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1) Your question states that, until the compressor is switched off, a constant pressure of 5 atm is maintained in the box. This answers the 1st part of your question. (However, perhaps you mean that the compressor delivers a certain amount of gas per second while the 2nd hole is open, and you wish to know the pressure of the gas in the box when equilibrium ...

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It depends what exactly you mean by "coordinate". If your Lagrangian/Hamiltonian is time-independent, then you may consider time to be purely a parameter parametrizing e.g. the integral curves of the vector field associated to the Hamiltonian on phase space. If your Lagrangian/Hamiltonian is time-dependent, you should indeed properly consider your theory on ...

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I think this issue is best clarified by closely looking at the way time is mixed into coordinate frame transformations in Classical Mechanics as opposed to Relativistic Mechanics. Let's take the case of an observer, Alice, moving at velocity $v$ in the positive $x$ direction away from her friend Bob. Both Alice and Bob are looking at an object situated at ...

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The simplest approach to a problem like this would assume that the collision is elastic, and that you have some knowledge of the elastic constant. But a collision between car and human is not that. Instead, let us assume that the "elbow sized object" hits the human in the mid section, and that it doesn't simply go right through him. Then the next thing that ...

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One of ideas associated with string theory is the ekpyrotic universe. This starts with brane cosmology i.e. the idea that our universe is a four dimensional brane floating around in the ten dimensional string theory spacetime. There will be many such brane worlds and the ekpyrotic idea is that a collision between two branes would appear just like the Big ...

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Yes, but by definition. Not by any meaningful physics. Imagine a path through 3-space. You can define the path by a function of time that returns a position. ${\bf f}(t)=(x(t),y(t),z(t))$. Then the velocity as a function of time is ${\bf v}(t)={\bf f}'(t)$. Easy. You could do the same thing through 4-space, by describing a path parameterized by some other ...

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Yes, this statement is true, in the sense that the four-velocity $u^\mu = (\gamma, \gamma \vec{v})$ always satisfies $$u^\mu u_\mu = 1$$ as you can check using the definition of $\gamma$. (I'm setting $c=1$.) Therefore the magnitude of the four-velocity is always equal to the speed of light. However, this statement can be really misleading. It's true that ...

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This paper explains the importance of physical mechanisms existing which can function as clocks at various eras. Your question is not simple Abstract We provide a discussion of some main ideas in our project about the physical foundation of the time concept in cosmology. It is standard to point to the Planck scale (located at ∼ 10−43 seconds after ...

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See the special relativity holds only in inertial frames of reference and in the absence of gravity. Now consider a train moving with uniform velocity comparable to the speed of light. Even at the speed of light an observer in the train cannot tell whether he is moving or the rest of the universe is moving. He feel the exact feeling as he is at rest. This is ...

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I want an answer which is free of mathematical relations.I want an insight rather than a mathematical relation. Very well. Do you see?

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If we think little more complex and consider every particle in the universe, each particle should be moving with some initial velocity caused by something happened before, due to some other particle You do not state the level of your physics knowledge. I will assume you are a highschool student. What you are describing is the way classical mechanics ...

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The general relativity model of the universe is a mathematical model, and in this all of time and space are defined in frameworks. Going from one framework to another requires going through GR transformations. The variable of time within the framework of a planet close to a large sun, for example, is defined and stable within it. There is no slowing or ...

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I read a few lines about general relativity and [... an equation for] the eigentime of a time-like curve. I suppose that this is referring to an equation similar to $$\tau A_J^Q := \int_0^1~dt~\sqrt{g[~\dot\gamma, \dot\gamma~]},$$ where $A$ denotes a particular participant ("material point", "principal identifiable individual"), the quantity being ...

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Exactly as an ideal clock at rest with the observer (here pictured as a timelike curve) measures the proper time of the observer, ideal rulers at rest with the observer measure the distances in the rest space of the observer. Mathematically these rulers are pictured as an orthonormal basis made of $3$ vectors normal to the unit tangent vector to the ...

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In GR the notions of space and time are no longer different, they are combined into spacetime. Points in spacetime are labelled by coordinates, which can be arbitrarily chosen, and can in the special case of Minkowski space be the familiar x, y, z and t. The only physically meaningful quantity however is the line element: ds^2 = g_{\mu \nu} dx^\mu ...

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The proper time of a time-like curve is its length.

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The counting is done by the signal generator. The clock contains a signal generator that generates the 9,192,631,770 Hz signal going to the microwave transmitter. This generator contains a counter that counts every cycle the generator creates (though as The Photon says it may use a prescaler).

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Nowadays it's reasonable to make an actual digital counter that operates at 10 GHz. Even so, you might rather use a prescaler to divide this frequency down to 1/4 or 1/8 of the microwave frequency before you actually start counting cycles. In olden times you might have generated your 10 GHz signal by multiplying up a lower frequency (maybe in the 100's of ...

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