OK, first of all, I said a half of a lightyear, because I was assuming that half of the length of the scissors was handle, so the vertex would start off halfway between here and there. And yes, half a lightyear in a second is very much faster than light.
If we had the (impossible) perfectly rigid blades, then you could transmit information this way: I could, for instance, use “scissors open” to represent a 1, and “scissors closed” to represent a zero. If they’re perfectly rigid, then the handle end opens and closes at the same time as the blades, so this would be instantaneous transmission of information. Again, though, this is impossible.
The problems with FTL come about whenever you’re transmitting information faster than light. In principle, you’re even allowed to move matter around FTL, but it’s hard to think of a way to move matter without sending information with it. There’s also some “things” which can move faster than light (such as shadows), but which do so in a way that neither mass nor information is moving any faster than c.
Issac Asimov talks about this in one of his books on physics. He also uses the example of how fast the ‘spot’ that a police or ambulance rotating beacon makes is travelling. His point is that, as others have said, it is all completely meaningless because neither ‘thing’ has any mass. They’re not real objects.
In electromagnetic fields classes that EE students have to take, the subject of “phase velocity” is brought up, and the scissors question is the same idea.
Imagine two straight-line waves approaching each other at an angle (not exactly head-on). You can look at the location of the peak height where the waves intersect, and watch it as the peak changes position. How fast does it travel? Faster than the waves themselves. The students in these classes will be shown how to find equations that describe the position of the crest, and then comes the question: the crest is always travelling faster than light - how can this be so?
The answer is that the crest is not really anything but an idea that we imagine, so we can make it move at whatever rate we want. There’s nothing real there, just like there’s not anything real moving at the point where scissors intersect.
But I’ll take a “stab” at finding how fast that might go. The scissors I just grabbed have blades about 100mm long, and at the point where the tips are almost together, the straight edges are pointing back to points around the pivot, maybe 5mm each side of it. So the shallowest angle they’re closing at is about arcsin(10/100), or 5.7 degrees.
The velocity of the intersection would be faster than that of the blade tip by a factor of 1/sin(5.7/2), or around 20. So how fast are the tips going? If I close them from 90 degrees in around 50ms, which I think is somewhat on the fast side of realistic, then the tips would be travelling about 3 m/s, so the intersecting point would be travelling at around 60 m/s, or around 200 km/hr (130 miles per hour). Not quite light speed.
the contact between the blades is not a physical thing, so yes, with a perfectly rigid material it could go faster than the SOL.
I can do you one better. You can make a contact point go INFINTELY fast in your own house. Right now.
Take a ruler, or any straight, flat object (pencil will work). Stand it up on a flat surface at 90 degrees, pointing straight up at the ceiling. Then, keeping the end (i.e. the pencil eraser) touching the flat surface, let the pencil fall down…or lay it down flat, whatever. The contact point from the eraser will move infintely fast towards the tip of the pencil at the moment it lays down flat on the surface.
We have mistakenly assumed that the scissors do in fact close when you close the handle. But, in fact, according to Special Relativity, this is not at all what happens. What does happen is that the blades of the scissors flex. No matter what material you use for the scissors, SR sets a theoretical upper limit to the rigidity of the material. In short, when you close the scissors, they bend.
The point at which the blades bend propagates down the blade at some speed less than the speed of light. On the near side of this point, the scissors are closed. On the far side of this point, the scissors remain open. You have, in fact, sent a kind of wave down the scissors, carrying the information that the scissors have been closed. But this wave does not travel faster than the speed of light. It will take at least one year for the tips of the blades, at the far end of the scissors, to feel any force whatsoever, and, ultimately, to come together to completely close the scissors.
As a practical matter, this theoretical upper limit to the rigidity of the metal in the scissors is far higher than the rigidity of any real material, so it would, in practice, take much much longer to close a real pair of metal scissors with blades as long as these.
One can analyze this problem microscopically as well. The electromagnetic force which binds the atoms of the scissors together propagates at the speeds of light. So if you displace some set of atoms in the scissor (such as the entire handles), the force will
not propagate down the scissor instantaneously, This means that a scissor this big must cease to act as a rigid body. You can move parts of it without other parts moving at the same time. It takes some finite time for the changing forces on the scissor to
propagate from atom to atom, letting the far tip of the blades “know” that the scissors have been closed.
