## classical physics vs relativity: parallel electron beams

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trevbus
Posts: 59
Joined: Sat Apr 26, 2008 12:50 am

### classical physics vs relativity: parallel electron beams

Can someone explain to me how two parallel electron beams can be attracted to each other according to special relativity.

Classical physics says each beam will generate a magnetic field so the beams will be attracted to each other.

Relativity says the magnetic field only exists for observers moving relative to the electron beam, hence there is no magnetic field if the beams are moving in parallel and at the same speed.

I have been searching for an explanation, here is the closest I got to a discussion of this issue and the so-called expert doesn't even understand the question!

http://en.allexperts.com/q/Physics-1358 ... -LAW-2.htm

I am not concerned with relativistic speeds - relativity should explain magnetism at any speed.

There are numerous other discussions explaining how conducting wires are attracted (ie Ampere's experiment), due to the electrons moving relative to the positive metal atoms in the other wire, but there is no equivalent conductive medium in an electron beam!

Farsight
Posts: 142
Joined: Thu Mar 26, 2009 3:39 pm

### Re: classical physics vs relativity: parallel electron beams

Trevbus: can you give me a reference re the beams being attracted to one another?

People don't quite understand the electromagnetic field. They don't understand that there's a dualism. There's only one field there, but there's two different ways of seeing it, feeling it, detecting it. It's one field and two forces, not two fields. See Jefimenko's_equations and note this paragraph:

"There is a widespread interpretation of Maxwell's equations to the effect that time variable electric and magnetic fields can cause each other. This is often used as part of an explanation of the formation of electromagnetic waves. However, Jefimenko's equations show otherwise. Jefimenko says, "...neither Maxwell's equations nor their solutions indicate an existence of causal links between electric and magnetic fields. Therefore, we must conclude that an electromagnetic field is a dual entity always having an electric and a magnetic component simultaneously created by their common sources: time-variable electric charges and currents."

If you think about a single electron, it's got an electric field, which is kind of spherical. An electron doesn't have a magnetic field. Now think about a line of electrons: it's got an electrical field, which is kind of cylindrical. But this line of electrons doesn't have a magnetic field. However if you move down this line of electrons, or if it moves past you because it's an electron beam, you see a magnetic field. The electric field hasn't "generated" this magnetic field. It's just how you see the electromagnetic field when you're in relative motion with respect to it.

This is because the electric field is a "twist" field. But if you move through it, or it moves through you, you see it as a "turn" field. It really is this like. This is why we have alternators and dynamos and electric motors. Look at the right hand rule:

The red line is the current in a wire. It's just a line of electrons moving upwards, causing this rotation. Now find a reamer and grip it in your right hand. Push up on the bottom with your left. It's got this twist to it, so it turns. If you could see a column of electric field around the wire, that's what it would look like:

The electron's electric field is isotropic in three dimensions, like a ball studded all around with Fibonacci spirals. Contrive a line of electrons in a wire or a beam, and move past it, and you experience a net orthogonal turn. This is how it is, how it's always been, and it goes back at least as far as Minkowski. Take a look at Space and Time, two pages from the end:

"Then in the description of the field produced by the electron we see that the separation of the field into electric and magnetic force is a relative one with regard to the underlying time axis; the most perspicious way of describing the two forces together is on a certain analogy with the wrench in mechanics, though the analogy is not complete".

The wrench is important. It's associated with a screw thread. Like that reamer. All this is legit stuff, it's both old, and it's new. It's called relativity+. Take a look at the Institute of Physics "PhysicsWorld" website http://physicsworld.com/cws/article/news/40780 and look at the bottom right. Everything comes down to electrodynamics in the end, which is where relativity began. It's an electric universe, and it's really really simple. Sometimes I think it's too simple, and people can't believe how simple it is, and prefer instead to look for something complicated.

