New answers tagged faster-than-light
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The radius of the observable universe is about 46 billion light years, which is considerably greater than its age of about 14 billion years. Since the radius of the observable universe is defined by the greatest distance from which light would have had time to reach us since the Big Bang, you might think that it would lie at a distance of only 14 billion ...
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Firstly, the light year measures distance, and not age. But I see your question here: "Can the radius of the universe(in ly) be more than its age (in y)?"
The answer is (surprisingly) yes. In fact, this is indeed the case.
Firstly, a little side story:
This is something that confounded Einstein himself, way before we even knew about the Big Bang. When he ...
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If you take an aluminum rod and tap one end with a hammer, the disturbance travels along the rod at the speed of sound in aluminum, which is about 5000 m/s. This speed is what determines the frequency of the ringing that you hear. The speed is many orders of magnitude less than c. If it were higher than c for some other substance (one that was very stiff and ...
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About faster than light...
I know (in fact I am currently yet studying) different extensions of relativity. Some options naturally arise:
1) Yes, Ben... Sudarshan's (and Recami's) Meta-relativity is one "option", somewhat oldfashioned. Problems: tachyons have not been observed in Nature yet.
metarelativity paper
metarelativity paper 2012
2) Carlos ...
1
Nice question.
I don't understand the Lorentz-violating possibilities very well, so I'll only try to comment on Lorentz-invariant theories.
The classic papers are Tolman 1917, Bilaniuk 1962, and Bilaniuk 1969. Bilaniuk 1969 can easily be found online by googling, and gives a good overview. Tolman proposed a causality paradox involving tachyons, known as ...
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Your second equation is incorrect. In both Newtonian Mechanics and Relativistic Mechanics, force is the time rate of change of momentum:
$\vec F = \dfrac{d \vec p}{dt}$
Where, in special relativity, momentum is:
$\vec p = m \dfrac{\vec v}{\sqrt{1 - \frac{v^2}{c^2}}} = m \gamma \vec v$
and $m$ is the invariant mass.
Thus, when the time derivative is ...
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Maybe the thing you are seeking for is a dynamics of a tachyon. I will briefly introduce it. Below I use $m=\mathrm{const}$ as a rest mass or simply the mass (mass changing with speed is a pedagogical mistake), and $c=1$ - a usual convention to simplify formulas without information loss. $\gamma$ is an abbreviation for $1/\sqrt{1-v^2}$ and is called Lorentz ...
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You can't travel faster than light. And anything with mass can't travel at the speed of light, so if you set $v=c$ in any of those equations you need $m_0=0$, and so you would be talking about a photon or some other massless particle. As $v\to c$ in those equations, the force goes to infinity, so you can never reach $c$ for $m_0\ne 0$.
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Of course it wouldn't - and to be honest here it's not even hard to imagine. If the lever was absolutely hard and could not bend (normally it must bend - the speed of waves in material is also limited) you'd need more energy to move it faster.
To imagine this, take your bicycle and try to rotate one of its wheels. As you put your finger closer to he centre, ...
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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 ...
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One way to think of a "moving shadow" is by following the last photon that was allowed through. In that case, the speed of a shadow is exactly the speed of light.
On the other hand, you could also define the speed of a shadow as the speed of the boundary between dark and light. In that case there is no thing that's actually moving, so there's no bound on ...
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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 ...
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Because the neutrinos follow a straighter line.
The visible light that reaches your eye/telescope has been pulled back and forth by various influences such as gravitational pull along its long path to you. The neutrinos have taken a straighter route because they are much less influenced.
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Here's the reported article on the neutrino detection which has the phrase. To answer your title, neutrinos have a very small mass. They don't carry charge which makes them invulnerable to EM radiation. But, they still interact with charged particles such as electrons, protons and muons. Fast neutrinos can interact with electrons in some medium (like water) ...
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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 ...
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This is essentially the same as lurscher's answer, but from a different perspective.
Special Relativity is often thought of as some kind of mystical force that acts on objects and stops them moving faster than light. This misconception is the reason for questions like this one. Special Relativity is actually just a prescription for telling us what events in ...
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There are several experiments where photons are claimed to travel faster than the speed of light. Most notable among them are Nimtz double-prism experiment. Here is a bibliography on the subject.
As it is said in the link, physicists basically agree on the observations, but differ in the interpretations of those observations. Confusion between phase ...
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Faster-than-light tunneling appears only in non-relativistic quantum mechanics. As soon as you introduce the concept of relativity to QM, faster-than-light tunneling disappears.
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The speed of light seems to be the undisputed speed limit of the universe, in relation to the fact that to travel faster than a massless photon is able to travel would not only be physically impossible because no object containing mass would be able to stand the blinding speed, even in the vacuum of space without atmosphere to create drag.
Also, there is ...
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in relation to anything else that can make such measurements.
As the speed of light is universal, nothing can see any other massive field moving at the speed of light (which is reserved for massless fields)
your 0.51 number suggests that you expect that naive addition of velocities holds when velocities approach the speed of light. This is wrong. Here is ...
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One of the consequences of the FTL motion is that there is always a reference frame where the object is at different places at the same time. This is opposite to the time-like motion, where there is always a frame where object is at the same place in different times.
Now consider the structure of proton. It is known that the number of observed proton ...
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