# Whether the speed of alternative/direct current is faster than light?

1. Aug 17, 2011

### Mr.GaGa

Whether the speed of alternative/direct current is faster than light???

What's the speed of alternative and direct current in metals? c, less or greater? It is impossible to be c because metal is not vacuum.

2. Aug 17, 2011

### space guy1

Re: Whether the speed of alternative/direct current is faster than light???

according to what I know, the charges move anywhere from 66-99% the speed of light. the electrons themselves only move on the range of millimeters per hour.

3. Aug 17, 2011

### ghwellsjr

The charges are the electrons and move rather slowly but not that slowly, I don't think. The voltage signals travel down pairs of wires at about two-thirds of c although the charges travel down one wire and back on the other one.

4. Aug 17, 2011

### Drakkith

Staff Emeritus
Re: Whether the speed of alternative/direct current is faster than light???

Also, in an AC circuit, each electron only moves a few millimeters one way before being forced back the other way when the direction of current changes. A DC circuit would be different as the direction of current never switches.

5. Aug 17, 2011

### pervect

Staff Emeritus
Re: Whether the speed of alternative/direct current is faster than light???

The actual speed with which electrons move in metals is very slow. Google for "drift velocity".

http://en.wikipedia.org/w/index.php?title=Drift_velocity&oldid=444660015" has a calculation of this for an example of 3 amperes through a 1mm copper wire, getting .00028 meters/second.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/ohmmic.html" [Broken] also has some calculations for drift velocity.

Now, you might not be interested in the actual (slow) speed with which the electrons move, but rather the speed at which the signal propagates.

The speed of signal through a propagation through a wire is hard to define, the wire distorts the signal a and it depends on the environment and the frequency.

A high bandwidth "wire", like coaxial cable, doesn't distort the signal and the speed is easier to define and measure. However, the speed through a cable depends mostly on the insulator, and not very much on the metal. The usual coax cable transmits signals about 75% of c, you get close to 'c' if you use an air dielectric (i.e. air insulator).

See Wiki again, http://en.wikipedia.org/w/index.php?title=Wave_propagation_speed&oldid=444855003.

Last edited by a moderator: May 5, 2017
6. Aug 18, 2011

### Q-reeus

Re: Whether the speed of alternative/direct current is faster than light???

It's amazing how the old Drude model of conductivity in metals continues to be perpetuated, even at eg Wiki and Hyperphysics as per Pervect's links in #5. The Wikipedia article there starts off right in mentioning that 'free' electrons rattle around at the Fermi velocity, but then uses a calculation going back to the Drude model concept. Fact is Sommerfeld around 1927 figured out that picture of an extremely small mean drift velocity of at most mm's/sec contributed by all the 'free' electrons is wrong. Actually only a tiny fraction, those unpaired and close to the Fermi surface, are free to conduct and move with a mean 'drift' velocity close to the Fermi velocity, typically around 106 m/sec! A brief article comparing the Drude and Sommerfeld values: http://tau.nanophys.kth.se/cmp/hall/node1.html [Broken]

Last edited by a moderator: May 5, 2017
7. Aug 18, 2011

### ghwellsjr

Re: Whether the speed of alternative/direct current is faster than light???

A million meters a second!! I find that really hard to believe.

8. Aug 18, 2011

### Drakkith

Staff Emeritus
Re: Whether the speed of alternative/direct current is faster than light???

Why's that? It's not that fast. Light itself travels at 299,792,458 m/s.

9. Aug 18, 2011

### Mr.GaGa

Re: Whether the speed of alternative/direct current is faster than light???

Why the value is 66-99% c ? Would you like to give some references to show the result?

10. Aug 18, 2011

### Drakkith

Staff Emeritus
Re: Whether the speed of alternative/direct current is faster than light???

Per here: http://en.wikipedia.org/wiki/Electric_current#Drift_speed

That is referring to the propagation of the force I believe, not the charges (electrons) themselves.

11. Aug 18, 2011

### chaszz

Re: Whether the speed of alternative/direct current is faster than light???

A few questions.

1. Is it correct to say that in a current the movement, or drift, of the electrons themselves is small, but the movement of the charge is much faster? That is what I gather from the preceding posts.