Farsight
Posts: 142
Joined: Thu Mar 26, 2009 3:39 pm

### Re: classical physics vs relativity: parallel electron beams

Trevbus: see what I said above, have a think about it, and then look up "braided jets" to find articles like this:

http://sci.esa.int/science-e/www/object ... ctid=37721

"NASA's Hubble Space Telescope has provided a detailed view of a ten thousand light-year long jet of plasma which has been ejected from the core of a galaxy 270 million light-years away. Observations made with the European Space Agency's Faint Object Camera (FOC) reveal that the jet has an unusual braided structure, like a twisted pair of wires. "This is the first time that such a structure has been seen in an optical jet," says F. Duccio Macchetto, ESA's Principal Investigator on the FOC and Head of the Science Programs Division at the Space Telescope Science Institute."

If two parallel electron beams are travelling at different speeds, the right hand rule applies, and each "sees" the electric field of the other as a magnetic field. Hence the twist field appears to be a turn field, and the two beams spiral around one another.

earls
Posts: 275
Joined: Thu Mar 20, 2008 6:48 am

### Re: classical physics vs relativity: parallel electron beams

So stationary charge = electric field; moving charge = magnetic field?

I'm not sure you answer his question though...

If the two beams are moving at the exact same speed (appear stationary to each other), then there appears to be no magnetic field, and if there is no magnetic field, what is pulling the beams together?

"Sometimes I think it's too simple, and people can't believe how simple it is, and prefer instead to look for something complicated."

Absolutely, positively agree. We can talk about this, that and the other, but our "basis" - quantum mechanics is based on EM. Regardless of how large you scale up, THE FOUNDATION IS STILL EM. At no point does EM magically become irrelevant, contrary to what is generally purported.

Farsight
Posts: 142
Joined: Thu Mar 26, 2009 3:39 pm

### Re: classical physics vs relativity: parallel electron beams

earls wrote:So stationary charge = electric field; moving charge = magnetic field?
Yep. And since motion is relative, if it's you moving instead of the charge you see its electric field as a magnetic field. There's only really one field there.
earls wrote:I'm not sure you answer his question though...

If the two beams are moving at the exact same speed (appear stationary to each other), then there appears to be no magnetic field, and if there is no magnetic field, what is pulling the beams together?
Nothing. That's why I asked for a reference. If you simplify it to two single electrons moving at the same speed, then simplify it further to say they're not moving at all, they don't pull together, they repel. You have to have two electron beams with different velocities to get that braided galactic jet, then an electron in beam 2 sees the electric field of an electron in beam 1 as a magnetic field, and moves in a helical path:

earls wrote:Farsight: "Sometimes I think it's too simple, and people can't believe how simple it is, and prefer instead to look for something complicated."

Absolutely, positively agree. We can talk about this, that and the other, but our "basis" - quantum mechanics is based on EM. Regardless of how large you scale up, THE FOUNDATION IS STILL EM. At no point does EM magically become irrelevant, contrary to what is generally purported.
I totally agree. It's an electric universe. And the quantum of quantum mechanics is simple too. See Planck's constant. It's the h in E=hf, and it's hidden in plain view:

"The Planck constant has dimensions of energy multiplied by time, which are also the dimensions of action. In SI units, the Planck constant is expressed in joule seconds (J·s). The dimensions may also be written as momentum multiplied by distance (N·m·s), which are also the dimensions of angular momentum".

Sorry, I'm going off topic there. maybe this deserves its own thread.

jjohnson
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Location: Thurston County WA

### Re: classical physics vs relativity: parallel electron beams

If you need a more rigorous textbook reference as to how parallel electron beams end up attracting each other (regardless of relative electron velocities) refer to A. Peratt's book, Physics of the Plasma Universe, Chapter 3, Biot-Savart Law in Cosmic Plasma, especially the parts after the electrostatic force considerations, starting at 3.8 on p. 108. He sets up a net neutral plasma to begin with, with 2 current-conducting plasma filaments in parallel alignment in the same magnetic guide field. The plasma particles are initially thermalized at some temperature - "a few kiloelectron volts" - which is constant at all points - to keep starting conditions as simple as possible for a particle-in-cell (PIC)simulation of the forces which accrue. This note is a brief summary of the parts referring to motion.

