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  • #46
    Whew ... I've been working 17 hour days and haven't had time to keep up with the board.

    I originally approached the issue of the relative motion averaging to zero by considering the motion to be in one dimension only. Then the motion is that of a mechanical oscillator relative to some stationary point. If you assume that the two reference frames are equal and indistinguishable then one frame moves forward and stops, then the next frame moves forward and stops so the relative motion averages to zero. But we've made several assumptions.

    I'm pretty sure there would be a dilation, but it will be unique to rotational motion. I haven't had time to actually work out the math on paper, but I think I can see what to do. I've also emailed one of my professors who will be teaching the course on general relativity so I'll see what he has to say on the matter.

    ... on an unrelated note:
    Evan - I finally found the bit of "pipe" (I think cored round is probably a better term) that I've been looking for to make my rotary table. I also made a deposit on a new lathe so when I get that I'll be off to the races and I'll be able to put that bearing to good use!


    • #47
      As a person with some experience doing experiments in physics, I have a couple of suggestions. First, define very carefully your hypothesis and the mathematics that support it. An experiment is a test of a hypothesis. Don't start thinking about stress or how to build equipment until that part is complete. Before you start the next step, bounce your hypothesis and experimental approach off professors, graduate students and any one who will listen. You will learn a lot in this part of step one. Second, don't build anything you don't have to build. For example, if you can use an existing centrifuge - don't build something that emulates one. It is a waste of your time, despite the fact that it would be fun. You don't want to spend any of your time on something that does not lead to your desired result for one big reason - unanticipated effects or outcomes. For example, in you description of the experiment you planned, have you considered the physical effects of your "centrifuge" on the electronic components? Will capacitances change? Will that impact the result? Using a crystal? Any effects there? More often than not, some unanticipated effect will more than drown out the desired signal. So you want to leave most of your time available to sort out these effects. Most of the time spent in a successful experiment is spent after the initial setup is running. This time is used to make revisions to the experiment to solve problems that arise. Often several approaches are tried and abandoned before a successful approach is developed. Give yourself time for this.
      Good luck!!


      • #48
        Thanks Bruce

        I think I mentioned somewhere that there is a huge effect on the electronics. In fact, it will cause a greater change in frequency than any relativistic effects, but there is a well defined empirically derived equation for the effect of acceleration on crystal oscillators. Crystal oscillators were the basis for the atomic clocks that were flown around the world and are highly accurate (if you get good ones). The packages I'm looking at are a little pricey at 30 bucks a pop but they have a high level of precision - the error should be several order of magnitudes less than the effect from relativity.

        Advanced lab is a pretty free form class and the professors encourage students to pick something and basically play with it. In the field of physics that I am interested in, most of the "experiments" are based on hunches or loose theories. Unfortunantly, experimentalists sometimes don't see eye to eye with theorists and go there own way on occassion.

        Plus I've got all summer to fool around on my own time


        • #49
          I've been thinking some more on the problem. First of all, time dilation can only happen in respect of a different frame of reference. There is absolutely no way to measure time dilation that is occuring in your frame of reference. This makes the question "Is the object on the centrifuge in a different frame of reference?". Surprisingly, I don't think so.

          If we observe the centrifuge from outside the radius of rotation then no matter where we observe it from the average velocity in respect of the observer equals zero. If we observe it from within the radius of rotation the average velocity still equals zero and a special case exists as well. If we observe from the center of rotation then the average velocity and the instantaneous velocity are zero. All the object in the centrifuge has then is relative angular velocity and that cannot cause time dilation since it isn't a vector quantity. In fact, if we sit at the center of rotation and rotate as well then there isn't even relative angular velocity yet in none of the observations have we changed our average velocity (we have not accelerated) relative to the object in the centrifuge.

          The problem with a null result is that it proves nothing other than the fact that you failed to find a non-null result. The most a null result can do is set limits on a positive result.
          Last edited by Evan; 05-21-2008, 10:53 PM.
          Free software for calculating bolt circles and similar: Click Here


          • #50
            The twin paradox occurs in the case of circular motion as well as linear motion. IOW, time dilation occurs when the acceleration is associated with orbital motion. Here is a great reference:



            • #51
              Hoop snake

              Lottsa hoop-related strees in these links:





              • #52

                That is avery interesting paper. However, I detect a problem, at least in the general presentation of the examples. It constantly makes statements that require time dilation be observed in one frame from another. This is in direct contradiction to a prediction made in the 1950s by Roger Penrose and independently by James Terrell.

                It elegantly proves that the Lorenzt-Fitzgerald contraction cannot be observed from any frame of reference. By corollary, neither can time dilation. In order to make any measurement of time dilation the clocks used must be in the same frame of reference.

                Can You See the Lorentz-Fitzgerald Contraction? Or: Penrose-Terrell Rotation

                I also have an uncomfortable feeling about the idea of a N-gon tending toward a circle in this instance. It reminds me of Xeno's Paradox. As n grows larger the acceleration to make the "course changes" diminishes in inverse proportion. It can then be argued that in the limit case of n=infinity=circle the acceleration required is the sum of an infinite amount of infinitely small accelerations = zero.

                Also, in the appendix the author invokes changes in acceleration even though it was stated earlier that it makes no difference.

                When the traveling twin accelerates at
                each vertex of the polygon they will see the Earth clock at
                that vertex advance more quickly during the acceleration.
                These advances accumulate so that when the traveling
                twin is again next to the Earth twin both will agree the
                clock carried around the polygon has recorded less time
                than the one held by the Earth twin. Exactly the same
                thing happens in the limit as the polygon path becomes
                a circular path
                At the least it is a bad example because it contradicts earlier statements and also seems to invoke yet another paradox.

                Interesting stuff though.
                Free software for calculating bolt circles and similar: Click Here


                • #53
                  There is another perspective on SR that makes this clearer (hopefully). In this perspective you travel through space-time at a constant velocity wrt a given frame. As a parallel, imagine that you are travelling north at 100mph. In one hour you move 100 miles north. If you change direction to NorthEast, your progress North in one hour is now diminished by the square root of 2. Back to space time. At rest, you make progress through the time dimension a distance of ct for a time t. But if your velocity through space increases in ANY direction, that velocity increase comes at the expense of your progress through the time dimension. So your clock slows down wrt the "fixed frame".
                  I have not read the Penrose paper, but my guess is that he is referring to something a little more esoteric when he says observable. There are legions of examples of observation of the time dilation effect. The classic case the is decay of muons incident on the atmosphere. Based on the known decay rate, muons should not get as far as they do. They travel farther than expected because their clocks run slower wrt our "fixed" frame. The paper I referenced also give examples of experimental confirmation.


                  • #54
                    Certainly there are numerous examples of time dilation. However, they all depend on the observation being made in the observers frame of reference. Time dilation cannot be observed directly in another frame of reference. In other words, you can't somehow peek at the clock in another frame to see if it is running slower. It's values must be communicated to your frame which then makes it subject to the Penrose rotation as well as simultaneity.

                    So your clock slows down wrt the "fixed frame".
                    And that is a subject of much debate. The "fixed" frame is like the holy grail. Much sought after but never confirmed as found. Some ideas serve well such as using the distant stars but even that is only an approximation.

                    Any "though experiment" that invokes the possibility of somehow being able to observe time dilation in respect of two different frames is placing us as observers outside of both frames and into an impossible frame with a world line that intersects the other frames regardless of their relative velocities.

                    This is seen in the question about "what is the relative velocity of two photons traveling in opposite directions?". The answer is that they don't have a relative velocity since their world lines don't intersect.

                    It's all very interesting to me and I shall have to contemplate the implications of that paper you presented as it does raise questions that are new to me (and apparently to many others as well).

                    Thanks for that link.
                    Free software for calculating bolt circles and similar: Click Here


                    • #55
                      I took a look at the Penrose paper and it has to do with the visual appearance of objects moving relative to the observer. It has nothing to do with detecting time dilation. Other methods, like radioactive decay, which provide their own clock, have been used to detect time dilation. Penrose does not say that it is impossible to measure time dilation, which is the subject of Fasttrack's proposal. I see no reason why in principle, for circular motion, that you cannot observe it directly by electronic means. However, I do see a great number of problems in doing a successful experiment - it won't be easy.


                      • #56
                        It's the reason for the Penrose rotation that prevents one from observing time dilation in the accelerated frame. Let's say there is a pendulum swinging on the accelerated spacecraft. Time is slowed but the entire frame is contracted so it still seems to have the same period to an observer in the accelerated frame.

                        We try to observe it through a window in the spacecraft as it passes us. The pendulum is contracted so it has a shorter distance to swing. If we could see the contraction we would realize that the period, although the same, is for what appears to us a shorter swing meaning the time is dilated. But, because of the Penrose rotation all we see is the pendulum displaying the same period and the same degree of swing when we first measured it in our frame.

                        In the example given in the paper it's clear this is an issue of simultaneity which affects all possible observations, not just the geometry of reflected light.

                        An example of this in the "real" universe is an object falling into a black hole. If time dilation in the object's frame were observable then it would appear to come to a halt at the event horizon and never actually cross the horizon since time is dilated to infinity at the velocity of light.
                        Last edited by Evan; 05-22-2008, 07:55 PM.
                        Free software for calculating bolt circles and similar: Click Here


                        • #57
                          Both Bruce and Evan are correct, in so far as it goes. For time dilation to be observed, the object must return to the initial frame of reference. That is the solution to the twin paradox; one twin never changes reference frames and does not expierence relativistic effects. The second twin leaves the first reference frame, hurtles around the universe and then returns to the original reference frame and suddenly the effects are realized.

                          I'll post more as it relates to my "experiment" soon.


                          • #58
                            This has turned out to be quite an interesting problem! The spacetime metric is distorted by the spinning disk - in fact it is distorted due to the stress and strain within the body, not the mass specifically.

                            The degree to which the spatial geometry or temporal geometry is changed I have not determined. If it has been determined, its mired somewhere in general relativity with many qualifiers and advanced mathmatics. I'll see what more I can dig up on it. The rotating disk was mentioned in Einstein's 1916 paper but for his purposes, he assumed that there was no temporal distortion, but gave no explicit reasons for this. According to Max Born, a spinning disk is a contradiction (relativistically anyway) since the circumfrence contracts but the radius does not. (i.e. it is a non-euclidean circle lying in euclidean space)


                            • #59
                              "For time dilation to be observed, the object must return to the initial frame of reference."

                              Not so. Consider atmospheric muon decay. The muon does not slow down until it decays - thus sending a signal to the observer. In the case of the flying atomic clocks, the clock was returned to land only for convenience - with proper equipment it could have been still flying. Consider Thomas precession - another example of the object not returning to the observers reference frame.
                              I am not sure why you make this statement. --??


                              • #60
                                Originally posted by knucklehead
                                special relativity?
                                why didn't you say so...
                                36000ipm is only about 35mph.

                                can you run your experiment in a car?

                                how long do you plan to run for?

                                That's funny, I get 375 MPH. A bit of a different ball game as regards using a car. But I guess there a few out there. And finding a stretch of road may be just as big of a challenge.
                                Paul A.
                                SE Texas

                                Make it fit.
                                You can't win and there IS a penalty for trying!