GRED Answer: Scissor vertex speed

[Henning Makholm]

Make your blade edge and baseline out of stiff wires, and put a bead at their intersection. If you now move the blade edge down, the bead moves horizontally along the baseline wire, marking the intersection of the two. It will travel different distances on each wire, in exactly the same time.

Ignoring any relativistic effects, of course. :–)

Yes, obviously this "vertex" is a physical object and cannot exceed c.

No, what I meant was that when we switch to measuring the bead's travel in the blade-comoving frame, we need to take time dilation into account. An observer fixed to the blade will say that more time has passed while the bead moves from one end of the baseline to the other. Not very much more at ordinary speeds, but "exactly the same time" is a very exacting claim to make.

(We could imagine that the bead keep bouncing back and forth along the baseline and just coincidentally followed the vertex. An observer on the blade will see the "bead clock" ticking slower. (At first sight this argument would seem to be ruined by symmetry, but it is really not symmetric: the two observers agree that the baseline runs at right angles to their mutual velocity whereas the blade edge doesn't, and that makes a difference)).

[Chris Peterson]

No, what I meant was that when we switch to measuring the bead's travel in the blade-comoving frame, we need to take time dilation into effect. An observer fixed to the blade will say that more time has passed while the bead moves from one end of the baseline to the other. Not very much more at ordinary speeds, but "exactly the same time" is a very exacting claim to make.

Agreed, although for the purposes of this discussion, I'm willing to allow "exact" for the case of the bead moving a few meters per second. As you note, the relativistic effects are small (parts per trillion), but the difference in velocities could easily be an order of magnitude or more.

[hstarbuck]

Interesting note for guillotine example: The vertex travel 2 distances, the bottom length of right triangle (width of device) and hypotenuse of right triangle (length of blade edge) at the same time, further lending to fact that it is not a physical object.

Hah... you had me thinking about this for a minute. But really, this doesn't suggest the point is non-physical. It just means the point moves at a different velocity along the baseline than along the blade. This could be accomplished just as well with a physical object. Make your blade edge and baseline out of stiff wires, and put a bead at their intersection. If you now move the blade edge down, the bead moves horizontally along the baseline wire, marking the intersection of the two. It will travel different distances on each wire, in exactly the same time.

Oops, I see it now. The horizontal v relative to horiz wire is just a component of the diagonal v relative to diag wire. They are, however, moving in 2 different frames of reference. If I walk forward a meter in a moving bus I move further relative to the road. Any examples of something moving 2 linear distances in same time in a single reference frame?

[Henning Makholm]

Any examples of something moving 2 linear distances in same time in a single reference frame?

No, by definition. If you find a way to measure a different distance, you have found a different reference frame, because what a reference frame means is how you measure times and distances.

[makc]

Clearly, if we work the scissors exclusively from one end, we cannot make the vertex travel faster than light.

This would sound about right, especially in light of Amir question, except that my parallel guillotine case doesn't quite fit. Well, you could say that in order for guillotine blades to go absolutely parallel and without any deformation it cannot be trigerred "exclusively from one end", and you have to have numerous blade-releasing devices along the blade that cannot be triggered faster than it takes light to travel along the blade, blah blah blah, which is basically right (and answers Amir question, actually) but then it doesn't really matter in context of original question, where - yes - we can make the vertex move at infinite speed.

[makc]

I think the confusion over this question might be because the question does not really describe an experiment.

Here you go:

0.GIF

edit: sorry for completely ignoring last 2 pages of discussion, I just had to make a point that in it's original form, the question has "yes" as an answer

[wonderboy]

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.


Paul

[Chris Peterson]

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.

[Henning Makholm]

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.

I got out my ordinary kitchen scissors and measured:
Blade length: 95mm.
Pivot offset: 8mm.
The blades are stainless steel (let's assume a density of 8 g/cm³), 2 mm thick, width tapered from 15mm at the pivot to about 6 mm at the tips

Let's estimate, conservatively, the energy it would take to close the scissors fast enough to make the vertex move at above c. The blade tips will have to move at transverse speed ½c*8/95 = 12,622 km/s. Thus, every part of the outer half of each blade moves at at least 6,311 km/s. The mass of that outer half is at least 0.6*4.8*0.2*8 = 4.6 g. This gives each blade a kinetic energy of above 91 GJ. Bringing those blades to a stop must dispose of the equivalent energy of more than 44 tons of TNT.

Somehow I don't think I usually close my scissors quite that fast.

[Chris Peterson]

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.

