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There is a 1961 paper by Aharonov and Bohm on this subject, in which there is defined, among other things, a characteristic time for an operator's expectation value to deviate significantly, measured by the initial dispersion in that operator. This result is essentially a theorem we will prove here (Theorem 2). Let $\mathcal{S}$ be a Hilbert space, $A$ a ...

4

It's really an either/or proposition, i.e. either space is expanding or the time experienced by distant objects is dilated, depending on how you view the situation. We choose the former description because it is better. To expand (excuse the pun!) on what I mean, the measurable result of time dilation is red-shift and indeed distant cosmological objects ...

4

To measure time, a duration, you need two moments – when you press "start" and "stop" button on the stopwatch, respectively. But because the two objects are moving relatively to each other, it isn't possible for them to "meet" at both moments. If their locations coincide at the "start" moment, for example, so that their clocks may be compared at this "start" ...

3

Ok, so the Energy-Time "Uncertainty Principle" is often way misrepresented, but it does mean something. In $\Delta t \Delta E \geq \frac{\hbar}{2}$ the $\Delta t$ represents the amount of time is takes for the energy expectation value to change by one standard deviation. It does not represent a measurement. Note: This is explained in Griffith's "Quantum ...

2

The uncertainty principle is still true in its usual form, but it refers to your knowledge of the state. Suppose your state is just one electron, you can confirm this if you observe the system for a time $\Delta t$ and you don't see additional particles. However, due to the uncertainty principle you can only measure particles that increase the energy of the ...

2

You raise two issues: ΔT, and the HORIZONS timescales. Let us tackle each in turn. 1. What is Delta-T? You are correct that HORIZONS is using a confusing term here. What the HORIZONS menu calls Delta-T is an entirely different quantity than the ΔT you will see defined and used in many other references on astronomy. Briefly: What HORIZONS calls Delta-T ...

2

The basic confusion is in your comment that "During $\Delta t_3$ an event occurs in $O_3$'s frame that is measured as $\Delta t_2 = \gamma^\prime \Delta t_3$". In SR a single "event" occurs at a single point in spacetime--an interval like $\Delta t$ can only describe the time between a pair of events. What's more, the time dilation formula $\Delta t_B = ... 1 As @Hypnosifl points out, a single event cannot have$\Delta t$. You must define two events such as a light flashing or the beginning and end of a process or a particle moving from point A to point B. You must the define the pair of events (call them$A$and$B$with both a time coordinate and a spacial coordinate, e.g.$$\pmatrix{ct_A \\ x_A} \text{ and } ... 1 force = acceleration * mass, hence acceleration will be$a=50N/22kg \approx 2.27m/s^2$Distance it moves might be found by integration:$\int_0^{1.2}v(t)dt=\int_0^{1.2}atdt$, since speed$v(t)=at$Answer to (B) then is 1/2*1.2*(2.27*1.2)=1.63, which seems pretty close to what you have got 1 suppose it is possible to accelerate matter at speed of light By this you must mean suppose that relativistic mechanics is, at its root, wrong. What will the time reflects on these two clocks? Since you've stipulated that relativistic mechanics is wrong, which incorrect, non-relativistic mechanics would you like to apply to this problem? 1 Where is the flaw in my thinking? In your concept of time. It's little more than a cumulative measure of local motion, see A World without Time: The Forgotten Legacy of Godel and Einstein]. Your macroscopic motion relative to some other guy results in you measuring his local motion to be slow, whilst he measures your local motion to be slow. This sounds ... 1 You are entirely correct: when assigning JD real numbers to UTC calendar dates, it is simply impossible to name any moment during the leap second — while an analog rendering of a UTC time can say “23:59:60.25”, the JD will provide no name for any moment of that entire second. This can be seen if you visit the standard JPL HORIZONS system: ... 1 The relativity of simultaneity is not an axiom, the axiom is that the light velocity is the same in every frame of coordinates. A spot of light travels at the same velocity, c with respect to you, and at the same velocity$c\$ with respect to a traveler traveling with respect to you at an arbitrary velocity. So, assume that you send two spots of light to ...

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In classical mechanics, time is the unique parametrisation of dynamical systems. In relativity theory, one then sees that time is somewhat more than this, because there exists a global symmetry (the Poincaré-group) that involes time and space on an equal basis (called spacetime). Also, one can show that parametrisation by time is not the only way to do ...

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