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This isn't a complete answer, but John Baez gave a pretty good treatment of this in a series of blog posts (part 1, part 2, part 3, part 4; arXiv paper with some more stuff). Basically, he defines what he calls the "quantropy", which is just the classical entropy formula with $\beta$ replaced by $-i/\hbar$ and the energy replaced with the action. (Note ...


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A logical analysis of absolute motion ongoing within an absolute 4 dimensional Space-Time continuum, leads you to the awareness of the constant motion of all objects. That constant motion turned out to be the speed of light. If one analyzes the concept of constant motion of all objects located within Space-Time, and that this ongoing motion is the equivalent ...


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No. My answer is negative, even if I confirm the statements of other answers: "The first thing is almost completely arbitrary, especially in full general relativity. The second thing is an unambiguous result of an experiment."(Jerry Schirmer) "In Einsteinian relativity all observers can still agree on a number of facts, they are just ...


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It means someone in a different frame of reference would observe events happening slowly in the other frame of reference. All observers in their own frame of reference perceive time to be flowing at the same rate. Differences only arise when observing different frames of reference. The phrasing is an oddity and peculiarity of English. It is imprecise. It ...


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There's a little mistake in the signs, since the potential energy is given by $U=-\dfrac{GMm}{r}$. The problem of finding the time elapsed between two points of the trajectory may be done by realizing that at any point $$\frac{1}{2}m\dot{x}^2-\dfrac{GMm}{x}=E=-\dfrac{GMm}{H},$$ where $H$ is the maximum height of the particle. Hence ...


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I think what you are missing is that these energies are eigenvalues of the time-independent Hamiltonian. i.e. They correspond to stationary states that do not change in time. The scenario you describe is not time-independent - therefore the difference between the energy levels will carry some uncertainty corresponding to the lifetime of the excited state.


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The solution might be the fact that it is supposed that gravitation is propagating at light speed. Movements at light speed are particular as it is shown for photons in vacuum: The (hypothetical) proper time of photons is always zero, that means that there is no time passing from the hypothetical point of view of photons. By consequence, photons cannot ...


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The "relativity of simultaneity" is not a statement about what "exists"--that is a matter for philosophy--but just about the fact that the laws of physics obey the same equations in all the inertial coordinate systems related to one another by the Lorentz transformation, which dictates that different inertial systems define simultaneity differently (i.e. two ...


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The question seems to imply that the OP has a fundamental problem with existential questions. Those are for psychology and philosophy to ponder. Physics simply observes that one can build very precise clocks that agree with each other reasonably well under certain circumstances and not at all under others. The theory of special relativity clarifies when ...


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First of all, physics does not ever talk about the question of existence, but about useful descriptions and predictions of observations. No physicist will ever prove to you he is not just a figment of your imagination but he can prove to you that Newton's law works pretty well for what you see. In the scientific method, a theory is indeed used until it ...


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The aim of special relativity and of spacetime (in particular: the Minkowski space time) is not to know about what time is. Spacetime is showing a relation between space and time from an observer's view only - and this whatever time is in reality (including the question if time exists or not). The result is that time (i.e. the value measured by clocks) may ...


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If we were to try to standardize a unit of time with another alien species based on something fundamental to the laws of physics rather than an arbitrary division of an arbitrary planet rotating an arbitrary sun, do we have anything fundamental and universal reference point to base it on? Yes. For example, the second is currently defined according to an ...


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You have to be careful about the difference between speed and velocity. Saying that two clocks are moving at the same speed is different from saying that the relative speed between the two clocks is zero. For example, as measured in some inertial frame of reference, two clocks can be moving at the same speed but in opposite directions, in which case their ...


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The answer is: Solve Newton's second law. Really, $\vec F = m\vec a$ is meant to be a second-order differential equation, with the force dependent on position (and, sometimes, time). Writing it as $$ \vec F(\vec x,t) = m \frac{\mathrm{d}^2\vec x}{\mathrm{d}t^2}$$ makes manifest that the distance travelled by something, is, in general, the solution $\vec ...


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As for "why", that is either simple or complex! The simple answer is that it is a consequence of the speed of light being constant for all observers. That means when travelling relative to each other they both measure time differently. This site provides a simple math explanation OTOH, time is measured differently in different gravitational fields, and that ...


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You don't have to be an astronaut traveling at near the speed of light to experience this effect. It can be measured quite precisely here on Earth and it has been measured both on elementary particles in accelerators and by flying atomic clocks around the world in planes. Humans are simply not used to it because the differences between the flow of time in ...


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As an example, http://en.wikipedia.org/wiki/Particle_decay, you can regard $\Delta t$ as the lifetime of the particle decayed.



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