Starship Asterisk*

RJN wrote:

Chris Peterson wrote:I think you can have the intersection point of the blades can still move faster than c. The reasoning is that with scissors (unlike the guillotine) the angle is changing, and therefore the velocity of the intersection point is changing (assuming constant angular closure). The intersection starts out moving slowly, but is moving very fast as the scissors are nearly closed.

Yes, but this situation can only occur when an entire scissor blade is already moving. If both scissor blades start at rest, however, the information to start moving must still move along the length of one blade. So even a scissors with a vertex angle of zero must have each point along one blade start to move before that point can be considered closed.

Chris Peterson wrote:

b0bb0 wrote:This is way over my head, but... I think there may be an alternate answer. Assuming the speed of a photon is the speed of light. That the speed of a photon is variable in an "Atmosphere". That in a dense enough atmosphere will bring a photon to a stop. Then anything moving scissorswise would be moving faster than the speed of light

The limiting factor isn't the speed of light, but the universal constant c, which happens to be the speed that light travels in a vacuum. C isn't determined by the speed of light, the speed of light is determined by c.

Aside from this, making an atmosphere denser simply makes it opaque, which isn't the same as slowing down light. The slowest light will get (assuming it isn't absorbed) is determined by the index of refraction of the atmosphere either in its liquid or solid phase, depending on just how dense it gets. The materials with the highest indexes of refraction are around 3, meaning that light travels one third of c. That's still a long ways from standing still.

http://en.wikipedia.org/wiki/Speed_of_light wrote:
<<In a medium, the speed at which light waves propagate can differ from c; to properly discuss the meaning of this statement, several different concepts of the "speed of a light wave" need to be distinguished. The first is the speed of a wave of a single frequency f; this is called the phase velocity v_p. The refractive index of a material is defined as the ratio of c to the phase velocity v_p in the material: larger indices of refraction indicate smaller speeds. The refractive index of a material may depend on the light's frequency, intensity, polarization, or direction of propagation; in many cases, though, it can be treated as a material-dependent constant. The refractive index of air is approximately 1.0003. Denser media, such as water, glass, and diamond, have refractive indexes of around 1.3, 1.5 and 2.4 respectively for visible light.

In transparent materials, the refractive index generally greater than 1, meaning that the phase velocity is less than c. In other materials, it is possible for the refractive index to becomes smaller than 1 for some frequencies; in some exotic materials it is even possible for the index of refraction to become negative. The requirement that causality is not violated implies that the real and imaginary parts of the dielectric constant of any material, corresponding respectively to the index of refraction and to the attenuation coefficient, are linked by the Kramers–Kronig relations. In practical terms, this means that in a material with phase velocity less than 1, the absorption of the wave is so quick that no signal can be sent faster than c.

The second concept of the speed of light in a material is the average velocity of a pulse consisting of different frequencies. This is called the group velocity and depends not only on the properties of the medium but also on the distribution of frequencies in the pulse. A pulse with different group and phase velocities (which occurs if the phase velocity is not the same for all the frequencies of the pulse) is said to undergo dispersion. Certain materials have an exceptionally low group velocity for light waves, a phenomenon called slow light. In 1999, a team of scientists led by Lene Hau were able to slow the speed of a light pulse to about 17 metres per second; in 2001, they were able to momentarily stop a beam. In 2003, scientists at Harvard University and the Lebedev Physical Institute in Moscow succeeded in completely halting light by directing it into a Bose–Einstein condensate of the element rubidium, the atoms of which, in Lukin's words, behaved "like tiny mirrors" due to an interference pattern in two "control" beams.

It is also possible for the group velocity of light pulses to exceed c. In an experiment in 2000, laser beams traveled for extremely short distances through cesium atoms with a group velocity of 300 times c. It should even be possible for the group velocity to become infinite or even negative, implying pulses traveling instantaneously or backwards in time. None of these options, however, allow information to be transmitted faster than c. It is impossible to transmit information with a light pulse any faster than the speed of the earliest part of the pulse (the front velocity). It can be shown that this is (under certain assumptions) always equal to c.>>

b0bb0 wrote:This is way over my head, but... I think there may be an alternate answer. Assuming the speed of a photon is the speed of light. That the speed of a photon is variable in an "Atmosphere". That in a dense enough atmossphere will bring a photon to a stop. Then anything moving scissorswise would be moving faster than the speed of light

b0bb0 wrote:This is way over my head, but... I think there may be an alternate answer. Assuming the speed of a photon is the speed of light. That the speed of a photon is variable in an "Atmosphere". That in a dense enough atmossphere will bring a photon to a stop. Then anything moving scissorswise would be moving faster than the speed of light

Beta wrote:

neufer wrote: It seems to me that [speed of light response] straight edge scissors would be strain distorted under the closing forces into Archimedes spirals and thus would proceed to close outward at a constant speed (= c).

If you can start with straight blades that distort into outward curves in motion, you can start with inward-curved blades that distort into straight edges in motion. The vertex will start out behind the propagating distortion, moving much more slowly, then catch up >c (but not overtake it).

• 1) light speed travel along the blade edge => light speed travel from star to reflection nebula
  2) light speed travel of the closing blade edge => light speed travel from reflection nebula to earth

• If the upper (moving) scissors blade is initially defined by y(x)
  and the distance along it by S(x) = ⌠ sqrt [1-(dy/dx)²] dx
  
  Then the minimum time of travel for the vertex
  to close at distance R(x) = sqrt(y²+x²)
  is t(R) = {S + R arcsin(y/R)}/c
  
  so the instantaneous vertex speed is
  dR/dt = c/{dS/dR + arcsin(y/R) + R d[arcsin(y/R)]/dR}
  
  And the average vertex speed
  = c / {(s/sqrt[y²+x²]) +arctan(y/x)} < c

RJN wrote:Yes, but this situation can only occur when an entire scissor blade is already moving. If both scissor blades start at rest, however, the information to start moving must still move along the length of one blade. So even a scissors with a vertex angle of zero must have each point along one blade start to move before that point can be considered closed.

