Hot answers tagged

83

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 ...


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 ...


59

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 ...


49

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 ...


41

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 ...


36

The thing about the speed of light $c$ is that it's not just a number associated with a certain type of particle. While we could talk about the mass of the proton, and there would be no problem assuming non-protons had greater or lesser masses, the value $c$ is an entirely different beast. $c$ is an intrinsic property of spacetime itself, not of the ...


34

This was a reference to the apparent measurement that neutrinos travel faster than light. FTL travel can be used to travel back in time (though the procedure for doing so is somewhat involved). Sadly the apparent superluminal speed turned out to be due to experimental errors: a fibre optic cable attached improperly, which caused the apparently ...


30

(There's a couple of these questions kicking around, but I didn't see anyone give the "two boosted copies" answer. Generically, I'd say that's the right answer, since it gives an actual causality violation.) In your scenario, the two planets remain a hundred thousand light years apart. The fact is, you won't get any actual causality violations with FTL that ...


27

Shine a flashlight on a wall. Rotate the flashlight so the illuminated spot moves. Q: How fast does the spot move? A: It depends how far away the wall is. Q: How fast can the spot possibly move? A: There is no limit. Put the wall far enough away, and the spot can move with any speed. Q: What is moving across the wall? A: Nothing. The light that makes up ...


27

In the case of relativity, "information" refers to a signal that enforces causality. That is, if event A causes event B, then some signal must travel from A to B. Otherwise, how would B "know" that A had occurred? Some examples: Light (signal) from a candle (A) hits your eye (B), causing you to see it. Electricity (signal) flows from a connected switch ...


24

It's a bit more complicated than that. Given any two events, there is a quantity, called the interval (also 'spacetime interval' or 'invariant interval'), denoted $\Delta s^2$, and which equals $\Delta s^2=c^2\Delta t^2-\Delta \mathbf r^2$, which determines how the two events can relate to each other causally. If $\Delta s^2>0$, then we say $A$ and $B$ ...


22

It's not possible to communicate faster than light using entangled states. All you get out of entanglement is a correlation between the values of two measurements.; the entanglement doesn't allow you to influence the value measured at another location in a non-causal way. In other words, the correlation only becomes evident after combining the results from ...


21

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 ...


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 ...


19

Physics is the discipline that studies natural phenomena, and finds mathematical models that fit the measurements and observations and also predict future behavior of the system under study. Mathematics is a discipline which studies numbers with sophisiticated methods, it has axioms and theorems and can prove statements or disprove them absolutely. To use ...


18

Nobody has explained to me how Shor's quantum factorization algorithm works under the transactional interpretation, and I expect this is because the transactional interpretation cannot actually explain this algorithm. If it can't, then chances are the transactional interpretation doesn't actually work. (I have looked at some of the papers that purport to ...


17

This is really the same as Adam's answer but phrased differently. Suppose you have a single wire and you connect it to a battery. Electrons start to flow, but as they do so the resistance to their flow (i.e. the resistance of the wire) generates a potential difference. The electron flow rate, i.e. the current, builds up until the potential difference is ...


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} = ...


16

Edit regarding 3+1 spacetimes and causality I'll keep adding to the answer as I get more information, and hopefully everything will just evolve along. At the very least, I'll have a set of notes to work from in the future :) This is also the first, broadest, cut at an actual answer regarding causality. Alcubierre sets out to find his warp drive metric ...


16

One approach to exploring this question is to study the Glider in Conway's Game of Life. Where does its movement "come from"? It is a direct and easily-verified result of the rules of its universe. I highly recommend you take a few minutes with graph paper to verify its behaviour for yourself. What is really important to see is that motion is not a law ...


15

Suppose you and I have a conversation from a long distance away. We're at rest with respect to each other and communicate much faster than light. I say "How are you", and you wait a short time and say, "I'm fine thanks." From our point of view, you were responding to my question. However, from a reference frame moving from me to you at relativistic ...


15

In special relativity, you think of a 4-dimensional space-time. The key point here is that two events, 1, and 2 happening at $t_{1}, x_{1}, y_{1}, z_{1}$ and $t_{2},x_{2},y_{2},z_{2}$ have a distance given by ${}^{1}$ $$(\Delta s)^{2} = -c^{2}(\Delta t)^{2} + (\Delta x)^{2} + (\Delta y)^{2} + (\Delta z)^{2}$$ Now, we can therefore give any two events a ...


15

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

Recall that commuting observables in quantum mechanics are simultaneously observable. If I have observables A and B, and they commute, I can measure A and then B and the results will be the same as if I measured B and then A (if you insist on being precise, then by the same I mean in a statistical sense where I take averages over many identical experiments). ...


14

In reality there's no such thing as a perfect rigid body. There will always be a delay in the motion propagating along the body. Under "normal" conditions you don't notice this delay as it's infinitesimal when compared to the size of everyday objects you interact with. However if you had a rod several light years long (assuming that's at all possible) the ...


14

What follows is certainly not a comprehensive answer addressing all of your concerns. It is an answer to the question is there a way to see something clearly pathological like superluminal signals in the heat equation? I would argue that yes, there is. The general solution to the initial value problem $T(x,0) = T_0(x)$ for the heat equation on the ...


13

Excellent question. You are correct about wavepacket spreading, and in fact you do get superluminal propagation in non-relativistic QM - which is rubbish. You need a relativistic theory. You should read the first part of Sidney Coleman's lecture notes on quantum field theory where he discusses this exact problem: http://arxiv.org/abs/1110.5013 The short ...


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

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 ...



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