Einstein's Thought-Experiment: Disgruntled Observer's Perspective

[ch@rlatan]

Let’s put an observer in a 3-D frame of reference at x=0, y=0, z=0 to observe one of Einstein’s thought-experiments. You know the one - where a spaceship is equipped with a photon emitter, a mirror and another observer whose frame of reference is at rest with the spaceship. Let’s have the spaceship moving left to right along the x-axis (as is the convention) at a significant fraction of the speed of light.
But, because I have placed our observer in the same x-y plane (where z=0) in which the spaceship will be moving he will not be able to observe any sideways motion of the event. So we pull him out into a parallel x-y plane (where x=0, y=0, z>0) and allow him to face the x-y plane in which the event will take place. Let us assume that the event takes place so that a) the photon starts and finishes its journey on the x-axis (y=0, z=0) and b) the photon hits the mirror at the point where x=0 i.e. directly in front of our observer.

But wait. Our observer points out to me that as far as he’s concerned he would now no longer observe the spaceship moving at a constant speed, with him no longer sharing the same x-axis. He shows me a time-distance graph of the movement of the craft with respect to his positioning in his frame of reference (x=0, y=0, z>0) and indeed the numbers indicate a real and observable parabolic speed. In fact, he goes on to say that the only time that his measurement of speed agrees with the ‘significant fraction of the speed of light’ of the craft is at the maximum of that parabola i.e. the shortest distance between him and the spacecraft ’s flight-path, which, he reliably informs me, is ascertained with an instantaneous measurement. He goes on to say, “For any object with constant speed to move with constancy in a point-observer’s frame of reference, the object must be moving directly toward or away from the observer or be moving in a fixed-radius orbit with the observer at the centre”.

“Oh….kay?”, I say and pull out my book on relativity and show our discontented observer the standard side-view diagram of the photon’s movement through the event. “No, no, no!”, he cries tugging at his hair, “This diagram is all wrong”. He continues, “For me to observe the photon in the two-dimensional way that the diagram suggests I must observe it at perpendicularly equidistant points between my x-axis and the craft’s x-axis throughout the duration of the event. In which case, I have entered into the same moving frame of reference as the observer on the craft. Indeed, any measurements I make along the x-axis of the craft, either during the event or retrospectively will always put me in the same moving frame of reference as the observer on the craft”.

“The only way that sense can be made of this diagram is if the whole of the event takes place instantaneously, at the point of closest distance i.e. at the top of the parabola mentioned earlier, but having an event that takes time - happen instantaneously - makes no sense at all. The best that the measurements taken from this diagram can offer is an approximation, that is made under one of two assumptions, a) the dimensions of the event are infinitesimally small with respect to the distance of the observer from it or b) the event is observed from an infinite distance with respect to the dimensions of the event. In either case, we can no longer talk about how the photon in this event moves for observers in at-rest frames of reference when even in the realms of the thought-experiment it has become imperceptible”.

“But the event can still be thought-experimentally observed”, I put to him, mindlessly flipping through the pages of my book, searching for a leg to stand on. “Yes,” he replies, snatching it from my sweaty hands and frisbee-ing into my own thought-experimental void, “ but not in the two spatial dimensions that the diagram suggests. As far as a point-observer is concerned the photon moves through all three of his spatial dimensions i.e. the craft moves toward (1) the observer and to the right (2) as it approaches the y-axis - while the photon is moving up and down (3). What’s more, any meaningful measurement would have to take into account both the perpendicular distance between the observer and the spacecraft ’s flight-path and the height of the mirror with respect to the emitter”.

Is this observer just being awkward, pedantic, playing with perspective or does he have a point?

