READERS: In another [thread=51810]thread[/thread] after lengthy discussion about Special Relativity's claim of spatial length contraction, Pete has posted a thread which (making certain assumptions) purportedly proves the issue of length contraction. This thread is an effort to enlighten readers to certain facts (not assumptions) and how they mandate that such spatial contraction and assumptions are therefore invalid concepts. First one does not need to even concern himself with the postulates of relativity. You need only to accept (not assume) the fact that at least a clock with velocity which has accelerated while under the enfluence of F = ma, will have a slower clock tick rate (time dilation) than a clock which remains inertial. I specify the above conditions since reciprocity has never been demonstrated and a clock has never been shown emperically to tick slow due to relative velocity alone but only due to actual accelerated velocity. It is mentioned here in that in absence of some future supporting emperical finding there should be no consideration given the issue of reciprocity advocated by SRT. Now take a long piece of paper and draw a 1m long horizontal line. Mark the scale of this line as 3E<sup>8</sup>/1. That is each cm is 1 light second. In a rest frame that makes this line 100 light seconds long. Now envision an observer at the right end of the line and a moving observer going from left to right along the line at 0.866c. If we now mark the crafts location along and above this line each second of the trip you will have 115 one second time marks with a minor 0.473 second remainer to the rest observer. Each time mark is 0.866 light seconds long. We know that it has been emperically demonstrated that a clock with this motion will tick at 1/2 the rate of the rest clock. That is you should make a mark below the 1m line for each two marks made according to the rest clock marks. Therefore based on the rest observers view of velocity the moving clock will only accumulate 57 seconds during the trip and have a 0.7367 remainder to the rest observer. Based on the rest observer velocity, rest line length and rest clock tick rate the moving clock will (can) only accumulate 57 seconds IF the 1m long line remains in 1/1 correspondance between frames. That is its length CAN NOT have changed otherwise the moving clock could not accumulate the 57 ticks if you acknowledge the fact of time dilation on moving clocks. Therefore it is clear that spatial length contraction did not and cannot occur but what does occur is that velocity becomes frame dependant, not length. Given at rest: d = 1m, v = 0.866 cm/sec, t = d / v = 100cm / 0.866cm/sec = 115.473 seconds trip time. Given in moving frame: d = 1m, t = 57.7367 seconds, v = d / t = 100 cm / 57.7367 seconds = 1.732 cm/s = 1.732c!. Let me suggest you forget arguements about invariance of 'c'. Forget arguements about MM. Stick with the facts and then see if they do not mandate that we reconsider our prior interpretations of such matters. I think they must. The failure in SRT is the equating of t and t' time intervals when one is known to be different than the other. SRT changes measurement standards between frames but then treats them as equal in the formula d = vt.
For the record, the other thread does not "purport to prove length contraction". It presents a situation which allows us to investigate whether length contraction follows from an invariant speed of light. Mac thinks it does not, I think it does... but I haven't presented any argument to that effect, only invited interested participants to investigate for themselves. Mac has unfortunately declined to do so.
can you provide a link that shows the time dilation... is the result of acceloration... and not mearly velocity differences??? as such is fundamental. -MT
No need. I base my arguement on the fact that there has been no evidence supporting a relative velocity affect. All data for over 100 years has been for accelerated clocks. Certainly if one can supply such data then I would be forced to retreat. I don't think I need worry much about that prospect. Please Register or Log in to view the hidden image!
Mac, your argument appears to be missing something. Can you expand on the logic involved in this step?
I still have the view that your thread is an SRT thread in sheeps clothing. In my thread I address the issue strictly from the known physics and emperical data. If that data demonstrates a conflict then it supports the view that the interpretations of measured invariant 'c' is flawed, hence your exercise is only useful IF 'c' were truly invariant in the manner you think it is. My effort shows that assumption MUST be in error. So why waste time plotting the basis for SRT if SRT is flawed?
I thought you were debunking length contraction, rather than invariance of 'c'? You were quite adamant that length contraction doesn't follow from invariant c, so my thread was the logical next step. If you don't want to follow through, why make a claim in the first place?
Not sure what you think is missing. The logic is acknowledging emperical data about accumulated time dilation on clocks which supports it as a real physical fact, it simply follows that the accumulated trip time of the moving clock is entirely due to clock dilation and not a change in distance. Once you recognize that must be the case it then is apparent that what is frame dependant is velocity, not distance. Notice no where have I attacked the invariance of 'c'.
You have missed the point. As I am demonstrating, the invariance of 'c' is not at issue. That is length contraction can be shown inconsistant with known physics without attacking the assumptions of invariant 'c'. It is not that you cannot make an arguement for length contraction making that assumption. It is that the length contraction which follows from such assumption is invalid. Hence that leads to the ultimate conclusion that the basic assumptions about the basis for measured "Invariant 'c' " must be flawed.
The conclusion in that line doesn't appear to follow from the premises. Can you spell out the link between the two, using deductive reasoning?
That's not what you said before. You said "... I have shown that based on your assumption length contraction does not occur...", hence the other thread. I'm glad you now agree that if c were invariant, then length contraction would follow. So it seems that your argument is now that because invariant c implies length contraction, and that length contraction is false, then c is not invariant? That's certainly a valid argument. I agree with the first premise, but not the second... which is of course the reason that this thread exists - to demonstrate that length contraction can't be true. Carry on!
