Alright, I’m not saying you guys are wrong (I realize you’re right) but I don’t understand the argument here. Basically, you’re saying “Nothing can travel faster than light; therefore, the pole must bend”. Which is true if nothing can travel faster than light. But the reason given for this is that the pole bends, making the hammerhead travel slowly. But, the only reason we assume that the pole bends is because we assume that the hammerhead can’t pass C, and the only reason we assume that…
What am I missing here?
Nothing. The universe is set up so nothing can go faster than c. The impossibility of a rigid pole is one of the (many) things which ensure that (because if a rigid pole were possible, c would be higher than it is).
You’re kinda looking at it backwards. We can measure c. And c is what it is because of the way the universe is set up. If the universe were set up differently (such as with the existence of rigid poles, or one of a thousand other things) then we’d measure c and it would be a different value.
You’re trying to apply Newtonian physics in a relativistic world. Things don’t extrapolate up from the speeds we’re used to. There’s lots of experimental evidence that shows that things don’t work the way your common sense says they do. It’s part of the fundamental nature of the universe.
We don’t assume the pole bends, we see that it bends. Everything else is describing why it bends.
I’d put it differently.
A solid object looks solid to us, but really it’s a bunch of force fields. The speed at which those forces can be transmitted is limited to c, same as everything else.
Even gravity has to propogate (though this hasn’t been tested definitively yet)
I actually made that up myself, clearly I’ve missed my calling
(on first draft I did mention that it was my What if, but then I dropped the explanation)
We don’t need relativistic speeds before things bend, so we’re not just assuming there are no perfectly rigid substances, we’ve observed that things like hammers actually bend. And as has been pointed out, that’s what we expect from what we know of how substances are put together from atoms.
I like the way someone put it in one of these threads before:
(sorry, don’t remember the attribution)
Accelerating an object with mass toward the speed of light (actually, c) is a game of diminishing returns - because mass increases as you get faster, and that increases the amount of force you need to apply to accelerate the object some more.
This means that as the end of the rod gets faster, it gets harder to rotate it, so it bends. It can’t do anything but bend, because to get the tip up to light speed, you’d have to apply infinite torque.
No material, real or theoretical, could come anywhere close to being strong enough to withstand the forces required to get even halfway through this experiment - the centrifugal force would tear the rod apart, for example.
And you can’t get around it by positing some hypothetical indestructible material, because no such thing is possible, because at the microscopic level, it would have to violate causality - and it can’t have infinite tensile strength, because nothing in the universe that has a value (such as mass, width, elasticity, etc) can have that value set at infinity.
We know for a fact that there is no such thing as an unbendable object. What is your unbendable unbreakable oject made out of? Steel? Titanium? Diamond? Carbon nanotubes? Neutronium?
If your object is made out of substances that exist in this universe, it is not unbendable and not unbreakable.
And of course, with leverage you can swing a stick 1 centimeter on one end, and have the other end swing 1 meter. But you need the same amount of energy to move the high speed end 1 meter as you would if you were holding the high speed end. A lever lets you transform a small force over a large distance into a large force over a small distance, or the reverse where you transform a large force over a small distance to a small force over a large distance.
So when you move a hammer, it takes the same amount of energy to move the end of the hammer whether you move it via the handle/lever, or whether you move it by the head. You don’t get extra energy by using a lever. So when you try to swing a mile-long hammer by swinging the handle, it takes more energy than a human being can produce. And the faster you want your distant hammerhead to move, the more energy you have to provide. The energy doesn’t come for free. So you need greater and greater energy to move the hammerhead, and to move the hammerhead at c would require infinite energy.
Excellent approach and explanation. We don’t need to invoke fictional materials, just explain what a lever does. Nice one.
sigh…I hate coming here and seeing all these posts and realizing i’m just not as smart as I like to think I am… but I like to think I’m a bit smarter when I leave.
I’ve been thinking about this, and I’m pretty sure it’s not true. It seems to me that the speed of the point of the intersection couldn’t possibly move faster than the speed of sound in the material of the blades, and that will always be less than C. Of course, I’m not entirely sure how macroscopic motion propagates through materials. It may be possible to set something up so that the total time from the application of force to the blades to the intersection of the blades at point X is dependent on the speed of sound, but the apparent motion of the intersection over some distance is not.
In the case of inwardly curved blades, for example, the tip of the blades won’t move until the force applied to the opposite end propagates at the speed of sound. Once that happens and the tips of the blades meet, though, could the intersection travel back faster than the speed of sound? I don’t know. If it could, then I assume it could travel arbitrarily fast, even exceeding the speed of light, since as you say, it’s not an actual object, but I can’t visualize it.
ETA: The more I think about the curved blade example, the less sure I am that you’re wrong. I just don’t know.
But the whole point is that the scissor point is not a physical object therefore is not bound by the speed of light, much less the speed of sound in the material.
I find it helpful to think in equations. Like imagine a Cartesian x-y plane, where the units of the axes are in metres. Imagine the line given by y = 0.0000000000000000000000001 * x, which is an almost horizontal line. This line goes through the origin, so the x intercept of the line is zero.
Now imagine lowering that line by one centimetre. The equation of the moved line is now y = 0.0000000000000000000000001 * x - 0.01. The x-intercept of this line is now 100000000000000000000000. Now despite the fact that we’ve only moved the line down by 1cm, we’ve moved the x-intercept by quite a lot.
In fact, you can show that as you move the line up and down, the x-intercept moves uniformly at 10000000000000000000000000 faster than the up and down motion. If we move that line down 1cm over the space of 1 minute, the x-intercept has still moved faster than the speed of light.
Now if we realized the x-axis and our line as physical objects, we can move one up or down past the other with ease, and we’re not moving them so fast that we can no longer think of them as rigid, but we’re still getting the intersection moving faster than the speed of light.
