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jester1989
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will a 2m(rest length) car moving near lightspeed fall in a 1m hole?
The question is, in your thought experiment, under what conditions does the car fall into the hole. If you answer that question is a rigorous manner then you will find that the answer is the same in all frames.jester1989 said:the car's length is 2m, and the holes length is 1m, the hole's width>car's width.(since this doesn't contract. Car's direction of travel is parallel to the car's and hole's length.
jester1989 said:will a 2m(rest length) car moving near lightspeed fall in a 1m hole?
yuiop said:This is a fairly well known paradox, but it is not popular because it is very "messy" and has a number of practical issues that have to be resolved. Here are some of the issues outlined:
1) A car would normally have suspension, which would complicate the calculations, so I will take the liberty of replacing the car with a flat ice puck moving on a frictionless surface. The ice puck would have to be traveling at a velocity somewhat greater than 0.866c relative to the surface, to get the required length contraction. At that the velocity the time for the front edge of the ice puck to traverse the hole would be 1.926E-9 seconds. Assuming a downward gravitational force of 10m/s^2 the leading edge of the puck would fall a distance of 0.0000000000185 millimetres. That would hardly register as a bump in the pucks straight line path across the top of the hole. To make the puck fall a noticeable distance (say 1 cm) into the hole the gravity would have to be over 500,000,000,000 times greater than the Earth's surface gravity.
2) In the reference frame in which the puck is rest, the hole is only 0.5 meters wide and the car is 2 meters wide. The only way the puck can enter the hole is if the puck bends. This requires that the rigidity of the puck material has to be limited and as already mentioned, the gravitational force has to huge.
3) In the rest frame of the surface, there is point at which more than half of the puck is unsupported as it starts to cross the gap. At this point the edge of the hole acts a fulcrum and the puck starts to rotate. This rotation means the puck approaches the far side sideways on and is unlikely to cleanly pass under the far edge even if the puck and surface are paper thin. In the rest frame of the hole, there is never a point at which more than half of the puck is unsupported and there no reason why the puck should rotate in this frame. Presumably the rotation is replaced by the bending of the puck in this frame. This is one of the more messier aspects of the paradox.
4) It should be noted that the acceleration due to gravity is effectively greater (by gamma squared) in the frame in which the puck is at rest due to time dilation. For example if the puck falls 5m in one second in the rest frame of the surface then it falls 5m in less than than half a second in the puck frame.
So as you can see, in order to determine if the "vehicle" falls into the hole or not, we need to know the height of the vehicle and the thickness of the surface, the force of gravity, the tensile strength or rigidity of the material the vehicle is made of and the suspension arrangement (if any). All we can be sure of without knowing all those details is that whatever the fate of the vehicle in any given reference frame, that the same fate happens in any other reference frame. If it can be shown that different outcomes are predicted in different reference frames, then relativity is a broken theory or (more likely) we have not taken everything into account.
jester1989 said:will a 2m(rest length) car moving near lightspeed fall in a 1m hole?
This scenario is a thought experiment used to demonstrate the effects of time dilation in Einstein's theory of relativity. In this scenario, the car is traveling at a speed close to the speed of light, which causes time to slow down for the car relative to an outside observer. This means that from the perspective of the car, the hole may appear to be only 1m deep, allowing the car to fall into it.
Time dilation is a phenomenon where time appears to pass more slowly for an object in motion compared to an object at rest, as observed by an outside observer. In this scenario, the car is moving at a high speed, causing time to dilate and allowing the car to fall into the 1m hole.
This thought experiment is based on Einstein's theory of relativity, which states that the laws of physics are the same for all observers in uniform motion. This means that the perception of time and space can vary depending on the observer's perspective, as demonstrated in this scenario.
While this thought experiment is based on scientific principles and theories, it is not physically possible for a car to reach speeds close to the speed of light. The laws of physics prevent objects with mass from reaching the speed of light, which would require an infinite amount of energy.
This scenario challenges our traditional understanding of time and space, showing that it is not a fixed concept but rather relative to the observer's perspective. It also highlights the complexities of Einstein's theory of relativity and its impact on our understanding of the universe.