imaplanck, according to a ground observer, the bottom of the tread is stationary, the axels (and the body of the tank) are moving to his right at .866c, and the top of the tread is moving to his right at 2 x .866c. Can't you understand that the top of the tread is moving to the right of the ground observer at twice the speed of the tank body? According to an observer inside the tank, the top of the tread moves forward at .866c and the bottom of the tread moves rearward at .866c. Both top and bottom would be contracted by the same amount, according to the tank observer. The observer on the ground sees a different scenario. He sees the bottom of the tread at rest with the ground, the tank moving to the right at .866c, and the top of the tread moving to the right at twice the speed of the tank itself. The tank tread moves in different directions at the top and bottom. This creates the paradox in the ground frame. The ground observer does not see the top of the tread and the tank moving to the right at the same speed. The tread still moves relative to the tank body and its axels.
Thats what we have been trying to tell you and you haven't bee able to understand, not the other way around. Yes we have never said otherwise, you though have : Yes again we had to tell you that(several times). Where is the paradox though????
Posted by stupidasshole, What the fuck is wrong with you? What the f**k is this supposed to mean, dickhead? What frame of reference are you using? Don't you know the very basics of stating which frame you are using? I have repeatedly stated THE GROUND FRAME moron. Are you stating both the top of the track and the bottom of the track are doubled in the ground frame? You don't have a clue as to what is being discussed.
IT APPLIES IN ALL FRAMES FUCKWIT. THERE IS NO NEED TO BE FRAME SPECIFIC IF IT APPLIES IN ALL FRAMES(ALL THOUGH THIS WAS ONLY A REITERATION OF A STATEMENT I MADE WHERE I DID ACTUALLY SPECIFY THAT IT APPLIES IN ALL FRAMES). JESUS YOU ARE AN IMBECILE.
Look 2imbecilic, could we take this to PMs I have no wish to get Petes brilliant thread thrown in the bin(if its not already too late).
So, plank-for-brains, you are stating the top of the track is stretched by a factor of two according to a stationary observer sitting on the bottom track. You are stating the bottom of the track is stretched by a factor of two according to a stationary observer sitting on the top track. Do you even realize that each of these observers 'see' the other frame (track) moving past his 'at rest' frame by 2 times .866c? Do you realize a stationary observer sitting on a spot in between the top and bottom tracks would see the top track moving in one direction at .866c and the bottom track moving in the opposite direction at .866c? JESUS, YOU ARE AN IMBECILE IF YOU CLAIM THE TRACK IS 'STRETCHED' BY A FACTOR OF TWO IN ALL FRAMES.
I give up! You are just not capable of understanding this. I would like it to be noted that I ran angry based on your repeated fuckwitted false claims of correction, not based on your misunderstanding of the premise. Its not a crime to not get something.
Pete, this is your thread, so you don't have to take my suggestion, of course. Your 'tank' scenario can be replaced by a conveyor belt that incorporates all the same features and frames of reference, but with an easier-to-understand relationship between frames. At least I think it will be easier to understand for all readers of this thread. Tell me what you think of my suggestion. The conveyor belt corresponds to the tread of the tank, of course. The body of your tank corresponds to the axels at the ends of the conveyor belt. The ground frame in your tank scenario would correspond to the bottom of the conveyor belt. The 'ground' could also correspond to the top of the conveyor belt, if the ground were at rest with respect to the top of the belt in that particular frame of reference. We can make this conveyor belt any length we want, measured in kilometers. The proper length is the axel-to-axel distance the belt revolves around. The axels have no relative motion wrt each other, hence the proper length of the conveyor belt as a whole. Assume the proper length of the conveyor belt as 1,000 kilometers and the velocity of each belt surface (top and bottom) as .866c in the axel frame of reference for the following. Do you now see that both the top and bottom of the conveyor belt would contract by one half ONLY IN THE AXEL (or tank body) FRAME OF REFERENCE? In the axel rest frame, the belt would have to 'stretch' by a factor of two, or break, according to Special Theory. In the rest frame of an observer riding along on the belt, the distance between the axels would contract by 1/2 to 500 kilometers, but the section of the belt he is riding on would not contract, it would still measure 1,000 kilometers. If the ground were in contact with his section, it would not contract.This observer riding on one section of the belt would see the other section as moving past his position at 2 times .866c, necessitating the use of SR's velocity addition formula. I think the rest observer on the track (same as ground observer) would see the other track as measuring 142.8 kilometers. I didn't work the velocity addition formula, but relied on your 'factor of seven' statement for the 2 x .866c contraction factor.
Hi 2inquisitive, If you go back to the first page of the thread, and look at the two animations by Pete, you will see that the length of the entire track is represented by 22 ruler-marks all around the track. It is difficult to count them because they are moving, but you can take my word for it that there are 22 of them. Now if you scroll down that page a little further, you will see that I have posted a static picture of the tank (non-animated) in which both the tank and the embankment are at rest. In that picture, there are only 11 ruler-marks around the outside edge of the track. So, considering the entirety of the track, the length of the track is increased by a factor of 2 (gamma) in both of the animations. Please note that Pete considers my drawing to be incorrect because he does not consider those marks to be ruler marks. He considers them to be spikes on the tread, and in that case, he is correct in claiming that there must be 22 of them in all frames. Spikes cannot appear and disappear, after all. So my drawing does not represent what the tank actually looks like. But I think you will find it useful for measuring lengths (even though the units on the track are obviously different from the units on the embankment.)