(And even the large velocities and energies you come up with in your calculation are physically feasible; you aren't stepping on any hard limits. You'd need something stronger than steel, but I don't think that breaks the solution.)

[Henning Makholm]

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.

Sure, but then I'd dispute the ordinariness of the scissors.

Once we are going to reengineer, let me repeat that my ordinary kitchen scissors have blades that bend slightly into the plane of rotation. As I close the scissors, they successively pry apart by forces transmitted through the vertex. This is by design, as it ensures a cleaner cut by making sure that the blades actually contact instead of moving past each other with a gap that the material being cut could pass through. However the successive-prying-apart works only for vertex speeds below the speed of sound in the steel. Above that, the blades would likely collide head-on instead of slicing past each other. (Opening the scissors appears to present no such problems).

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.

Agreed. It's just that it helps at least me thinking of the practical consequences if we don't have to work in terms of picoseconds. I'd settle for several light seconds...

[neufer]

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

Given the tensile strength of steel (vs. it's density) it is hard to imagine a pair of scissors (of any length)
closing at an angular velocity faster than about 1 km/s without being torn apart by centrifugal force.

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

However, there is nothing to prevent two long bars of steel passing by each other with constant velocities approaching c.

[swainy]

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.

tc

[Chris Peterson]

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.

Of course I get that... it's what I said, after all! Now make a very tiny angle between them, so that there actually is an intersection point, and it's obvious that you can get that intersection to move at any arbitrary speed, for any particular speed of closure between the two cards.

[wonderboy]

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.

The little radio signals from the crudely drawn (just joking) ground based array made me believe it was radio ignited. It sure looks like it. I did actually think that he must have meant pre timed igniters, but hey ho.


Paul.

[makc]

yes, in my picture they were triggered by radio signal coming "from one end" of scissors; however, it doesn't say anywhere that we can't add pre-programmed delay between signal reception and ignition in fact, it is absolutely needed to make "rockets ignite simultaneously in observer's frame", as the picture said.

[neufer]

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

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

<<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.>>

[Henning Makholm]

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.

Why, we have to find some way to make the majority right, don't we?

[RJN]

I believe the best answer is "Yes, I have no problem with that." Much of the analysis given below is correct. In fact, this discussion thread is the best general analysis of this problem of which I am aware, and possibly even a good example of "Citizen Science."

In sum, the vertex of a scissors is not a physical object and can exceed the speed of light. If you could close a one light-year long scissors in one second, for example, then the vertex would need to move much faster than light.

The guillotine-scissors example, given below, makes this particularly clear. Here consider two lines with a very small angle between them. Now consider the tilted line slowly dropping past the straight line. The intersection of them is the vertex and can move down either line arbitrarily fast, even faster than light.

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. In that sense this example has similarities to the Twirling Pole GRED posted earlier here: http://asterisk.apod.com/vie ... 30&t=19641

A neat twist, posted below, which I had not previously considered, is that of a scissors that does NOT start with straight blades. This scissors, when closing, can have a vertex or even multiple vertexes that can actually break the speed of light even when the starting time is known only at the handle.

- RJN

[Chris Peterson]

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.

[makc]

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.

I think it should be very possible in "from one end" situation too, now. Check out this picture:

0.jpg

Thick line is moving blade edge supposed shape at t=1. We can see that although the blade has to deform, the vertex speed in marked interval can still be very close to what it would be in the world where blade was able to move as a rigid body. I am not that strong in math to actually express it as a formula, however.

edit: actually, nvm. looking at my picture again, I see that it demonstrates subluminal vertex speed for superluminal speed, it would have to be this:

[neufer]

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.

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).

[Beta]

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).

[Henning Makholm]

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).

That analysis assumes that you keep pushing at the handles.

Say instead that you stop pushing after you've poured a finite amount of angular momentum into the blades. If the mechanical properties of the blade includes sufficient vibration damping (by heat loss, which cannot make angular momentum go away) the blade could settle down into rigid rotation with a constant angular velocity before it has finished closing. That's really just a matter of starting with the scissors at a sufficiently large angle. If it's not enough, just declare that the initial angle was more than 360° and it's the next time around that really counts.

Once you've stopped pushing and the blade has settled down into smooth rotation, there seems to be nothing in theory to prevent the vertex to exceed c.

Now the trick: Even if you did continue pushing, how could that possibly retard the vertex? (Hmm, it could make it cross any point earlier, but by less at larger distances, thus decreasing the speed. Disregard this non-trick, please.)

[RJN]

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.

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.

- RJN