How Can We Measure the Speed of Light Over a Long Distance?

[Bullington]

The main question stems from the answer for this one:

If I have a light year long rod and push it on one end, how long would it take for the other end to move?
Still Unsure of this answer.

Main Question:

If I had 2, light-year long conductive rods with a voltmeter attached at the ends then applied a voltage to it, how long would it take for the voltmeter to read the voltage?

Resources/tutorials/wiki pages please for this as well. Thanks!

 

[andrewkirk]

If I have a light year long rod and push it on one end, how long would it take for the other end to move?

I'm pretty sure there are physical reasons why, even if a rod that long could be created, it could not stay intact. But let's leave them aside and imagine it can.

The answer is that the time it takes for the other end to move is one light year divided by the speed of sound in the rod. That speed of sound will depend on things like stiffness (see here) but, whatever it is, it will be enormously slower than the speed of light, so the other end will take much longer than a year - possibly millions of years - to move.

The reason is that your push on one end transmits through the rod as a pressure wave that travels at the speed of sound.

For the second question more info is needed for any sort of a sensible answer to be possible. What is the resistance per unit length of the rods? How is the voltage applied, and to what points on the rod? Why are there two rods and how are they connected? A circuit diagram is needed.

 

[Bullington]

Thanks for the reply! Yes, I just want a conceptual understanding of the question, so everything is perfect: resistance is zero; the two rods are spaced very far apart. What else might be required for the voltage to reach the end?
Although; what I'm really after is: Which would travel faster, pushing a rod or a voltage through the two rods? Would they travel at the same speed?

 

[andrewkirk]

The voltage, at the ends where the Voltmeter is connected, arises from the flow of a disturbance in electric field that flows away from each terminal of the voltage source, towards the other end of the rod that is connected to that terminal. Both those flows propagate as waves through the rods, at a speed equal to the speed to electricity through the rod which, if it is made of metal, will be 60-90% of the speed of light (source here). So it will be about 1.1-1.6 years before the voltmeter registers a potential difference. Note also that the voltage source will need to be absolutely gigantic to propagate the electric field so far.

The voltmeter will register a potential difference long before the pressure wave from a physical push reaches the end of the rod.

 

[Bullington]

Thanks for your help! Thanks for the sources too, I really Appreciate it!
I still have some misunderstandings of the whole process. So when you push the rod, the molecules inside the rod move, but; they can only propagate as fast as the speed of sound. But if you apply a voltage source, then it travels at a speed much faster than the speed of sound; Well, what if instead of using a voltmeter we measure the current, would it still be as quick? If so, how? Isn't current just electrons that are pushing other electrons?

 

[andrewkirk]

Well, what if instead of using a voltmeter we measure the current, would it still be as quick? If so, how? Isn't current just electrons that are pushing other electrons?

The result if we measured current would be the same as for measuring voltage. Electrons move to make a current when a voltage is applied to them.

The propagation of the voltage is the movement of a wave in the electric field, not of electron(s). The movement of electrons due to current in a conductor is actually very slow, around 1mm per second. But the movement of the wave is very fast. This is (somewhat) similar to how, in a water wave, individual water molecules move neither far nor fast, but a wave can travel fast.

So we can't think of the propagation of the current as electrons pushing each other. If it were limited to that then the voltage would travel much more slowly than the push from the end of the rod.

Here's a page that discusses the important difference between speed of current propagation and speed of electrons.

 

[sophiecentaur]

Here's a page that discusses the important difference between speed of current propagation and speed of electrons.

In a discussion like this, it is best to approach it, for a start, in classical, macroscopic terms. Ignore photons, phonons and electrons and stick to EM and Mechanical waves. You get a good answer from that approach and you won't risk getting embroiled in how electromagnetic energy actually travels on a conductor.

 

[Dale]

what if instead of using a voltmeter we measure the current, would it still be as quick? If so, how? Isn't current just electrons that are pushing other electrons?

Just want to "second" what @sophiecentaur and @andrewkirk both just said. There is definitely no need to think of this in terms of electrons or molecules, classical continuum mechanics is fine.

In that sense, the acoustic behavior is not so different from the electrical behavior. In each case the speed of the wave (acoustic or electromagnetic) is different from the speed of the material. If you pound very hard on a steel rod you might make some of the material move at a few hundred m/s, but the acoustic wave will travel at about 6 km/s. If you tap very lightly then the material may only move at a few dozen m/s, but the wave will still move at the same 6 km/s. The wave velocity is a property of the medium, and is independent of the motion of the material which is partially dependent on the strength of the excitation. Similarly for current.

