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.(adsbygoogle = window.adsbygoogle || []).push({});

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 thata)the photon starts and finishes its journey on the x-axis (y=0, z=0) andb)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 areal and observableparabolic 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?

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# Disgruntled observer

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