(I got the idea for this one while racing cars on my bicycle this morning.)
StarValleyWy, physicist, interrupts the idyllic stupor of RHP one day, shouting incoherently about how Einstein is a fraud. After being calmed down, he explains that he has constructed a machine that could, in theory, propel one to any arbitrarily large velocity. He explains:
The machine as it is consists of a straight 80-mile stretch of highway, at one end of which is placed a flatbed truck 60 miles in length, such that it covers all but the last 20 miles of the highway. On top of this truck is another, placed so that the ends are flush, 40 miles in length. On top of this is a truck 20 miles in length placed in the same manner. At a signal, the bottom truck starts moving at 20 mph with respect to the road. The second moves at 20 mph wrt the bottom truck. The third moves at 20 mph wrt the truck below it. After one hour, the bottom truck has traveled to the end of the road. The second truck has traveled to the end of the first truck, and to the end of the road. The third truck has traveled to the end of the second, and thus to the end of the road. Thus, while each truck used energy necessary only to propel it at 20 mph, the top truck traveled 60 miles in one hour, for an average speed of 60 mph. Enlarging distances and adding arbitrarily many trucks could clearly propel the top truck at any velocity desired, namely one faster than light. Thus Mr. Einstein was a fraud.
There is one seemingly tiny flaw. What is it?
Originally posted by royalchickenThere are two huge flaws - the bottom truck has to use enough energy to accelerate all 3 trucks up to 20mph. Same goes for the second wrt the third.
(I got the idea for this one while racing cars on my bicycle this morning.)
StarValleyWy, physicist, interrupts the idyllic stupor of RHP one day, shouting incoherently about how Einstein is a fraud. After being calmed down, he explains that he has constructed a machine that could, in theory, propel one to any arbitrarily large velocity. He expla ...[text shortened]... er than light. Thus Mr. Einstein was a fraud.
There is one seemingly tiny flaw. What is it?
It would undoubtably be less expensive, energy-wise, to just accelerate the top truck to 60mph. If you pile up an arbitrarily large number of trucks, the bottom one would require an arbitrarily large amount of energy to get them all going, and the next one up would need almost as much.
Originally posted by royalchickenAhem...
There is one seemingly tiny flaw. What is it?[/b]
I know, I know! I have two answers. I'll give my smart ass one now and a better one later... chuckle , tee hee...
From Smoot to Alpine... Star Valley is only 30 miles in length! The damned trucks won't fit! 🙄 And the county road commissioner is gunna be on you like flys on stink! 😲
Second reply... hoping i don't make a fool of myself...
There are valid reasons for both the Newtonian and the Einsteinian universes that shoot down the great "smoot to alpine" race.
Newtonian - Newtons second and third laws. Equal and opposite forces are exherted by each "child" truck upon it's parent as it's wheels push its parent backward in order to move forward. This force is proportionate to mass, but opposite in direction, and the total energy of the system must be conserved. f = ma for entire system. Hence the smallest stacked trucks' "speed" never exceeds the vector average of the system. ( not sure of the mathematical correctness of that last sentence, RC... Close?)
Einsteinian - We all hear the term "relativity". Einstein (well, acutally Lorentz) used this term to mean "one frame of reference in relationship to another", or their relative mass-energy states. The system of trucks in "the great Star Valley race" , are all one "frame", so even ignoring newtons equal/opposite force of child to parent... even if the children trucks could "magically" accellerate without force upon their parent , which they can't ... even if they could, none of the children would exceed the limits of the frame of reference. To put it in plain english, the children trucks would ALL BONK into the cab of their parent, imparting energy to it and destroying themselves in the doing. The total energy of the "system of trucks" AS SEEN FROM WITHIN the cab of the massive "monster mama" remains constant as it approaches the speed of light. You do, however eventually obtain a "single really, really massive truck, if observed FROM OUTSIDE the "frame", because the truck gains mass/energy as each child destroys itself in the "collision" with it's parent. (the mass to energy thingy, e = mc 2) Eventually all the children have destroyed themselves, imparting energy to the "big mama" truck rig, but the speed limit is safe.. Big mama gets fatter and fatter, but she cain't run no faster!
Relativity might be said to be the information differential as observed from inside big mama's cab as compared to an observer watching her pass from the grandstand down the final straightaway! She's doing 99.999997! Oh my God! She is flying!
From the grandstand... the sixty mile long truck would seem like a big flat plate as it whizzed by you. She would be a "paper thin", borg cube at full impulse! (Not to be confused with Barb'Q which is cooked in the parkin' lot before the race!)
As one approaches the speed of light, (or as i prefer to think of it... the "maximum information interchange rate"😉 if you were in the cab of the "monster mama" truck, your vision would shrink from all sides until you observed a large "cone" straight ahead of you. Ever nearer the speed of light, the cone shrinks to become a single overpoweringly bright, tiny dot. The reason is that all other information coming from the sides, and behind you... never arrives. An "information cone" to the front shrinks smaller and smaller until it becomes a single dot. The universe at near the speed of light is strikingly analogous to a black hole in this sense. It is truely a weird place in which we live. I apologize if this does not make sense. I have a "sort of" feel for relativity, but words fail, and i am sure i might be off on several important aspects. Without "math" ability, i am stuck in a world of guess and hope. That is why i envy RC and the rest of you who can actually do math. What a wonderful thing to not have to rely on verbs and adjectives! Mike
After thinking about this some more... I don't think i responded correctly to your basic question, Mark. I can see in my head that "maybe"... just maybe this has something to your question "where are they?"... something about each truck being 'half as long as it's parent'... we never do get to a full integer, do we?
Originally posted by royalchickenCool! see... i'm so freaked out by math that i "don't know success when it bites me in the butt" ! 😵
Actually, Mike, your large explanation, when taken along with what richjohnson said, isolates all the flaws in it that I could find. Good job to both of you 😀!
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Originally posted by royalchickenHere's another way of pointing out the flaw:
Actually, Mike, your large explanation, when taken along with what richjohnson said, isolates all the flaws in it that I could find. Good job to both of you 😀!
Say there are two trucks. If they accelerate at the same time they must both have their brakes off. So if the truck on top doesn't accelerate then it will roll off the back. Neglecting frictional effects it must apply exactly the same force to its wheels to stay still on the accelerating platform as would accelerate it to 20mph if it was on a stationary platform, so the truck on top gets no acceleration for free at all!
First i must ask if this event is taking place on earth? Well if it is there is one relavent flaw. Everyone know that the horizon is fifty miles of in the distance. Therefore a sixty mile long truck could not be FLAT. But rather would have to be curved along with the Earths surface.