163

First of all, let's get some important 'sociological' aspects out of the way: While website you've linked to, phys.org, tries to pass itself off as a science-journalism site, it is nothing of the sort. Instead, its core business is to aggregate press releases written by universities themselves. For most of the press releases they publish, phys.org does not ...


65

To be honest, much of this feels like very irresponsible journalism, partly on the part of the BBC and very much so on the part of Science alert. If you're looking for an accessible resource to what the paper does, the cover piece on APS Physics and the phys.org piece are much more sedate and, I think, much more commensurate with what's actually reported ...


40

The direction of the gravitational force would not change under time reversal. Your object would feel a force downward, just as it does usually. It might be easier to imagine you had a movie of an object under the influence of gravity. Drop the ball from rest some distance above the floor. You'll see it move downward and speed up. You'd interpret this as a ...


35

You missed something: the gravitational waves. A black hole merger spacetime contains gravitational waves leaving the merger at the speed of light. Time reversal reverses time across the entire spacetime, and this converts those escaping gravitational waves into a converging gravitational wave front, as well as the black holes into white holes. These waves ...


32

Good question. Let's first consider the ball falling immediately before it hits the table. Neglect friction with the air for simplicity. The ball has a velocity in the downward direction. If we reverse time, the ball is in the same position right above the table, but now it has an upward velocity. A ball with an upward velocity will rise with a negative ...


32

The articles are a little on the hysterical side, but I think they are just saying that violation of CP-symmetry means there must be violation of T-symmetry. T-symmetry means that physical laws are unchanged if we reverse the direction time flows. Classical theories obey T-symmetry, and it seems intuitively obvious that quantum mechanics would as well. But ...


25

They did not reverse time, they reversed the "arrow of time", meaning that time continued forward but entropy decreased a little, for a moment. Small temporary violations of the second law happens spontaneously all the time on a microscopic scale, wherever the thermal energy comes together in just the right way to be absorbed into an atom or molecule. It is ...


21

The simplest example in condensed matter physics that spontaneously breaks time reversal symmetry is a ferromagnet. Because spins (angular momentum) change sign under time reversal, the spontaneous magnetization in the ferromagnet breaks the symmetry. This is a macroscopic example. The chiral spin liquid (Wen-Wilczek-Zee) mentioned in the question is a non-...


16

I would say that it is a result of time reversal symmetry. If you consider the projectile at the apex of its trajectory then all that changes under time reversal is the direction of the horizontal component of motion. This means that the trajectory of the particle to get to that point and its trajectory after that point should be identical apart from a ...


15

When one is exactly at the critical angle, the light behaves in a way that may be interpreted as "something in between" refraction and reflection: it continues in a direction that is tangent to the boundary of the mediums. When the angle is smaller than the critical angle, we get refraction. At the critical angle, $\theta_2$ of the refraction becomes 90 ...


14

It's more correct to say that light rays split into reflected and refracted subcomponents at boundaries, rather than reflect or refract. Figuring this out is done by rigorously looking at the boundary conditions of the electric and magnetic fields at the interface. The result ends up being polarization-dependent, and is known as Fresnel's equations. Per ...


14

There is no mistake. The laws of physics themselves are reversible in time, but the solutions not necessarily so. Thus, the "behavior" of the universe itself does not show symmetry under time reversal, primarily due to the second law of thermodynamics. The second law is about the behavior of the solutions, is not a fundamental law in itself. In your specific ...


13

Reference (page $13$, formula $17.71$) The time-reversal operator is $\Theta = Ke^{-i\pi S_y/\hbar}$, where $K$ is the complex conjugation operator. Taking a spin $1/2$, we have a wavefunction which is a $2$- component spinor $\psi(x) = \begin{pmatrix} \psi_+(x) \\ \psi_-(x) \end{pmatrix}$, Note that, for spin $1/2$, $e^{-i\pi S_y/\hbar} = e^{-i \large \...


12

If $\Psi(x,t)$ solves the Schrodinger equation, so does $\Psi^*(x,-t)$ , so no, there is nothing at all that must increase.


12

Stated differently, why does EM radiation not "ripple inwards" and collect at some point? These are perfectly possible, by time-reversal. Well, in most cases observed or measured, EM radiation does not ripple outwards from a point either; usually, the radiation is connected to a body with non-zero spatial dimensions. In fact, radiation of point charges may ...


