Information transmitted faster than light?

[preen]

Hi everyone, neat forum you got here. This one's been bothering me for a while, I hope you can help me. I've often seen this question satirized, but I've not yet come across the answer.

I've often heard it asserted that information of any kind cannot be transmitted from one place to another faster than the speed of light. For example, to send information to someone on Mars from Earth by any means, would take at least 3 minutes at it's nearest point. This makes sense to me in that it enforces a fixed causality between events across all observers.

1. Does this apply to communicating with a destination that you are in physical contact with? For example, if you were connected to the fellow on Mars by a string, and you communicated with him by tugging on the string, would he feel the string tugged immediately as you pulled it (assuming it is a magic string with no stretchiness), or would some process delay that information by at least the speed of light?

2. Does this put a speed limit on the propagation of a force through space? If the sun were to vanish and it's mass removed, we would still see the sun for 8 more minutes, but would we still experience the gravitational pull, and orbit the spot the sun -was- in for another 8 minutes? Or, if a magnet suddenly demagnitizes, do nearby paperclips learn of this event immediately, or do they continue to experience an attraction until the necessary delay elapses based on their distance?

 

[Calrid]

1)It applies as more or less a law of nature.

No information can be transmitted faster than light and AFAIK as yet none has in any experiment I know about.

2) Yes it does that's a fundamental part of Einstein's general relativity theory. We would indeed have some sort of gravitational lag due to the propogation of gravity through a vacuum in the same way we would have a lag in the time it would take us to notice the sun was gone because it went dark.

Speed of gravity
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In the context of classical theories of gravitation, the speed of gravity is the speed at which changes in a gravitational field propagate. This is the speed at which a change in the distribution of energy and momentum of matter results in subsequent alteration, at a distance, of the gravitational field which it produces. In a more physically correct sense, the "speed of gravity" refers to the speed of a gravitational wave.

The speed of gravitational waves in the general theory of relativity is equal to the speed of light in vacuo, c.[1] Within the theory of special relativity, the constant c is not exclusively about light; instead it is the highest possible speed for any physical interaction in nature. Formally, c is a conversion factor for changing the unit of time to the unit of space.[2] This makes it the only speed which does not depend either on the motion of an observer or a source of light and/or gravity. Thus, the speed of "light" is also the speed of gravitational waves and any massless particle. So far, the only candidates for massless particles in physics are the photons that light waves consist of, and also the theoretical gravitons which make up the associated field particles of gravity, if a quantum mechanical theory for gravity is ever successfully constructed.

Wiki is your friend.

 

[DaveC426913]

1. Does this apply to communicating with a destination that you are in physical contact with? For example, if you were connected to the fellow on Mars by a string, and you communicated with him by tugging on the string, would he feel the string tugged immediately as you pulled it (assuming it is a magic string with no stretchiness), or would some process delay that information by at least the speed of light?

The string is made of atoms. Those atoms can only transmit as fast as the speed of sound in the material it is made of - way way slower than the speed of light.

Diamond, the hardest substance known to man, only transmits forces at 12 km/s - 1/10,000 that of light.

2. Does this put a speed limit on the propagation of a force through space? If the sun were to vanish and it's mass removed, we would still see the sun for 8 more minutes, but would we still experience the gravitational pull, and orbit the spot the sun -was- in for another 8 minutes?

Yes. Changes in gravity, as in all forces, travel no faster than c.

 

[preen]

Thanks guys, that makes sense, but one more thing.

A maximally rigid ideal material would transmit a force at no faster than the speed of light.

Dude A on Earth would pull the string, and see it move. Dude B on Mars would -not- see the string move for 3 minutes. The string must temporarily become longer. What bends to allow the string to change length? (assuming the string is ideal and doesn't stretch).

Or, the the limit on the propagation of forces demand that the string must change length? (at least from a god's eye view)

 

[Andrew Mason]

If the sun were to vanish and it's mass removed, we would still see the sun for 8 more minutes, but would we still experience the gravitational pull, and orbit the spot the sun -was- in for another 8 minutes?