2. Is the movement of the charge the same thing as the propagation of the electromagnetic waves? If so, is the charge somewhere on the electromagnetic spectrum, and if so, where on the spectrum? Or is the charge itself the 'electro' component of 'electromagnetic', and the magnetic component is caused by it (the charge)?

3. If the direction of the current in AC is continually reversing, how does the current do any work? It would seem to me to cancel itself out.

12. Aug 18, 2011

### sunroof

Re: Whether the speed of alternative/direct current is faster than light???

The speed of charge(electron) has nothing to do with that of the electromagnetic field. It is much slower than the latter. (Wiki: http://en.wikipedia.org/wiki/Drift_velocity )

13. Aug 18, 2011

### Drakkith

Staff Emeritus
Re: Whether the speed of alternative/direct current is faster than light???

Replace charge with EM field or force and you are correct.
No, a Charge is a property of matter (particles) that causes it to experience a force. An Electron is an Electrically Charged particle. Hence we call it an electric charge: http://en.wikipedia.org/wiki/Electric_charge

I think that if the frequency was so high as to reverse before the EMF (electromotive force) can propagate through the circuit, then it would interfere I believe. However the frequency of AC circuits is low enough to give the EMF plenty of time to propagate throughout the circuit. Remember, it's speed is a high proportion of c, the speed of light.

14. Aug 18, 2011

### ghwellsjr

Re: Whether the speed of alternative/direct current is faster than light???

An electron has a negative charge which means two things:

1) Surrounding the charge is a negative voltage that is inversely proportional to the distance from the charge. If you move this charge, this field of voltage adjusts itself at the speed of light to its new position.

2) A charged particle will experience a force along the direction of a spatial change in voltage field. So two charged particles separated by a distance will experience a force along a line between them because the voltage field is changing in that direction.

The same could be said for the positive charges on protons. For all practical purposes, the number of positive and negative charges are approximately equal so the voltage field in any area is generally quite low. However, if you can get an electron to vibrate, you can create a wave in the voltage field that propagates outward at the speed of light. When this voltage wave reaches another electron far removed from it, it will cause it to vibrate.

There, now you have the condensed theory of light.

If you can collect an excess of charge on a piece of metal which allows the free-flow of electrons, you can create a voltage on it. At any location on the metal, there will be enough charges in the surrounding metal to add up to the same voltage everywhere. Now if you take two such pieces of metal and put charges of opposite polarity on them, you will have a measureable voltage between them. You can then put a piece of wire between them, you will get a momentary measureable current flow in the wire.

There, now you have the condensed theory of electricity.

Now instead of a short piece of wire going directly between these two pieces of charged metal, you take a very long piece of wire going many miles distance and coupling back along a parallel path, before you connect both ends to the pieces of metal, there will be no voltage on the wire but as soon as you make both connections, all of a sudden the electrons in the two pieces of metal are transferred to the beginning of the two pieces of wire and electrons start to flow. These moving electrons create a changing voltage difference between the two wires that propagates down the wires at a substantial fraction of the speed of light and the disturbance in the charges along the wires propagate along with it but the charges are not moving very far.

There, now you have the condensed theory of a transmission line.

Last edited: Aug 19, 2011
15. Aug 19, 2011

### Per Oni

Re: Whether the speed of alternative/direct current is faster than light???

Chapter 1 The Drude Theory of Metals, bottom of page 16 “Solid State Physics; Ashcroft / Mermin”
Chapter 2 The Summerfield Theory of Metals, halfway page 51 same book:
That book was written in 1975 and is generally accepted as a brilliant piece of work. However I do accept that the differences between Fermi speed, thermal velocity, drift speed, signal speed are never well explained anywhere.

Last edited by a moderator: May 5, 2017
16. Aug 19, 2011

### PhilDSP

Re: Whether the speed of alternative/direct current is faster than light???

It's probably worth considering the 2 types of current: conduction current and displacement current. Conduction current is the movement of the charge while displacement current is the movement or transport of EM (light) energy which propagates at c.

You can calculate the displacement current using the Poynting theorem. The displacement current travels often at a 90 degree direction to the direction of travel of the charges. The displacement current is what creates EM waves.