Only if the force is applied evenly along it’s entire length. The scissors example is different, the force is applied at a point and takes time to propagate along the length of the object (which can’t be truly rigid…)
But no force need be applied during the observation period in my example (if you make as-rigid-as-possible physical representations of the two lines). I can hold one line (the x-axis, say) still, and set up the other almost-parallel line on rails a dozen times the length of the segments away. If I push the moving line towards the non-moving one, the impulse from my push will have propagated throughout the line long before to gets to the non-moving one and the moving line will be moving as one object as it passes over the non-moving line.
Yes, but that wouldn’t be scissors in the ordinary sense. Of course arguably any pair of scissors designed specially to model the FTL motion of non-physical conceptual “objects” isn’t going to be scissors in the ordinary sense anyway. But my objections were specifically to a pair of scissors operating as a set of objects attached at a fixed pivot with force applied to a pair levers extending from the pivot in the opposite direction. Sorry if I wasn’t clear about that.
I’m still not sure though how the scissors I’m talking about move once the initial force has propagated through the entire length of the blade. It may be a similar thing to what you’re describing, in that once the scissors are in motion, no force has to propagate, so there is no limit to consider. I’m not sure that the angle of closure could ever travel faster than the force propagates, but I think maybe the scissors could be designed so that that wouldn’t matter. I’m thinking of a design such that the handles extend on both sides of the pivot, so that when the scissors are open, the blades don’t intersect at all and when they are closed there is a gap between the pivot and the blades. (Think of a pair of pliers with rounded jaws that don’t meet along their entire length.)
I hope someone better at physics (or at least better at visualizing thought experiments) weighs in on this.
I don’t see the problem here at all. It is exactly as leahcim explained.
If you’d like a better visualization, compare it to a shadow: Imagine that I am near the sun, casting a shadow upon Neptune. It takes 4.1 hours for the shadow to reach Neptune. Then, I move at some ridiculously slow sub-light speed, and just a few minutes later, I’m casting a shadow upon Pluto. The shadow will appear on Pluto about 5.4 hours later. Now, if Neptune and Pluto are at opposite ends of the solar system, then they are 9.5 light-hours away, yet it took less than two hours for the shadow to move from one to another.
The trick is that the shadow doesn’t really exist. So it can move at any speed, even faster than light.
Alternatively, try this simplified version of what leahcim wrote with far too many decimal points for my taste:
Imagine a triangle made of whatever material you like. It is twenty inches wide, and only one inch tall. You can make it yourself from paper. The base is running along the edge of a table. Now, suppose you pull the triangle down at whatever speed you like, past the edge of the table.
Let’s say it took you one second from the time that the edge of the triangle was against the edge of the table, until the triangle was totally off the table. It should be easy to see that the diagonal line (which is about 10 inches long) also took one second to get off the table. Here’s the good part: The point at which the diagonal touched the edge of the table traveled ten inches in that same second, thus moving at ten inches per second. This corresponds EXACTLY to the point where the blades of the scissors cross. And the moving point goes at a speed ten times that of the triangle.
Now, Imagine that the triangle is not moving at one inch per second. Rather it is moving at one fifth the speed of light, at which relativistic effects (like time dilation and length shortening) are pretty minor. The crossing point moves ten times as fast as the whole triangle, which will now be double the speed of light.
QED. No bending, no twisting, no infinite amounts of energy required.
Keeve, I don’t know how to explain it any more clearly. The problem is that unlike a beam of light, the blade of the scissors is not a rigid line segment and will curve in response to the force applied to the handle. Imagine instead of scissors made of metal you have a pair of scissors made of licorice. Closing the handles won’t make the blades snap shut; instead it will bend the licorice blades and cause a wave to travel down the length of the blades. the part of the blades closest to the handles will move first before the tips move at all. Eventually the wave of motion will travel down the length of the blades moving them together like a pair of whips.
This is how real scissors made of metal move, but we don’t notice it because the wave travels down the length of the metal blade much, much faster than it would through licorice. It will still be much slower than the speed of light, though. If the scissors are constructed normally, I don’t think the point of intersection can travel faster than that wave. The wave can travel much faster than the blades, but it can’t exceed the speed of sound in the material of the blades.
The intersection of two straight lines can be made to move at any arbitrary speed. The intersection of two physical objects can’t. If you try to close the scissors fast enough to move the intersection point faster than the speed of sound in the blades, the blades will just flex (or shatter). The speed of light has nothing to do with it, but the speed of sound will always be much slower, so you can never get the wave of motion to travel along the scissors anywhere close to C.
If you had a perfectly rigid pair of scissors that never flexed or shattered, then of course you could do it, because in a perfectly rigid material sound would travel infinitely fast. Since information can’t travel faster than C, we know that a perfectly rigid material is impossible.
In regards to your triangle example, if you start the triangle accelerating above the surface of the table so that it is moving at a uniform speed when it crosses the edge, then yes, that would work. (Leahcim already suggested something like that.) But you can’t do that with scissors. One end of the blade always starts moving before the other end does.
The scissors can easily be contrived in such a way that the force propagates along the blades, setting them in motion, then they start to intersect.
Consider a very small scale thought experiment:
It’s possible to construct a pair of scissors where the point of intersection moves away from the handles as they are closed. These are normal scissors.
It’s possible to construct a pair of scissors with hooked blades that result in the intersection moving toward the handles as they close (I’m taking about normal handheld-sized scissors here - diagram later if it’s not clear what I mean)
Therefore, it must be possible to construct a third pair of scissors that are intermediate between the two cases above, where the blades close simultaneously all along, all at once.
Therefore, it must be possible to construct any fourth pair of scissors where the intersection moves at arbitrary speed, by very slightly tweaking case 3.