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If we restrict ourselves to within the steady state and measure some properties Steady states do not exist in isolation . Any mass/body in isolation in space will radiate black body radiation and its thermodynamic variables will be changing, and thus will not be in a "steady state". (hence the entropy production cannot be measured since it is ...


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As the moon is continually receding from the earth due to the tides, the end result will be a stable orbit. about 2.3 billion years from now, the increase of the Sun's radiation will have caused the Earth's oceans to vaporize,[13] removing the bulk of the tidal friction and acceleration. The orbit should be stable. But the sun will finally become a ...


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The Sun will collide with the Earth. The orbits are stable. But in about 5 billion years, the Sun will run low on hydrogen and begin burning helium. This will make it expand and engulf the Earth.


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You have to distinguish between spacetime and proper time: The vacuum would still continue to be part of the Minkowski spacetime continuum of the observers, in particular with respect to simultaneity (e.g. of events happening at this place before or after your experiment). If your experiment is lasting one hour, during this hour the clocks of the observers ...


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There's an interesting phenonemon known as the quantum Zeno effect which concerns extremely rapid measurements (like your hypothetical camera) and objects remaining stationary. To tell which state a system is in, eg. whether an electron's spin is up or down, we must measure it. According to classical physics, the system is in one particular state, and ...


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I believe that the currently attainable limit of imaging is around 10's of atto-seconds per time slice (around 10^-17) from which it is possible to observe individual state transitions of an electron in silicon (which takes around 450 atto seconds, or about half a femto-second). as per Ryan Colyer's answer, uncertainty can prevent imaging in a single pass, ...


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Relative speed can be greater than "c". This does not mean that in an inertial frame fixed on one ship the other ship looks like it is going faster than "c". In an inertial frame fixed on one ship the other ship looks like it is going slower than "c", so light from one could in principle reach the other. In an inertial frame fixed on one ship the other ship ...


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The observation that "π seconds is a nanocentury" is attributed to Tom Duff, who is known to computer programmers as the inventor of "Duff's Device". There's nothing magical about the fact that 1/10,000,000 of a planetary orbit should equal roughly π/86400 of a planetary day (not the same thing as a planetary rotation, btw, since the orientation of the side ...


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I've worked on a camera that has as one of its core features the ability to increase the FPS until you are counting single photons. Here is one of the pdfs about it. You will see from the figures that there is an intrinsic tradeoff between the noise/image-quality and the FPS, which is simply due to the statistics of photon counting noise as you get fewer ...


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The Planck-Time is a little higher than $t_p=5\cdot 10^{-44} \, \text{sec}$ so the maximum frame rate allowed by quantum mechanics is less than $1 \, \text{frame}/t_p = 2\cdot 10^{43} \, \text{frames/sec}$.


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In addition to the good answer of MSalters it is worth pointing out that individual photons arrive on the detector of the camera at different times. The way that cameras work is that they convert photons arriving into a signal that can be read out. No matter how high the fps rate there will be some point in time where one frame is finished and the new one ...


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Are you aware that light consists of quanta (Sophia might have been a bit premature in her comment to say QM is not involved). Each photon captured by the camera is captured in one frame, for practical purposes. So the problem as we increase the FPS is that each frame is now based on fewer and fewer photons. This isn't just theory. We've done this ...


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To say that something is a (linear) operator you have to specify the space where it acts. You may say that, for example, wavefunctions of quantum mechanics are maps: $t\to \psi(t)$ that are continuous in $t$ with values in $L^2(\mathbb{R}^d)$. If we restrict to compact time intervals $[0,T]$, we may denote the space of these maps by ...


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You are touching on the subject of relativistic quantum mechanics where time and space $(t,x)$ are handled on the same footing as operators. The accepted description is to not use quantum wavefunctions as describing one particle but rather the state of a quantum field. Doing this turns into the subject of quantum field theory and is the basis of modern ...


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You cannot boost a massive particle to the speed of light, which is what you're trying to do. The infinities you are finding when you set $v=c$ are closely related to the fact that it would take an infinite amount of energy to accelerate a massive object, like a pebble or an electron, to the speed of light. So this is a mathematical manifestation of the ...


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Where does that precise time come from? Is it just the energy / Hamiltonian $H$ that determines it? Yes. $\newcommand{\ket}[1]{|#1\rangle} \newcommand{\bra}[1]{\langle #1 |}$ Suppose I have an atom which can be in one of two states $\ket{0}$ or $\ket{1}$. Suppose that atom is coupled to another atom via an interaction Hamiltonian like this $$H_I = ...


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Coordinates and momenta of the system are called variables by convention. Time is sometimes called variable, after all its nature is to keep changing. But to distinguish time from coordinates and momenta, people call it parameter in some cases. Parameter is a word used instead of variable when the quantity is a different kind of argument of a function. ...


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Consider this: the space traveler is flying at near light speed relative to you. But for him you are flying at near light speed, just in opposite direction. So he must think then that you have to experience all the "effects of the increased mass", mustn't he? The answer is in the fact that the very basis of Special Relativity is the postulate of ...


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With respect to ground: After push-off, man moves upwards at $0.8\text{ft}/\text{sec}$, pillow downwards at $8\text{ft}/\text{sec}$. It takes the pillow $1\text{s}$ to hit the ground, by which time the man has moved to $8.8\text{ft}$ up. Pillow (being weirdly elastic) returns at exactly the same speed it departed with, has to close the $8.8\text{ft}$ gap at ...


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Time is what an ideal clock measures. So what's an ideal clock? It's something that measures time. In other words, physicists don't quite know what time is. That's okay. They don't quite know what space is, either. What they do know, and know very, very well, is how to measure both, and how the two (time and space) relate to one another. That the speed of ...


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Being able to sense phenomenon and being able to explain them are different animals. Consider how many millions of magnetic coils we employ in our daily lives. "Science" still cannot give a single, congruent, fully observable at every level, without referring to other phenomenon, explanation of WHY they work. Obviously they do, and we have figured out that ...



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