You are asking a question that presuposes that the laws of physics do not apply. In effect, you are asking how the laws of physics would apply if the laws of physics did not apply.

In the scenario you have given, the magical instantaneous disappearance of the sun would result in a magical disappearance of gravity immediately for the entire solar system thereby magically sending a signal moving at a speed greater than c. This is why mass cannot disappear like that.

Or, if a magnet suddenly demagnitizes, do nearby paperclips learn of this event immediately, or do they continue to experience an attraction until the necessary delay elapses based on their distance?

The stoppage of current in the magnet cannot be instantaneous. The rapid change in the magnetic field results in an electromagnetic wave being sent out at speed c. Paper clips cannot learn of this event before that wave arrives.

AM

 

[preen]

In the scenario you have given, the magical instantaneous disappearance of the sun would result in a magical disappearance of gravity immediately for the entire solar system thereby magically sending a signal moving at a speed greater than c.

Ok, I'm confused again. Right, the mass can't just go away. I'll rephrase the question. It can be a change in the mass, or just the position of the object. I'm curious about the delay of notification of any event involving a change in a force.Object A is 1 light year away. You measure it's gravitational force as coming from a particular, consistant direction.

Object A moves. Do you wait a year before becoming aware of a change in the direction of it's gravitational pull?

I understand gravitational and EM waves zip along at c, but I'm wondering about the fields themselves. Is the field fixed around the entity that exerts it in a rigid way, or does it sort of lag behind depending on that entity's speed? Is a change in the strength of the field experienced in the entire field simultaneously, or does the change sort of expand from the source entity like a ripple?

 

[michaelwoodco]

You are asking a question that presuposes that the laws of physics do not apply. In effect, you are asking how the laws of physics would apply if the laws of physics did not apply.

In the scenario you have given, the magical instantaneous disappearance of the sun would result in a magical disappearance of gravity immediately for the entire solar system thereby magically sending a signal moving at a speed greater than c. This is why mass cannot disappear like that.

The stoppage of current in the magnet cannot be instantaneous. The rapid change in the magnetic field results in an electromagnetic wave being sent out at speed c. Paper clips cannot learn of this event before that wave arrives.

AM

Wait...I just watched a video explaining that ripples of gravity moved at the speed of light. So by instantaneous do you mean that as soon as we know the sun is gone? It seemed like the video said the Earth would continue rotating for a few minutes

 

[Doc Al]

Thanks guys, that makes sense, but one more thing.

A maximally rigid ideal material would transmit a force at no faster than the speed of light.

Dude A on Earth would pull the string, and see it move. Dude B on Mars would -not- see the string move for 3 minutes. The string must temporarily become longer. What bends to allow the string to change length? (assuming the string is ideal and doesn't stretch).

Or, the the limit on the propagation of forces demand that the string must change length?

Exactly! Relativity implies that there can be no perfectly rigid bodies.

 

[russ_watters]

magic string

Magic string? So in other words, assuming we can violate the laws of physics, can we violate relativity? Um...sure. That doesn't tell us anything useful about reality, though, does it?

 

[Ryan_m_b]

Any object when pulled stretches somewhat. With some materials this is obvious (rubber) with others it is less so (concrete). Whilst some objects are elastic and stretch a lot before breaking others are not and quickly break (if you were to pull at a brick it would stretch ever so minutely before it broke, most likely stretching at the molecular scale). So if you had a string that was any length (whether it was between Earth and Mars or your left and right hand) when you pull one end it ripples all the way down it's length at its speed of sound stretching.

Imagine it this way, you have 100 people each standing in 100 one metre wide squares. These people have to remain the same distance between either neighbour preferably exactly 1 metre from the person on either side. If i take the person at one end and move them 1 metre then you will observe a ripple as one by one every one hops one metre to catch up with the person that just moved.