 

[fresh_42]

Both those flows propagate as waves through the rods, at a speed equal to the speed to electricity through the rod which, if it is made of metal, will be 60-90% of the speed of light (source here).

I have a short question here, because I don't get two statements aligned. In a TV documentary (I know...), Hawking stated that Maxwell observed electricity propagates with the speed of light. How does this fit?

 

[Dale]

Maxwell observed electricity propagates with the speed of light. How does this fit?

EM waves propagate at the speed of light in vacuum. A wire is not vacuum.

 

[fresh_42]

EM waves propagate at the speed of light in vacuum. A wire is not vacuum.

I know. But I assumed (maybe mistakenly) that Maxwell hasn't been able to measure it in a vacuum at his time, but in a wire instead.

Edit: Or might it has been, that he measured something so fast, that he only could think of the speed of light?

 

[sophiecentaur]

Maxwell had no suitable electrical equipment for measuring the speed of a signal at the time. He was a theoretician and predicted the speed from other electrical measurements.

he only could think of the speed of light

Lol. I think he was smarter than that. And he did quite well. Pretty much all he calculated has been verified experimentally, once the measurement techniques became available.

 

[andrewkirk]

I have a short question here, because I don't get two statements aligned. In a TV documentary (I know...), Hawking stated that Maxwell observed electricity propagates with the speed of light. How does this fit?

The reports I found on a quick search about what Maxwell said were that an EM wave propagates at the speed of light, which is not the same as saying that a wave in a wire (electric current) propagates at the same speed as light in a vacuum. Perhaps Hawking was just being loose with his use of language and should have said 'electromagnetic waves' rather than 'electricity'.

I assume that electricity propagates in a wire at the same speed that light propagates in a wire but, since visible wavelengths traveling through copper are heavily attenuated, the comparison is somewhat moot.

Looking at the chronology of measurements of the speed of light, I see that Maxwell (writing his equations in 1865) would have known of the Fizeau-Foucault experiments (1850) that demonstrated that the speed of light in water was slower than in air, so I expect he would have been aware that it was probably different again in metal. But I don't think there were any experiments in his time that could measure the speed of EM waves in metal. So I think he would have assumed that the speed in metal was different from that in a vacuum, but of the same order.

 

[sophiecentaur]

So I think he would have assumed that the speed in metal was different from that in a vacuum, but of the same order.

An electrical wave does not propagate 'through' a wire. It propagates through the region around the wire. In the more common case of a signal along a pair of wires the majority of the energy is carried in the space between and in the case of a coax cable, it all travels in the cylindrical space between the inner and outer. The 'reason' it doesn't travel quite at c is because of the interaction with the wire structure and also any dielectric / insulating material in the cable.
The relative speeds of light through glass / water / air were not measured directly (the path length used was far too long for water or glass in those days) but finding the refractive index by noting the way the angles of the rays change at an interface.

should have said 'electromagnetic waves' rather than 'electricity'.

Not really, because he was probably just talking generally and 'electricity' is a non-specific, conversational term.
Carry on with your reading. It's a fascinating area of study and, being strictly classical, it doesn't call for knowledge of QM, photons or electrons. Nonetheless, it delivers the goods.

 

[Dale]

But I assumed (maybe mistakenly) that Maxwell hasn't been able to measure it in a vacuum at his time, but in a wire instead.

Well, historically Maxwell just made the prediction and Hertz is the one who did the actual measurement that confirmed the prediction. I am not sure the historical details are important for this thread.

 

[fresh_42]

Well, historically Maxwell just made the prediction and Hertz is the one who did the actual measurement that confirmed the prediction. I am not sure the historical details are important for this thread.

No, and I'm aware it was slightly off topic. I just wanted to get the two seemingly contradicting statements cleared. (And the original questions had already been answered, so I thought a little detour wouldn't harm.) Thanks for your (pl.) answers, though.

 

[Dale]

Sure, also I think that Hertz just confirmed the presence of electromagnetic waves, but I don't think that he measured their speed at that time. So my response may also not be exactly relevant either.

 

[sophiecentaur]

Maxwell hasn't been able to measure it in a vacuum at his time, but in a wire instead.

It is often convenient to measure the speed of a wave, using the formula
c = fλ because it may be much easier to measure frequency and wavelength than measuring the transit time of a wave over a long distance. This link is a fun approach to a seriously useful technique. (Sorry if it's approach is too 'noddy' but the idea is there)
The technique is suitable for all frequencies of waves, including optical frequencies.