42

It is both. Or even indeterminate. It is important to note that $\Sigma \vec F = m \vec a$ does not express a cause-effect relationship. Causes always preceed effects, so a causal relationship is given by an equation of the form $f(t)=g(t_r)$ where $t_r<t$ or more commonly $f(t)=\int_{-\infty}^{t} g(t_r) \ dt_r$ and $t_r$ is called the retarded time. ...


16

That isn't really the right question to ask. We never measure wave functions. We measure properties like position, momentum, energy of an electron. Whether the electron is spin up or spin down. The behavior of these properties doesn't match what you would expect from classical physics. Wave functions are a mathematical construct that help predict what ...


13

The EL equations for your proposed potential would be $$m\ddot q -\frac{d}{dt}\frac{\partial U}{\partial \dot q}= \frac{\partial U}{\partial q}$$ which can be re-expressed as $$\left(m- \frac{\partial^2 U}{\partial \dot q^2} \right)\ddot q = -\frac{\partial U}{\partial q} +\frac{\partial^2 U}{\partial q \partial \dot q} \dot q$$ Non-linear dependance of $U$ ...


13

What is a wave function? It is a mathematical function depending on energy and momentum or space and time,$Ψ(p_x,p_y,p_z)$ or $Ψ(x,y,z,t)$ ( in its simple form). This function is a solution of a wave equation, a second order differential equation. Mathematical functions are a billion, what is the wave function's connection with measurable physical ...


13

There is no way to tell if wavefunction collapse is immediately everywhere (whatever that might mean in a relativistic universe), because wavefunction collapse has no observable consequences. The Everett Interpretation of quantum mechanics (also misleadingly known as the 'Many Worlds Interpretation') explains all observations without requiring wavefunction ...


12

This is a question about philosophy not physics. Here is the answer. If I kick a ball it accelerates. It is not because of the ball accelerating that I kick it, for what would be the point of football (EU English) if it was the other way around?


11

Wormholes in GR do not require higher dimensions. It easier to imagine curved spacetime as being embedded in higher dimensions, but the usual mathematical description of curved spaces does not require that.


10

Newton's law does not specify or predict any propagation speed for gravitational disturbances at all. As a nonrelativistic treatment of gravity, it implicitly assumes infinite speed. Einstein's development of general relativity does specify the speed of light as the propagation speed for gravitational disturbances.


10

Beware of using the word "measurement" to smuggle in an ill-defined or impossible physical process. The notion that there could be a position measurement resulting in a delta-function wavefunction is an example of an unphysical idea. Even if we replace the delta-function by a function of finite height and very small width, the whole calculation ...


9

A block universe is simply one in which all the laws of physics are deterministic and reversible. In such a universe, complete and precise knowledge of the configuration of the universe at one point in time (or across one "slice" of the block) contains enough information in principle to determine the configuration of the universe at all past and ...


9

the time of the density corresponds to the scalar potential. This is not correct, precisely because of causality considerations. If the charge distribution is time-dependent, the potential at time $t$ will instead depend on the configuration at some retarded time, $t_r=t-\frac{|\boldsymbol{r}-\boldsymbol{r}'|}{c}$.


9

In the Lorenz gauge $\vec{\nabla}\cdot\vec{A}+\frac{1}{c^2}\frac{\partial V}{\partial t}=0$, the Maxwell equations in terms of the potentials are, for $V$: $$-\frac{1}{c^2}\frac{\partial^2V}{\partial t^2}+\nabla^2V=-\frac{\rho}{\epsilon_0},\tag{1}$$ where $\rho=\rho(\vec{x},t)$ is the charge distribution. The general solution to this is $$V(\vec{x},t)=V_0(\...


8

For what it's worth, higher powers of velocities (or momenta) do appear in many Lagrangians, e.g. as a power series in relativistic corrections, say, from square root terms.


8

Past, present and future in special relativity are separated by the light cone. Past and future are inside the light cone, which is what is called a timelike distance apart, or $$\Delta t^2-\Delta x^2 > 0$$ Past is characterized by $\Delta t < 0$, future by $\Delta t>0$. The inside of the light cone represents all events that might have a causal ...


