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42

I assume you used the formulae $f_o = fs\sqrt{\frac{1+v/c}{1-v/c}}$ for the clocks ahead of you and $f_o = fs\sqrt{\frac{1-v/c}{1+v/c}}$ for the clocks behind you. Those formulae do imply a singularity for the clock that is closest to you. Which equation to use? The answer is neither. Those expressions assume the travel is along the line of sight to the ...


30

Which year? The sidereal year? The tropical year? The anomalistic year? The calendar year (and whose calendar)? The sidereal year is the average amount of time it takes the Earth to make one complete orbit about the Sun with respect to the fixed stars. The tropical year is the amount of average amount of time between successive spring equinoxes. The ...


16

There are a few ways to answer your question, and I will try to list some of them. According to Quantum Mechanics, and due to the Heisenberg Uncertainty Principle, we cannot predict the future state (position and momentum) of any system. Given the state of a system in classical phase space $(\textbf{r}(t_0), \textbf{p}(t_0))$, we cannot determine the state ...


15

A deterministic universe need not be predictable. And even a deterministic universe not hampered by any limits to observability need not be predictable. As an example take a toy universe consisting of an infinite chain of $0$'s and $1$'s. This 1D cellular universe evolves according to cellular automata rule-110: the state of a cell becomes $1$, unless the ...


10

It sounds like you're interested in when a spacetime admits a Cauchy surface. The answer is that every spacetime that is globally hyperbolic has this property. This was proved by Geroch in 1970 (article here, see Section 5). This includes most of the textbook relativistic spacetimes --- Schwarzschild, Kerr, FLRW, and many others. But there are some ...


9

What you're asking about is the existence of surfaces of simultaneity. In SR, surfaces of simultaneity can be defined by measurement procedures such as Einstein synchronization, and they turn out to depend on one's frame of reference. In GR it gets a lot tougher to do this. We don't even have global frames of reference. It turns out that what you need in ...


6

Yes, quantum tunnelling in the double well potential can be solved in a Wick-rotated Euclidean formulation $$ S_E[x]~=~\int \! dt_E \left[ \frac{1}{2}\left(\frac{dx}{dt_E}\right)^2 - (-V) \right], $$ see e.g. Ref 1. Here $t_E=it_M$ denotes Euclidean time. The Euclidean action is in turn interpreted as the usual kinetic minus potential term with a potential ...


4

At a "frozen" instant of time, the arrow may not be moving - but this is a tautology, since movement is something that requires time. However, even in that frozen instant the arrow does have a velocity (instantaneous velocity, if you will). Imagine that time is a series of huge number of discrete frames (or instead imagine that it is continuous, and that we ...


4

You're mixing up two things in this question: 1) How we label individual points (Einstein calls them "events") in space-time 2) What results someone would get when looking at their clock when they pass through spacetime points. The first thing is almost completely arbitrary, especially in full general relativity. The second thing is an unambiguous result ...


3

Yes, really. But that doesn't mean that we're floating around loose without a foundation. In Galilean relativity all observer could agree on a number of things about a interaction of process. Things like How long it took (the same for all the bits) How far each part of the system traveled in that time What the mass of bit ... In Einsteinian relativity ...


3

It does not mean that it switches the hyperfine state that often. I means that, if you hit the atom with a photon that (by $E = \hbar\omega$) corresponds to exactly that frequency, then the energy of that photon will precisely be the energy to lift the electron from the lower hyperfine state to the upper hyperfine state. If hit, it will then, as with all ...


3

If you measure the absorption of microwaves by a gas of caesium atoms you'll get a spectrum looking something like this: NB not a real spectrum - I drew this as an illustration When the microwave frequency is 9,192,631,770 Hz the microwave photons have exactly the right energy to flip the outer electron spin, so at this frequency they are more strongly ...


3

Even in a quantum universe, all evolution is deterministic if interpreted under Many-Worlds interpretation. So all possible futures could be "already determined", but you would still be unable to know which of those futures will be directly experienced by your qualia, since qualia experiences are always described by non-unitary probabilistic projection ...


3

The signal from the clock moving towards you is the Doppler shifted version of the value you "know" it to be - that is, first slow it down by gamma (clock moving relative to your frame of reference), then speed it up by Doppler shift. Ditto, with sign reversed, for clocks behind you. Now the clock moving at right angles shows what you expect and there is no ...


