GRED Answer: Scissor vertex speed

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Re: GRED Answer: Scissor vertex speed

Post by Beta » Thu Jun 24, 2010 6:25 pm

Henning Makholm wrote: Clearly, if we work the scissors exclusively from one end, we cannot make the vertex travel faster than light. (At least not unless the blades have some very weird elastic properties such that they won't meet close to us until our impulse has had time to travel down to points far from us, in which case it would be a stretch to describe the thing as a scissors).
I disagree. I think that it is possible to get vertex speed > c even if the impulse travels down the blades at < c, and the vertex can still form and move slowly while it's still close to the handles. As a proof of concept, consider a pair of scissors of ordinary size with slightly concave edges (like a lobster claw). Close it at ordinary speeds; first a vertex forms near the handle and begins moving out, then the points meet and another vertex forms and begins moving in. Just before the two vertices meet, their speed increases without limit.

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Re: GRED Answer: Scissor vertex speed

Post by Chris Peterson » Thu Jun 24, 2010 6:57 pm

Beta wrote:I disagree. I think that it is possible to get vertex speed > c even if the impulse travels down the blades at < c, and the vertex can still form and move slowly while it's still close to the handles. As a proof of concept, consider a pair of scissors of ordinary size with slightly concave edges (like a lobster claw). Close it at ordinary speeds; first a vertex forms near the handle and begins moving out, then the points meet and another vertex forms and begins moving in. Just before the two vertices meet, their speed increases without limit.
This problem overlaps the previous long pole problem. In thinking about the scissors, it is important to remember that we still can't convey any information faster than c. That means that if we decide the vertex can move at greater than c, we have to allow for the fact that it can't reach any arbitrary point in space faster than a photon released by the scissors operator when he starts the scissors closing. Another way of saying this is that (assuming the operator is very near the vertex when it starts moving) the average velocity of the vertex over its travel time must be less than c, even if it has a velocity greater than c over part of its movement.
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Re: GRED Answer: Scissor vertex speed

Post by Beta » Thu Jun 24, 2010 7:26 pm

Chris Peterson wrote: In thinking about the scissors, it is important to remember that we still can't convey any information faster than c. That means that if we decide the vertex can move at greater than c, we have to allow for the fact that it can't reach any arbitrary point in space faster than a photon released by the scissors operator when he starts the scissors closing.
Agreed.

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Re: GRED Answer: Scissor vertex speed

Post by alter-ego » Thu Jun 24, 2010 7:43 pm

Beta wrote:
Henning Makholm wrote: Clearly, if we work the scissors exclusively from one end, we cannot make the vertex travel faster than light. (At least not unless the blades have some very weird elastic properties such that they won't meet close to us until our impulse has had time to travel down to points far from us, in which case it would be a stretch to describe the thing as a scissors).
I disagree. I think that it is possible to get vertex speed > c even if the impulse travels down the blades at < c, and the vertex can still form and move slowly while it's still close to the handles. As a proof of concept, consider a pair of scissors of ordinary size with slightly concave edges (like a lobster claw). Close it at ordinary speeds; first a vertex forms near the handle and begins moving out, then the points meet and another vertex forms and begins moving in. Just before the two vertices meet, their speed increases without limit.
It appears we are in agreement in principle, but have questions about demonstrating this in practice with a hand-held pair of scissors?? I believe it is physically possible to demonstrate this, but would likely take a lot more than scissors and a lot of details to account for. $$$$$$
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Re: GRED Answer: Scissor vertex speed

Post by hstarbuck » Thu Jun 24, 2010 7:56 pm

I was thinking pivot point when I voted no, but now, realizing it is the meeting of the blades, switch to yes because I agree with posts supporting. Maybe more words describing this thought exp would have been better this time.

