Question

We can measure Lorentz contraction for fast moving objects, but we also assume that the contraction exists for all velocities, although it would be difficult to prove the contraction of slowly moving snail.

You might then argue that it is a situation where the model might give you an affirmative answer but that you couldn’t actually prove it. There are posts about this but I see no attempt of proof.

Here is an attempt to do that: We imagine a conveyor belt moving at the speed of a snail. On top of this moving belt we imagine another belt moving at the same speed so that a snail on the second belt would move with double speed. We then add belt upon belt until the snail on the last belt moves with half the speed of light. In this case we might prove the effect.

Would that be a proof that the effect exists for the lowest speed component, based on the symmetry of the build-up of speed in the arrangement?

Answer 1

Adding conveyor belts to accelerate a snail to relativistic speeds cannot serve as practical proof of Lorentz contraction at low velocities, though such contraction is real and has been observed at high velocities in particle accelerators.

Step-by-step explanation:

The question is asking whether adding multiple conveyor belts, each increasing the velocity of a snail incrementally until it is moving at relativistic speeds, could serve as proof that Lorentz contraction occurs at low velocities as well. The student is suggesting an experiment that raises the question on the validity of length contraction for very slow-moving objects.

According to the theory of special relativity, length contraction is indeed a real phenomenon that affects all objects in motion, regardless of their speed. However, the effect is only noticeable at velocities approaching the speed of light.

In real-world experiments, such as those conducted at particle accelerators like the Stanford Linear Accelerator Center (SLAC), charged particles moving at relativistic speeds exhibit length contraction, which has been experimentally verified. The fields around these particles are observed to interact more briefly with detectors, which is a consequence of the length contraction predicted by special relativity.

Although the proposed conveyor belt experiment is a creative idea, in practice, it would not be feasible to use this method to demonstrate Lorentz contraction at low velocities because the effects at such speeds are imperceptibly small.

The contraction at low speeds is several orders of magnitude smaller than can be measured with current technology. Therefore, while the thought experiment aligns with the symmetrical build-up of speed, it cannot serve as a practical proof of length contraction for the snail's initial slow motion.