2

If you consider a straight-on trajectory, there really will be a discontinuity. That is the same as with the audible Doppler effect. There is a smooth drop in frequency of a fire truck's siren passing you on the street. The reason is, that there is a certain distance between you and the truck at the closest point. If that were not the case, i.e. the siren ...


2

First off, there are a couple of reasons why we don't have complete symmetry between space and time: We have 3 spatial dimensions and only one timelike one. The particles in the standard model have timelike or lightlike world-lines; as far as we know, there are no tachyons. For these reasons, it only makes sense to talk about laws of physics that take ...


2

Yes, the two are intimately related. One way, as in QMechanic's answer, is via Wick rotations, but in general there is a lot more freedom once you allow integration contours to go over into the complex plane. In my area, strong field physics, the use of complex time to understand tunnelling problems is everyday bread and butter for many people, and it is the ...


2

The most common explanation for the "matter-antimatter asymmetry of the Universe" is $\rm CP$ violation in interactions involving leptons. This scenario is usually called leptogenesis because it generates a net excess of leptons compared to anti-leptons. This $\rm CP$ violation is currently unconfirmed by experiment (though there is also not yet any evidence ...


2

What makes heat move from hot to cold? Entropy. How can you calculate entropy microscopically? Start counting states! What makes the universe change irreversibly from yesterday to tomorrow? Start counting states!


1

Take a landscape. It can be modeled by a function f(x,y,z). If all the derivatives, df/dx, df/dy, df/dz are zero, the landscape is flat to infinity and nothing interesting exists in the landscape. If one of the derivatives is different than zero, then we perceive a shape, and generally a landscape has a shape. As an example, suppose that we have a cone ...


1

Even though the forces started at different times, is there any displacement of the metal box in any of the situations? Or is there any movement at all but is the net displacement zero? Sure. If you think of each force as causing an acceleration, the first one begins an acceleration in one direction, the second an acceleration in the other (or a ...


1

CPT does exchange particles with their antiparticles, so if there were a time direction associated with particles then it might make sense to say that, by CPT, the antiparticles would have to have the opposite time direction. But there's no time direction associated with particles. It doesn't even make sense to say that something is "going forward in time"; ...


1

In quantum mechanics velocity is not an easy concept. Here particle motion is replaced by a wave. Momentum, is easier to define in quantum mechanics. A complex wave $\exp(ikx)$ describes a particle with momentum $p=\hbar k$ where $\hbar$ is Plancks constant divided with $2\pi$. It is fundamental in quantum mechanics that momentum cannot strictly be defined ...


1

"How do we know that clocks slow down relative to each other?" Experimentally. This has been observed many times in the lab. The same answer is true for ANYTHING in physics and science in general. We only know that it is true, because we have experimental evidence for it.


1

Duration is certainly a more physical concept than time. Duration is something you may measure between timelike separated events while time is always something you compute by adding up duration measurements + an arbitrary constant to fix the origin. Duration is experimental and relational while time (e.g. GPS time) is an abstract a posteriori ...


1

Okay, I am going to try and give this a shot, but this is most probably not going to be a decisive answer. Let us operate with the term event time and duration and consider only special relativity (SR). The conclusions of general relativity should be the same for reasonable space-times. (e.g. without closed time-like curves etc.) We expect event time to ...


1

I'd like to add something to these answers. In the classical mechanics, we cannot distinguish a moving body from the body at rest, if we look at it at any particular instant. So, we have to add some hidden information to the picture, that is instantaneous velocity. But that's what physics only knew in the 19th century. In 20th century physics, there have ...


1

We know that to position objects in spacetime requires four coordinates e.g. $(t, x, y, z)$. So time certainly exists. The point you're addressing is about the flow of time. Incidentally this point is discussed in some detail in the question Is there a proof of existence of time?. Any object traces out a worldline that is a curve in spacetime, and we can ...


1

You could use the Length contraction equation of Special Relativity to determine speed. If you know the dimensions of an object at rest relative to you, you would know its velocity relative to you by finding which dimensions are length contracted and by how much when you measure the body in motion relative to you. But, full disclosure, I think time exists.


1

Philosophically, both time and distance are illusions. Distance is actually more disturbing than time. So first, let's define what "time" is. It is the number of transitions of an atomic state (see atomic clock wiki). Distance, a meter, is defined to be the length a photon (light) travels in $\frac{1}{299,792,458}$ of a second (source) which ...



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