 

[JesseM]

Let’s put an observer in a 3-D frame of reference at x=0, y=0, z=0 to observe one of Einstein’s thought-experiments. You know the one - where a spaceship is equipped with a photon emitter, a mirror and another observer whose frame of reference is at rest with the spaceship. Let’s have the spaceship moving left to right along the x-axis (as is the convention) at a significant fraction of the speed of light.
But, because I have placed our observer in the same x-y plane (where z=0) in which the spaceship will be moving he will not be able to observe any sideways motion of the event. So we pull him out into a parallel x-y plane (where x=0, y=0, z>0) and allow him to face the x-y plane in which the event will take place. Let us assume that the event takes place so that a) the photon starts and finishes its journey on the x-axis (y=0, z=0) and b) the photon hits the mirror at the point where x=0 i.e. directly in front of our observer.

Are you aware of the fact that when physicists talk about an observer "observing" something, they are not referring to what an individual at a particular location sees but rather what coordinates he assigns to events in his own coordinate system? So line-of-sight issues don't matter, putting the observer at a different z-coordinate isn't going to change things either way.

But wait. Our observer points out to me that as far as he’s concerned he would now no longer observe the spaceship moving at a constant speed, with him no longer sharing the same x-axis. He shows me a time-distance graph of the movement of the craft with respect to his positioning in his frame of reference (x=0, y=0, z>0) and indeed the numbers indicate a real and observable parabolic speed.

You appear to be talking about some sort of "visual speed", but that has nothing to do with the speed in his frame. If he places a ruler that's at rest in his frame along the path of the spaceship, and at each ruler-marking he attaches a clock also at rest in his frame, and he "synchronizes" the clocks using the Einstein synchronization convention (which is based on the assumption light moves at c in his frame, so he could synchronize two of his clocks by setting off a flash at the midpoint between them and setting the clocks to read the same time when the light from the flash hits them), then if he notes the position on the ruler and the time on the clock at that position as the rocket passes various points on the ruler, he will find that the rocket is moving at constant speed in his frame. For example, if the rocket passes the 0 light-second mark when the clock there reads 0 seconds, and it passes the 10 light-second mark when the clock there reads 20 seconds, and it passes the 20 light-second mark when the clock there reads 40 seconds, and it passes the 30 light-second mark when the clock there reads 60 seconds, then he'll conclude the ship is moving at a constant speed of 0.5c. It doesn't matter when the light from these events actually reaches him, and it also doesn't matter what the visual distance between these marks is from his position (because of the way perspective works, marks which are farther from his position will look like they're bunched closer together...but this is true in Newtonian physics as well, of course). If you read section 1 of Einstein's 1905 paper, you can see he always used the idea that the time coordinates assigned to a given event should ideally be based on the readings of clocks "in the immediate neighborhood" of the event, not on the time that some distant observer actually sees the event with his own eyes.

“Oh….kay?”, I say and pull out my book on relativity and show our discontented observer the standard side-view diagram of the photon’s movement through the event. “No, no, no!”, he cries tugging at his hair, “This diagram is all wrong”. He continues, “For me to observe the photon in the two-dimensional way that the diagram suggests I must observe it at perpendicularly equidistant points between my x-axis and the craft’s x-axis throughout the duration of the event. In which case, I have entered into the same moving frame of reference as the observer on the craft. Indeed, any measurements I make along the x-axis of the craft, either during the event or retrospectively will always put me in the same moving frame of reference as the observer on the craft”.

You're not talking about what he "observes" in the standard sense of what coordinates he assigns to events in his frame; you're just talking about what he sees, which is a totally different matter. Diagrams in relativity textbooks are based on the former notion.

Is this observer just being awkward, pedantic, playing with perspective or does he have a point?

Just playing with visual perspective, and ignoring the standard explanations of how coordinates are assigned to events which should be found in any textbook.

 

[ch@rlatan]

Hey JesseM

Originally posted by JesseM

...then if he notes the position on the ruler and the time on the clock at that position as the rocket passes various points on the ruler, he will find that the rocket is moving at constant speed in his frame.

Of course. The same constant movement that the observer on the craft observes - because measurements have been taken from the craft's moving frame of reference. If at each of those points along the ruler there was also a camera that took a thought-experimental photo of the craft at the same time as the measurements were made - all the photos would be identical. It would be quite valid for the observer on the craft to use your measurements to determine his constant speed through the (now integrated) frames. But for the observer in the inertial frame to use them violates his inertial frame with non-inertial observations which say nothing about what he observes - either visually or in the textbook sense. Here's what I proposed in my OP..

