Is it possible for information (like 1 and 0s) to be transmitted faster than light?
For instance, take a rigid pole of several AU in length. Now say you have a person on each end, and one of them starts pulling and pushing on his/her end.
The person on the opposite end should receive the pushes and pulls instantaneously as no particle is making the full journey.
Would this actually work?
The answer is no. The pole would bend/wobble and the effect at the other end would still be delayed.
The reason is that the force which binds the atoms of the pole together - the Electro-Magnetic force - needs to be transmitted from one end of the pole to the other. The transmitter of the EM-force is light, and thus the signal cannot travel faster than the speed of light; instead the pole will bend, because the close end will have moved, and the far end will not yet have received intelligence of the move.
EDIT: A simpler reason.
In order to move the whole pole, you need to move every atom of the pole.
You might like to think of atoms as next door neighbours If one of them decides to move, he sends out a messenger to all his closest neighbours telling them he is moving. Then they all decide to move as well, so they each send out messengers to to their closest neighbours to let them know they are moving; and so it continues, until the message to move has travelled all the way to the end. No atom will move until he has received the message to do so, and the message won't travel any faster than all the messengers can run; and the messengers can't run faster than the speed of light.
/B2S
The information about the pushes will be received on the other end with the speed of sound in the substance of the pole. For any real material it is much slower than the speed of light (for a steel rod it would be about 5000 m/s).
No.
In relativity you cannot consider extended objects to be infinitely "stiff" - they must bend and stretch, as real objects do. When you move one end of the steel rod, it makes part of it bend and stretch which exerts a force on the next section which makes that move and which makes a new part bend and stretch and so on and so on until you reach Alpha Centauri. This moves along at some speed which is characteristic for the metal which is fast enough that we don't really notice in day to day life. All relativity tells us is that that characteristic speed is less than the speed of light - it turns out for real metal its much less than the speed of light.
The signal will propagate at the speed of sound in steel. I happen to know the speed of sound in aluminum, because my students measure it in lab; it's about 5000 m/s. This is many orders of magnitude less than the speed of light.
Here is an interesting site about this idea and similar ideas: http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#3
Essentially the problem with this idea is there are no such thing as perfectly rigid bodies. So as you push, it sends a little compression wave through the material, which travels at the speed of sound in the material, as sound is just a type of propagating compression.
A simple explanation why the speed of sound can never be faster than the speed of light:
Consider two atoms $A$ and $B$. Give the nucleus of $A$ a slight push. As we know, this push will carry over to $B$, but why? It's due to their electrostatic repulsion. So for $B$ to even react, you first need at least an electromagnetic wave/photon travel from $A$ to $B$. This can of course not get there faster than the speed of light. The nucleus of $A$ itself can obviously not be faster, either, so even with brute force it's not possible to get a sonic speed $\,>\!c$.
Is it possible for information (like 1 and 0s) tO be transmitted in anyway faster than light.
No.
Born2Smile said the same thing (which I +1'd) but I figured it's worth repeating for emphasis. It'd be a violation of causality. For some more details on why this is not allowed, in addition to Born2Smile's answer, see What are some scenarios where FTL information transfer would violate causality?.
Relativity says that different inertial reference frames will have different time measurements, but causality is respected in all reference frames. That is, unrelated events A and B may appear to some observers to happen simultaneously, others may see A before B, or B before A. But if A causes B, A will be seen to precede B by all observers (though different observers may disagree on the amount of time between A and B).
If any information traveled faster than the speed of light, there would be an inertial reference frame from which it would appear that the signal got to its destination before it left its source. So far, there is no evidence that the universe is non-causal. (Another reason to strongly doubt faster-than-light neutrino speeds.)
For instance, take a rigid pole of several AU in length. [...] The person on the opposite end should receive the pushes and pulls instantaneously as no particle is making the full journey.
As other answers have pointed out, you can't have perfect rigidity, and the signal would propagate at the speed of sound in the material.
If tap a steel rod with a small hammer at one end, it doesn't instantaneously budge at the other end (though it may look that way to the naked eye). Instead, tapping merely compresses the material at one side, and the compressed area stretches out at the speed of sound in the material until the other end does move, and eventually the rod returns to a relaxed state. In the course of all this the rod undergoes mechanical oscillations and may produce audible sound as a result.
You can think of "rigid" materials as having very stiff springs between atoms. The more rigid the material, the stiffer the springs. But motion must still propagate through the springs at the speed of sound in the material, and always below the speed of light. The reason it must always be below the speed of light is that the inter-atomic forces are electrostatic forces, which themselves cannot propagate faster than the speed of light.
What would happen if you were to tap a steel rod with such force that you would impart a velocity larger than the speed of sound in the material? The answer is it would undergo plastic deformation. Rigidity breaks down much sooner than relativity.
When you said "actually" as in "Would this actually work?" the answer is no since the rigidity assumption of the pole itself is just an approximation and each approximation fails in some critical limits. Also the several-AU-long pole is another non-real thing at least as far as I can say. But let consider your question as a mind consuming game, then it's an interesting question. Here is my two-cent on it:
Pushing and pulling in the first place are act of applying a force, so we are more probably in the Dynamics playground not the Statics yard. The net force will cause motion that you can model it using either the Classic physics or relativity, both based on experiments, never axiomatic or fully rational. However, depending how the pole is considered in the space (if there is any friction or else) and at the two ends (the supporting reactions) the free diagram might change such that we would have also other forces in the play, then if the exerted push/pull force is resisted, even locally, we will enter the yard of Statics and the Strength of material where we can talk about how the information travels inside the pole, through a compression or rarefaction wave.