Incidentally, Peratt shows that even with three or more parallel filaments the forces tend to bring only two parallel currents together and initiate a twist or pinch (3.10.6). The "ignored" filament(s) remain quiescent. I doubt that the Standard Model could predict any of this, in its current (NPI - I should call it "non-current") state.

Schlieren photographic images of parallel 15mm stainless steel wires, which are vaporized into parallel plasma filaments, indicate that the two filaments, after 250kA pulse initiation, radiate (X-ray) for about 5 ns, and then the two filaments move toward each other (he notes asymmetrically at first, one moving initially) and as they get rather close the forces start them into the spiral around one another. This is what creates stars or galaxies if scaled up to truly cosmic dimensions, instead of just little 9/16" diameter wires pulsed by a megaW discharge in a vacuum tank.

This is not a trite simulation. 3-D forces are involved, and any perturbation one place affects everything else. In real (more or less analog) conditions, this is a smooth process (although smooth and ultra-fast and ultra-slow can all happen, depending on the evolution and energy release rates, etc.). In the digital computer, it has to be stepped. How this is done is generally described in Chapter 8 and Appendix E (TRISTAN program code). The experiments with real plasmas are well simulated by the PIC computer simulation.

The Biot-Savart forces generated by the parallel currents are long-range attractive and short-range repulsive, Figure 3.13. This moves the filaments together at first but prevents their actually simply merging under free plasma conditions. The current electrons spiral around magnetic field lines (domains of equal magnetic field strength) perpendicular to the net flow direction of the currents , in helices in one direction, while the positive ion component of the current spiral similarly in the opposite direction. The gyroradii of the two species are different because their masses are different Polarization occurs in each converging filament since it is moving across the field lines of the longitudinal guide magnetic field. The cross sections of the converging filaments, initially circular, "thin out" in section and deform into oval shapes and then into "jelly bean" shapes as they twist around each other, seen end-on, or axial view. This does not get into a lot of detail as to how the entrained plasma material is compressed and heated, or how various atomic weights are or are not separated, or the influences of grainy and dusty inclusions in the plasma, but that is not the question at hand.

Hope this helps. Wish this text hadn't had such a short press run. It deserves far wider dissemination than it gets, and its relative rarity has driven the price out of reach of all but wealthy collectors or investors in rare books. I just happened to luck into a sale and get it for a few hundred bucks. It really explains a lot.

Farsight
Posts: 142
Joined: Thu Mar 26, 2009 3:39 pm

### Re: classical physics vs relativity: parallel electron beams

jj: you mentioned "generated" and the Biot-Savart law. Can I just point out that what we read here in wikipedia http://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law is wrong:

"The Biot–Savart law (pronounced /ˈbiːoʊ səˈvɑr/ or /ˈbjoʊ səˈvɑr/)[1] is an equation in electromagnetism that describes the magnetic field B generated by an electric current".

I'm not saying the Biot-Savart law is "wrong", just that the idea of an electric current generating a magnetic field is wrong. There's only one field, the electromagnetic field. See Jefimenko's equations at http://en.wikipedia.org/wiki/Jefimenko's_equations and note this:

'There is a widespread interpretation of Maxwell's equations to the effect that time variable electric and magnetic fields can cause each other. This is often used as part of an explanation of the formation of electromagnetic waves. However, Jefimenko's equations show otherwise. [3] Jefimenko says, "...neither Maxwell's equations nor their solutions indicate an existence of causal links between electric and magnetic fields. Therefore, we must conclude that an electromagnetic field is a dual entity always having an electric and a magnetic component simultaneously created by their common sources: time-variable electric charges and currents".'