Chris Peterson wrote: This may need some clarification, or additional analysis. I think you can have the intersection point of the blades can still move faster than c. The reasoning is that with scissors (unlike the guillotine) the angle is changing, and therefore the velocity of the intersection point is changing (assuming constant angular closure). The intersection starts out moving slowly, but is moving very fast as the scissors are nearly closed.

neufer wrote:It seems to me that "infinitely stiff" (i.e., with speed of light response) straight edge scissors would be strain distorted under the closing forces into Archimedes spirals and thus would proceed to close outward at a constant speed (= c).

neufer wrote: It seems to me that [speed of light response] straight edge scissors would be strain distorted under the closing forces into Archimedes spirals and thus would proceed to close outward at a constant speed (= c).

Chris Peterson wrote:

RJN wrote:Conversely, however, the "no" answer is actually correct in the most classic example of a scissors closing -- that when the two blades start as rigid, straight, at rest, and the time when the scissors will start to close is only known at the handle. For this case, the information that the scissors is closing can only move up the blades at the speed of light, so that the end of the scissors, say one light year away, could not know to close before that information arrives from the handle.

This may need some clarification, or additional analysis. I think you can have the intersection point of the blades can still move faster than c. The reasoning is that with scissors (unlike the guillotine) the angle is changing, and therefore the velocity of the intersection point is changing (assuming constant angular closure). The intersection starts out moving slowly, but is moving very fast as the scissors are nearly closed. Causality limitations only require that information not get from the hands closing the scissors to the scissor tips in less time than a photon could. But there is nothing that says the intersection velocity can't start at less than c and end at more than c. As long as the average speed is less than c, the Universe should be happy.

Chris Peterson wrote:The intersection starts out moving slowly, but is moving very fast as the scissors are nearly closed. Causality limitations only require that information not get from the hands closing the scissors to the scissor tips in less time than a photon could. But there is nothing that says the intersection velocity can't start at less than c and end at more than c. As long as the average speed is less than c, the Universe should be happy.

RJN wrote:Conversely, however, the "no" answer is actually correct in the most classic example of a scissors closing -- that when the two blades start as rigid, straight, at rest, and the time when the scissors will start to close is only known at the handle. For this case, the information that the scissors is closing can only move up the blades at the speed of light, so that the end of the scissors, say one light year away, could not know to close before that information arrives from the handle.

neufer wrote:Here (I assume) we have an attempt to explain the simple concept
of "apparent superluminal motion" using an enormous pair of scissors
and our Asternauts have run off in all directions with those scissors.

http://en.wikipedia.org/wiki/Faster-than-light wrote:
<<Apparent superluminal motion is observed in many radio galaxies, blazars, quasars and recently also in microquasars. The effect was predicted before it was observed by Martin Rees and can be explained as an optical illusion caused by the object partly moving in the direction of the observer, when the speed calculations assume it does not. The phenomenon does not contradict the theory of special relativity. Interestingly, corrected calculations show these objects have velocities close to the speed of light (relative to our reference frame).

Light spots and shadows: If a laser is swept across a distant object, the spot of light can easily be made to move at a speed greater than c. Similarly, a shadow projected onto a distant object can be made to move faster than c. In neither case does any information travel faster than light.>>

Chris Peterson wrote:

wonderboy wrote:It would take longer for the rocket to the right of your blade to ignite if your remote igniting them, the signal would travel at c and would take considerably longer to reach the last rocket than the first.

They are not remotely ignited. They are ignited by local timers, using a preset plan. Again, this is just the "timed wave" that was discussed in the long pole problem, and it doesn't violate any sort of causality.

This whole problem is complicated by talking about very long scissors and complex movement mechanisms. You can apply simple math to see that an ordinary pair of kitchen scissors will have the vertex moving faster than c just as they close. Or you can change the guillotine angle to be arbitrarily close to 0° and get any vertex speed you want, even with a very slow falling blade. There is no need to worry about relativistic effects in the experimental apparatus.

swainy wrote:If i have two equal sheets of card, which are square. I put them next to each other. I choose the angle to be zero. so when i move them apart, the vertex is instant? Faster than light. I think i get you now Chris.

Chris Peterson wrote:You'd need something stronger than steel, but I don't think that breaks the solution.

• Maximum Scissors Velocity = Constant x sqrt (tensile strength/density)
  (Constant depends on the amount of taper of the scissors blade.)

Chris Peterson wrote:

Henning Makholm wrote:Somehow I don't think I usually close my scissors quite that fast.

I meant to suggest modifying the ordinary kitchen scissors slightly by placing the pivot point very close to the blade edges. Unless we start talking atomic thicknesses, that's just engineering.

In any case, my point was only that this problem is easier to work with if we don't start invoking light year long scissors. It isn't necessary to the concept, and it certainly adds an entire level of complexity not suggested by the initial question. If the vertex can go faster than c, it can do so whether the scissors are abnormally long or not.

Henning Makholm wrote:Somehow I don't think I usually close my scissors quite that fast.

Chris Peterson wrote:You can apply simple math to see that an ordinary pair of kitchen scissors will have the vertex moving faster than c just as they close.