Or rather the energy travels in a direction that is 90 degrees from the direction of the conduction current vector while the displacement current is in the opposite direction.

Last edited: Aug 19, 2011
17. Aug 19, 2011

### harrylin

Re: Whether the speed of alternative/direct current is faster than light???

Thank you - that little piece of information had not reached me!

Last edited by a moderator: May 5, 2017
18. Aug 19, 2011

### Mr.GaGa

Re: Whether the speed of alternative/direct current is faster than light???

I read http://en.wikipedia.org/wiki/Drift_velocity and the velocity of charge(electron) is very slow. Actually, it is the electromagnetic fiel in conductors to transimit energy and signal whose velocity is much faster than light in vacuum. In particular, it is infinity according to the reference (Energy transport faster than light in good conductors, arXiv:/1101.1840v2). Really?

19. Aug 20, 2011

### Q-reeus

Re: Whether the speed of alternative/direct current is faster than light???

from Per Oni in #15:
"That book was written in 1975 and is generally accepted as a brilliant piece of work. However I do accept that the differences between Fermi speed, thermal velocity, drift speed, signal speed are never well explained anywhere."

I include a pdf version of an article (Conduction.pdf) that gives a nice summary of Drude and Sommerfeld models (unfortunately original online link no longer works). Note it makes the point that the net result gives the same overall figure for conductivity (but very different results for other parameters of interest). That's probably what Mermin meant by classical models working so well. https://www.physicsforums.com/attachment.php?attachmentid=38139&stc=1&d=1313832109

from harrylin in #17:
"Thank you - that little piece of information had not reached me!"

from Mr.GaGa in #18:
"I read http://en.wikipedia.org/wiki/Drift_velocity and the velocity of charge(electron) is very slow. Actually, it is the electromagnetic fiel in conductors to transimit energy and signal whose velocity is much faster than light in vacuum. In particular, it is infinity according to the reference (Energy transport faster than light in good conductors, arXiv:/1101.1840v2). Really?"

How that article got published in a peer-reviewed journal is beyond me. No way can be true. For a near monochromatic wave propogating in a hollow waveguide for instance, the phase velocity vp (speed a crest moves at) exceeds c, but the signal velocity vs (speed an actual signal moves at) is correspondingly less according to vpvs = c2. When dispersion is high this relation gets a bit fuzzy and the peak value of a pulse can, within the pulse envelope and over a limited duration, move faster than c, but never can the pulse leading edge exceed c, no matter what. See eg http://en.wikipedia.org/wiki/Superluminal_motion [oops - better one at http://en.wikipedia.org/wiki/Faster-than-light] [Broken]

Finally, wondering why I have received just one email notification on this thread since my last entry #6!! And yes, my settings are still set for automatic 'instant' notification.

#### Attached Files:

• ###### Conduction.pdf
File size:
404 KB
Views:
423
Last edited by a moderator: May 5, 2017
20. Aug 20, 2011

### Per Oni

Re: Whether the speed of alternative/direct current is faster than light???

This part I don’t agree with. When looking at the article you provided in #19 you can see in the picture of the Fermi spheres that the whole surface is displaced by a certain distance. This means that all conduction electrons have changed their speeds towards –E. Of course I accept that they are not all moving with the same velocity. But since they are all moving towards –E, the average speed is still given by v=j/ne, which is extremely slow.

21. Aug 20, 2011

### sunroof

Re: Whether the speed of alternative/direct current is faster than light???

Yes. A superluminal phase velocity vp>c is corresponding to a signal velocity vs less than c because vpvs = c2. However, a subluminal phase velocity vp<c might represent vs>c. See http://en.wikipedia.org/wiki/Phase_velocity

Last edited by a moderator: May 5, 2017
22. Aug 21, 2011

### Q-reeus

Re: Whether the speed of alternative/direct current is faster than light???

