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Min/max Time dilation 
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#19
Feb1412, 10:46 PM

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Now in your first post, you said that time dilation can vary between 0 (clock stopped), as a lower limit, to near 1, as an upper limit. But you were really talking about tick rate which is the reciprocal of time dilation. "Dilation" means "getting bigger" not smaller. I attempted to point out that the time dilation factor can vary between exactly 1 and has no upper limit. You were attempting to point out that one of the limits could be reached by a clock traveling at a speed of c and wondering where the corresponding limit was for gravitational time dilation. I wanted you to see that if you properly view time dilation as a number greater than or equal to one, then both types of time dilation (one due to speed and one due to gravity) have no upper limit. You also need to be aware that every clock keeps time with no time dilation, in other words, its time dilation is 1. This is what we call Proper Time. This is one of the tenets of relativity, that time is relative for every clock. It isn't until we assign a clock to a Frame of Reference in which it has a speed relative to that FoR that we then can talk about its time dilation factor as defined by that FoR. It gets a little more complicated when one (or both) of them is accelerating but essentially the same principle applies. But I'm not sure if I have addressed your Zeno issue. I really don't know what your concern is. 


#20
Feb1512, 12:29 AM

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Rate of time = the 'length' of a second. Is this the more accurate way to describe time dilation? I also do understand that observer's travelling at some portion of c will have no innate awareness of time dilation. A hapless stranger waking in an enclosed, windowless room would have no way to distinguish between being on board a spaceship travelling at 90% c and being a mile underground on Earth. Infinities are usualy sought to be removed from theory, as I understand it. Has anyone attempted to address the ever decreasing movement of an observer at speeds approaching c? Noone has ever tried to argue that there is a point where such a fractional movement is impossible? Wouldn't Planck's constant become involved, where the energy of such a small motion is below the constant (or does the increasing energy required to accelerate the object overcome this??). The line I put in bold: My first mention of Zeno was just an observation. This is the first time I've ever seen it come in a realistic situation. My second comment about a "nonZenolike step" was a pun; a hope that we would do more than move by half the remaining distance between our respective positions. ;) The nonbold paragraph. Hmm. Let's say Anthoney is in the middle of a supervoid, at rest with respect to the CMB. Cleopatra is travelling at 99.9999% the speed of c. They both have time pieces. It seems to me to be true that there is no other clock in the universe that could record Cleopatra's clock as running slower than Anthony does, because it is impossible for anyone to be experiencing any less time dilation than Anthoney is (assuming that we have placed him at a point that is as distant from any source of gravity as can be found). The only way for either to observe a slower rate of time is if Cleo continues the infitessimal crawl ever closer to c (I also recognise that each tiny increase is exponentially bigger than the previous one). Again, is the above paragraph accurate? 


#21
Feb1512, 01:49 AM

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1) "Cleopatra is travelling at 99.9999% the speed of c". In relativity, this is an inherently meaningless statement. I assume you mean Cleopatra is traveling 99.9999% c relative to Anthony. This also means Anthony is traveling 99.9999% c relative to Cleopatra. 2) Cleopatra perceives Anthony's clock running very slow. Anthony perceive Cleopatra's clock running very slow. This is the reciprocal time dilation pointed out at the very beginning of this thread, that you seem unwilling to accept, even though it is the most elementary concept of SR. Why not read part 1 of Einstein's 1905 paper that Gwellsjr gave you a link for. Read it carefully, with an open mind. 


#22
Feb1512, 02:27 AM

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γ = 1/√(1β^{2}) where β is v/c. More often, gamma is applied to the tick rates of clocks because we are more familiar with how they keep time rather than how long a second is. Then we can say that the Proper Time on a moving clock is the reciprocal of gamma times the Coordinate Time of a real or virtual stationary clock. τ = t√(1β^{2}) where τ (tau) is the Proper Time on the moving clock (or observer) and t is the Coordinate Time on the stationary clock (or observer). First off, just say that you have a Frame of Reference in which Anthoney is at rest and Cleopatra is traveling at 99.9999% the speed of c. The CMB is not a factor. Since Cleo is the one that is traveling, her clock is the one that is time dilated meaning it is ticking more slowly than Anthoney's according to our selected Frame of Reference. You can apply the formula above for the Proper Time rate of both clocks. I have no idea what you mean by: However, in a different FoR, say where Cleopatra is at rest and Anthoney is traveling at 99.9999% of c, Anthoney's clock will be time dilated and Cleo's will have no time dilation. We could also pick a FoR kind of "half way" between the two of them so each of them is traveling at about 99.9% of c in the opposite direction and they will both be experiencing the same time dilation. But again, this doesn't take into account how each one observes the other clock for which, as I said, you need to use Relativistic Doppler. Relativistic Doppler is the same in all Frames of Reference, in fact it is not related to any theory but an analysis of what can be measured. 


#23
Feb1512, 02:45 AM

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Your number 1) statement is slightly less settled from my point of view. 


#24
Feb1512, 02:49 AM

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It's late, so on that blunder, I shall retire for now. 


