Parth G | To Understand ALL of Relativity, You Need to Know This One Concept. @ParthGChannel | Uploaded 2 years ago | Updated 8 hours ago
Can we discuss the equation that transforms from one reference frame's coordinates to another, in 5 minutes?
In this video we look Galilean relativity in some basic detail. We start by recalling that two observers, moving relative to each other, may observe the motion of an object differently to each other. Observers moving at a constant speed to each other can be described by the "standard configuration" in relativity, as discussed in episode 1 of this series!
The special case we look at here is when the first observer sees the object as being stationary, while the other (moving at a speed v to the first) measures the object to be moving at a constant speed. We see how this looks from either perspective, and then plot a distance-time graph for each observer.
In order to transform from one observer's coordinate values for the object to the other observer's values, we need an equation that links the two. When calculating the second observer's coordinate values, we can see this should depend on the first observer's values, the time elapsed since the two reference frames crossed, and the relative speed between the two frames. The equation is x' = x - vt, where x' is the second observer's coordinate value at a time t, the time elapsed since the frames crossed, and v is the relative speed.
We also see that from one observer's perspective, the other seems obviously wrong as their coordinate system is "moving". However, switching to the other reference frame gives us the opposite perspective.
Interestingly, we assume a "universal time" in this analysis. We imagine that both observers agree on how long it's been since t = 0, which is when the two reference frames exactly align. This implies there is some unique reference frame in the universe, whose time measurement applies to every other reference frame. This, however, is not true in reality. We can use this discussion about universal time to set up a discussion about special relativity in a future episode!
Episode 1: youtu.be/1fJwbpS_OZg
Thanks for watching, please do check out my socials here:
Instagram - @parthvlogs
Patreon - patreon.com/parthg
Music Chanel - Parth G's Shenanigans
Merch - https://parth-gs-merch-stand.creator-spring.com/
Here are some affiliate links for things I use! I make a small commission if you make a purchase through these links.
Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
My Camera: https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
Microphone (Fifine): https://amzn.to/2OwyWvt
Gorillapod: https://amzn.to/3wQ0L2Q
Timestamps:
0:00 - Basic Equations of Galilean Relativity
0:35 - Two Observers and their Reference Frames
2:08 - The Equations!
3:11 - Is One of the Reference Frames "Wrong"?
3:59 - The Assumption of Universal Time
4:49 - Setting Up for Special Relativity
Can we discuss the equation that transforms from one reference frame's coordinates to another, in 5 minutes?
In this video we look Galilean relativity in some basic detail. We start by recalling that two observers, moving relative to each other, may observe the motion of an object differently to each other. Observers moving at a constant speed to each other can be described by the "standard configuration" in relativity, as discussed in episode 1 of this series!
The special case we look at here is when the first observer sees the object as being stationary, while the other (moving at a speed v to the first) measures the object to be moving at a constant speed. We see how this looks from either perspective, and then plot a distance-time graph for each observer.
In order to transform from one observer's coordinate values for the object to the other observer's values, we need an equation that links the two. When calculating the second observer's coordinate values, we can see this should depend on the first observer's values, the time elapsed since the two reference frames crossed, and the relative speed between the two frames. The equation is x' = x - vt, where x' is the second observer's coordinate value at a time t, the time elapsed since the frames crossed, and v is the relative speed.
We also see that from one observer's perspective, the other seems obviously wrong as their coordinate system is "moving". However, switching to the other reference frame gives us the opposite perspective.
Interestingly, we assume a "universal time" in this analysis. We imagine that both observers agree on how long it's been since t = 0, which is when the two reference frames exactly align. This implies there is some unique reference frame in the universe, whose time measurement applies to every other reference frame. This, however, is not true in reality. We can use this discussion about universal time to set up a discussion about special relativity in a future episode!
Episode 1: youtu.be/1fJwbpS_OZg
Thanks for watching, please do check out my socials here:
Instagram - @parthvlogs
Patreon - patreon.com/parthg
Music Chanel - Parth G's Shenanigans
Merch - https://parth-gs-merch-stand.creator-spring.com/
Here are some affiliate links for things I use! I make a small commission if you make a purchase through these links.
Quantum Physics Book I Enjoy: https://amzn.to/3sxLlgL
My Camera: https://amzn.to/2SjZzWq
ND Filter: https://amzn.to/3qoGwHk
Microphone (Fifine): https://amzn.to/2OwyWvt
Gorillapod: https://amzn.to/3wQ0L2Q
Timestamps:
0:00 - Basic Equations of Galilean Relativity
0:35 - Two Observers and their Reference Frames
2:08 - The Equations!
3:11 - Is One of the Reference Frames "Wrong"?
3:59 - The Assumption of Universal Time
4:49 - Setting Up for Special Relativity
