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The problem relates to some observations as to how forces act in "Einstein's elevator", a case which can be considered to be modeled by special relativity even though many methods commonly used to address the problem are introduced in General relativity. It's also case which involves both the concept of forces and (gravitational) time dilation, that illustrate how they interact. Thus it serves as a vehicle for discussing the laws of physics in cases where time dilation exists.

Consider a weight hanging from a cable of constant cross section in an accelerating elevator. The cable is considered to be "massless" though perhaps it would be better to say that the density of the cable is zero, thus the cable doesn't have to support its own weight. This is not realistic, but does not violate any fundamental laws of physics. It does violate the weak energy condition, but that's not a fundamental law. IT's also noteworthy that this idea of a zero-density cable is frame dependent, so this part of the problem specification is a bit coordiante dependent.

We can ask the question "Is the tension in the cable constant along it's length". And the answer to that question is no - the tension in the cable is not constant.

At the I level, we can draw this conclusion from considerations of the conservation of energy. The work done in lifting the weight by a certain distance through the rope, which is assumed for simplicity to be well approximated by Born rigidity, must conserve energy, and this requires that the tension not be constant. The issue involves Bell's spaceship paradox, whereby the proper acceleration at the top of the cable is dfferent than the proper acceleration at the bottom of the cable where the weight is attached.

The A-level answer is more interesting and I personally find it more convincing than the I-level argument, but it does require graduate level concepts.

For the A-level approach, we use the Rindler metric, and we note that the relativistic replacement for F=ma, an ordinary differential equation, is ##\nabla_a T^{ab} = 0##, a partial differential equation, where the concept of force is replaced by an entity known as the stress-energy tensor ##T##, in which tension in the rope is just one component of the tensor. The components are basically density and tension, and we set the density to zero, as the rope is (in the frame of the elevator) specified as being massless. It is worth noting that the concept of "massless" here is frame dependent.

Solving this partial differential equation in previously mentioned Rindler coordinates (which is convenient, though of course other coordinate choices could be made, as long as some attention is paid to sepcifying the idea that the density of the rope is zero in a coordinate independent form), and converting the tension in the rope from a coordinate basis to an orthonormal basis, we observe that the stress in the cable is not constant, and that the total force exerted by the rope on it's attachment point at the top of the elevator is not equal to the total force exerted by the rope on the weight at the bottom of the elevator.

I'm pretty sure I posted the details of this calculaltion elsewhere in the PF forums once upon a time - if it becomes necessary I believe I can dig it up.