Speed of Electricity: Is it Possible for Electrons to Travel at c?

[fred2028]

What is the speed? If the speed of electricity is c, then how is it possible that an electron, with a rest mass, can travel at c?

 

[Troels]

What is the speed? If the speed of electricity is c, then how is it possible that an electron, with a rest mass, can travel at c?

(I assume that by "speed of electricity" you mean the time it takes between you flip the switch and the bulb lits)

First: The speed of electricity is *not* the same as the speed of the electrons. A single electron in a wire moves at snails pace. But there are a huge number of them, and once you aply a potential difference (electric field) over the wire, they all start to move at onces. Picture it, if you like, as a long lane of small balls. If you push the one end slowly, they all start to move, and you transmit your push to the end of the lane immediately.

Second: They do not start to move at entirely the same time. The electric field will move trough the wire at the speed of light in that material of which the wire happens to be made - but that's not c. It is slower. But still, way faster than human perception for any household wirering.


Edit: Okay, so "speed of electricity" commonly referes to the drift velocity of electrons, so I got that part wrong.

 

[stewartcs]

What is the speed? If the speed of electricity is c, then how is it possible that an electron, with a rest mass, can travel at c?

Here you go...

http://howthingswork.virginia.edu/search.php?searchs=speed+of+electricity&searchq=yes&searcha=yes

http://en.wikipedia.org/wiki/Speed_of_electricity

CS

 

[drv]

Contradiction

(I assume that by "speed of electricity" you mean the time it takes between you flip the switch and the bulb lits)

First: The speed of electricity is *not* the same as the speed of the electrons. A single electron in a wire moves at snails pace. But there are a huge number of them, and once you aply a potential difference (electric field) over the wire, they all start to move at onces. Picture it, if you like, as a long lane of small balls. If you push the one end slowly, they all start to move, and you transmit your push to the end of the lane immediately.

Second: They do not start to move at entirely the same time. The electric field will move trough the wire at the speed of light in that material of which the wire happens to be made - but that's not c. It is slower. But still, way faster than human perception for any household wirering.


Edit: Okay, so "speed of electricity" commonly referes to the drift velocity of electrons, so I got that part wrong.

The movement of electrons in an antenna does not work this way. The electron distribution over a length of 1/4 wavelength is sinusoidal. The zero voltage point moves across the wire at the speed of light. Therefore, the current movement is not transferred immediately from one end to the other.

If you believe atoms having orbiting electrons, then there is another contradiction. It takes time for an electron to move from one point on the orbit to another. At times, it will take the time to move 1/2 wavelength to get to the opposite side. According to the old Bohr model of the atom, this speed is less than 1% of the speed of light. Therefore, it would require a lot of atoms to get one electron to move at a speed approaching the speed of light.

Another consideration is the inductance of the line, which also slows the electrons. At low frequencies, an antenna is longer and the (total) inductance is higher. The wave still moves at the speed of light.

Adding up all of these consistencies, it is tempting to believe that the electrons do move at the speed of light in an atom. In order to accommodate this new inconsistency, a new physical model of the atom is needed (which is not a bad idea).

 

[Astronuc]

What is the speed? If the speed of electricity is c, then how is it possible that an electron, with a rest mass, can travel at c?

The electric (and magnetic) field propagates at the speed of light, but the changes in the electric field are affected by the speed of the electrons. Photons (EM radiation) move at the speed of light, but they have different frequencies, and therefore energy.

 

[drv]

A profound question: Can electrons move at the speed of light?

The electric (and magnetic) field propagates at the speed of light, but the changes in the electric field are affected by the speed of the electrons. Photons (EM radiation) move at the speed of light, but they have different frequencies, and therefore energy.

Both of the above observations are correct. However, this situation is even more complex. When an electron moves, its mass changes from its rest mass. As the electron approaches the speed of light, the mass approaches zero. Therefore, for fast-moving electrons, the mass change must be taken into account, especially when integrating the energy equation as a function of the distance to other charges in the vicinity. Another complexity is that high-speed objects have two masses: the longitudinal mass and the transverse mass. These facts have profound consequences, especially since these little details are generally disregarded.

 

[Astronuc]

When an electron moves, its mass changes from its rest mass. As the electron approaches the speed of light, the mass approaches zero.

According to Special Relativity, as objects approach the speed of light, the mass increases. This is observed in accelerators (cyclotrons, synchrotrons, linacs, . . . ) which accelerate electrons or protons to relativistic speeds.

