# Transmitting Information Faster than C

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This is not true' date=' except in the case of quantum teleportation.

So in other words, it's true.

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So, you claim that it moves through the rod at the speed of light regardless of the material, huh? That sounds like a claim that we know all there is to know about any and all materials....

The speed cannot exceed c. It can go slower.

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The speed cannot exceed c. It can go slower.

The only thing slowing it down though is compressibility even though materials like diamond and osmium are regarded as incompressible. To say it cannot be faster is to say that these materials have no compressible limit such that no force applied to one end of their structure could appear at the other end simultaneously. I'm leery that this claim could actually be proven.

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doG: the materials are defined as incompressible because for most conditions we can create outside the pressures at the detonation of a nuclear device, they are practically incompressible.

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Back to the stick example...

What if we had the system set up so that the long rod was held in a hinge set up by a long rod of great strength.

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When we drop the rod, assuming the mass increases infinitely, wouldn't the rod exceed the speed of light? In this case, the infinitely increasing mass aids in the rotation. Am I missing something?

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Ignoring the assumption of the mass increasing (you need to define which mass you are talking about), the rod would bend.

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Ignoring the assumption of the mass increasing (you need to define which mass you are talking about), the rod would bend.

Say the mass is a single electron. If you push on one side of the electron then how long does it take the force to appear at the other side? I'd say instantaneously unless the electron itself is compressible...

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Say the mass is a single electron. If you push on one side of the electron then how long does it take the force to appear at the other side? I'd say instantaneously unless the electron itself is compressible...

however long it takes for light to cross the electron. the force is transmitted by particles that travel at the speed of light, hence, the force travels at the speed of light.

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however long it takes for light to cross the electron. the force is transmitted by particles that travel at the speed of light, hence, the force travels at the speed of light.

OK, so change the mass to the smallest particle. Now what carries the force from one side of that particle to the other and at what speed if the particle is at maximum compression? In short, what is the limit of the equation we are evaluating? I believe it is higher than C.

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OK, so change the mass to the smallest particle. Now what carries the force from one side of that particle to the other and at what speed if the particle is at maximum compression? In short, what is the limit of the equation we are evaluating? I believe it is higher than C.

The relevant factor is how fast can one charge exert a force on another. "One side of a particle to the other" has very little meaning in QM.

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there are a few arguments going around as to whether the effect of gravity travels instantly or at C

the problem is, no one can "create" gravity in substantial enough quantities to measure the speed of it's transmission experimentally.

also, are tachyons likely to be real? apparantly they have a lower speed limit of C and possibly no upper limit.

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there are a few arguments going around as to whether the effect of gravity travels instantly or at C

the problem is' date=' no one can "create" gravity in substantial enough quantities to measure the speed of it's transmission experimentally.[/quote']

I've always wondered myself if there is a "speed of gravity" and just how fast is it if there is. Then again I continue to run into people that insist that the speed of light is some natural speed limit even though they cannot actually prove their claim.

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I've always wondered myself if there is a "speed of gravity" and just how fast is it if there is.

I´ve always wondered what people mean when they are talking about "speed of gravity".

Then again I continue to run into people that insist that the speed of light is some natural speed limit even though they cannot actually prove their claim.

That might depend on what you accept as a proof. I have a flask of water in my hand. If I open my hand, it will fall down and hit the floor afterwards. If the bottle falls down slower than c, the order of the events "I open my hand" and "flask hits the floor" will always be the same. That is very neat considering that relativity -which is where the speedlimit of c comes from- demands that anyone can watch me dropping the bottle and that none of them is more or less correct in what he sees. If the bottle fell down with >c, the order of dropping and hitting the floor would not be unique anymore. Some people would see me dropping the bottle before it hits the floor, some others would see the bottle hit the floor before I even dropped it. That arises a whole lot of problems/questions: How can the bottle hit the floor when I am still holding it in my hand? Who is correct in what he sees? Why do I throw water bottles around at all?

In short: The best reason for a speed limit of c that I can think of is that velocities above c cause a real lot of (still unresolved) headaches.

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there are a few arguments going around as to whether the effect of gravity travels instantly or at C

the problem is' date=' no one can "create" gravity in substantial enough quantities to measure the speed of it's transmission experimentally.

also, are tachyons likely to be real? apparantly they have a lower speed limit of C and possibly no upper limit.[/quote']

Yes there are arguments, but the validity of them varies widely. The ones I've seen that insist on instantaneous gravity have serious flaws.

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I've always wondered myself if there is a "speed of gravity" and just how fast is it if there is. Then again I continue to run into people that insist that the speed of light is some natural speed limit even though they cannot actually prove their claim.