10

Conservation of energy follows from invariance under translation in time, not inversion. This symmetry states that no matter when you do your experiment, it will give the same results. All isolated systems obey this symmetry (and therefore conserve energy) and no violation of it has ever been detected. (Needless to say, it would be a huge event if it were.) ...


10

As an update on this old thread, the 2015 version of the Particle Data Group review on tests of conservation laws (the 2009 version of which was rightly pointed to by invisiblerhino) has an interesting update: The BABAR experiment has reported the first direct observation of $T$ violation in the $B$ system. The measured $T$-violating parameters in the ...


10

You have all the elements in your question, your difficulty is about what is meant by "time reversal symmetry". Time reversal symmetry holds if, when "playing backwards", the motion observed obeys the same law. With friction it is not the case : friction opposes movement, when playing backwards it (seemingly) promotes it. You can also go to equations for ...


10

One of the problems you will encounter is causality. Imagine you have a ball resting on the ground. Without already knowing how it behaved in the past you cannot uniquely define the next frame of your game. You cannot tell if the ball should: move upwards vertically. move upwards in any direction. roll on the ground towards any direction. do nothing. You ...


10

No, Newtonian gravity is perfectly time-reversal invariant. Suppose I throw a ball up, it falls back down, and my friend catches it. In the time-reversed picture, my friend throws a ball up, it falls back down, and I catch it. Gravity is doing precisely the same thing in both cases: attracting the ball and Earth together. The reason you might think ...


10

The time ordering enters as a consequence of the definition of the Hamiltonian as the generator of time translations. In the Schödinger picture: $$|\psi(t)\rangle \approx \left(1 - \frac{i}{\hbar} H(t') [t - t'] + \mathcal{O}([t-t']^2)\right) |\psi(t')\rangle,$$ where the relationship becomes exact in the limit as $t-t' \rightarrow 0^+$. It's an exercise in ...


10

Indeed, one of the definitions of spontaneous symmetry breaking is in terms of its susceptibility: Suppose we add a symmetry breaking perturbation $h \; \delta H$ to our Hamiltonian (as you do), if $$ \lim_{h \to 0} \lim_{N \to \infty} \langle m \rangle \neq 0 $$ then we say our system has spontaneous symmetry breaking. (Note: $N$ is the number of ...


9

The point is that the symmetries in QM (bijective operations sending states to states preserving the transition probability) can be represented by either unitary or antiunitary operators. This is the statement of a famous theorem due to Wigner. It is possible to prove also that, if the Hamiltonian of a system is bounded below, time reversal must be ...


9

I would consider that since acceleration is a constant vector pointing downward, that the time the projectiles downward component takes to accelerate from V(initial) to 0 would be the same as the time it takes to accelerate the object from 0 to V(final)


9

The popular press's description of this experiment is wildly wrong. It's hard to tell whether they just got it completely wrong on their own, or Scheck got it wrong and they're accurately describing what he said, or if it's some combination of the two. Scheck is a co-author but not the first author, and none of the ridiculous things they represent him as ...


9

They are called symmetries because (when the symmetry exists) they commute with the second quantized Hamiltonian: $$\hat{H} = \sum_{AB}\hat{\psi}^{\dagger}_A H_{AB} \hat{\psi}_B,$$ where $H_{AB}$ are the matrix elements of the single particle Hamiltonian: Time reversal: $$\hat{\mathcal{T}}\hat{H}\hat{\mathcal{T}}^{-1} = \hat{H}$$ Particle hole: $$\...


9

Yes, to the same extent as falling egg violates time reversal symmetry (have you seen a broken egg spontaneously jump from the floor to your cup?). This is called "second law of thermodynamics" and it is not time-symmetric.


8

I) First of all, one should never use the Dirac bra-ket notation (in its ultimate version where an operator acts to the right on kets and to the left on bras) to consider the definition of adjointness, since the notation was designed to make the adjointness property look like a mathematical triviality, which it is not. See also this Phys.SE post. II) OP's ...


8

As the neutron is not point-like, consider it has a continuous distribution of charge $\rho(\mathbf{r})$ confined in a volume $\Omega$. The dipole electric moment is then given by $\mathbf{D}(\mathbf{r})=\int_\Omega \rho(\mathbf{r}')\delta(\mathbf{r}-\mathbf{r}')d^3r'$ where the coordinates are measured from the centre of mass of the ...


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