Special Relativity: Grokking for a Female Neurobiologist in her 60s

[Chava]

I'm a female neurobiologist in my 60s with a lifelong passion for physics (but my math was not strong enough). I have a special interest in special relativity and a decent grasp of the basics. I can solve Lorenz calculations 'til the cows come home'. I don't need help with homework of any type. I get frustrated with lots of the illustrations given in books for lay people. They conflate mass with waves. I made a deep foray into wave theory and recognized that you can't push on a wave -- any wave - and make it move faster. This is a point that get lost when people talk about SR.

Right now, I'm trying to reconcile the notion that any inertial frame can take itself to be stationary. So, how do we get to solve real world problems when space ships are traveling to Mars, for example? I only recently learned that it is not only the length of an object that contracts along the axis of motion, relative to a different 'stationary' observer, but also the pathlength. That is boggling me.

I've worked through the full 43 lectures of Michel van Biezen. In lesson 34 (if memory serves) he addresses the issue of path length shortening. However, if the spaceship is traveling at a fixed velocity of some fraction of 'c', why doesn't it "perceive" itself to be stationary? Is the velocity and all the related calculations really dependent upon whether the pilot "knows" his ship is moving? Does it have anything to do with the velocity that the target (maybe space station) is moving toward the ship?

 

[PeroK]

Reading your post it's clear that you have fundamental misunderstandings of the basics.

For example:

Right now, I'm trying to reconcile the notion that any inertial frame can take itself to be stationary.

This is something fundamental to classical, non-relativistic mechanics. E.g. if two objects collide, you can study the collision in the "laboratory" frame, the rest rame of either object or the centre of momentum frame. This is something that is done all the time in introductory physics homework problems. The laws of Newtonian mechanics are the same in all inertial reference frames: $F = ma$ etc.

 

[Ibix]

Is the velocity and all the related calculations really dependent upon whether the pilot "knows" his ship is moving?

No. The calculations depend on whether the pilot chooses to treat the ship as stationary and Mars as coming to him, or Mars as stationary and him going there. Relativity brings extra complexity, but really this is something so familiar we don't even notice it, and it's mind boggling when it gets pointed out. Imagine you are sitting on a station platform sipping coffee, and you see me passing through on a train sipping coffee. Describing how you are sipping the coffee is easy. But your description of me drinking coffee features a cup of liquid doing 60mph, which I manage to bring to my lips which are also doing 60mph, and rotating and translating the cup so that only a little goes in my mouth. It's complicated - but I can do it without thinking because I do all my calculations in a frame where I am at rest and it's you whose cup is doing 60mph.

I strongly recommend looking up Minkowski diagrams. They are what made relativity 'click' for me, because you can see on one diagram all the different things being measured and really understand how length contraction, time dilation, and the relativity of simultaneity all fit together.

 

[Dale]

However, if the spaceship is traveling at a fixed velocity of some fraction of 'c', why doesn't it "perceive" itself to be stationary?

I am a little unsure about your question. The spaceship is indeed stationary in its own frame.

 

[FactChecker]

I only recently learned that it is not only the length of an object that contracts along the axis of motion, relative to a different 'stationary' observer, but also the pathlength. That is boggling me.

You are mixing two different perspectives here. The length of a moving object is contracted from the perspective of the other "stationary" observer. The path length is not shortened in the perspective of the other "stationary" observer, but it is shortened in the perspective of the observer moving with the object. Both effects are just due to the perspective of an observer in another inertial reference frame.

 

[robphy]

Right now, I'm trying to reconcile the notion that any inertial frame can take itself to be stationary.

This is the Principle of Relativity.

I almost always suggest that folks watch
"Frames of Reference" by Hume & Ivey 1960
archive.org/details/frames_of_reference



In addition,
watch video #41 and onward from
https://en.wikipedia.org/wiki/The_Mechanical_Universe
Here is #42 from YouTube

 

[Sagittarius A-Star]

Right now, I'm trying to reconcile the notion that any inertial frame can take itself to be stationary. So, how do we get to solve real world problems when space ships are traveling to Mars, for example? I only recently learned that it is not only the length of an object that contracts along the axis of motion, relative to a different 'stationary' observer, but also the pathlength. That is boggling me.

Assume for simplicity, that Earth and Mars are at rest in the same frame, so that their distance is constant.

Then the path length is length contracted in the rest frame of the space ship, because this path is moving with velocity $-v$ in the space ship's rest frame.

For intuition you can imagine, that a very long ruler connects Mars and Earth, which is length contracted in the rest frame of the space ship. There is no reason, why the length of the path should depend on, if this ruler is present or not.

 

[A.T.]

I'm trying to reconcile the notion that any inertial frame can take itself to be stationary.

This is also true in Galilean Relativity, so maybe start with that, before you get into Special Relativity.

I only recently learned that it is not only the length of an object that contracts along the axis of motion, relative to a different 'stationary' observer, but also the pathlength. That is boggling me.

This might help: