Hot answers tagged

86

Entanglement is being presented as an "active link" only because most people - including authors of popular (and sometimes even unpopular, using the very words of Sidney Coleman) books and articles - don't understand quantum mechanics. And they don't understand quantum mechanics because they don't want to believe that it is fundamentally correct: they always ...


63

Since general relativity is a local theory just like any good classical field theory, the Earth will respond to the local curvature which can change only once the information about the disappearance of the Sun has been communicated to the Earth's position (through the propagation of gravitational waves). So yes, the Earth would continue to orbit what should'...


60

I understand your confusion, but here's why people often feel that quantum entanglement is rather strange. Let's first consider the following statement you make: 2 things have some properties set in correlation to each other at the point of entanglement, they are separated, measured, and found to have these properties A classical (non-quantum) version ...


52

I wish to complete @Luboš Motl's answer, to which I agree. My point is on why people continue to make this mistake of an active link. This mistake is connected with one of the most interesting properties of quantum mechanics, Bell's theorem. One can argue that any physical theory is an hidden variable theory, the hidden variable being the description of the ...


42

Gravitational influences do propagate at the speed of light, not instantaneously. The question of what would happen if the Sun instantly disappeared is actually a funny one in general relativity. The equations of general relativity imply as a mathematical consequence that energy must be locally conserved. Therefore, there is no valid solution to the ...


22

All observations are consistent with standard GR so far, but I don't think the speed of gravity, in particular, has ever been measured. Experimental measurements of the speed of gravity was quite a controversy a few years ago when a paper came out claiming that the speed of gravity was very close to $c$ as measured by the Shapiro delay. To see papers on the ...


21

The higher the number of derivatives the more initial data you have to provide. If you have some Lagrangian that contains an infinite number of derivatives (or derivatives appearing non-polynomially, such as one over derivative) then you have to provide an infinite amount of initial data which amounts to non-local info, in the sense explained below. If you ...


19

Rather than repeat some very good standard answers, I want to discuss this issue from the perspective as to why classical systems should be viewed as strange. If we accept quantum mechanics as being fundamental, then in some sense we shouldn't really find things like entanglement to be strange at all. As pointed out by the answer given by joshphysics, as ...


17

The force does not change instantaneously, the correct way the electromagnetic field of (and thus the force exerted by) a moving electric charge is given by the Liénard-Wiechert potential, where one can see that the effect of the charge does not travel faster than light.


17

To add to ACuriousMind's answer on the Liénard-Weichert potentials, you can put these formulas into an even more wonderfully descriptive form since you can derive Feynman's formula from them for the radiation from a moving charge: $$\vec{E} = -\frac{q}{4\,\pi\,\epsilon_0}\left(\frac{\vec{R}}{R^3}+\frac{R}{c}\frac{\mathrm{d}}{\mathrm{d}t}\left(\frac{\vec{R}}{...


16

Your question was first asked by Laplace. The following is from the Wikipedia article on "The speed of gravity" Laplace The first attempt to combine a finite gravitational speed with Newton's theory was made by Laplace in 1805. Based on Newton's force law he considered a model in which the gravitational field is defined as a radiation field or ...


14

From Hacker News https://news.ycombinator.com/item?id=6253263 This is a far more interesting question than it might seem at first glance, and it deserves some attention because it tells us something fundamental and wonderful and just bloody awesome about the universe. But I don't know how to tell the story succinctly. So I'm going to do that thing I do. I ...


12

In classical mechanics, the lagrangians of two particles may be added only if the particules do not interract. I wouldn't say that. You can always write a Lagrangian $L$ for a system of two particles. In general, it takes the form $$L = L_1 + L_2 + L_i$$ where $L_i$ is an interaction term that depends on the coordinates and/or velocities of both ...


12

I agree that these terms —especially 'locality'— are used for different concepts and this is annoying. I will list several notions of causality and locality. Causality (or Einsteinian locality): Results of experiments carried out at a space-like distance are not correlated. This assumes that there are not previous correlations before making the experiment. ...