If the surrounding forces and support reactions stop the pole from moving, then if the applied forces are small in amplitude the waves will travel at the speed of sound. If you artificially assume the pole is fully rigid (fully incompressible) then you have already assumed the wave speed to be infinitely large, far greater than speed of the light. But as already told you the rigidity of no object in the real world is complete, so no infinity speed for information wave and no violation of the relativity theory necessarily. As others have addressed this issue in other answers, the speed information will have through the pole will be less than the speed of light, indeed.
However, what if the pole is free to move? Right after you exert the force the pole will sense an intrinsic resistance keeping it from moving, its own inertia. The inertial force (the D'Alambert force) might itself transform motion into compression so that again we will have the story stated above. Note that such a long pole would be a lot inert, that is, even if is totally free in the space to move you will still need an infinitely large force by applying which the pole can achieve a finite acceleration. So again it is not any realistic as you cannot set such a big pole in any observable motion. The only possibility is when you have a very long pole of infinitesimally small density, then yes, if it is RIGID-ENOUGH I think you should be able to break the record of information transport speed. But I don't know how you may achieve all these three together!
Is it possible for information (like 1 and 0s) to be transmitted faster than light?
No.
This answer has been given already. I'd like to point out, however, that this is utterly self-evident:
It is not possible for signals to be transmitted faster than any signals being transmitted at all.
(In the context of relativistic kinematics "light" plainly means any signal at all having been exchanged between systems constituted of electro-magnetic (or even electro-weak) charges, such as atoms or humans or any sort of observable matter that may be imagined in thought-experiments.)
It is only on this basis that geometric relations are being determined; such as (referring to the example given in the question) whether two people are separated from each other, or whether they meet; or whether two (separated) ends moved rigidly (in relation to each other), or one lagging behind another.
Concretely, the flaw of your example is that two participants who communicate instantaneously are called "meeting" each other; their distance from each other is evaluated as zero. And otherwise, considering two participants, A and B, who always find being separated from each other, and at rest to each other, they may well find "two ends of a pole" such that A pushing one end was simultaneous to B ejecting the other end (or likewise such that B pushing one end was simultaneous to A ejecting the other end); but only if those occurences are not recognized/considered as exchanges of signals.
No, even if no particle does the entire trip, the pole has elastic properties, i.e., you push some molecules, and those push the next ones, and so on, until the information that travels with the pushes reaches the other side. You're basically sending a density wave through the pole. This video of a falling slinky in slow motion shows that.
No, special relativity totally forbids information from travelling faster than light. Suppose you have a pole made of the most rigid substance on Earth, diamond. If you push the end, it will just buckel under compression. Longitudinal waves in a solid have a different speed than transeverse waves. If you pull the end, you will send a longitudinal wave through it and if you twist the end, you will send a transverse wave through it. I read that the speed of sound in diamond is 12/km per second but I don't which type of wave that was for but I'm sure neither of them travel anywhere near the speed of light. There might actually be a substance whose bulk modulus is larger than its density times c^2 so the wave equation would predict that a longitudinal wave in it will travel faster than light, which is what a neutron star is made of. The reason I'm wondering that is because I read that some neutron stars have a photon sphere. Obviously, even if that is the case, if you bombard its surface, the shockwave in it will not travel faster than light because then it would be travelling backwards in time in another frame of reference and therefore it doesn't obey the wave equation. It does not however violate any laws for it to obey the wave equation in certain situations and have a sinusodial wave travel through it faster than light. The movement of each part would be determined only by the part right beside it and not by a far away part.
The answer is No.
The keyword is that the Coulomb force (which hasn't been spelled out), the main forces binding the atoms together in the lattice of solid-state or condensed matter for the long pole, supposed to have retarded time to transmit the force/information between the atoms.
Again, Coulomb force, is part of Electromagnetic (E&M) force, which has been emphasized already by others. All E&M forces somehow become consistent between different reference frames only if we take into account the constant speed of light, and the retardation effect of E&M potential/force.
You can easily read the retarded electromagnetic potential$ (\varphi,\mathbf A )$/force here:
$$\mathrm\varphi (\mathbf r , t) = \frac{1}{4\pi\epsilon_0}\int \frac{\rho (\mathbf r' , t_r)}{|\mathbf r - \mathbf r'|}\, \mathrm{d}^3\mathbf r'$$
$$\mathbf A (\mathbf r , t) = \frac{\mu_0}{4\pi}\int \frac{\mathbf J (\mathbf r' , t_r)}{|\mathbf r - \mathbf r'|}\, \mathrm{d}^3\mathbf r'\,.$$
where 'r' is a position vector in space, 't' is time,
The retarded time is: $$t_r = t-\frac{|\mathbf r - \mathbf r'|}{c}$$
There is also gravity, and strong-force binding the nucleus; but they are in the much weaker energy scale comparing to E&M concerning binding atoms on the lattice. Also, all forces and all massless particle (photon/gluons/gravitons) may have the same speed of propagation, the speed of light.
No, a simple explanation with no math is that any force applied at either end will send either a compression or expansion wave through the object no faster than the material's speed of sound which is always much slower than c.
Your solution to distant instant communication is indeed appealing, but it has its shortcomings. The pole vibrates and thus produces sound waves within the pole; sound of course traverses at a much lesser velocity compared to light, thus what ever force is exerted by person A,it will produce sound waves which will reach B in ages (considering the distance), consequently information will NOT be transmitted instantly.