IMHO this dualism is crucial to understanding the electromagnetic field.

junglelord
Posts: 3693
Joined: Mon Mar 17, 2008 5:39 am

### Re: classical physics vs relativity: parallel electron beams

How can you have a e- or a p+ without a magnetic moment?
Of course its a dual and even more its a triad, Magnatism, EM, ES.
If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.
— Nikola Tesla
Casting Out the Nines from PHI into Indigs reveals the Cosmic Harmonic Code.
— Junglelord.
Knowledge is Structured in Consciouness. Structure and Function Cannot Be Seperated.
— Junglelord

Farsight
Posts: 142
Joined: Thu Mar 26, 2009 3:39 pm

### Re: classical physics vs relativity: parallel electron beams

You can't, see http://en.wikipedia.org/wiki/Spin_magnetic_moment, but note that this bit is wrong: In quantum mechanics, elementary particles are points, which have no axis to revolve around. This means these particles do not have spin in a classical sense. The electron is not a point particle, just as a radio wave is not a point particle, because annihilation tells us that the electron is a special configuration of a 511keV photon.

jjohnson
Posts: 1147
Joined: Mon Feb 16, 2009 11:24 am
Location: Thurston County WA

### Re: classical physics vs relativity: parallel electron beams

Farsight: conceded! - thanks; I should have said "accompanied by". On a different identification - calling elementary particles "points" is a result of physicists' constant confusion between math and the real world of real things. And while we are talking dualities +, don't forget that gravity forces accompany those particles which we postulate to have mass. Also, how can a "point" have a spin, which implies revolution at some distance from a center (where, mathematically, the "point" resides!)

Here we get to go on another field trip with Miles Mathis. He postulates that even photons have mass, even if it is not rest mass (they don't stop and rest!) - because they have energy, and cannot violate the energy equivalence postulated by Einstein's E = mc². He has a paper on the photon's mass that I won't get into here, although it is photons which create the forces which we observe, in his view of reality. Today's Forum reference to his latest paper, on calculating the position of the Earth's magnetopause or ionopause using his Unified Field (gravity + EM) seems right on, and although he doesn't agree with ALL of either EU or conventional physics, he has some stunningly absorbing ideas for us to investigate in hunting down how and why things behave as they do. He also is adept at pointing out where conventional math has gone south, and is not shy about substituting his vision for theirs. I have a question in to him right now about the feasibility of solving a 3-body problem in his Unified Field system, after reading his paper on the Saturn-Jupiter orbital anomaly and Laplace's mathematical obfuscations about that. Damn, so much to learn about...

Farsight
Posts: 142
Joined: Thu Mar 26, 2009 3:39 pm

### Re: classical physics vs relativity: parallel electron beams

Good stuff jj, we're singing from the same sheet here.
jjohnson wrote:Here we get to go on another field trip with Miles Mathis. He postulates that even photons have mass, even if it is not rest mass (they don't stop and rest!) - because they have energy, and cannot violate the energy equivalence postulated by Einstein's E = mc². He has a paper on the photon's mass that I won't get into here, although it is photons which create the forces which we observe, in his view of reality.
Somebody pointed him out to me yesterday, and I was looking at his website. There's some interesting stuff there, and I've emailed him saying we've got a lot we ought to talk about. I'll check out his paper on the photon mass. Meanwhile can I say that photons don't have mass in the usual sense. E=hf applies, not E = mc². But maybe the problem here is that people use the word mass in different ways. The "accepted" definition of mass is rest mass*, which is defined as the total energy of a system divided by c². It's a measure of how much energy is not moving in aggregate with respect to you. A photon is moving at c, hence mass doesn't apply. But put it inside a mirrored box so it bounces back and forth, and it increases the mass of that system. By the by, rest mass is a misnomer, it ought to be rest energy, only that's a misnomer too, because it isn't at rest. The electron has spin. It's like a photon going round and round inside a spherical mirrored box, only there is no box. All this stuff is something I feel I know like the back of my hand. Here's another excerpt to give an indication of how so:
Farsight wrote: MASS EXPLAINED

You know that energy is an intangible thing. You can’t hold energy in the palm of your hand, because energy is to do with stress, which is the same as pressure, and you need a volume of stress to get the dimensionality right.

