GRED Answer: Scissor vertex speed

[Chris Peterson]

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.

Yes, but I don't see how that changes my point. We can take a reasonably physical pair of scissors (I'm not talking about light year long blades here) and close them at a reasonable speed. Certainly there will be a propagation delay of the movement from one end to the other, but the system will reach a steady state. And in that state, there can be a time when the intersection point velocity is exceeding c. This doesn't violate any rules of causality.

[neufer]

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).

Correct.

A scissors blade can have jagged vertical "pinking shear" teeth that perfectly replicate the apparent superluminal motion of a light echo.

• 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

http://antwrp.gsfc.nasa.gov/apod/ap091122.html
http://asterisk.apod.com/vie ... t=0#p90968

http://antwrp.gsfc.nasa.gov/apod/ap080212.html

• 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]

Yes OK, the average speed of the vertex of a scissors with both blades starting straight and at rest is constrained to be less than c. More specifically the length of the blade divided by the time it takes for the blades to close, both measured in the frame of the handle, must be less than c. Once one of the blades is already moving, the instantaneous speed of the vertex at the moving blade position(s) can exceed c, so long as the total average speed remains so constrained. - RJN

[b0bb0]

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

[neufer]

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

Special relativity explicitly involves the speed of light in a vacuum.

[Chris Peterson]

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

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.

[neufer]

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.

<<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.>>

[Henning Makholm]

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.

Isn't all you're saying here that the vertex speed cannot jump instantaneously from 0 to >c? That seems to me to be so trivial that we don't have to invoke relativity to conclude it; F=ma does it for any nonzero vertex angle.

In the zero-angle case, I'd deny that the idea of a single vertex that can be assigned a speed applies in the first place. But in principle, we could certainly make a entire finite interval of the blade edge begin to move at the same time. That's just a question of delaying the impluse from reaching the nearer end of that edge interval while it propagates to the farther end through a different portion of the blade. If we're allowed to construct the blade out of materials with different propagation speeds, then including appropriate lensing elements into it should do the trick.