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In special relativity an event E is mapped to coordinates (x,t) in one inertial frame, and to coordinates (x',t') in another, and SR provides the relation between (x,t) and (x',t').

What is the empirical content of this theory (e.g. how would you operationally test it)? Since there are two frames, two observations are required - one that measures the (x,t) of E in one frame, and another that measures (x',t') of E in the other frame.

Classically this presents no problem, since we can assume an ideal measurement exists that would not disturb whatever is being measured (the event E), and so two of these measurements can be made in rapid succession, one in each frame.

But in QM, the result of measurement is intrinsically tied to the measurement apparatus and also the very act of measurement affects what is being measured. So when you observe an event E (say, particle position x at time t) in the first frame, using the apparatus in that frame, you can no longer observe that same event E in the second frame. Your second observation will at most be measuring the position of the particle after it has been observed in the first frame.

So, in effect, a single event E does not have well defined (empirically/operationally) coordinates in all frames of reference at once. How then can we even talk about a relation between (x,t) and (x',t'), when these are not well defined?

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In QM measurements are not restricted to one event, we need many-many of them. One event says nothing. Think of a point on a screen in a double-slit experiment.

In QM the events have probabilities to occur. Lorentz transformations serve to transform the observable event properties and probabilities from one reference frame to another. For ensembles of events they serve. Thus it is not implied that we only deal with one event.

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