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 Be the first pioneers to continue the Astronomy Discussions at our new Astronomy meeting place...The Space and Astronomy Agora What About... Forum List | Follow Ups | Post Message | Back to Thread Topics | In Response ToPosted by Harvey on September 30, 2003 20:54:12 UTC

Here is a conflict cited by philosopher of science J.A. Barrett in "Are Our Best Physical Theories \\ (Probably and/or Approximately) True?" (Jan., 2003):

QUOTE

Consider an electron (e^-) and two boxes E and F equipped with alarm clocks. The clocks are synchronized, the alarm on clock E is set to noon on 1 January 2050, and the alarm on clock F is set to noon plus
one minute on the same date. The electron is put into a superposition of being in each box. An observer Fred then carefully carries box F far from Earth (further than one light-minute away); and another observer Elle carefully positions box E near Earth. Fred and Elle are each instructed to look for the electron in their box when the alarm on their clock rings.

Suppose that the initial state of the electron before (in any inertial frame!) either observer makes a measurement to locate it is:

[frac{1}{\sqrt{2}}(|\mbox{Earth}\rangle_{e^-} + |mbox{Far Away}\rangle_{e^-})]

Now suppose that the standard formulation of quantum mechanics is right and that the collapse dynamics describes the time-evolution of quantum-mechanical states whenever there is a measurement interaction. What is the physical state of the electron when Fred measures it?

Since the measurement events are space-like separated, there will be an inertial frame Frame(E) where Elle makes her measurement first. In this case, Elle's measurement caused a collapse, and the state of the electron when Fred makes his measurement is either:

(1) (|\mbox{Earth}\rangle_{e^-})

or

(2) (|\mbox{Far Away}\rangle_{e^-}) with probability (1/2) in each case.

But since the measurement events are space-like separated, there will also be an inertial frame Frame(F) where Fred is the first to look for the electron. In this case the state of the electron when Fred makes his measurement is:

(3) (\frac{1}{\sqrt{2}} (|\mbox{Earth}\rangle_{e^-} + |\mbox{Far Away}\rangle_{e^-}))

since Elle has not yet interacted with the electron. States (1), (2), and (3) are mutually exclusive. On the standard interpretation of quantum-mechanical states, state (1) describes an electron that is determinately in the box on Earth, state (2) describes an electron that is determinately in the far-away box, and state (3) describes an electron that has no determinate position whatsoever. And again, there are
experiments that would in principle empirically distinguish between state (1) or (2) and state (3).

Since the standard formulation of quantum mechanics requires mutually incompatible states for different inertial frames, it is flatly inconsistent with the principle of relativity. So quantum mechanics and special relativity taken together are logically inconsistent.

UNQUOTE (note: minor changes to text due to incompatibility with ASCII)