12

Everything doesn't expand equally because of cosmological expansion. If everything expanded by the same percentage per year, then all our rulers and other distance-measuring devices would expand, and we wouldn't be able to detect any expansion at all. Actually, general relativity predicts that cosmological expansion has very little effect on objects that are ...


10

This is an area rife with potential misunderstanding, so we need to be absolutely clear what we mean. Suppose I take a ruler and a clock and I use rulers to mark out $x, y, z$ axes in space and the clock to note the positions of events in time. Assuming spacetime is flat, I now have a universal coordinate frame that everyone who is stationary relative to me ...


9

Just a nice analogue Prof. Jürgen Audretsch told me once: Imagine at home you put one glove in your coat without looking (and noticing it's only one of the two). After exiting the train you notice it's cold and you pull out that single glove. At this very instant you know it's either the left or the right glove, and you therefore know which one is left ...


9

In fact your view is quite close to the 'official' one; entanglement occurs just because both particles are described with one wave-function; the magic is in our classical habit of thinking that separate objects are described with separate "coordinates".


9

You assume that you can instantly measure the momentum to arbitrary precision, and this isn't the case. Let's consider a plane light wave to keep things simple, and suppose you want to measure the momentum so precisely that the position uncertainty becomes exceedingly large. How precisely do we have to measure the momentum? Well the uncertainty principle ...


8

Clearly, an interaction involving $\phi(x+h)$ deserved to be called nonlocal. But since $\phi(x+h)=\sum_{k=0}^\infty \phi^{(k)}(x) h^k/k!$, any nonlocal interaction can be expressed as a power series involving arbitrarily many derivatives. Therefore an action (or Lagrangian) is called nonlocal if it involves infinitely many derivatives. If there are only ...


8

Disillusionment with systems described by higher order Lagrangians harks back to a 1950 paper by Pais and Uhlenbeck, in which they showed that such systems were prone to pathologies, including states with negative energy and states with negative norm. There's a more recent discussion of this in arXiv:hep-th/0408104.


8

the fact that distortion travels 'as soon' as a mass is removed or not is not implied in any way by gravity being due to a distortion of spacetime. In fact distortions of spacetime are as limited to travel to the speed of light as any other physical influence.


8

What happened here? I am in complete shock that so many respondents are answering "yeah, no big deal, nothing really spooky going on, yeah it's just correlation..." What in the world is everyone talking about? Peter Oakey, forget all the math for a minute. This will take a few minutes of detailed but entirely non-mathematical setup, but if you can bear with ...


8

Here is the answer that made me realise what the big deal is. The description below is basically an expanded version of this blog post, which I came across a long time ago. Imagine we are going to play a game. It's a cooperative game, so we'll either both win or both lose. If we win, we get lots of money, but if we lose we both die, so we should do our best ...


7

You are confusing the concepts of "interactions" and "nonlocality". In realistic field theories, including all theories we ever used to study phenomena in the world around us, the interactions exist but they keep the physics local. As David mentioned, the Lagrangian density takes the form $${\mathcal L} = \sum_i \left[ (\partial_\mu \phi_i)^2 + m^2 \phi_i^2 ...


7

What is a local lagrangian density? A classical field theory on Minkowski space $\mathbb R^{d,1}$ is specified by a space $\mathcal C$ of field configurations $\phi:\mathbb R^{d,1}\to T$, and an action functional $S:\mathcal C\to\mathbb R$. The set $T$ is called the target space of the theory, and is often a vector space. If there exists a function $L:\...


7

It looks like this loophole is not explicitly discussed in the "axioms", but it is mentioned in the paragraph before equation (2) which I copy here: A symmetry transformation is said to be an internal symmetry transformation if it commutes with P. This implies that it acts only on particle-type indices, and has no matrix elements between particles ...



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