A 4D Physics Tale for Young Minds.
Tim is a clever young lad who has a 20 minute walk (1 mile) to school every school day. Tim's mother gave him a nice durable stop watch to help him make sure he made it to school on time every day. One tick each second. If he left the house at 7:40, and walked steadily along the way it was a nice easy stroll and he was always in his seat by 8:00am. 1200 ticks. 12 blocks. 100 ticks per block. Two steps per tick. So 7:40am was always when he left.
There was a small neighborhood grocery store between his house and the school. A distraction. Two minutes (120 ticks) from home. Some days he would pause there to spend a nickel or dime if he had either. That usually took 3 minutes (180 ticks) of the trip. What Tim realized was that he had already spent 5 minutes (300 ticks), but still had 18 minutes (1080 ticks) of walking to get to school. He knew if he ran he could stretch those 15 minutes (900 ticks) to cover 18 minutes (1080 ticks) of walking distance in just 15 minutes. The store distraction slowed down his ticks per distance travelled to a stop. Running stretched his ticks to cover more distance per tick. But Tim was panting and sweating when he got to school. Running required more work than walking would have needed.
Another day Tim wanted to get to school early so he could have time to finish his homework before class started. His homework was in his classroom desk. He realized that if he could run the whole way he could get 20 minutes (1200 ticks) worth of distance with just 15 minutes (900 ticks) and have 5 minutes (300 ticks) to work on his homework. He did make it to school with 5 spare minutes, but again he spent more energy to get there. Tim learned that he would need some eggs and bacon and toast and juice for breakfast on those running days. On walking days a bowl of cereal with milk was enough. Speeding up requires more energy.
Tim's Grandmother lives 1091 miles away. Tim had a dream about using his 1200 ticks to visit her. His dream said it was easy, just 1,309,200 ticks of his stopwatch to walk there. 363 hours and 40 minutes. But eating enough breakfast to get there in 1200 ticks may be impossible. Great Great Grandpa Albert would have agreed.
Two lessons for Three:
Rod and Miles are fraternal twins. Both are in the same class as Tim. All three volunteered for a race to show how ticks get used up when a longer path is taken. Or distance is lost when you stop moving but keep ticking.
Rule 1. Walking only. 2 steps per tick. Each student gets a stopwatch with 20 minutes (1200 clicks) countdown set on it. Start the countdown when you start walking. Stop walking when the countdown reaches 0.
- Tim wisely wants the straight path. The straight path is 1:1 aging speed to cosmic speed
- Miles wants to take the curved path.
- Rod will stop along the way to rest 3 minutes, or 180 ticks, before continuing.
All three should walk, 2 steps for each tick, and stopped when they used up their 1200 ticks. Rod and Miles will have used up their 1200 ticks before they caught up to Tim. To Tim, they would have seemed to have slowed down, aged faster, relative to him. Relativity.
The next day the three decide to have another race. Each one gets a stop watch with 1200 seconds (ticks) to use up. Tim walks. Rod takes baby steps. Miles runs. 20 minutes after the race starts we see how far each one got with the same 1200 seconds (ticks).
- Tim walked 1200 ticks. Tim's path is "preferred" time spent.
- Miles ran 1200 ticks.
- Rod waddled 1200 ticks. Baby steps.
Each one aged 20 minutes, but relative to Tim, Rod's aging ticks ended where half of Tim's ticks were. To Miles, Tim 's aging ticks ended where 2/3 of Miles tick were. Speed slows down aging, but consumes more energy to speed up.
- Tim's breathing and heart rate was only slightly above resting rates.
- Miles was panting and sweating after his 1200 ticks.
- Rod was so bored he nearly fell asleep. Relativity.
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