Empirical meaning of relativity in the context of QM

[bobcat321]

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?

 

[K^2]

Sam way we deal with all uncertainties in QM. Statistics. While a particular event cannot be measured from more than one frame, if the event is not reproducible, it is not scientifically relevant anyhow. For reproducible experiment, you need reproducible events. Setup identical conditions, do experiment a bunch of times in every frame you are interested in, and you should have your results.

 

[cragar]

yakir aharonov studies this and has papers on it that you might find interesting.
The paper is titled
Can we make sense out of the measurement process in relativistic QM
http://astrophysics.fic.uni.lodz.pl/100yrs/pdf/14/029.pdf

 

[Darwin123]

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?

Quantum mechanics has been shown to be consistent with special relativity. The issue of consistency between quantum mechanics and general relativity has not been completely resolved. Therefore, I am speaking in terms of special relativity.

An experimental apparatus is associated with the inertial frame where it is stationary. If the ruler factory marked off a ruler in inches, then the markings designate inches for every camera that is stationary with respect to that factory. If you want to know what the markings mean for a camera moving at high speed relative to that factory, then you have to use the Lorentz transformation. Similarly, if a clock factory sets each tick on a clock to a second interval, then that tick designates a tick is a second for each microphone that is stationary with respect to the clock factory.

Experimental measurements are events. If a camera takes a picture of clock and ruler, then the picture the camera takes takes represents an event. A local measurement represents an event with specific spatial coordinates and a specific time.

The above hypotheses are the same in both classical and quantum mechanics. For instance, locating a "particle" at a specific location and a specific time is an event whether the particle was a baseball, a bacterium, a proton, and electron or a photon.

The main confusion in QM may be the uncertainty principle. The Lorentz transformation describes how different instruments may measure location and momentum, or energy and time. These quantities can't be simultaneously measured at the same time due to the uncertainty principle. There is an indeterminacy associated with pairs of measurements. However, the indeterminacy transforms according to the Lorentz transformation. So even the "uncertainties" can follow SR.

The photon is a special case of interest. Detection of a photon immediately destroys that photon. So if a photon is detected at a specific place and time, there is no photon left to check the results. There are only two events where a photon can be detected: its creation (by energy and momentum transfer to the source and its destruction (by energy and momentum transfer at the absorber). The Lorentz transformation applies to these two terminal events.

Since the photon can not be positioned "in flight", there is no "event" associated between the events of creation and destruction. There is no indeterminacy associated with the terminal events. SR only has to be accurate with these two terminal events. QM can hypothesize all sorts of weird anomalies in between. Observers only have to agree at these two events.

 

[bob900]

Experimental measurements are events. If a camera takes a picture of clock and ruler, then the picture the camera takes takes represents an event. A local measurement represents an event with specific spatial coordinates and a specific time.



The above hypotheses are the same in both classical and quantum mechanics. For instance, locating a "particle" at a specific location and a specific time is an event whether the particle was a baseball, a bacterium, a proton, and electron or a photon.

Ok, but special relativity relates two (location,time) pairs with each other,via the Lorentz transformation : a (location,time) in frame A, and a (location',time') in frame B. In all presentations of special relativity that I've seen, an event is some physical occurrence to which we can assign, through measurement, different (space,time) coordinates in any inertial frame of reference. So in order to even have two (space,time) coordinate pairs to relate together, we need to make two measurements - one in each frame.

The main confusion in QM may be the uncertainty principle. The Lorentz transformation describes how different instruments may measure location and momentum, or energy and time.

But what about just simply measuring compatible observables such as position, with different instruments. Suppose the event is an electron hitting a detection screen. Clearly we can measure the position X and time T of this event in frame A, where the detection screen is stationary. But to test (or even apply) the formulas of special relativity to this event, we would need a second pair of coordinates (X',T') in another frame B.



My question is how do we obtain this second pair? It would seem the only way is through a second measurement, with a detector that is stationary in frame B. But then we are not measuring the same event - "the electron hitting a detection screen in frame A". Instead, with this second measurement, we are measuring the event "the electron hitting a detection screen in frame B, after it was measured by a screen in frame A".