Here’s my take. This works out well on a two dimensional plain. It wouldn’t actually work with a physical pair of scissors because you could never get them to actually close. The important thing here is that you have a single point at the vertex of two lines. This point has no dimensions in itself, it’s just infinitely close to the place where the lines intersect but doesn’t actually touch them. This means that the smallest motion of bringing the “blades” together takes up this point. The point is infinitely small. In a finite amount of time you need to move 1 divided by infinity. Actually you guys should check out the “slice of time” thread…it relates to this a lot. So in a two dimensional, euclidian plain this theory works to the extent that the point between the vertex has to move at an infinite speed to escape the closing of the blades. In reality though it doesn’t work because the fastest it could go would be a planck speed and the scissors could only move a planck distance. In a “slice of time” it was argued that this is the speed of light. Of course none of this really applies because the blades of scissors don’t meet anyway…there’s a very small gap between them. This only applies with a wide variety of hypothetical scissors.
Note: The things I say generally don’t make sense. Ignore me and maybe I’ll go away.
A similar thing, but not quite the same (a substance almost, but not quite, entirely unlike tea): I read somewhere or other in some layman-oriented cosmology book that pretty much the point when a neutron star, squeezed under its own mass, will collapse even further to form a black hole is the point at which the neutron packing would, if it were to become any more dense, cause the speed of “sound” within the medium to propagate faster than c. The universe says “no you won’t,” and voop, a black hole. “Voop”, of course, being the sound of a superluminal sonic boom.
Or rather, not necessarily *the[/i[ point it would do so, but definitely the upper bound of when it would.
That, Drastic, is an interesting question. I seem to recall it being one third the speed of light, but then, I’m not a neutron-star astrophysicist. I’ll ask around.
Neutron degeneracy pressure enables the neutron star to withstand the force of gravity. And since speed of sound is proportional to square of pressure, and sound speed must be less than speed of light, there has to be an upper mass limit, thought to be 2-3MO.
For objects more massive than this, gravity wins and star becomes a black hole
I do have a fun fact of my own, which is every bit as amazing as the scissors “fact”: If I stand outside and point my finger at a spot millions of miles in space, when I move my arm a little, the spot I’m pointing at moves faster than the speed of light!
If we have two rods parallel to each other and bring them together, the point of intersection move infinitely fast. If we rotate the moving rod by a small angle, the points of intersection are no longer simultaneous, but rather the point moves faster than light. This is not a material object moving faster than light, so it’s not prohibited. However, this cannot be used to transmit information from one point to another along the rod. In order to transmit information you have to have a source and a target. The points along the rod are all targets of the information that the gap has closed. So we haven’t transmitted information faster than light. For the point of intersection to move faster than light, the source of the information must be outside the rod. If you are on the rod and try to pull them together, then you run into the problem that Chronos pointed out; that there are no rigid rods; in this case the point of contact moves no faster than the speed of sound in the rod. The point of intersection can move faster than light, but the source of the decision to close the gap cannot be on the rod.
I thought not being able to transmit information FTL would imply you cannot move matter FTL.
Drastic
That doesn’t sound right. If I recall correctly, you can make a black hole out of any material. The critical mass increases as the radius increases. So, you can create a black hole out of anything, if you just have enough of it. I don’t see how the speed of sound in neutron star material would be special.
Virtually yours,
DrMatrix - That’s not a muon-neutrino in my pocket; I’ve got a hadron.
To my understanding, neutron stars are the material they are because the density of the formal material crushes the whole thing into only neutrons. They’ve got a lot of material because the star was massive enough in the first place that its own mass provided the necessary pressure to do that once it could no longer sustain enough outward force from fusion. So if you took, say, the Earth and applied equal pressure from all around outside using a Ultra Nega-gravity Pressor Beam Sphere (patent pending), eventually it’d form a black hole once below a certain radius. (Saw a table of that in a childhood book, “The Science in Science Fiction” ages ago–the event horizon would be something like a couple feet? Inches? Less? Don’t remember.)
The less the radius, the greater the density of the material. At a certain point of density, the earth would turn to all neutrons, in effect being sort of a neutron star itself–though I guess it’d probably be more of a neutron marble. The greater the density, the greater the speed of sound within the medium.
Or is it (theoretically) possible to take X amount of mass and have a black hole come of it, without that same mass passing through a degenerate-neutron state?
There is no critical density. For any density, there is a critical radius. The lower the density, the greater the critical radius. If you gather enough styrofoam it will collapse into a black hole.
FWIW, I’ve womdered about the OP’s question for years also! I love the SDMB!!
But you have all missed a very basic and critical point: even if you’re running at the speed of light, don’t run with scissors! You’ll put someone’s eye out!