Pete says that the tank and embankment both at rest should look like this. Please Register or Log in to view the hidden image! Then, once it is turning, the length contraction of the entire track causes it to have to stretch in order to reach around the wheels. Unless it breaks first, at .866c it will stretch to the point where the distance between the treads doubles in its own frame (therefore, it becomes evident along the bottom tread which is at rest with the embankment). This makes more sense than my explanation, so I retract my above post.
Hi Neddy. Yes, I saw your drawing earlier. According to Special Theory, the bottom track frame is pretty simple. Did you read my conveyor belt explaination? In the tank's rest frame (which is also the axels rest frame), the bottom track appears contracted by a factor of two. In the bottom track's rest frame (which is also the ground's rest frame), the axels (and tank) appear contracted by a factor of two. The track is its proper length in the ground rest frame, not contracted or stretched. This is according to Special Theory. Any other explainations are not SR, but the posters distorted version of SR. Also, according to Special Theory, an observer sitting on the bottom track will see the top track moving past at 2 x .866c unless the velocity addition formula is used. Using the velocity addition formula, an observer sitting on the bottom track will see the top section of the track contracted by a factor of seven. The same is true for an observer sitting on the top section, he will see the bottom section contracted by a factor of seven.
I thought we were going to move on to more challenging things? Please Register or Log in to view the hidden image! If the mentally retarded relativity knockers wont look past their own pre-conceived ideas and see for themselves that these animations are correct, thats their own problem is it not? Can we not ignore the arrogant stragglers and progress?
Hi everyone, The tank tread must be able to physically stretch, a tread that could not stretch would be perfectly rigid and would have a speed of sound > c. Both of these are well known to be incompatible with relativity. "Space geometry in rotating reference frames: A historical appraisal" is a pretty interesting paper that really addresses the history of this argument, or rather the argument from CANGAS' original thread about wheels instead of tank treads. There are two points made repeatedly in the paper that I think are important to this discussion. First, if you want to consider the system (wheel or tank treads) in two different states of motion then you must consider the material properties. Second, even if you only want to consider the system in a single state of motion you have to be really careful about simultaneity and about what exactly you are describing, simultaneity is not global in rotating reference frames so it makes "proper circumference" difficult to define. I think that a full treatment of the material properties is probably beyond the math of anyone on this forum (particularly since you would have to use some four-vector or tensor formulation of Hooke's law). So I would personally recommend limiting the discussion to the case where the tank is moving at .866c wrt the ground and not considering the case with the tank at rest wrt the ground. -Dale
Yes lets be pragmatic about this. Lets consider actual physical parameters. A tank tread is not a friction drive it is driven by a positive mechanical mesh with a drive cog. Therefore your contraction theory requires different stretch over different areas of the tread and different stretch in different views. Therefore if you actually take tensil or yield strength into account you have the tread breaking at different velocities as a function of the observers view point. A common problem with the theory of relativity. It wants to claim physical actions as a consequence of observation of a disassociated enity to the event.
Can you actually demonstrate that mathematically using the Lorentz transform? You like to wave your hands and claim SR paradox, but I have yet to see you actually correctly produce a SR prediction let alone show that it is paradoxical. If you can indeed rigorously show that the tread would break at different speeds then you would have succeeded in your long-time ambition, but simply claiming it is insufficient. Find the relativistic formulation of Hooke's law and Young's modulus, set up the problem carefully, use the Lorentz transform, and back up your claim. -Dale
Do you really think that trying to shift the attentioon somehow changes the facts. THE TANK TREADS ARE MECHANICALLY SYNCHRONIZED TO HAVE UNIFORM DISTRIBUTION OF CLEATS ACROSS THE UPPER AND LOWER SECTIONS. THAT CANNOT CHANGE AS YOU HAS SHOWN IT UNLESS YOU HAVE THE TREAD SKIP TEETH ON THE COG IN ADDITTION TO DIFFERENTIAL CONTRACTION AS A FUNCTION OF OBSERVER VIEW. SPEAKING OF WAVING HANDS.
I talked of a simultaneity earlier but noone acknowledge simultaneity as a consideration encompassed in this tank track (which is of course is a rotating reference frame). May we attempt to illustrate loss of simultaneity here? instead of feeding the monkeies.
Mac has brought up an interesting simultaneity issue. There are two simultaneity issues in the scenario. Mac's issue is related to the tank getting up to speed. The other, which is related and easier to address first, is related to the tank cruising at constant velocity. First issue In the rolling tank's reference frame, there are the same number of cleats on the top section as on the bottom section. But in the ground reference frame, the rolling tank has more cleats on the top section than the bottom. How is this possible? Second issue In the ground reference frame, there are the same number of cleats on the top section as on the bottom section before the tank starts rolling. But the rolling tank has more cleats on the top section than the bottom. The driving wheels are both going at the same speed (as we know from the tank reference frame), and there is no slipping of the tread on the wheels (again, we know this from the tank frame), so how do the extra cleats get to the top section?