Originally posted by ch@rlatan

Indeed, any measurements I make along the x-axis of the craft, either during the event or retrospectively will always put me in the same moving frame of reference as the observer on the craft”.

It doesn't matter how or when you take observations/measurements this statement always holds true.

You also seem to want to separate the observer from his frame once he has created it and have him move about in it. But in doing so you are creating a third absolute frame in which the two observers can measure and be measured. The observer's frame is always with him and will move with him. And whether an event is directly observed or by proxy -through some device - when one observer is taking measurements from along another observer's axis of movement, he will, by his actions and positioning enter into that moving frame.

If, as you suggest, the reference frames are the important element, why don't we just have reference frames and state 'what is' and be done with the observers?

 

[JesseM]

Of course. The same constant movement that the observer on the craft observes - because measurements have been taken from the craft's moving frame of reference.

What constant movement? In the craft's frame of reference, the craft is at rest. Every inertial observer is supposed to use rulers and clocks at rest relative to themselves, if there's a ruler at rest relative to the craft next to it, then the craft will remain next to the same marking on this ruler forever. Only if you pick the frame of an observer moving relative to the craft will the craft's position on a ruler at rest in that frame be changing over time.

If at each of those points along the ruler there was also a camera that took a thought-experimental photo of the craft at the same time as the measurements were made - all the photos would be identical.

Not if the photos showed the marking on the ruler next to the craft, and the reading on the clock at that marking.

It would be quite valid for the observer on the craft to use your measurements to determine his constant speed through the (now integrated) frames. But for the observer in the inertial frame

Both the observer on the craft and the observer who sees the craft in motion are in "inertial frames", assuming the craft isn't accelerating. "Inertial" just means not accelerating.

to use them violates his inertial frame with non-inertial observations which say nothing about what he observes - either visually or in the textbook sense.

But the "textbook sense is that each inertial observer observes things using only local measurements on rulers and clocks at rest relative to themselves. And I don't understand what you mean by "violates his inertial frame with non-inertial observations"--what is a "non-inertial observation", exactly? As long as all his rulers and clocks move inertially, how can local measurements on them be called "non-inertial"?

Here's what I proposed in my OP..

Indeed, any measurements I make along the x-axis of the craft, either during the event or retrospectively will always put me in the same moving frame of reference as the observer on the craft”.

It doesn't matter how or when you take observations/measurements this statement always holds true.

Why does it put you in the same moving frame of reference? You can just sit in one place and look through your telescope at which markings on your ruler the telescope passes, and look at the reading on the clock next to each marking as the craft is passing it. Or you can have a bunch of friends who are all at rest in your frame at different positions, each making local measurements of the craft as it passes them.

You also seem to want to separate the observer from his frame once he has created it and have him move about in it.

Again, there is no need for any movement of the observer relative to his ruler/clock system.

But in doing so you are creating a third absolute frame in which the two observers can measure and be measured. The observer's frame is always with him and will move with him. And whether an event is directly observed or by proxy -through some device - when one observer is taking measurements from along another observer's axis of movement, he will, by his actions and positioning enter into that moving frame.

You really seem to have some confused notion about what a "frame" means, it has nothing to do with your spatial position, only with your state of motion. You can imagine each observer having a 3D grid of rulers and clocks which fill all of space, with the grids of different inertial observers in motion relative to one another being able to freely pass through one another without colliding. This corresponds to the notion that each frame is a coordinate system that assigns coordinates to events throughout space, not just along some particular line.

If, as you suggest, the reference frames are the important element, why don't we just have reference frames and state 'what is' and be done with the observers?

Yes, you're quite free to do that. Most problems in relativity books don't specifically imagine that there is actually a human at rest in every frame that you're making use of in the problem, imagining that each frame represents the perspective of an "observer" is just an idea that can be useful in teaching relativity to new students, I think.