of light with respect to the green fleet.
The blue dots represent pulses of light. One cycle of lightpulses between two green ships takes two seconds of "green time", one second for each leg.
As seen from the perspective of the reds the transit time of the lightpulses they exchange among each other is one second of "red time" for each leg. As seen from the perspective of the greens the red ships cycle of exchanging lightpulses travels a diagonal path that is two lightseconds long. (As seen from the green perspective the reds travel 1.73 (<math>\sqrt{3}<math>) lightseconds of distance for every two seconds of green time.)
One of the red ships emits a lightpulse towards the greens every second of red time. These pulses are recieved by ships of the green fleet with two-second intervals as measured in green time.
Relative
The time dilation is relative: the green perspective and the red perspective are in all respects mirror images of each other.
All physics phenomena that can be used to measure lapses of time yield outcomes that are consistent with each other. (Intriguingly, most forms of time-keeping can be readily seen to count time by counting cycles of some oscillation.) There are no exceptions known to this inner consistency of time-keeping. If there would be an exception, then inertial motion would not be relative in the way that is described by special relativity.
In this example the rate of time as measured by any sort of clock is seen to be consistent with a velocity of light propagation that is invariant across the entire range of inertial frames of reference. --Cleon Teunissen | Talk 00:36, 6 Jun 2005 (UTC)
- YES! That is what I want. It is more involved that what I envisioned, but the extra details are such that they help to drive the point home. Unless someone objects, please place it and a description into the article as a sub-section of the velocity time dilation section. Perhaps call it "The physics of velocity time dilation". Be advised that I will edit your wording when I get a chance, but yours will do for now. Just start with a basic description of what the overall physics is, and then start refering to the GIF.
- You may also want to do the same thing from the standpoint of the red fleet, with the green ship moving upwards to show the symmetry of this effect. However, only do this if you are comfortable with using it.
- Once again, thank you for this fine illustrative GIF.
- Sounds good to me. Impressive GIF-fu :). --Christopher Thomas 23:09, 6 Jun 2005 (UTC)
The "spacetime geometry ..." subsection
Cleon -
That GIF looks great. Thanks again for it.
As you can see, I have already done an edit on your text. You wrote:
- There is no physics phenomenon known that would allow either the greens or the reds to identify themselves as "the non-moving ones".
However, there in nothing wrong with being non-moving (or at rest) in relativity. You just have to specify what it is that you are at rest with respect to. In one part of your animation, at-rest is with respect to the green fleet; In the other part, at-rest is with respect to the red fleet.
Be warned that I (and maybe others) will tweak your text even more. Some work is needed to better describe the overall physics of what is being illustrated. As I see it what you earned with the GIF was the right to have the first crack at explaining it. You have now exercised that right, and the rest of us can now "play" with your work. Even so, I for one will take care in how it is editted: It may not be perfect, but you have done a good enough job that a sloppy edit will make the text worse instead of beeter.
--EMS | Talk 02:02, 9 Jun 2005 (UTC)
- there is nothing wrong with being non-moving (or at rest) in relativity. --EMS | Talk 02:02, 9 Jun 2005 (UTC)
As so often you have found a way to misunderstand. I should have mentioned that I was referring to the following: "There is no physics phenomenon known that would allow either the greens or the reds to identify their own state of inertial motion as non-moving with respect to some overall absolute reference."
I think there is something you are confused about: any distinction between being at rest and being in inertial motion is meaningless in the context of special relativity.
- No. It is not meaningless. It just is a relative concept, not an absolute one. If I see something as maintining its distance and orientation with respect to myself, then I will consider it to be at rest. Period. End of discussion.
- Now mind you, the object that is "at rest" in my frame of reference could be a ball on the end of a string which is keeping the ball from flying away from me as I spin around and around in circles. However, note that since I am spinning with the ball it orientation with respect to my face is constant and the string is also keeping its distance constant. So by the formal definition of being at rest, it is. The issue is that this rest is not an inertial state of motion.
- Then again, you are probably at rest right now with respect to your chair, and both you and the chair are in an accelerated frame of reference.
- (Actually there is one way that being at rest is an absoute, but being at rest with respect to one's self is awfully trivial.)
The dichotomy 'being at rest'/'being in inertial motion' is ingrained in our language, but we need to get away from that dichotomy.
In order to perform calculations the greens apply a coordinate system that is stationary with respect to the green fleet, and then, and only then, it is possible to apply the relativistic laws of physics in calculating what frequency they will actually detect as they receive signals from the reds that are emitted at an agreed frequency, say the frequency of a characteristic line in an atomic emission spectrum. (Or they can calculate from the measured frequency shift the magnitude of relative motion.)
In special relativity, when you have two emitters/detectors with a relative velocity, and you want to calculate for both what they will actually measure, then you choose two coordinate systems, one that is stationary with respect to "the greens" and one that is stationary with respect to "the reds", and then transformations between those coordinate systems can be performed. A phrase like "the greens are at rest in their own coordinate system" is a meaningless tautology, for the only way to "deploy" any coordinate system is to first specify with respect to what that coordinate system is stationary.
--Cleon Teunissen | Talk 11:17, 9 Jun 2005 (UTC)
- It seems to me that "stationary" and "at rest" are synonomous. So you have ended up saying the same thing that I am: Once you specify the coordinate system, you can specify the rest state(s) within it. Contrary to what you implied, the construction of a rest state is easy. That there is not abosolute rest is a different matter.