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Re: GRED Answer: Scissor vertex speed

Post by Henning Makholm » Thu Jun 24, 2010 8:09 pm

Beta wrote:
Henning Makholm wrote: Clearly, if we work the scissors exclusively from one end, we cannot make the vertex travel faster than light. (At least not unless the blades have some very weird elastic properties such that they won't meet close to us until our impulse has had time to travel down to points far from us, in which case it would be a stretch to describe the thing as a scissors).
I disagree. I think that it is possible to get vertex speed > c even if the impulse travels down the blades at < c, and the vertex can still form and move slowly while it's still close to the handles. As a proof of concept, consider a pair of scissors of ordinary size with slightly concave edges (like a lobster claw). Close it at ordinary speeds; first a vertex forms near the handle and begins moving out, then the points meet and another vertex forms and begins moving in. Just before the two vertices meet, their speed increases without limit.
Yes, of course.
alter-ego wrote:It appears we are in agreement in principle, but have questions about demonstrating this in practice with a hand-held pair of scissors?? I believe it is physically possible to demonstrate this, but would likely take a lot more than scissors and a lot of details to account for. $$$$$$
The most immediate difficulty is that for a practical demonstration, the angle between the blades would have to be so small that it is difficult to define the location of the vertex with sufficient precision. If we close the blade at a reasonable transverse speed of a few meters per second, an uncertainty of a atomic width in where the edge of the blade is will move the vertex hundreds of meters. That calls for a very long scissors.

Also, if we want to time the movement of the vertex from point A to point B, we'll need to exclude the possibility that a new vertex forms close to point B together with an anti-vertex that travels backward along the scissors to eliminate the original vertex. It's not even clear to me how to make sure of that in any concrete experiment (which points to the more general fact that the whole idea of a single traveling vertex is strictly speaking bogus).
Last edited by Henning Makholm on Thu Jun 24, 2010 8:29 pm, edited 1 time in total.
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Re: GRED Answer: Scissor vertex speed

Post by bystander » Thu Jun 24, 2010 8:22 pm

alter-ego wrote:It appears we are in agreement in principle, but have questions about demonstrating this in practice with a hand-held pair of scissors?? I believe it is physically possible to demonstrate this, but would likely take a lot more than scissors and a lot of details to account for. $$$$$$
It can probably be modeled mathematically as a function of the closing rate of the blades and the angle of incidence.

Any argument about the length of the blades and their material construction is extraneous.

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Re: GRED Answer: Scissor vertex speed

Post by Henning Makholm » Thu Jun 24, 2010 8:41 pm

Henning Makholm wrote:The most immediate difficulty is that for a practical demonstration, the angle between the blades would have to be so small that it is difficult to define the location of the vertex with sufficient precision. If we close the blade at a reasonable transverse speed of a few meters per second, an uncertainty of a atomic width in where the edge of the blade is will move the vertex hundreds of meters.
Whoops, I misplaced an exponent somewhere. It would be only a few centimeters, not "hundreds of meters". However, since manufacturing irregularities as well as the detectable gap between the blades would surely be much greater than a single atom, it still presents a practical obstacle.
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Re: GRED Answer: Scissor vertex speed

Post by Henning Makholm » Thu Jun 24, 2010 9:15 pm

Henning Makholm wrote:Also, if we want to time the movement of the vertex from point A to point B, we'll need to exclude the possibility that a new vertex forms close to point B together with an anti-vertex that travels backward along the scissors to eliminate the original vertex.
Coincidentally, something quite analogous to this can happen in quantum electrodynamics and make particles such as electrons appear to have moved faster than light. It turns out that this effect cannot be used to send information faster than light (for which there are precise and impeccable mathematical arguments, but heuristically speaking, histories where it happens tend to interfere destructively and either cancel completely or at least smear out enough to leave you in doubt what message was sent) -- which is all relativity really requires.
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Re: GRED Answer: Scissor vertex speed

Post by hstarbuck » Thu Jun 24, 2010 9:16 pm

Lets set this up with a attempt to be reasonable even though thought experiments do not require this: If we have a 1000m (1km) wide guillotine with a blade coming down at the speed of sound (344 m/s), set the vertical distance from the part that first touches the flat receiving blade (block, surface, whatever--just flat) to the end that last touches to 1 mm (0.001m), then the distance (1000m) will be covered in 2.907*10-6s for apparent velocity of 3.44*108m/s-----greater than c. Is this possible to set up?--probably not with the precision in today's technology haha, but no laws seem to be broken.