To add to Atheist's example: I accelerate an electron, but even giving it more and more energy, the speed it attains follows the special relativity formula, asymptotic to c. More confidence that relativity is correct, and that c is a limiting speed.

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I´ve always wondered what people mean when they are talking about "speed of gravity".

Whether there are retardation effects as in electromagnetic interactions. There aren't but AFAIK it's because gravity is a different type of interaction, so not having behavior analogous to EM interactions doesn't mean what some people claim it does.

e.g. if the sun were to suddenly disappear, how fast would we notice it, from the loss of light and loss of gravity? Where does the sun appear to be, from a standpoint of the direction of the light travel and the direction of gravity's pull? They apparently differ.

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That contact point moves up and down the blades when you open or close the scissors, and it moves much much faster than the blades themselves because it has to travel along the whole length of the blades in the time it takes to close or open the scissors. A pair of 300 km long scissors, that are only opened 1 m, the scissor blades move 1 m to close, but the contact point moves 300 km in the same time. If you closed those blades very very fast, and also made the blades much much longer, then the contact point can travel along the length of the blades faster than C without any problem.

Hi IMM, yes that is right. The contact point can travel along the length of the blades faster than C without any problem.

I believe swansont answered the question in post #19

The two blades need not be connected. As such' date=' there is no causal relationship between the position of two, so there is no limit to how fast the contact point (or apparent contact point) can move.

It's similar to a light beam from a source rotating at [math']\omega[/math]. The speed of the projected beam is $\omega r$, so if you are far enough away, this can exceed c. But there is no information contained there, and the photons do not have a causal relationship.

It is always possible for two (or a series of) unrelated events to be temporally separated by less than t = d/c

I believe he is saying that the contact point can move faster than c (as long as the scissors are closing steadily).

But if you try to send morse code by abruptly opening or closing in a jerky unpredictable fashion then the long blades will behave a bit like rubber. the information that you suddenly changed from closing to opening will not be able to ripple down the blade any faster than light. It is information that cannot travel at over the speedlimit.

that was a nice question, neat illustrations! I don't know if you decided your question was answered or not, or if you just havent been back. I expect everybody would like it if you would push with more questions (if you have further puzzlement about anything.)

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e.g. if the sun were to suddenly disappear, how fast would we notice it, from the loss of light and loss of gravity?

I would suppose instantly ... just like you´d instantly realize the change of an electric field if the sun had charge.

(I´m a bit Martin-inspired today so I try to break out of the "give the same answer for the x-th time" routine and rather give a controversial statement)

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To add to Atheist's example: I accelerate an electron, but even giving it more and more energy, the speed it attains follows the special relativity formula, asymptotic to c. More confidence that relativity is correct, and that c is a limiting speed.

But the force of gravity is not conveyed by electrons and we don't know what, if anything, it is conveyed by. Since we know so little about it I don't think we cannot even speculate that the speed of gravity, if it exists, is limited to the speed of light.

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I would suppose instantly

what happened to the 8 minutes?

 my question sounds naive, given what swansont said in post #41

however I must confess that is how I picture it: the sun would cease to exist and, by some unphysical means, its effect on the gravitational field would be abruptly turned off. I picture a WAVE of change in the gravitational field propagating outwards at speed c.

after 8 minutes, just as it becomes dark, the earth would exit from its orbit and begin traveling in an approximately straight line

I would be very happy to learn that this picture is wrong, since it would surprise me. If possible, please explain more!

 Is there a problem with assuming that the sun ceases to exist in an unphysical way? We cannot simply assume that it is converted to radiant energy which then disperses, because that would be a different problem gravitationally (there would be be the gravity associated with the radiant energy, among other inconvenient side effects )

How about we picture a PHYSICAL process that abruptly removes the sun from the center of the solar system: a neutron star traveling at near the speed of light suddenly looms out of the darkness and collides with the sun, sending it careening off like a billiard ball. Then one asks, how soon would the effect be noticed? Shucks. The incoming neutron star has gravity which perturbs things.

Atheist and swansont I would appreciate any clarification. I keep thinking that a change in the gravitational field can only propagate at speed c. It is like a groove in my head.

(Atheist, I find you inspiring too )

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what happened to the 8 minutes?

They are having a poker game with the continuity equation, I´d suppose. At least I think their absence is related to another.

EDIT: Or let me ask the other way round: Except for the heuristic "exchange particle is photon which travels at lightspeed => it takes 8 minutes to note a change"-argument, is there a way to do an explicit calculation that gives me the 8 mins? I get the instant change directly from electrostatics which seems valid due to the charge not moving.