No, the article Conduction.pdf makes it clear it is only the small fraction of unpaired electrons that form a potential reservoir for conduction, and it is from this fraction only that the distorted Fermi surface has relevance. There are a number of contributing factors and the full details are way beyond my capabilities. However, typically at room temp a fraction of ~ 10-3 are unpaired. At the same time, owing to the electronic wave nature, mfp is greater than the Drude picture suggests, by about an order of magnitude, but this is countered by the random speed ~ vF ~ an order of magnitude greater than Drude value v0, so that the mft is roughly equal in the Drude and Sommerfeld models. The picture so far gives almost no enhanced drift velocity per electron if one assumes only initially random emissions of electrons being accelerated for the mft - the Drude concept. This still leaves then about three order of magnitude deficit in conductivity to explain. The other main factor is that emission is suppressed in directions away from the applied -E (unpaired electrons 'sink' into the paired conduction band levels), and enhanced in the direction of -E. That is what I believe is implied in the linked article. The actual level of vectoring I'm not sure of, but the author writes "j = nqvF" for the current, suggesting only a small fraction of that ~ 10-3 of unpaired electrons appreciably carries the current. Then there is the question of scattering being elastic or inelastic and to what degree correlated etc. For a full treatment things get quite complicated and Brillouin zones, Bloch modes and all that quantum physics stuff comes into play, which is taking this right away from SR & GR.

Last edited: Aug 21, 2011
23. Aug 21, 2011

### Q-reeus

Re: Whether the speed of alternative/direct current is faster than light???

No doubt that is referring to the part under sub-heading 'Slow phase velocity and superluminality'. Another example where Wikipedia cannot always be trusted. Conceivably the author of that piece was the same one who wrote the arXiv.org article linked to in #18. For an EM wave to propagate freely through a metal, it must have a frequency well above the plasma frequency fp, which for eg copper is in the ultraviolet range. Even then, it won't get far beyond the micron range typically, as damping is pretty high. At mains frequency, permittivity is almost purely imaginary, and severe attenuation and reflection occurs - skin depth for copper at 50 Hz is slightly under 1 cm. Interestingly the speed of such a severely attenuated wave is much less than the speed of sound in the metal - so much for superliminal transmission! Try http://farside.ph.utexas.edu/teaching/315/Waves/node49.html for some finer details. As discussed in #5, transmission velocity is owing to coupling by the fields, not motion of the charges, and can only approach c, being considerably less if dielectric insulation is present. This is all standard transmission-line theory stuff.

24. Aug 21, 2011

### Per Oni

Re: Whether the speed of alternative/direct current is faster than light???

@ Q-reeus
So far you admit that you are at odds with both articles in Wiki and Hyperphysics. To support your view you quote one ambiguous article which shows Fermi sphere pictures explaining one thing and a text explaining a different thing. Now just like you this whole theory is far beyond my capabilities, therefore we are both dependent on what the profs in physics tell us. Let’s take Kittel’s “Introduction to Solid State Physics” page 142 and look at figure 10. There, the whole Fermi sphere is (again) moved by a certain distance. But more important look at equation 42: j=nqv. where v is (as he calls it) the “incremental velocity” and n is the number of electrons per unit volume. This a different formula from the one your article suggests: j=n(Fermi) q V(Fermi).

As an aside: in my opinion your article mixes up the number of scattered electrons with the number of conduction electrons.

And yes I also don’t know why this thread is posted here.

25. Aug 21, 2011

### Q-reeus

Re: Whether the speed of alternative/direct current is faster than light???

The ambiguity is with your interpretation of what is being said there, not the article itself. As per last entry, vast bulk of 'free' electrons are velocity paired and make no net contribution. Displacement of Fermi surface therefore can only be relevant for unpaired fraction. The author makes this plain.
Don't have Kittel but there is practically no chance any real conflicting viewpoint exists between the two. Try looking at the context a bit closer - sure he's not just deriving an *equivalent* expression in terms of Drude model? The author in my article does the same, in the same equation line to that I quoted. Point being shown there is that the Sommerfeld and Drude models finish up with roughly the same overall result for electrical and thermal conduction (but far apart for e.g. electronic specific heat). My copy of Solid State Physics, 2nd Ed'n, - J.S.Blakemore, p185 backs up precisely the account given in my uploaded article - only a tiny fraction of the 'free' electrons carry the current.
You may feel that, but I see no mix up. It is a brief but perfectly standard treatment - that fully qualified university lecturer is no idiot.
Well only that the OP thought faster-than-light might be a realistic prospect. It has gotten sidetracked since, which is pretty typical! :zzz: