Make a ruler with a rigid material, one end of the ruler is in my hand, the other, in my brother’s hand. There is a door with a hole big enough for the ruler to go through. This all takes place in a vacuum.
We agree that if the ruler is parallel to the ground, it means 0. If it’s perpendicular to it, it means 1.
When either of us rotates the (rigid) ruler, a bit of information is transmitted, seemingly instantly.
Does it actually take time for the rotation to propagate from one end to the other?
If I am understanding the setup correctly, it is going to take you some miliseconds to rotate the ruler after you make the decision which data bit to communicate.
We have done this one a bunch of times although the most common scenario is some vast distance in space connected by a rod. In any case, the information is being transmitted by the speed of sound and not the speed of light which is an incredible difference as you already know. It doesn’t work as a cheat at all.
What gazpacho and Shagnasty said. The motion will not instantly propagate down the ruler; rather, the ruler will flex and then straighten out, with the deformation transmitting across it at the speed of sound in the material it is made up of.
Another similar case is the “superluminal scissors”. If you make scissors with long enough blades, and close them, mustn’t the tips of the blades be going faster than light speed?
This is an old idea. Its usually explained as a lighthouse. You get a lighthouse and your spin it at c. Now the lighthouse light creates an arc of light across a nearby mountain. Is that light arc violating the speed of light? No. The arc is not a physical thing, its a construct we put together in our minds. You cant encode information in this arc that could ever go faster than light. We’re not seeing a photon go faster than c, we are seeing the illusion of movement caused by the photons bouncing off the mountain and our monkey brains interpreting that as a photon path.
Just to clarify, that would be the speed of sound in the presumably stiff material of the ruler (3000-6000 m/s for most solid materials), which is much faster than air (~340 m/s at STP) but still way slower than the speed of light (3x10[sup]8[/sup] m/s). And even if you did have a perfectly inelastic material, you would still have the inertia of the material to contend with. Moving any mass “instantaneously” (i.e. moving two distant but causally connected points at simultaneously) would require an instantaneous change in momentum which would require infinite force. This may seem like an abstract point because in basic physics and dynamics texts it is assumed that forces are just big blue arrows and masses are all large pinkish inelastic and slightly transparent potatoes, but in reality when you apply a force to a body you get internal acoustic and shock effects
[Not sure why the last part of my post got cut off…grr]
…but in reality when you apply a force to a body you get internal acoustic and shock effects that account for this internal elasticity, even if the body itself appears to be rigid. There are no perfectly rigid, or even perfectly elastic bodies; every real material substance will flex, and that flexibility will result in some hysteresis losses.
Is this like those experiments where a signal is supposedly sent faster than light, but in fact it’s just the group velocity that exceeds c? As in the lighthouse example, nothing is actually traveling faster than c but the illusion is there. (Or is that the phase velocity? I fail at physics.)
Phase velocity, which is the rate of propagation of one particular component of the group, i.e. it describes the rate of change of the signal group. The group velocity cannot exceed c except under special circumstances in which any information within the group is destroyed (or at least unavailable to the recipient).
Even though in an anomalous medium the group velocity appears to travel ftl no information is actually being transmitted that fast.
The illusion of ftl occurs because all the information necessary to rephase the pulse as it exits the anamolous medium exists at the very front of the pulse and this info does not exceed c.
