On Monday, December 30, 2024 at 6:13:18 AM UTC-7 Quentin Anciaux wrote: Chatgpt is your friend and accept an infinite amount of trolling, here is its a correct answer:
The scenario you're referring to is a classic thought experiment in special relativity called the "ladder paradox" or "pole-and-barn paradox". It illustrates how the effects of Lorentz contraction and the relativity of simultaneity work together to resolve what seems like a paradox. The Setup: Imagine a car moving at a relativistic speed (close to the speed of light) towards a garage. The car is longer than the garage when measured in their respective rest frames. The question is: can the car fit entirely inside the garage for a moment, given Lorentz contraction? Lorentz Contraction: 1. In the garage's frame of reference (rest frame of the garage): Due to the Lorentz contraction, the moving car appears shorter than its rest length. This contraction occurs along the direction of motion. >From the garage's perspective, it seems that the car becomes short enough to fit entirely inside the garage for a moment. 2. In the car's frame of reference (rest frame of the car): The car perceives the garage as moving toward it at relativistic speed. Due to Lorentz contraction, the garage appears even shorter than its rest length. >From the car's perspective, it seems impossible for the car to fit inside the garage, as the garage is too short. Relativity of Simultaneity: The apparent paradox arises because different observers disagree on what events are simultaneous. Here's how this resolves the situation: 1. In the garage's frame: The garage can be equipped with two doors: a front door and a back door. At one specific instant (according to the garage's clock), both doors can close simultaneously, with the car fully inside the garage. 2. In the car's frame: Simultaneity is relative. The car's frame does not agree that the front and back doors close at the same time. Instead, it perceives the back door closing first and the front door closing later (or vice versa, depending on the direction of motion). *How does this guarantee no collision? AG* Resolving the Paradox: 1. In the garage's frame, the car can fit entirely inside the garage due to Lorentz contraction. 2. In the car's frame, the car never fits entirely inside the garage. *This is exactly my result using length contraction. AG * *What would a Bird's Eye Observer resident in an overhead satellite observe if the garage had no roof? AG* However, because simultaneity is relative, the sequence of door closures ensures that no collision occurs, and the situation is physically consistent in both frames. *This result, a disgreement between the frames is what, on the Internet, is called a paradox. Everyone knows about simultaneity being relative. We all know about it. Why then do videos trying to resolve it, try to get the car fit in garage from the car frame? AG * Key Takeaway: The apparent paradox arises from treating simultaneity as absolute (like in classical mechanics). Special relativity shows that simultaneity depends on the observer's frame of reference, and Lorentz contraction is observed differently depending on the frame. This resolves the contradiction and maintains consistency with the principles of relativity. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/bb0d21dc-e599-43c1-a9aa-c2050d5012b1n%40googlegroups.com.
