Tue 12 Jan, 2021 10:57 pm
We have the following two situations:
Viewing the A1-M1-B1 frame at rest:
A2(.8c---->)(The clock at A1 reads 4:45)
A1 M1 B1
Viewing the A2 frame at rest:
A2(The clock at A1 reads 5:00)
A1 M1 B1
(<-----.8c) (5:00) (5:15)
When the clock at A1 reads 5:00, A2 is simultaneously in 2 different locations.
Yes, both elapsed time and location are based on your frame of reference
You are doing all of this work... let me ask again. This is material covered in an AP high school class. For the amount of work you are putting into this, you could just learn it.
Why don't you simply take a Physics class so you can learn how this actually works
There are two things interesting in this example.
1. Any system to measure time is arbitrary.
We actually have come up with a "universal" definition of a second. We can send a paragraph explaining to intelligent extraterrestrials what as second is... and assuming they can count, and can do an experiment relating to the speed of light, they will come up with the same unit of measurement.
However, a second is a measure of elapsed time. Any intelligent extraterrestrial can build a clock that will properly mark off the second. That doesn't answer the question "What time is it now?"
The time that a clock reads depends on when you started it running. Different time zones have different times depending on when noon is. And even when noon is is arbitrary (based on when the sun is at its highest point over some observatory in some god-forsaken country that used to be in Europe).
So when a clock reads 5:00... all it tells me is that (assuming the clock is well built) that 5 hours ago it as 12:00. It doesn't tell me anything about the universe. The clock was just set by intelligent mammals on one small planet based on some accident of politics and astronomy.
2. Any system to measure location is arbitrary.
We also have a "universal" definition of a meter (and a foot, and a mile) that can be understood and replicated by our intelligent extraterrestrials. I can tell you with certainty how far something is (in a given reference frame).
When we talk about location, we are really talking about a distance from arbitrarily chosen reference points. My house is just outside of Boston. I can tell you how far I am from downtown Boston. That doesn't answer the question "Where is your house located".
So we created a system of longitude and latitude which provides a global way to determine location with two coordinates. Of course, this system is based on an arbitrary grid starting on some choice made due to an accident of politics and astronomy (same as the clock).
Any system to measure location needs a fixed reference point (i.e. a point that can be assumed to not be moving). I like to think that my house is not moving... it will be at the same geographic coordinates tomorrow that it is today.
Of course on another perspective... my house is moving. Yes, my house is fixed to a planet that is not only circling the Sun at one time a day, it is also spinning. From this perspective, the whole system of measuring location... those imaginary gridlines that mark longitude and latitude... are also moving.
3. The interesting problem with this example. In the OP location is treated as some absolute. Of course in space, each spaceship will have its own system of measuring time, and its own system of measuring location that will be arbitrarily determined based on the convenience of its inhabitants.
They can't be the same... because these systems assume a fixed reference point, and people in different spaceships don't chare a fixed reference point.