If the person at the other end can't move then the line is stretched with the ripple passing back and forth as everyone tries to both maintain an equal distance between each other as well as trying to obey the rule of being 1 metre away from both neighbours in this now 101 metre line of 100 people. If i was to let the end person jump back to his original place the ripple would travel down again.

The "ripple" speed in an object is the speed of sound within the object. It is impossible to build a magic string where all objects move at the same time to reposition themselves because it would require each atom to react instantly to what happens to every other atom.

Do you understand why using a magic string is a bit like asking "if we could travel faster than light could we travel faster than light?" hope I helped :)

 

[preen]

Thanks. So the granular nature of matter prevents anything from being in 'contact' with anything else. The particles communicate with forces, and their own accelerations are limited to finite values (and large accelerations sap energy via gravitational waves).

Though can someone clarify the propagation of a change in the magnitude of a force throughout a field; I think that's the root of my confusion.

If a force generated by an entity changes in any way (eg. if it changes mass, or moves), is the change immediately felt in the entire extent of the force's field instantly, or does the change propagate throughout the filed at the speed of light?

Like in the sun example. Are we feeling the gravity from the sun from where it is now, or where it was 8 minutes ago? Is it correct to think of gravity as being transmitted by particles exchanged between bodies at the speed of light?

 

[Ryan_m_b]

Yes, the field would change at the speed of light. If the sun disappeared then it's gravitational well would disappear in a wave propagating at the speed of light.

If you move a magnet the magnetic field moves along at the speed of light

 

[Andrew Mason]

Yes, the field would change at the speed of light. If the sun disappeared then it's gravitational well would disappear in a wave propagating at the speed of light.

This is rather speculative. No one knows if gravitational waves exist. The premise is that mass can disappear instantaneously. It is not known how that would be possible.

AM

 

[Ryan_m_b]

This is rather speculative. No one knows if gravitational waves exist. The premise is that mass can disappear instantaneously. It is not known how that would be possible.

AM

I agree, but Preen wants to know if there is anyway to transmit faster than light. Whilst disappearing suns are entirely in the realm of hypothetical you could propose another scenario to answer Preen's question;

If a large body is moving relative to a probe that can measure gravity and has a telescope both of those instruments will agree as to where the object is. If it was light minutes away and moving at a high speed perpendicular to the probe then the image seen by the probes telescope will show the object to be at a place that it no longer inhabits. The gravity data should agree because the gravity isn't propagating at superluminal speeds.

 

[DaveC426913]

I agree, but Preen wants to know if there is anyway to transmit faster than light. Whilst disappearing suns are entirely in the realm of hypothetical you could propose another scenario to answer Preen's question;

If a large body is moving relative to a probe that can measure gravity and has a telescope both of those instruments will agree as to where the object is. If it was light minutes away and moving at a high speed perpendicular to the probe then the image seen by the probes telescope will show the object to be at a place that it no longer inhabits. The gravity data should agree because the gravity isn't propagating at superluminal speeds.

Good point. If changes in gravity occurred at superluminal speeds, we would look up into the sky and be able to sense where a moving object "actually" is, ahead of its light image (like seeing and hearing a jet plane overhead at two different points in the sky.)

And we'd also instantly have a form of superluminal communications. I could wave a moon around and you could detect its location well before its light reached you.

Realizing these are impossible, one can deduce that changes in gravity must propogate at no more than c.

 

[DrGreg]

No one knows if gravitational waves exist.

I think that is putting it a bit strongly. It is true that gravitational waves have not been experimentally detected, but general relativity predicts they do exist and it would be a huge shock if an experiment were ever to conclusively disprove their existence.

On the other hand, gravitons may or may not exist because we don't yet have any theory of quantum gravity.

 

[Cleonis]

If changes in gravity occurred at superluminal speeds, we would look up into the sky and be able to sense where a moving object "actually" is, ahead of its light image (like seeing and hearing a jet plane overhead at two different points in the sky.)

