# Tag Info

44

If I was on a bus at 60 km/h, and I started walking on the bus at a steady pace of 5 km/h, then I'd technically be moving at 65 km/h, right? Not exactly right. You would be correct if the Galilean transformation correctly described the relationship between moving frames of reference but, it doesn't. Instead, the empirical evidence is that the ...

42

The answer is no. The pole would bend/wobble and the effect at the other end would still be delayed. The reason is that the force which binds the atoms of the pole together - the Electro-Magnetic force - needs to be transmitted from one end of the pole to the other. The transmitter of the EM-force is light, and thus the signal cannot travel faster than the ...

37

The photons move at the speed of light in a straight line from the laser to the moon and back. The spot on the moon can move faster than light. There is no law against that. The spot is not a physical object, just an image. When you turn your wrist nothing happens to the photons which are already on the way to the moon - they continue on the same trajectory. ...

30

One of the results of special relativity is that a particle moving at the speed of light does not experience time, and thus is unable to make any measurements. In particular, it cannot measure the velocity of another particle passing it. So, strictly speaking, your question is undefined. Particle #1 does not have a "point of view," so to speak. (More ...

22

This question implicitly refers to the visible universe, but we should state that explicitly, as otherwise the question doesn't make any sense. It may seem like we shouldn't be able to see more than 13.7 billion light-years (13.7 giga-light-years, or glyrs) away, but that reasoning omits the expansion of spacetime according to General Relativity. A photon ...

20

Imagine a rock on a rope. As you rotate the rope faster and faster, you need to pull stronger and stronger to provide centripetal force that keeps the stone on the orbit. The increasing tension in the rope would eventually break the it. The very same thing would happen with bar (just replace the rock with the bar's center of mass). And naturally, all of this ...

20

There are quite a few common misconceptions about the expansion of the universe, even among professional physicists. I will try to clarify a few of these issues; for more information, I highly recommend the article "Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe" from Tamara M. Davis and ...

20

They are probaby talking about supernovae, like how SN1987A was first detected by neutrinos before the light arrived. In that case neutrinos and photons are both produced in the core of the supernovae explosion, but they have dense clouds of gas to get through before they get to empty space and travel freely to us. Since the neutrinos are weakly interacting ...

18

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 ...

18

Cute question! For a neutrino with mass $m$ and energy $E\gg m$, we have $v=1-\epsilon$, where $\epsilon\approx (1/2)(m/E)^2$ (in units with $c=1$). IceCube has detected neutrinos with energies on the order of 1 PeV, but that's exceptional. For neutrinos with mass 0.1 eV and an energy of 1 PeV, we have $\epsilon\sim10^{-32}$. The time of flight for ...

17

Before I answer, a couple caveats: As Adam said, the universe isn't going to start behaving any differently because we discovered something. Right now it seems much more likely (even by admission of the experimenters) that it's just a mistake somewhere in the analysis, not an actual case of superluminal motion. Anyway: if the discovery turns out to be ...

16

I read somewhere that $E=mc^2$ shows that if something was to travel faster than the speed of light then they would have infinite mass and would have used infinite energy. Nope, not true. For a couple of reasons, but first, let me explain what $E = mc^2$ means in modern-day physics. The equation $E = mc^2$ itself only applies to an object that is at ...

16

To answer this kind of question properly, it's important to clarify the foundational issues of why SR forbids superluminal speeds and what kind of superluminal speeds it forbids. There are several independent arguments of this kind that tell us several different things. Superluminal transmission of information would violate causality, since it would allow ...

15

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 ...

15

You should tell your son that this very question was asked by, explored by, and eventually answered by the some of the brightest physicists of the 19th century. Eventually two scientists named Michelson and Morley came up with an experiment to measure this effect, and were amazed to discover that it didn't exist! Rather: Light travelled at exactly the same ...

14

There is a real object with relativistic speed of surface - millisecond pulsar. The swiftest spinning pulsar currently known, spinning 716 times a second. Surface speed of such pulsar with radius 16 km is about $7*10^7$ m/s or 24% speed of light. It is calculated that pulsars would break apart if they spun at a rate of more than 1500 rotations per ...

14

The calculation is done for 1987A here. Basically, the neutrinos' fractional speed increase from the new paper is $2.48\pm0.28\pm0.30\times10^{-5}$ (statistical / systematic errors, respectively) . SN1987a was $166\,912\pm10.1$ ly away, so multiplying the fraction by the travel time gives $4.14\pm0.97$ years. In reality, we got the neutrinos a few hours ...

13

First, the existing theory: we know that special relativity is based on the Lorentz transformations, which for uniform relative motion in the $x$ direction take the form \begin{align} x' &= \frac{x + vt}{\sqrt{1 - v^2/c^2}} & t' &= \frac{t + vx/c^2}{\sqrt{1 - v^2/c^2}} \end{align} Now, suppose you arbitrarily choose one particular reference ...

13

Electromagnetic waves travel at the speed of light, and nothing can carry energy or information faster than light. Quantum entanglement doesn't carry information from one particle to another: all you get on one end is a random value from some distribution that has a relationship to a random number somewhere else. They can't be used to transmit information ...

12

Cute idea, +1. Let's think about where the slingshot boost of $2u$ comes from. In the center of mass frame, symmetry guarantees that the test particle exits with a speed equal to the speed with which it entered. If you set this up so that the deflection is nearly 180 degrees, then the problem becomes one-dimensional, so in the c.m. frame, the entry and exit ...

11

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 ...

11

This is what special relativity is all about.. In special relativity you cannot simply state that particle 2 is moving at c+c=2c in a reference frame where particle 1 is at rest. Speeds add like this (easily found in wikipedia): $$v_2^{'} = \frac{v_1+v_2}{1+\frac{v_1v_2}{c^2}}$$ i.e. the speed of particle 2 $v_2'$ in a reference frame where particle 1 is ...

11

In the expanding universe, you have to be a bit careful to define exactly what you mean by distance. The "proper distance" referred to here in that article means the distance measured at the present time. We have to be careful even to define what we mean by that last phrase -- time is relative, you know. But if the universe is approximately homogeneous, then ...

11

Collapsing an entangled pair occurs instantaneously but can never be used to transmit information faster than light. If you have an entangled pair of particles, A and B, making a measurement on some entangled property of A will give you a random result and B will have the complementary result. The key point is that you have no control over the state of A, ...

11

The question is not just about the question whether Superman's image represents a "real piece of information". It's clearly not actual matter located at the appropriate point in space. Instead, the image is a virtual place defined by certain criteria. But the fact that the image isn't quite material doesn't mean that you should switch back to Newtonian ...

11

Yes, if a particle would be travelling faster than light, it would always travel faster than light. This is what's called a tachyon, and they have in some sense imaginary mass. The three regimes, time-like, light-like and space-like (i.e. subluminal, luminal and superluminal space-time distances) are invariant under Lorentz transformation. Therefore ...

11

In principle, any of the fundamental "forces" could be used to transmit information. In practice, humans are only able to use electromagnetism. And in any case, none of these "forces" travel faster than light. Gravitational waves basically travel as fast, but no faster. Any massive particles (including neutrinos) will travel strictly slower than light. ...

10

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 ...

10

Yes, the expansion of space itself is allowed to exceed the speed-of-light limit because the speed-of-light limit only applies to regions where special relativity – a description of the spacetime as a flat geometry – applies. In the context of cosmology, especially a very fast expansion, special relativity doesn't apply because the curvature of the spacetime ...

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