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Measurement is a process in which by help of interactions one quantum entangles the quantum system under study and the environment and by rapidly utilizing decoherence cleans up the "off diagonals" of the entanglement into an apparent collapsed state. After this process, it effectively appears as the wave function of the system has been set to a distinct ...

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Susskind's original argument doesn't work. Alice just needs Bob to send a message to her saying "I'm still alive!" She doesn't have to illuminate Bob. Of course, it's hard to get a message out from the near-horizon region of a black hole because of the redshift, but there's no theoretical reason that this shouldn't work. Suppose you don't have a ...

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The most famous "terrestrial" experiment that I know of was the measurement of the speed of sound in Nevile's Court in Trinity College, Cambridge. As the tour guides will tell you, Newton stomped his foot and listened for the echo from the wall on the opposite end of the North Cloister. He timed the echo by making a (short) pendulum, and adjusting the length ...

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Conjecture: The distance to the moon was approximately known by astronomers in Newton's days. Once you know the orbital radius and period, a simple diagram shows you how much the moon "falls". When angle $q$ is small, the distance $d$ is calculated from $$\frac{d}{v~t}= \frac{v~t}{R}\\ d=\frac{v^2 t^2}{R}$$ Note - interesting details on this ...

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Advantages Very accurate ( In fact its accuracy allows it to be utilised to calibrate other thermometers) Wide Range Independent of gas used Disadvantages Large and bulky(inconvenient to carry and handke) Slow to Respond (due high heat capacity) Expensive to manufacture and keep I'm not sure about its use in any specific industries.

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Notice that the probability of measuring say the position of a particle whose wavefuction is $\psi(x)$ in the interval $I=(a,b)$ is $$\int_a^b \left|\psi(x)\right|^2 \mathrm{d}x.$$ We can define a multiplication operator on the state space much like the position operator $\hat{X}\psi(x)=x\psi(x)$ as follows. $P_I(\psi)=\chi_I(x)\psi(x)$. It is a projection ...

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You've incorrectly found that the matrix for $H$ is given by $$\left(\begin{array}{cc} 1&0\\0&H \end{array}\right)$$ where $H$ and $1$ are $2\times 2$ matrices, and we're using the following ordering of basis elements: $(|00\rangle,|01\rangle,|10\rangle,|11\rangle)$. This isn't true. An easy way to see that is to compute the matrix element \$\...

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If we measure length by a scale there is no change of energy. So it depends on subjects to be measured.

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First an important clarification about simultaneity you need to be aware of: In special relativity we learn that there is no such thing as two spatially separated events A and B happening 'at the same time', at least not in any absolute sense. If one inertial observer sees the events as simultaneous, another perfectly legitimate inertial observer sees A ...

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