Well, that ushers in the question of aberration.
Is there such a thing as aberration of the direction of gravitation? And does it coincide with aberration of propagating light?
That question has been examined by http://www.physics.ucdavis.edu/Text/Carlip.html" (in response to criticism of General Relativity by Tom van Flandern)

In the article http://xxx.lanl.gov/abs/gr-qc/9909087" Carlip demonstrates the following remarkable property of GR: When two celestial bodies are orbiting each other in circular orbits then the instantaneous direction of gravity is precisely towards the instantaneous position of the other body. No aberration.

Carlip shows that if that would not be the case then solar systems would be unstable; angular momentum would not be conserved.
According to GR in the case of perfect circular orbit there is no emission of gravitational waves by the system.

However, when two celestial bodies orbit each other in an ellipse-shaped orbit then there is a socalled quadrupole moment contribution in the orbital mechanics, and then the orbiting motion does emit gravitational waves.
That is what is corroborated by the Hulse-Taylor binary system. I find the distinction between emission of electromagnetic waves and gravitational waves truly remarkable.
As we know, cyclotron radiation arises because charged particles in circular motion radiate electromagnetic energy. (More generally, charged particles that undergo acceleration radiate electromagnetic energy.)
But inertial mass in circular motion does not give rise to gravitational waves.

In the case of circular motion the time derivative of the acceleration is constant, whereas with an ellipse-shaped orbit the acceleration varies over time. Compared to electromagnetic waves gravitational waves arise at a higher order, they arise only if the time derivative of the acceleration varies over time. Finally, returning to the question I raised at the start of this post: the aberration of gravity does not coincide with the aberration of propagating light.

 

[Andrew Mason]

Good point. If changes in gravity occurred at superluminal speeds, we would look up into the sky and be able to sense where a moving object "actually" is, ahead of its light image (like seeing and hearing a jet plane overhead at two different points in the sky.)

And we'd also instantly have a form of superluminal communications. I could wave a moon around and you could detect its location well before its light reached you.

Realizing these are impossible, one can deduce that changes in gravity must propogate at no more than c.

Is it necessary for gravity to propagate at all? Why would gravity have to propagate from one massive body to another massive body just because there is relative motion? Does gravity have to continuously propagate in order for the Earth to experience the changes in the gravity of the sun due to the changing distance between the Earth and the sun? Wouldn't that mean that gravitational waves would have to propagate from a massive body all the time?

AM

 

[Dale]

1. Does this apply to communicating with a destination that you are in physical contact with? For example, if you were connected to the fellow on Mars by a string, and you communicated with him by tugging on the string, would he feel the string tugged immediately as you pulled it (assuming it is a magic string with no stretchiness), or would some process delay that information by at least the speed of light?

Very amusing. Yes, if you assume a magic string which violates the laws of physics then you will reach a conclusion which violates the laws of physics.

 

[DaveC426913]

Very amusing. Yes, if you assume a magic string which violates the laws of physics then you will reach a conclusion which violates the laws of physics.

In his/her defense, one does not intuitively combine relativistic velocities with the distances on the scale of atoms in a piece of string. Once the realization is made though, in retrospect it can seem obvious.

 

[Dale]

Sure, but one generally assumes that magic violates the laws of physics.

 

[DaveC426913]

Sure, but one generally assumes that magic violates the laws of physics.

No I know, I mean it's not readily apparent that the mere stretchiness property of a piece of string would be so closely related the ultimate speed limit of the universe. Our naive understanding of materials is that they are just solid and inert, not involved in SR. It's an easy oversight for a novice.

 

[Cleonis]

Is it necessary for gravity to propagate at all?

Well, first thing to do here is to distinguish between a field, and waves.

Let's look at an electromagnetic field and electromagnetic waves.
That which propagates is a change of the field (change of direction, change of magnitude). An electromagnetic wave is a change in an electromagnetic field, it's that change that propagates away from some origin.

It seems to me that the capacity for propagation should be attributed exclusively to waves, not to the field itself.

Does gravity have to continuously propagate in order for the Earth to experience the changes in the gravity of the sun due to the changing distance between the Earth and the sun?