You know that mass is a tangible thing. You can hold an object in your hand and feel the mass of it. You even know that E=mc², and that the intangible thing called energy can be used to make the tangible thing called mass. But you don’t know how, because you don't know how simple it really is.

The answer is all down to motion. Or the lack of it. You have to get relative, because motion is relative, and you have to think in terms of momentum and inertia. A 10kg cannonball is a tangible thing, you can hold it in the palm of your hand and feel the mass of it. And if it’s travelling at 1m/s it’s “got” kinetic energy as quantified by KE=½mv2. It’s also “got” momentum, as quantified by p=mv, and it’s hard to stop. Brace yourself, then apply some constant braking force by catching it in the midriff. Ooof, and you feel the energy/momentum. Kinetic energy is looking at this in terms of stopping distance, whilst momentum is looking at it in terms of stopping time. The measure we call momentum is conserved in the collision because your gut and the cannonball shared a mutual force for the same period of time. The measure we call kinetic energy isn’t conserved, because some of the mass in motion is redirected into your deformation and heat and bruises, all of which involve mass in motion, but scattered motion instead of the tidy motion of a mass moving relative to you. Or you moving relative to it, because all the while you were never too sure whether it was you moving or the cannonball.

When we consider that the cannonball is stationary and it’s you moving at 1m/s, the cannonball hasn’t got any kinetic energy or momentum, all it’s got is inertia. You’re attempting to move it and accelerate it to your velocity of 1m/s, and that makes it harder to start, not harder to stop. In this respect momentum and inertia can be considered as two different aspects of the same thing, and that thing is energy...

* There’s also active gravitational mass which tells you how much gravity the energy causes, and passive gravitational mass, which is a measure of how much an object is attracted by gravity. People also talk of inertial mass, which tells us how much force we need to apply to accelerate or decelerate an object. Then there’s relativistic mass, which is just a measure of energy, which is why it applies to a photon.

trevbus
Posts: 59
Joined: Sat Apr 26, 2008 12:50 am

### Re: classical physics vs relativity: parallel electron beams

jjohnson wrote:If you need a more rigorous textbook reference as to how parallel electron beams end up attracting each other (regardless of relative electron velocities) refer to A. Peratt's book, Physics of the Plasma Universe, Chapter 3, Biot-Savart Law in Cosmic Plasma, especially the parts after the electrostatic force considerations, starting at 3.8 on p. 108. He sets up a net neutral plasma to begin with, with 2 current-conducting plasma filaments in parallel alignment in the same magnetic guide field. The plasma particles are initially thermalized at some temperature - "a few kiloelectron volts" - which is constant at all points - to keep starting conditions as simple as possible for a particle-in-cell (PIC)simulation of the forces which accrue. This note is a brief summary of the parts referring to motion.

Incidentally, Peratt shows that even with three or more parallel filaments the forces tend to bring only two parallel currents together and initiate a twist or pinch (3.10.6). The "ignored" filament(s) remain quiescent. I doubt that the Standard Model could predict any of this, in its current (NPI - I should call it "non-current") state.
OK thanks. So the slower electrons are attracted to the faster ones, and the faster ones are repelled by the slower ones. I will have to borrow Peratt's book again.

mharratsc
Posts: 1405
Joined: Mon Jan 26, 2009 7:37 am

### Re: classical physics vs relativity: parallel electron beams

<Everything jjohnson says>
Jim is so smart that he hurts my brain. o.O
Mike H.

"I have no fear to shout out my ignorance and let the Wise correct me, for every instance of such narrows the gulf between them and me." -- Michael A. Harrington

kschalm
Posts: 3
Joined: Tue Jul 28, 2009 4:50 pm

### Re: classical physics vs relativity: parallel electron beams

Can someone explain to me how two parallel electron beams can be attracted to each other according to special relativity.

Classical physics says each beam will generate a magnetic field so the beams will be attracted to each other.

Relativity says the magnetic field only exists for observers moving relative to the electron beam, hence there is no magnetic field if the beams are moving in parallel and at the same speed.