8

With the signature $(+,-[,-,-])$ and natural units, the square interval from P to Q is $$S_{PQ}=(Q_t-P_t)^2-(Q_x-P_x)^2$$ if Q is in the timelike future of P (inside the future cone), then $S_{PQ}>0$ with $Q_t>P_t$ if Q is in the lightlike future of P (on the future cone), then $S_{PQ}=0$ with $Q_t>P_t$ if Q coincides with P, then $S_{PQ}=0$ with $...


6

You seem to be conflating "causally linked" with "in the same reference frame". This is not correct. Two points in the spacetime are "causally linked" if there is a causal (timelike or null) curve that connects them (meaning you can reach one point from the other without moving faster than $c$), so two observers can be ...


5

In relativistic quantum mechanics it can be shown that time reversal operator commutes the same way as parity inversion operator : $$ {\text{T}}H{\text{T}}^{-1} \equiv {\text{P}}H{\text{P}}^{-1}$$ Where $H$ is energy operator, $T$ - time reversal operator and $P$ is parity transformation operator. What this means ? Consider this picture of a cannon shooting ...


5

It is difficult to know exactly what “moving backwards in time” means so I am going to interpret your question as “does replacing mass with negative mass give the same result as replacing $t$ with $-t$ ?”. Newton’s second law $F=ma$ does not change if you replace $t$ with $-t$. In other words, if a force accelerates a mass from $v_1$ to $v_2$ then if we ...


5

To enlarge a bit on Bob's answer (Hi Bob and welcome to the physics SE): It takes time for light to travel from its source to our telescopes and then into our eyes. This means that whenever we are "looking" at anything in our world by using light, we are seeing it as it appeared in the past, when those photons were originally emitted. For objects ...


5

There are no theories describing wave function collapse. The concept is pure interpretation and in my opinion problematic. Wave functions are fully specified as solutions of a wave equation, such as the Schrödinger or the Dirac equation. These equations do not allow for a collapse. The ensemble or statistical interpretation is among others does not require ...


5

Both are true. The answer could stop there, but apparently we need 30 characters or more!


4

Why can't effects propagate backwards in time, within the backwards light cone of a cause? For example, when I turn on a flashlight, why doesn't the light travel backwards in time just like it does forwards in time? I don't see why this is prohibited by the laws of physics. The raw differential equations describing, e.g. the propagation of light are time ...


4

The problem is that you assume that an event horizon is simply an area within which the escape velocity becomes greater than $c$. This isn't really the full picture, otherwise we could just model black holes using Newtonian gravity; rather, it's just a heuristic that we use to calculate the Schwarzschild radius. It gives the "right answer for the wrong ...


4

You seem to understand well the mathematical models that we use and describe these particles, and then we say wow, these models are perfectly describing reality, because they are all justified by our experiments, so massive particles can never travel at the speed of light in vacuum, that is what we see from the experiments, and the mathematical models show ...


4

There is nothing special about $\eta_{\mu\nu}=\text{diag}(-1,1,1,1)$ in special relativity - if we were working in oblique co-ordinates or in spherical co-ordinates then the metric tensor would have different elements. The key points are: The metric tensor is a tensor so we know how its elements transform if we change our system of co-ordinates. In special ...


4

Professor Padmanabhan is in OP's linked video talking about virtual paths in the path integral formalism. They are needed to construct the full amplitude. They are not actual paths and do not necessarily respect causality. See also e.g. this related Phys.SE post.


4

What is physics? Physics is the discipline that studies numerically nature and uses mathematical models, the theories, in order to describe the data and , important, predict new situations. Laws (also postulates, principles) of physics are extra axioms to the mathematical axioms in order to pick from the infinity of mathematical relations in the models, the ...


4

It is both, depending which object is the subject in the choice of point of view. A cause is an action that leads to another action. A consequence is an action that happened due to a previous action. If you push a ball, the cause is your body moving into the ball and the consequence is the ball moves. No net force on the ball causes the ball to have no ...


4

Many answers say the answer is “both” or that the question is really philosophical. Perhaps that is true, but it does not seem like a reasonable view to take in this context. Beginning physics students are usually taught that a force is a “push or pull”. Later, when they learn physics in a slightly more rigorous manner, they should be taught that a force is ...


4

I will try to rephrase a bit how I understand what Weinberg is saying. A priori we only know what for two different inertial reference frames we have $ds^2 = ds'^2$ when $ds^2 = 0$. We then try to find the most general coordinate transformations of spacetime which possess this property. This way we discover conformal transformations. However, when we try to ...


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