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Re: GRED Answer: Scissor vertex speed

Post by Craine » Sat Jun 26, 2010 1:40 am

As many people already have stated, the Vertex is not a physical point. It is a virtual point used in describing the relative position of the two scissor blades. However it should be noted that describing it from an observers viewpoint can be some fun. Imagine if you will lightyear long blades that can somehow move together and close within an hour. (lets forget about the engineering issues for now)

If an observer would be near the base of the blades (near the axis around which the blades rotate) when the scissor blades start to move together, the vertex may have moved far and fast, but the light from the blade tips is still underway to the observer for another year (minus one hour).

If the observer is near the blade tips, he might see the blade tips come together, an hour after he knows the blades started moving a lightyear away. And yet, it will seem the blades near the base are still wide apart...for another year.

And if the observer is in the middle he might see the blade edges come together when the vertex passes him, while the blades near the base as well as near the tips still seem to be wide apart for 6 months.

So, for a single static observer, the vertex does not seem to move faster then the speed of light. Simply because the light send out from any point along which the vertex passes can itself not move faster then light. Of course. But separate observers may each see the vertex pass in timeframes that are less then the time needed to travel that same distance at the speed of light.

So, the vertex itself can theoretically move as fast as you want, even faster then c. But a single observer will never be able to see it happen. Gotta love relativity. :D

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Re: GRED Answer: Scissor vertex speed

Post by Chris Peterson » Sat Jun 26, 2010 1:58 am

Craine wrote:As many people already have stated, the Vertex is not a physical point. It is a virtual point used in describing the relative position of the two scissor blades. However it should be noted that describing it from an observers viewpoint can be some fun. Imagine if you will lightyear long blades that can somehow move together and close within an hour. (lets forget about the engineering issues for now)
Your argument and most conclusions fail for a simple reason: you can't do the experiment the way you suggest, and it has nothing to do with engineering issues. If you have scissor blades 1 ly long, and you try closing the scissors, the motion cannot be conveyed to the other end of the scissors in less than a year. This has nothing to do with the vertex, it's just the basic rules of relativity. This can't be fixed by engineering "solutions" like infinitely rigid scissors, or anything like that.

An observer somewhere along a more reasonably sized pair of scissors is perfectly capable of observing the intersection point passing him by at greater than c, and he will actually observe it as greater than c.
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Re: GRED Answer: Scissor vertex speed

Post by Craine » Sat Jun 26, 2010 2:03 am

I think I have to correct my own statement....a single observer can see it happen. But it takes some funny scissors.

Imagine, if you will, scissors with blades a lighyear long, but curved into a circle. So, the tips of the blades are right behind the base of the blades (near the axis the scissor blades rotate around). The radius of the circle will then be 1/(2pi) lightyear. We stil assume the scissors can close within an hour.

An observer standing in the center of the circle scissors will have to wait 1/(2pi) or approximately 0.16 year before he sees the blades start to move. But then the light from all directions starts to come in within an hour. For that observer the vertex will seem to move all the way around him for a total distance of 1 lightyear within that single hour.

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Re: GRED Answer: Scissor vertex speed

Post by Craine » Sat Jun 26, 2010 2:16 am

Chris Peterson wrote:Your argument and most conclusions fail for a simple reason: you can't do the experiment the way you suggest, and it has nothing to do with engineering issues. If you have scissor blades 1 ly long, and you try closing the scissors, the motion cannot be conveyed to the other end of the scissors in less than a year. This has nothing to do with the vertex, it's just the basic rules of relativity. This can't be fixed by engineering "solutions" like infinitely rigid scissors, or anything like that.

An observer somewhere along a more reasonably sized pair of scissors is perfectly capable of observing the intersection point passing him by at greater than c, and he will actually observe it as greater than c.
Sorry, but I disagree. Instead of scissors perhaps you can imagine two long lines of rocketships spaced out along what would have been the edges of the scissors, the rockets aimed directly at each other. Each rocket preprogrammed to start at the same time, only the distance between the lines of rockets determines the time it takes to hit its opponent rocket, which of course happens when the vertext passes.

With my assumption of all engineering issues aside, I believe my arguments stand.

