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 Subject: electrons in wires Category: Science Asked by: glidera-ga List Price: \$5.00 Posted: 11 May 2004 23:13 PDT Expires: 10 Jun 2004 23:13 PDT Question ID: 345010
 ```If I drop an electron into a perfect, almost infinitely long conducting wire, does the fact that I can observe it at the other end of the wire essentially simultaneously mean that it moves faster than the speed of light?```
 Subject: Re: electrons in wires Answered By: eiffel-ga on 12 May 2004 04:43 PDT Rated:
 ```Hi glidera, Suppose you have a perfect conductor, and "push an electron into one end". You would be able to observe the electrical effect at the other end almost instantaneously, even though that electron has not travelled to the other end of the conductor. In the same way, an electric light comes on almost as soon as you flick the switch, even though the electrons have not travelled along the length of the wire from the switch to the light. Informally, that's because the wire is already "chock full of electrons", so pushing one in at the switch end will push another into the filament of the lamp. But the effect is not truly instantaneous. When you push an electron into one end of the conductor, it "nudges" the next one with its electric field, and so on all the way down the wire until the electrons at the far end are "nudged" and we can detect the signal. The electric field of each electron propagates at the speed of light, but the inertial mass of the electrons will mean that the speed at which the electric signal propagates will fall short of the speed of light: "For a very rough estimate I believe electricity (the field) travels in the range of about 0.66 to 0.9 times the speed of light in a conductor." Ask a Scientist - Voltage and Efficiency http://www.newton.dep.anl.gov/askasci/eng99/eng99174.htm "Electrical signals in a copper wire travel at approximately 2/3 the speed of light." WildPackets ? Technical Compendium, Technology Engineering Networking http://www.wildpackets.com/compendium/EN/EN-Propa.html "Speed of electricity/radio on copper wire: 2.3 x 10^8 m/sec" Metrics.pdf http://nest.cs.uiowa.edu/22C178f00/pdf/metrics.pdf Although for most purposes this appears "instantaneous" to us, there are some situations where the non-instantaneous speed is noticeable. One is the echo that we sometimes hear on a long-distance phone call, caused by the time taken for the electric signal to travel through the phone network and back again. Another is the resonance that can occur on a nationwide electric grid where a reflected signal arrives back in time to reinforce the next cycle. Two further points: Firstly, the same effect is obtained if we "pull an electron out of one end" of a conductor instead of "pushing it in". Secondly, the individual electrons in a conductor move VERY slowly. Here's a web page with some rough calculations (and discussion) showing a speed of 8.4cm (3 inches) per hour for a 100 watt bulb connected to typical lamp cord: Speed of electricity flow (speed of current) http://www.amasci.com/miscon/speed.html Now, having assured you that the propagation speed of the electric signal is very fast but still less than the speed of light (under all circumstances, in a conducting wire) I will whet your appetite with two pieces of recent research, one of which refers to a displacement current moving faster than the speed of light, and one of which (cautiously) refers to an electromagnetic signal moving faster than the speed of light: "We are developing a completely new type of solid-state light source, the Polarisation Synchrotron; the machine is based on the interchangability of displacement current and real current in Maxwell?s Equations. However, because displacement current has no inertial mass, it may be moved faster than the speed of light, resulting in extraordinary emission properties which our source exploits." Current Research ? Quantum optoelectronics (scroll to last entry on page) http://www.physics.ox.ac.uk/CM/QuanOpt.html "A near-field analysis ... indicates that the fields generated ... propagate superluminally in the nearfield of the source and reduce to the speed of light as the waves propagate into the farfield ... It is shown that relativity theory indicates that these superluminal signals can be reflected off a moving frame causing the information to arrive before the signal was transmitted (i.e. Backward in time). It is unknown if these signals can be used to change the past." Near-field Analysis of Superluminally Propagating Electromagnetic and Gravitational Fields http://arxiv.org/pdf/gr-qc/0304090 The math in these papers is beyond me, but it seems like fascinating stuff! Please request clarification if this answer does not yet meet your needs. Google Search Strategy: "speed of electric current" ://www.google.com/search?hl=en&q=%22speed+of+electric+current%22 "speed of electric current" light ://www.google.com/search?q=%22speed+of+electric+current%22+light "speed of electric" "speed of light" ://www.google.com/search?hl=en&lr=&q=%22speed+of+electric%22+%22speed+of+light%22 "propagation speed" "electricity" copper ://www.google.com/search?hl=en&lr=&q=%22propagation+speed%22+%22electricity%22+copper Regards, eiffel-ga``` Request for Answer Clarification by glidera-ga on 12 May 2004 11:15 PDT ```I thank you for your thorough search, but one thing I must mention. We observe a current almost instanenously, but not quite, under an applied voltage. The example I was referring to was an isolated, nearly infinitely-long wire NOT connected to any battery so electrons do not feel any force so they do not move due to an applied electrostatic field. What I was referring to was the fact that if the wire is indeed perfect, there will exist a molecular orbital called the Lowest Unoccupied Molecular Orbital (LUMO) extending through the length of the wire such that the electronic wavefunction will be delocalized over the entire wire, and the probability to find the electron is the same everywhere along the wire so that I can observe it indeed instantaneously at the other end infinitely far away from the other end where the electron was initially "dropped". Once again, I appreciate your input and your time.``` Clarification of Answer by eiffel-ga on 12 May 2004 13:27 PDT ```My apologies, glidera, I did not see anything in your question to suggest that you were seeking a quantum physics explanation - and indeed I would not be able to give one. Having said that, I have a few comments to add: 1. It's not clear to me how you can disregard electrostatic fields as you "drop an electron into" one end of a conductor. Even though we're not using a battery, won't we need to consider the electrostatic field of the added electron as it approaches the wire? 2. Suppose the wave functions of electrons in the (perfect) conductor are indeed delocalized over the whole length of the conductor. Won't it then be the case that as the length of the conductor approaches infinity the probability of finding our new electron at the other end approaches zero? And with a near-infinite conductor, doesn't the energy difference between the Highest Occupied Molecular Orbital and Lowest Unoccupied Molecular Orbital become vanishingly small (because we have so many molecular orbitals)? So how are we going to measure this effect? But your core point is that the effect of the new electron is not confined to a point but is present in the wavefunction across the entire extent of the conductor, and that is a fascinating point. Regards, eiffel-ga``` Request for Answer Clarification by glidera-ga on 12 May 2004 13:41 PDT ```Eiffel, you make excellent points, I've concluded that it was worth my \$5 to engage in this discussion, and once again I thank you for your time. You are completely right, the situation I presented is entirely artificial, and you would not indeed be able to ignore such electrostatic effects when the electron approaches the wire, but then again there is no such thing as a perfect wire either. :) As far as the band gap is concerned, I could modify the question to ask just about a long wire and not infinitely long, also I don't believe you would necessarily need the HOMO-LUMO gap i.e. there are methods other than spectroscopic ones such as scattering, etc. that I'm sure may be used. Once again, this situation would never exist and I applaud your rebuttle to my last point. Again I appreciate this discussion. (If you have nothing better to do, we could potentially continue this discussion - langaidin10@hotmail.com). Thank you and have a good day.``` Clarification of Answer by eiffel-ga on 12 May 2004 23:44 PDT `Thanks for the kind comments and tip, glidera.`

 ```Just a comment that's only tangentially related to your question. The specific electron that you ?dropped? will move rather slowly. In fact you can walk faster than it travels. However, the energy moves very fast.```
 ```Like I said, I wasn't talking about conduction through a wire under an EMF. This is a strictly a quantum mechanical effect, although one may argue that so is conduction; however, the conduction phenomenon may be reduced to a rather classical picture, which would suffice to get a superficial understanding. One cannot do that with wavefunction delocalization.```
 ```What struck me odd is - if all matter can be represented as energy, or structured energy in some formal system, it seems 'particle' or 'matter' are mute - as all is E - only particle when observed ? yes ?```
 ```Yes, using the word "particle" is very misleading since we KNOW that matter isn't particle-like, but wave-like. However, we find that a particle description serves often as a very good approximation. After all, fundamental "particles" and photons do have particle character to them. And you're right, the particle nature will only manifest when you observe your system.```