The usual interpretation, as far as I'm aware of, is that a field is thought of as something that permeates space, and if the source of the field is static then the field is static.

The field is thought of as extended in space, and everywhere particles interact with the portion of the field that they are in contact with. Another way of saying this is: particles interact with the local field.

The case of a planet orbiting a sun in an ellipse-shaped orbit is certainly not seen as a process where the planet and the sun are constantly re-negotiating their interaction, in response to change of their mutual distance.
The orbiting planet is thought of as interacting with the local field.Returning to the original question: 'Is it necessary for gravity to propagate at all?'
The usual interpretation, I think, is that the gravitational field does not propagate, but changes in the field do.That said, not all change at the source gives rise to change of the field at the perifery. For instance, if a dying star collapses to neutron star state, then at a distance there is no change of the gravitational field. For a gravitational field only the total inertial mass of the source counts, not the density of the source's matter. In collapsing to neutron star state the density of the star's matter goes up dramatically, but since the total mass remains the same the external gravitational field remains the same. So there's nothing to propagate.

 

[Andrew Mason]

Well, first thing to do here is to distinguish between a field, and waves.

Yes. But you are supposing that there are gravity waves. I am just suggesting that they may not be necessary for gravity.

Returning to the original question: 'Is it necessary for gravity to propagate at all?'
The usual interpretation, I think, is that the gravitational field does not propagate, but changes in the field do.

And all I am saying is that I don't see why it is necessary for anything to propagate. You are assuming that it is possible for changes to occur in a gravitational field. Can you explain how that occurs?

That said, not all change at the source gives rise to change of the field at the perifery. For instance, if a dying star collapses to neutron star state, then at a distance there is no change of the gravitational field. For a gravitational field only the total inertial mass of the source counts, not the density of the source's matter. In collapsing to neutron star state the density of the star's matter goes up dramatically, but since the total mass remains the same the external gravitational field remains the same. So there's nothing to propagate.

That is kind of my point. What kind of change would give rise to a change in the gravitational field that then has to propagate into space?

AM

 

[KingNothing]

Hi Preen, one thing that might help you understand is this: the molecules of any object (including your string) are held together by electrical forces (bonds) between the molecules. This is why the speed that a mechanical change propagates (such as pulling, stretching, moving, etc) has an upper limit of the speed of electromagnetic propagation.

 

[Ryan_m_b]

That is kind of my point. What kind of change would give rise to a change in the gravitational field that then has to propagate into space?

AM

How about the movement of the object? If a large body is moving relative to a gravity detector that information won't be superluminal.

 

[sophiecentaur]

The object needn't be moving; it can be changing shape or orientation - if not spherical. If, for example, the Moon were to be changed from a sphere to a dumbell shape and rotated (head over heels) on an axis parallel with the Earth's axis, you 'could' detect a change in gravitational force at the same rate as the tumbling of this dumbell. This is because the potential of the dumbell is different from that of a sphere, although they would both have a CM in the same place.
Your gravitational sensors would be in the same phase as the optical information you'd get in a telescope.

 

[Andrew Mason]

The object needn't be moving; it can be changing shape or orientation - if not spherical. If, for example, the Moon were to be changed from a sphere to a dumbell shape and rotated (head over heels) on an axis parallel with the Earth's axis, you 'could' detect a change in gravitational force at the same rate as the tumbling of this dumbell. This is because the potential of the dumbell is different from that of a sphere, although they would both have a CM in the same place.
Your gravitational sensors would be in the same phase as the optical information you'd get in a telescope.

The change in shape of the moon would change its moment of inertia. If the moon's rate of rotation did not change, in order to conserve total angular momentum, would the location of the CM (ie. the Earth moon CM radius) not have to change as well?

The bottom line is that these kinds of changes do not appear to change the gravitational effect of these masses. Nothing has to be communicated to distant objects about such changes.

AM

 

[Cleonis]

Yes. But you are supposing that there are gravity waves. I am just suggesting that they may not be necessary for gravity.

