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It is only in the Schroedinger picture (and those connected to it by time-independent $U$) that the Hamiltonian can be read off from the dynamical equation for $\vert\psi\rangle$. In all other pictures you would find there a kind of "effective Hamiltonian" which is different from the actual Hamiltonian in this picture. So $$\hat{H}_P = U^\dagger \hat{H}_S ...


0

At very high velocity, time is dilated with respect to an observer. The speed of light remains constant but since the distance that the light must travel increases, the time that it takes for it to travel from say a point A to a point B is longer than if it were stationary relative to the observer.


1

We wouldn't normally answer what is blatantly a homework problem, however I think there is an important principle here and it's instructive to go into detail. Any experimental physicist will tell you that when faced with experimental data the very first thing to do is DRAW A GRAPH: The blue squares are your data and the red line is a fit (see below). ...


2

Usually, when you want to probe the lifetime $\tau$ of a particle (or a quasi-particle), what you basically do is looking for the way the associated wave-function $\psi$ is significantly decreasing : $$\psi\sim\psi_0\,e^{-\left(\frac{1}{\tau}+\,i\frac{E}{\hbar}\right)t}$$ Let us consider a free particle with a given energy $E$. As $\langle E\rangle=E$ is ...


0

Let's say you're the one accelerating towards the other person who is at rest, so after meeting him you're clocks wouldn't agree because of time dilation, right? Let's make the thought experiment more precise. In some inertial frame of reference, a moving clock is located at $x = 0$ when both the coordinate time $t$ and the moving clock time $\tau$ ...


0

All inertial reference frames are equivalent. This is the most basic assumption of Special Relativity as well as Newtonian Mechanics. This means that if you are in an inertial reference frame, say, a car moving with constant velocity, you can never tell if the car is moving or not (unless you look out of the window of course). This is not true for a ...


0

Time dilation is linked to motion. Be it from acceleration, or velocity, or both. It is because the speed of light is invariant for all observers. If this speed is the same, then what changes is 'time.' As for the who experiences time dilation, the answer is both of you. You both feel time dilation with respect to each other. Time dilation is not 'whoah ...


0

The difference between unaccelerated (which includes stationary) and accelerated state is that in case of the latter you can actually feel (and measure) the force causing acceleration. Example: Without looking out the window, you cannot tell whether the train you are in is currently moving or not (relative to Earth) unless there is some acceleration ...


1

Extensive googling hasn't helped me to understand how this observed earth rotation angle is used to compute UT1 As explained in: this lecture Earth's angle of rotation = 2π(0.7790572732640 + 1.00273781191135448(Julian UT1date - 2451545.0)) radians. So one observes Earth's angle of rotation and calculates the Julian UT1 date as a decimal date from that ...


0

Anywhere there is energy there is time dilation. But you have used a linear approximation - which may hide the super - tiny effect of time change as a wave runs though a region of space. In other words, if there was a beam of gravity waves, and one person was in the waves, the other not, the person who experienced the waves would have a small difference ...


0

First, to clear something up, the amount of work done does not depend on the amount of time a force is applied, but on the distance over which the force acts. If you and your friend, Alfred, use the same force to push a block from point A to point B, but it takes you ten years and Alfred ten seconds, you both end up doing the same amount of work, and hence ...


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Exerting a force over a time interval is not always related to energy being put into the system. The amount of energy given to a system by a force is called the work. This is computed by calculating the projection of the force onto the displacement made by the object. $$ \text{(Change in Energy)} = W = \vec{F}\cdot d\vec{l} = F dl \cos(\theta)$$ This ...


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In general, it takes no energy to apply a force. Energy is described as the potential to do work, which has the same units as energy. Work is defined as a force applied during some distance. From these definitions, it is clear that the duration of the force does not directly impact how much energy is required. For instance, Earth exerts a force of gravity ...


0

The energy you input is equal to the work you perform, that is force times distance. Thus the energy will grow if you continue to apply force and the system on which you apply force continues to move. The rate at which you bring this energy to the system per unit of time is the power, if it is constant through time, then energy equals power times duration. ...


-3

Energy equals mass multiplied by the speed of light squared, and mass equals energy divided by the speed of light squared. What goes up, must come down. Nothing can escape a black hole. Every action has an equal and opposite reaction. Energy cannot be created or destroyed, it only changes form. All things in an enclosed system gain entropy, slow down, ...


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The simplest idea is that the collapse of the previous universe caused the big bang. I imagine it as black holes smashing into each other at great speed, immediately causing a nuclear reaction. There are some unproven theories that need to be adjusted, such as the idea that dark energy density remains constant as space expands. Black hole radiation has ...


0

Think of it as a resistors in parallel problem. You have a heat source inside the room and a constant temperature outside (if you assume that the outdoors is infinite and well connected to the walls. Then you have a thermal resistance/area for the wall, ceiling and floor material. Using the total area you have an overall thermal resistance and a ...


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You are confused about what is called the Observer Effect. Read about it from here Observer Effect. Also, read some parts of this. The Uncertainty Principle just says that there is a fundamental limit to which the position and momentum of an object can be measured. Also, as PhotonicBoom said, the Observer Effect for Quantum Mechanics is not experienced at a ...


0

A clock is a collection of particles that behaves classically, i.e its a combination of all the wavefunctions of its particles, and due to that "coupling" it does not behave probabilistically anymore. You are refering to the phenomenon of wavefunction collapse due to a conscious observer, but in reality decoherence occurs. Wavefunction collapse happens in ...


0

What muddies the waters a bit are that when I tried to search for the borde-guth thing, the first result was a Christian site, and of course when it was discovered that the universe was expanding, the big bang was taken by many Christian scientists as the creation of the universe by God, and that is still the most likely explanation for why the universe ...


0

In an inertial frame , the clocks at different points of space are synchronized. This synchronization issue is important. Once you synchronize Indian time with the American one, there is no paradox. So it is not a time travel. Anyways , the question was interesting.


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No, this is not time travel. Imagine you start in India and adjust your watch to US time before you leave. Nothing has changed. You have neither gained nor lost time, but when you get to the US your watch shows the correct local time.


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Time Travel does not mean going from one time zone to another. You did not get those 6.5 hours back again, they just appear to be back to you because you entered a different time zone. I think this definition of Time Travel by David Lewis’ is perfect and will explain why you are wrong: An object time travels if and only if the difference between its ...


0

If you leave earth at age 30 and live for 30 years near a black hole, time will pass more slowly for you and normal for the people on the earth. I don't know the exact age you will be when you spend 30 years near a black hole, but when you return to earth you will be younger than others who had the same age as yours when you left. In other words, others at ...


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The time used in describing the evolution of the universe is comoving time. This is the time that would be measured by a freely moving observer on their wristwatch (assuming the high temperatures didn't melt both the observer and the wristwatch :-). Time is not a simple thing to define in general relativity, however we can always unambiguously define proper ...


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This is a common point of confusion, not only with regards to inflation, but any time an expanding universe comes up... The "cosmic speed limit" as you call it says that no particle or signal can move through spacetime faster than the speed of light. Spacetime is a very specifically defined thing, described with a coordinate system. There is no restriction, ...



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