I have been searching for an explanation, here is the closest I got to a discussion of this issue and the so-called expert doesn't even understand the question!
Let me try to have a crack at this. technically, farsight has answered the question, but very briefly. I'm actually not qualified to answer this so if i need correcting, somebody please do... but i'll tell you how i think it works.

first i'd like to agree that the "expert" you asked is not trying very hard to understand what you're asking (or more accurately, where you're coming from). for one thing it is a red herring for him to say that the electrons are moving at different speeds. it is normal in science to construct an ideal scenario to simplify the discussion, and that's what you've done; you are certainly allowed to say that the electrons are all moving at the same speed. then the expert correctly implies that the magnetic field seen in one reference frame is not seen in the other and neither are its effects -- but doesn't say so directly, just talks about apples.

to be explicit, neither the magnetic field nor its effect of moving the electron beams closer together, are seen in the reference frame of the electrons. so, the distance between the beams, as measured by the electrons (!), is L1, and the distance as measured by the scientist in the lab is L2, and L2 < L1. which one is correct?

both!

in relativity there is no "privileged" frame of reference. you cannot ask "who is right?". both are right. they disagree about what is being measured, and that is in the nature of reality.

if i understood you correctly, you were starting with the belief that the distance between the beams would be observed equally in all reference frames -- that it is an absolute quantity, and thus there is a mystery force to be explained, the ghost of magnetism. but the relativistic equations that transform coordinates between reference frames also mess with distances (and EM fields, and time, and mass...). that might sound like a weasel answer, but it's the correct SR answer, and i am led to believe that it's also an experimentally observed fact (if we are even permitted to speak of facts in a world of relativity )

cheers!

edit - i should add that the various quantities (time, distance, mass, force fields...) transformed by SR are transformed in a "coordinated" way (npi) so that they are consistent *within* each frame of reference, i.e. the laws of physics work in all frames -- but the individual quantities differ between frames.

Shanti
Posts: 1
Joined: Mon Nov 08, 2010 1:04 pm

### Re: classical physics vs relativity: parallel electron beams

Hi, I'm new and I'm definitely not an expert in Plasma-Physics.

I'm happy I finally came across this forum, as it looks like people here know more about this matter, as everyone else I asked up 'til now wasn't able to really answer this question.
I had martered my brain now since several months about exactly this topic, but even with the answers currently given here, somehow this doesn't add up to me.
Please correct me and explain, wherever I'm wrong. I really want to understand this!!!

Example:
A quote from the LANL site:
In 1934 W. H. Bennett discovered that streams of electrons flowing in the axial or Z-direction, self pinch from the magnetic field they generate around themselves
According to your explanations this is only true if the electrons have different speeds.

But let's examine this.
If we have 2 streams. Within each stream the electrons do have the same velocity, but the beams as a whole do have different velocities.
From the reference frame of the faster beam, it looks as if the other beam is going in the reverse direction. But from the reference frame of the slower beam it looks as if the faster beam is going in the forward direction. But this results in different directions of the seen currents, so also of the seen magnetic fields. But then they should not pinch together as observed!

Another example:
If I have 1 beam with all electrons at the same velocity. From my reference frame, I see a current in space. Therefore I should see a magnetic field. Therefore shouldn't from my point of view the electron beam pinch? Otherwise the physics wouldn't be correct from what I observe in my inertial system.
But from the inertial system of the electrons in the beam, they don't move at all. so they do not see any magnetic field and therefore no pinching.
Sure you can say, that there's the usual observer based distance distortion. But here's a huge difference to the usual relativistic observing problems. Namely that in the usual observer problems, the distance distortion is always in the relative direction of travel. But in this problem not!
Another problem. In the usual relativistic observer problems, I just see a distortion, but not a different physical final result/reality.
But in this example this is the case!
From the inertial system of the beam, the electrons will separate due to repelling forces and no magnetic field. But from my viewpoint the beam should pinch and keep the electrons together. But these are completely different physical outcomes. This does not go together with the usual explanation of view distortion due to relativistic observing.
This really is a problem, I just cannot find an explanation.

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