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Re: GRED Answer: Scissor vertex speed

Post by Chris Peterson » Sat Jun 26, 2010 3:00 am

Craine wrote:Sorry, but I disagree. Instead of scissors perhaps you can imagine two long lines of rocketships spaced out along what would have been the edges of the scissors, the rockets aimed directly at each other. Each rocket preprogrammed to start at the same time, only the distance between the lines of rockets determines the time it takes to hit its opponent rocket, which of course happens when the vertext passes.
Yes, but that's an experiment that is physically very different from the scissors. Your timed setup doesn't violate causality. The line of rockets can be a light year long, and the time between the first and last one moving can be arbitrarily short (this is just the "timed wave" from the long pole problem). A scissor blade one light year long cannot be made to move unless it bends. From the time you move one end, it takes at least a year before the other end starts moving. That is not something that has an engineering solution. If you base a set of arguments on a setup that assumes 1 ly long scissor blades that need to move instantaneously, all those arguments fail because the conditions are unphysical.
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Re: GRED Answer: Scissor vertex speed

Post by alter-ego » Sat Jun 26, 2010 4:07 am

Craine wrote:Sorry, but I disagree. Instead of scissors perhaps you can imagine two long lines of rocketships spaced out along what would have been the edges of the scissors, the rockets aimed directly at each other. Each rocket preprogrammed to start at the same time, only the distance between the lines of rockets determines the time it takes to hit its opponent rocket, which of course happens when the vertext passes.

With my assumption of all engineering issues aside, I believe my arguments stand.
Hi Craine,
I'm confused over what point you're now driving at. It seems you wanted to show an observer couldn't see the vertex moving at >c by using scissors of infinite rigidity, then you realized how an observer could. Maybe you should have said: "With my assumption of all physics issues aside, I believe my arguments stand.
Do you question that a structure cannot be infinitely rigid??
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Re: GRED Answer: Scissor vertex speed

Post by bystander » Sat Jun 26, 2010 12:55 pm

I think the apparent velocity of the vertex is inversely proportional to the tangent (or sine) of the incidence angle. As the scissors close and the angle goes to zero, the apparent velocity increases without bounds. There is no need for super rigid blades light years long.

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Re: GRED Answer: Scissor vertex speed

Post by Henning Makholm » Sat Jun 26, 2010 1:38 pm

Chris Peterson wrote:A scissor blade one light year long cannot be made to move unless it bends. From the time you move one end, it takes at least a year before the other end starts moving.
There seems to be nothing in Craine's description that implies that force is being applied to the blade only at one point.

We could have a lot of people push on the blades along its entire length simultaneously, in just the right amount to set it rotating rigidly around the pivot, and then let it continue coasting by inertia as the scissors close. There will be some centrifugal stress in the blade (plus some second-order shear caused by differential width contraction), but it wouldn't have to bend as such.
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Re: GRED Answer: Scissor vertex speed

Post by Henning Makholm » Sat Jun 26, 2010 1:47 pm

Craine wrote:I think I have to correct my own statement....a single observer can see it happen. But it takes some funny scissors.
Not at all. The observer just needs not to be located exactly at the scissor line. If you place yourself some distance away from a point P which the vertex passes, in a direction perpendicular to the vertex "movement", then the lightspeed delay from the vertex to your eye will be constant (to first order) in a neighborhood of P. You will observe the vertex pass through that neighborhood at its true speed.
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Re: GRED Answer: Scissor vertex speed

Post by Craine » Sat Jun 26, 2010 2:41 pm

Perhaps there is some confusion about the original question. I assumed that the example of using scissors was merely to illustrate the concept. I approached the issue as that of a vertex, a virtual point, that in itself is moving in relation to two moving objects (the scissor blades). And thus, wether actual scissors or other physical objects are used is immaterial to the core problem. So, I suggested the timed rocketships as another way to illustrate the moving vertex issue.

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Re: GRED Answer: Scissor vertex speed

Post by Chris Peterson » Sat Jun 26, 2010 3:03 pm

bystander wrote:I think the apparent velocity of the vertex is inversely proportional to the tangent (or sine) of the incidence angle. As the scissors close and the angle goes to zero, the apparent velocity increases without bounds. There is no need for super rigid blades light years long.
That is correct.