 

[drv]

According to Special Relativity, as objects approach the speed of light, the mass increases. This is observed in accelerators (cyclotrons, synchrotrons, linacs, . . . ) which accelerate electrons or protons to relativistic speeds.

Your statement is quite correct. But there are two relativistic masses, as I have stated: the longitudinal mass and the transverse mass, both of which may vary with velocity. The relationship between the two masses is [m sub(tr)]/[m sub (lo)]= (1 - v^2/c^) , where v is the velocity of the mass point in a vacuum. As the velocity of the mass point approaches the speed of light, the ratio of the tranverse mass to the longitudinal mass approaches zero. This is a mathematical limit problem. If the tangential mass is slightly less than zero, then the longitudinal mass must be quite large. One can argue that both approach infinity as the velocity approaches the speed of light, in which case we are dealing with infinity divided by infinity. Many possible values can be assumed. Substitute [m sub(lo)] = N*[m sub(tr)] into this equation, and the limit does not approach zero. It always stay at 1/N on both sides of the equation. For the limit, N = infinity, the transverse mass goes to zero, which allows infinite velocity in the transverse direction!

Further comments on this important (but often overlooked) problem are most certainly invited.

 

[rewebster]

"AC voltages cause no net movement; the electrons "wiggle" back and forth in response to the alternating electric field."

http://en.wikipedia.org/wiki/Speed_of_electricity

I've always found this an interesting facet (bold type).

 

[drv]

You are misinterpreting this. AC voltages do not produce a "net movement". The electrons flow back and forth in the direction of the voltage source. There is an internal random current flow within metals that is a function of temperature. You will find this described in most physics texts, and the equations that I supplied are utilized in the design of semiconductors, etc.

 

[Doc Al]

Your statement is quite correct. But there are two relativistic masses, as I have stated: the longitudinal mass and the transverse mass, both of which may vary with velocity. The relationship between the two masses is [m sub(tr)]/[m sub (lo)]= (1 - v^2/c^) , where v is the velocity of the mass point in a vacuum. As the velocity of the mass point approaches the speed of light, the ratio of the tranverse mass to the longitudinal mass approaches zero. This is a mathematical limit problem. If the tangential mass is slightly less than zero, then the longitudinal mass must be quite large. One can argue that both approach infinity as the velocity approaches the speed of light, in which case we are dealing with infinity divided by infinity. Many possible values can be assumed. Substitute [m sub(lo)] = N*[m sub(tr)] into this equation, and the limit does not approach zero. It always stay at 1/N on both sides of the equation. For the limit, N = infinity, the transverse mass goes to zero, which allows infinite velocity in the transverse direction!

Further comments on this important (but often overlooked) problem are most certainly invited.

I see no problem at all, much less an important one. If you insist on using relativistic mass terminology, then both longitudinal and transverse "relativistic" masses go to infinity as the speed approaches c. What's the problem? No danger of any massive particle (invariant mass > 0, that is) traveling at the speed of light.

What do you mean by "If the tangential mass is slightly less than zero..."? How does that happen?

 

[rewebster]

You are misinterpreting this. AC voltages do not produce a "net movement". The electrons flow back and forth in the direction of the voltage source. There is an internal random current flow within metals that is a function of temperature. You will find this described in most physics texts, and the equations that I supplied are utilized in the design of semiconductors, etc.

I'm not misinterpreting it---I thought it was an interesting facet.

 

[Mentz114]

drv:

For the limit, N = infinity, the transverse mass goes to zero, which allows infinite velocity in the transverse direction!

This is an unphysical argument. N cannot reach infinity. Infinity is a mathematical concept, and you are talking out of your hat. Electrons cannot reach light speed, in any direction or inertial frame.

 

[Troels]

The movement of electrons in an antenna does not work this way. The electron distribution over a length of 1/4 wavelength is sinusoidal. The zero voltage point moves across the wire at the speed of light. Therefore, the current movement is not transferred immediately from one end to the other.

Have I ever said that the current movement in *any* wire is transferred immediately from one end to the other?

If you believe atoms having orbiting electrons, then there is another contradiction. It takes time for an electron to move from one point on the orbit to another. At times, it will take the time to move 1/2 wavelength to get to the opposite side. According to the old Bohr model of the atom, this speed is less than 1% of the speed of light. Therefore, it would require a lot of atoms to get one electron to move at a speed approaching the speed of light.