And all I am saying is that I don't see why it is necessary for anything to propagate. You are assuming that it is possible for changes to occur in a gravitational field. Can you explain how that occurs?

About the concept of 'field' in physics:
In physics it is very common to work with the concept of a field. And of course the two most well known examples are electromagnetic field and gravitational field.

But however common: we don't know whether these fields exist in the form they are described.

Describing electromagnetism in terms of a field theory is efficient and economical. Still, what we observe, what our instruments record, is not the fields, but trajectories of particles. We infer from the trajectories that particles are interacting, affecting each other's momentum. The existence of electromagnetic field, acting as mediator of the interaction, is hypothesized. Other ways to explain the phenomena are more convoluted, the value of the field hypothesis is in it's efficiency.

We have mathematical formalism that allows us to describe the behavior of the fields, but that is all. At present, if we want to use the concept of a 'field' we must accept its properties as irreducible.

Summerizing:
As far as I know the current situation is that we use the concept of field, but all we know is the properties, nothing beyond that.Electromagnetic waves
Interestingly, electromagnetic waves can be reduced. It has been pointed out that the existence of electromagnetic waves follows from the properties of the electromagnetic field.
When Maxwell developed the physics that nowadays we know as Maxwell's equations he predicted on theoretical grounds the existence of electromagnetic waves, and he derived from first principles the speed of propagation of these waves. As we know, this speed coincides with the speed of light, from which Maxwell inferred that light is propagating electromagnetic waves.

(For the relation between field and waves there is also the discussion by Daniel Schroeder: http://physics.weber.edu/schroeder/mrr/MRRtalk.html" .

The thing is, this speed of propagation is a property of the waves. The theory doesn't say anything about any sort of propagation of the field itself. It's meaningful to discuss speed of propagation of waves, but I think there's no meaning to some concept of "speed of the electromagnetic field".

Anyway, to my knowledge the standard view is that the waves are regarded as an epi-phenomenon. If the electromagnetic field exists it follows logically/physically that electromagnetic waves will exist.

Something analogous applies in the case of gravity and gravitational waves:
The orbital decay of the Hulse-Taylor binary is consistent with the energy that such a system radiates (in the form of gravitational waves), according to General Relativity. That is regarded as strong evidence for the existence of gravitational waves. For the sake of completeness: it's possible to have an overall configuration with sources of gravity, but without gravitational waves.
Conversely, gravitational waves arise if and only if the overall configuration involves sources of gravity.
Another way of saying that is that gravitational fields do not necessarily produce gravitational waves, but if there are gravitational waves then somewhere there must be the gravitational field(s) that produces those waves.
This is the point of view that waves are an epi-phenomenon; the view that the existence of the waves follows from the properties of the field.

 

[Calrid]

That's a good post^. Concisely put.

For completeness we could say it is impossible to describe all the interactions of any particle or interaction therein with just a wave model or just a particle model.

 

[sophiecentaur]

The change in shape of the moon would change its moment of inertia. If the moon's rate of rotation did not change, in order to conserve total angular momentum, would the location of the CM (ie. the Earth moon CM radius) not have to change as well?

The bottom line is that these kinds of changes do not appear to change the gravitational effect of these masses. Nothing has to be communicated to distant objects about such changes.

AM

Only spheres have no change in gravitational potential when they rotate.
Conservation of the dumbell Moon's angular momentum would just mean that it would rotate slower than it does now but, in our experiment, we could spin it at any rate we wanted. Why should there be a resulting first order change in the position of the Earth / Moon CM? What effect / interaction between Earth and Moon could change the radius of the Moo's orbit at the dumbell rotation rate. Tidal drag etc. would always apply but these have very long time constants c/w the spinning dumbell time.
Are you saying that there would be no periodic change of the 'dumbell' Moon gravity, measured on Earth? The field 'near' to a rotating dumbell is not isotropic so it would certainly change at the rotation rate - so how far away would you say the effect would not be noticed?