#25
Feb1512, 05:32 AM

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#26
Feb1512, 07:57 AM

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I see there is a different way to read a key sentence I responded to, and I misinterpreted what you meant. Unfortunately, the alternative interpretation is equally false. You say: " Let's say Anthoney is in the middle of a supervoid, at rest with respect to the CMB. Cleopatra is travelling at 99.9999% the speed of c. They both have time pieces. It seems to me to be true that there is no other clock in the universe that could record Cleopatra's clock as running slower than Anthony does" So, you are emphasizing that Anthony perceives Cleopatra's clock very slow (and don't care about what Cleopatra perceives). However, the statement is false anyway. Introduce Bob, moving at .9c relative to Anthony in the opposite direction as Cleopatra. Then Bob sees Cleopatra's clock going slower than Anthony sees it. Specifically, here is the order of time rates each perceives: Anthony: Anthony, normal; Bob slow; Cleopatra very slow. Bob: Bob normal; Anthony slow; Cleopatra very very slow (slower than Anthony sees Cleopatra). Cleopatra: Cleopatra normal; Anthony very slow; Bob very very slow. 


#27
Feb1512, 10:36 AM

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From the perspective of your "time dilation scale" you cannot ignore length contraction. There is a "scale" of sorts, length on one end time on the other, not zero and infinity. To say it differently time is a "unit", a I'm sure you would agree a "unit" is not actually representing any numerical value i.e. no zero through to infinity on this "scale". But, length measurements can "blend" into time measurements (&vice versa of course) and viola, time dilation/length contraction. This "blending" could be seen as a "scale" of sorts, with an interval being purely timelike on one end and purely spacelike on the other. Im not sure if your graphing calculator illustrates this, but consider that c is the fastest speed, any movement in a spacial dimension starts to "pull" the time dimension across that spacial dimension, that is the "blending" of the time & length measurements. Now after all this talk of time & length measurements, consider that speed (length*time) is relative. So it follows that time & length are relative, If you agree that motion is relative (i.e. no absolute rest), it is the exact same as agreeing there is no absolute measurement for time / length. I think I reitterated the inseperable relationship between time and length enough to get the point across that you cannot "zero in" on a time dilation "scale". Why is the "relationship inseperable"? It's motion that inherantly "blends" these units together. Specifically it is comparative motion where these units blend. "transform" might be the term used to describe this. There is a part of relativity that I find doesn't fit well with my intuition, and is simular to this thread. Time dilation /length contraction is not linear from "at rest" through to near c. That is, with the help of superman, we (me & superman ) accelerate our solar system to near c, using the stars to coordinate the starting position. A few years later, superman and I forgot we already did this, so we do it again, and again and again ect. all subsequent times we did this we recoordinated the start position again and accelerated from there obsvering our speed going from 0 through to near c again, following the same nonlinear whatever. These observations would be made each time the excersise was done. Relative to the original start position we are travelling nearer to c, despite having observations of accelerating from zero to near c numerous times. ( i get comparing the two observations is apples to oranges). Anyways, it's this "layering" of relative motion that starts to make me confussed why we can't find something/anything that we could coordinate speed to. Not that I question the validity of classical physics, just my ability to reason it , in this way. hint hint I think because momentum is a function of speed it would be relative, so there is no absolute "zero" momentum. Simular with gravity, free fall is zero gravity. 


#28
Feb1512, 02:43 PM

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I.e. Cleopatra will have gained mass, Anthoney will not. Cleopatra has the potential to blindly fly into a planet, Anthoney doesn't. If travelling at 99.9% c Cleo will have a Lorentz factor of just over 22. Am I interpreting this correctly as saying that over a distance of 22 lightseconds Cleo will only experience a second of time? As for Bob. If he and Cleopatra match speed in opposite directions, you are effectively saying that Anthoney will see them both tick at the same rate, and that their dilation will continue to infinity as they continue to accelerate. And that Bob and Cleo will see each other as slower and not that their clocks are moving the same? @George. In the section you asked me to look at the only thing I could see that seemed relevant was that he said we could ignore fourth and higher magnitudes. Is this what you were referring to? 


#29
Feb1512, 03:36 PM

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Traveling 22 light seconds of Anthony's distance, Cleo will experience 1 second. Traveling 22 light second of Cleo's distance, Anthony will experience 1 second. 


#30
Feb1512, 04:08 PM

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#31
Feb1512, 04:15 PM

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#32
Feb1512, 04:17 PM

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#33
Feb1512, 04:23 PM

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#34
Feb1512, 04:44 PM

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#35
Feb1512, 05:31 PM

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More physically, you can define distance using some reasonable procedure, e.g. parallax, image size, radar ranging. However, the first two relate a nearby size or distance with a distant size or big distance. Thus they need a definition of distance to get started. You can use radar ranging (or light travel time) to get started, or as your main definition. Going with radar for simplicity (in SR it is provable that they are all the same, for inertial observers), consider what Anthony and Cleopatra do. If each measures distance to some third object (in some state of motion), the round trip light paths will be radically different because of the relative motion between Anthony and Cleopatra. Thus, they measure the universe completely differently. 


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