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But the force of gravity is not conveyed by electrons and we don't know what, if anything, it is conveyed by. Since we know so little about it I don't think we cannot even speculate that the speed of gravity, if it exists, is limited to the speed of light.

But you don't have to speculate. This is science, and there are measurements we can make. The orbital decay of binary pulsars has been observed, and is consistent with gravity travelling at c, as well as other experiments.

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Martin- that's how I picture it, too, though this is certainly outside my area, and this is informed opinion, at best: Whatever is bending space is doing it continually, as if the interaction was with space as an intermediary. Hence the phrase "mass tells space how to bend, and space tells mass how to move." So there is no retardation for gravity, as the space is already bent, and the gravity vector is related to the gradient of the curvature. If the mass were suddenly "turned off" the unbending/flattening would propagate at c. But that's the item missing from the instantaneous gravity folks, who think that gravity should point in the direction of where the sun was 8 minutes ago, and why gravity and EM forces point in slightly different directions.

They are having a poker game with the continuity equation' date=' I´d suppose. At least I think their absence is related to another.

EDIT: Or let me ask the other way round: Except for the heuristic "exchange particle is photon which travels at lightspeed => it takes 8 minutes to note a change"-argument, is there a way to do an explicit calculation that gives me the 8 mins? I get the instant change directly from electrostatics which seems valid due to the charge not moving.[/quote']

If a charge a distance d away were to suddenly cease to exist, why wouldn't it take you d/c to find out? If you start the charge oscillating, you don't see a magnetic field instantly, you have to wait d/c for it to arrive.

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I think I'm in equilibrium now. thanks. so i will just listen

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that is how I picture it: the sun would cease to exist and' date=' by some unphysical means, its effect on the gravitational field would be abruptly turned off. I picture a WAVE of change in the gravitational field propagating outwards at speed c.

after 8 minutes, just as it becomes dark, the earth would exit from its orbit and begin traveling in an approximately straight line

I would be very happy to learn that this picture is wrong, since it would surprise me. If possible, please explain more! [/quote']

I absolutely don´t know what happens. And other than for fooling around a bit it doesn´t interest me as conservation of charge/energy forbids the scenario anyways (although investigating scenarios in which they aren´t conserved might be interesting in the sense of understanding why they have to be conserved).

The basic idea of why the change would be instantaneous revisited (sticking to EM since that´s easier but to some extend similar):

- There is one moment T or even a sufficiently small time-interval in which conservation of charge does not hold true. Charge goes to zero there.

- Since we have violated some fundamental equations of electromagnetism there, we cannot really expect electromagnetism to work at that point.

- So let´s try to approach this point from both sides (timewise) as close as we can:

t<T: There is a charge at rest. The electric field is just the normal q/r² - one for all times arbitrarily close to T.

t>T: There is no charge at all but that doesn´t nessecarily say that there´s no electric field at all. However, if you use the fact that an empty void is spherical symmetric, you can use gauss law (the one with "flux through sphere = charge inside", not sure about the name atm) to show that the field must be zero everywhere (as the "charge inside" will always be zero). This holds true up to arbitrarily close to T.

So if above arguments are valid, then you had an instant global change in the electric field.

Is there a problem with assuming that the sun ceases to exist in an unphysical way?

That is exactly the point, I think. If you pull the charged sun away rapidly, it would still be there so you couldn´t use the argument for t>T in above as easily (most probably not at all as the electric field should in fact not be zero, then).

We cannot simply assume that it is converted to radiant energy which then disperses, because that would be a different problem gravitationally (there would be be the gravity associated with the radiant energy, among other inconvenient side effects )

If I remember correctly the requirement for a Schwarzschild metric (gravitational field of the sun) is spherical symmetry of the energy-momemtum-stress tensor. I assume radiating away the sun at once would still result in a spherical symmetric energy-momentum tensor with the same "effective mass". So possibly there might not be any change at all, then (except for all living on earth dying after 8 minutes because the energy wave reached earth).

Atheist and swansont I would appreciate any clarification. I keep thinking that a change in the gravitational field can only propagate at speed c. It is like a groove in my head.

Well, for me "a force travelling at speed of light" probably means that the basic objects I build up the field upon have no mass and therefore a velocity of c (I have not seriously thought about that before). In that case, iirc the case is quite easy as in the linear approximation, the basic deviations from a flat metric have to obey a wave equation similar to that of photons and especially have a zero mass-term. So if you define the "speed of a force" in the way I just tried to sketch, you get your answer on what the speed of gravity is as soon as you have defined what you were asking for.

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