I *do not* believe so, nor have I ever said that I do. I am well schooled in solid state physics but please, do not ask me to account formally for the quantum mechanical transport theory of electrons in solids. It is so terribly crumblesome, let alone totally irrelevant for the question at hand.

Another consideration is the inductance of the line, which also slows the electrons. At low frequencies, an antenna is longer and the (total) inductance is higher. The wave still moves at the speed of light.

Here *you* are quite wrong; a straight wire has vanishing inductance, but for the sake of argument: the inductance opposes rapid chances in the current, but it doesn't matter where in the circuit you put the inductor. That is because it is accturally messing with the wave. Mind, not it's speed, but it's strenght.

Adding up all of these consistencies, it is tempting to believe that the electrons do move at the speed of light in an atom. In order to accommodate this new inconsistency, a new physical model of the atom is needed (which is not a bad idea).

Now, what kind of nonsense is this?

 

[Mentz114]

Adding up all of these consistencies, it is tempting to believe that the electrons do move at the speed of light in an atom. In order to accommodate this new inconsistency, a new physical model of the atom is needed (which is not a bad idea).

And throw away special relativity ? You don't know what you are talking about.

Now, what kind of nonsense is this?

Thank you, Troels.

drv obviously is pushing some crackpot theory

 

[drv]

And throw away special relativity ? You don't know what you are talking about.


Thank you, Troels.

drv obviously is pushing some crackpot theory

It may be easy for some to jump to this conclusion. Before you do this, however, consider the tangential mass equation and the longitudinal mass equation. Both relativistic equations do (mathematically) go to infinity as the velocity approaches the speed of light, just as has been stated below. However, there is also the equation that I presented below on 1/20.

Divide the tangential mass by the longitudinal mass as the velocity approaches the speed of light. The ratio of the tangential mass to the longitudinal mass goes to zero as the velocity approaches the speed of light. Hasn't anyone else ever wondered about these rather three odd simultaneous results - - for masses that have become quite different?

Now consider what this means. One way to interpret this is that the speed of the particle is unlimited when the mass reaches zero, but not infinity as Mentz points out, even though zero mass should be able to have unlimited velocity. This suggests to me that there will be a limited mass velocity. Then solve those three simultaneous equations. You may end up getting more than one solution, depending on your approach. I used vector analysis. The transverse velocity is orthogonal to the longitudinal velocity, and the sum of the absolute values of the vectors is the absolute velocity of the particle, which could be traveling in a stable circle. I obtained a very interesting result by invoking one other well known law of physics.

New theory? Perhaps. Crackpot theory? Perhaps. There are a lot of those going around. Does seem to be quite a simple little problem, though, with just two or three equations.

I am very curious as to what others might find in working this little exercise. Call me what you like, but let's try to deal with the facts, as we have them.

 

[Troels]

(Comment: When you state equations, please use the tex feature. Really, its not that difficult and it enormously increases the readability of your formalism)

It may be easy for some to jump to this conclusion. Before you do this, however, consider the tangential mass equation and the longitudinal mass equation. Both relativistic equations do (mathematically) go to infinity as the velocity approaches the speed of light, just as has been stated below. However, there is also the equation that I presented below on 1/20.

What, you mean this thing?

<br /> \frac{m_\mathrm{tr}}{m_\mathrm{lo}}=1-\frac{v^2}{c^2}<br />

One question: From *where* does that equation come? Surely you would have a reference or a calculation as basis for "your statement".

I obtained a very interesting result by invoking one other well known law of physics.

Care to explain which?

New theory? Perhaps. Crackpot theory? Perhaps. There are a lot of those going around.

There sure is, and the last thing we need is more of them. So please, try to come clean and share your enlightment with us fully and formally.

Call me what you like, but let's try to deal with the facts, as we have them.

Which is the favourite phrase of crackpot theory pushers, as is the lack of formalism and mysterious results pulled out of thin air.

And you still haven't further commented this bit:

Adding up all of these consistencies, it is tempting to believe that the electrons do move at the speed of light in an atom. In order to accommodate this new inconsistency, a new physical model of the atom is needed (which is not a bad idea).

*why* does your so-called results call for a new model of the atom? All that I have seen so far is a few vauge hints and statements concerning idealized single-particle movement in special relativity, which after all doesn't apply an inch to atomic structure, the undisputed realm of quantum mechanics.

 

[chroot]

Personal theories are not welcome here. drv, please do not use this forum as a sounding board for your own personal concepts. Furthermore, please do not derail legitimate threads about legitimate topics.