Your initial conditions are: 1) The traveller has a velocity of 0.866c in the rest frame. 2) The line has length of 100 light seconds in the rest frame. 3) Moving clocks ticks at half the rate of resting clocks in both frames. The valid premises drawn from these conditions are: 4) Moving clocks accumulate 57 seconds during the traveller's trip 5) The resting clock accumulates 115 seconds during the traveller's trip And you conclude that the line has a length of 100 light seconds in the moving frame . How do you reach that conclusion?
That must be the conclusion unless you do what is done in SRT which is equate the two different time intervals. As said: V = 0.866c (0.866 cm/sec), tick rate (tr) = 1 dilated tick/ 2 rest seconds. d = 100 cm. (accumulated time in dilated ticks) t' = tr * d / v = 0.5 * 100 cm / 0.866 cm/sec = 57.7367 dilated ticks. The error made in relativity is to equate the dilated ticks to equivelent seconds in the rest frame. They are only seconds in the moving frame. The two are not equivelent. If d were anything other than 100 cm (1/1 correspondance between frames) then the moving frame could not accumulate 57 seconds in the rest frame as predicted by time dilation. In the moving frame v = d / t' = 100 cm / 57.7 seconds = 1.732 cm/sec = 1.732c!.
Thanks for confirming the conditions and premises. A simple "that's right" would have sufficed. I don't think it follows. For counterexample: If d in the moving frame were 1000 cm, then the clock would still accumulate 57 seconds if the velocity of the line were 17.32c, yes?
Incorrect. 1 - You have no more basis to declare the line 1,000 cm than SRT does to declare it as 50 cm. 2 - If it were 1,000 cm and v in the moving frame were 17.32c then v in the rest frame would have to be 8.66c.
:bugeye: It's just a counterexample to your statement: ("If d were anything other than 100 cm..." ) Mac, you want to prove that it is 100cm in the moving frame, right? You're not going to start by assuming it to be 100cm in the moving frame, are you? Why? We know that the length of the line in the rest frame is 100cm. Are you assuming that the rest frame length is the same as the moving frame length?
MacM, If you are going to eliminate length contraction and account for time dilation, then when calculating the velocity of the moving frame you should calculate v = .866c. First and example of what I am talking about. You have clock A and clock B. Clock B ticks at the rate of 1 second for every 2 seconds on Clock A. Using Clock A, light travels 300,000km in 1 second. So in 2 seconds light would travel 600,000km. That means that using Clock B light should travel 600,000km in 1 second. So back to your example, the at rest clock reads 115 seconds. The at rest clock is still ticking at a rate where light travels 300,000km/sec, so the measured velocity of the ship is .866c In the moving clock, keeping in mind the clock is now ticking at a slower rate, (light should travel a greater distance per second, the ship should travel a greater distance per second), the clock reads 57 seconds. In both frames the distance covered is 300,000,000 km (I'm assuming that when you mentioned a light second you were refering to the distance of 300,000km). The ships velocity using the ships clock is 519,600 km/sec. This velocity should not be divided by 300,000 or you end up with 1.732c, which is an error. Remember that the ships clock is ticking at a rate of 1 second for every two seconds on the rest clock...so you should in this case calculate that in the moving frame, using the moving frames clock that c = 600,000km/sec. 519,600/600,000 is .866c So, velocity shouldn't be frame dependent, time dilation should occur as predicted, length should be the same in all frames and the speed of light is still constant (although the measured speed should vary based upon the rate of the clock) Of course I could be wrong, but this is my thought process...anyhow I'll let you get back to debating length contraction with Pete
Correct and as I point out if you adjust length and velocity in the moving frame you affect the calculation in the rest frame. I don't make any assumption. The dilated second in the moving frame is a longer time interval than the second in the rest frame. Hence to accumulate less trip time the distance traveled must remain constant. And we know that the dilated tick rate is twice the time interval of the rest second. Not assuming anything. The distance must be the same in both frames if time in the moving frame is ticking at 1/2 the rate as the rest frame and the clock accumulates 1/2 the amount of trip time. It seems that the conditions jof relativity confuse you. Lets approach this from another angle. Two cities 60 miles apart. Car "A" has a speedometer, odometer and clock. All working perfectly. Car "B" doesn't have a speedometer, he has an odometer but his clock is defective such that it only ticks at 1/2 the rate of the properly working clock in Car "A". Now the two vehicles set out to go between towns. Car "A" sets the pace and drives 60 Mph. At the end of the trip he records 60 Miles traveled in one hours time. Car "B" disagrees he says it only took 30 minutes and therefore they must have being going 120 Mph. Car "A" knows Car "B" clock is ticking slow and therefore does not think Car B only went 30 Miles. This is the precise situation in SRT at 0.866c.
MacM, if I am in my spaceship and I measure my own speed as 1.732c then, since light is going faster than me, I will measure the speed of light as something >1.732c. Therefore c is not invariant under the "MacM transform". I don't understand why you are willing to accept the body of impirical evidence supporting time dilation without accepting the much greater body of both impirical and theoretical evidence supporting the invariance of c. -Dale
There is absolutly no differance. When you go 0.9c light still exceeds that by 'c'. If you calculate 1.732c light still exceeds that by 'c'. This issue does not require challenging an invariant 'c'. I do not reject "measured" invariant 'c'. I reject the interpretation as to why it measures invariant. When you understand the "Why" then the falicy of SRT becomes more apparent.