Actually, this problem is much easier to understand if we consider the guillotine example rather than scissors. Scissors keep getting convolved with the long pole problem, which complicates things. If we construct a guillotine with an edge that is shallower than 45°, the intersection of the blade with the lower bar obviously moves faster than the blade itself. Since it is just an engineering problem to move the blade at any speed less than c, we can clearly make the intersection move at greater than c. The guillotine blade makes the causality issues simpler to grasp, and also gets rid of the tangent dependence (with scissors, the speed of the intersection point is not linearly related to the angular rate the scissors are closed; with a guillotine the speed of the intersection point is simply proportional to the speed the blade is dropped).
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Re: GRED Answer: Scissor vertex speed

Post by bystander » Sat Jun 26, 2010 3:53 pm

hstarbuck: http://asterisk.apod.com/vie ... 13#p125443
Chris Peterson wrote:Actually, this problem is much easier to understand if we consider the guillotine example rather than scissors. Scissors keep getting convolved with the long pole problem, which complicates things. If we construct a guillotine with an edge that is shallower than 45°, the intersection of the blade with the lower bar obviously moves faster than the blade itself. Since it is just an engineering problem to move the blade at any speed less than c, we can clearly make the intersection move at greater than c. The guillotine blade makes the causality issues simpler to grasp, and also gets rid of the tangent dependence (with scissors, the speed of the intersection point is not linearly related to the angular rate the scissors are closed; with a guillotine the speed of the intersection point is simply proportional to the speed the blade is dropped).
Wouldn't the speed still be inversely proportional to the tangent of the blade's angle? It's just that the angle is fixed, instead of diminishing as in the case of scissors.

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Re: GRED Answer: Scissor vertex speed

Post by Chris Peterson » Sat Jun 26, 2010 4:07 pm

bystander wrote:Wouldn't the speed still be inversely proportional to the tangent of the blade's angle? It's just that the angle is fixed, instead of diminishing as in the case of scissors.
Yes. But the speed that that the intersection travels is linearly related to the speed the blade moves, which I think is easier to understand than the scissors case, where the speed the intersection travels varies as the scissors are closed. In the case of the guillotine, all you need to know is that the blade angle is shallower than 45°, and the conclusion about intersection velocity follows logically. With the scissors, it's less obvious precisely because the angle is changing continuously.
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Re: GRED Answer: Scissor vertex speed

Post by bystander » Sat Jun 26, 2010 4:27 pm

Chris Peterson wrote:Yes. But the speed that that the intersection travels is linearly related to the speed the blade moves, which I think is easier to understand than the scissors case, where the speed the intersection travels varies as the scissors are closed. In the case of the guillotine, all you need to know is that the blade angle is shallower than 45°, and the conclusion about intersection velocity follows logically. With the scissors, it's less obvious precisely because the angle is changing continuously.
Yes but the inverse tangential relationship means that the shallower the angle of the blade, the faster the vertex moves, respectively.

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Re: GRED Answer: Scissor vertex speed

Post by Henning Makholm » Sat Jun 26, 2010 4:37 pm

bystander wrote:
Chris Peterson wrote:The guillotine blade makes the causality issues simpler to grasp, and also gets rid of the tangent dependence (with scissors, the speed of the intersection point is not linearly related to the angular rate the scissors are closed; with a guillotine the speed of the intersection point is simply proportional to the speed the blade is dropped).
Wouldn't the speed still be inversely proportional to the tangent of the blade's angle? It's just that the angle is fixed, instead of diminishing as in the case of scissors.
With scissors, the tangent of the vertex angle is only one factor in the speed; the other is the transverse speed of the blades which varies with the distance from the pivot.

To be precise, assuming that we can get each blade to move at a constant angular speed ω, the vertex point will move at speed bω/(sinθ·tanθ) where b is the perpendicular distance from the pivot to either blade's edge and 2θ is the angle between the blades. The tips of the scissors cannot move faster than light, so the length of the scissors is at most c/ω and θ must be at least asin(bω/c), or we have run out of blade! Noting that tan(asin(x))~x for small x, the theoretical maximal vertex speed becomes c²/bω. (Which is greater than c because bω, being the speed of the point on the blade edge right beside the pivot, is less than c).
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