# Not another false belief about magnetism?

#### AndrewS

The thread headed A basic question about magnetism describes magnetic and electric fields as being the same in each reference frame. That is to say there is no separate perpendicular magnetic field; motion just modifies the electric field. So this question concerns the situation where two positive ions initially move in the same direction and are side by side in a vacuum. An observer also co-moves with the ions at their speed of v. I will refer to the co-moving observer as C and an observer at rest as R.

1. C considers his moving frame to be at rest, so his clock is unaffected and the ions (which initially appear to be at rest) just have a rest mass of m0. C observes each ion accelerates at aC. From the equation F=ma we can say aC = FE/m0 where FE is the electrostatic repulsion.

2. For R at rest there is a magnetic force of attraction which varies linearly with the ions’ speed of v. This can be expressed as kv, so for R the repulsion is reduced to FE – kv. The mass of the moving ions is increased by the Lorentz factor of γ or (1 - v2/c2)-0.5 to give a further reduction in acceleration. Hence R should see a lesser acceleration of aR = (FE – kv)/γm0.

C and R see each other’s clock is slow by a factor of 1/ γ. So each can say the other’s measurement of speed is increased by a factor of γ and acceleration by γ2. But I don’t see how non-linear factors can reconcile acceleration differences which basically vary linearly with v. A single acceleration event seems to produce fundamentally different accelerations which cannot be reconciled by Lorentz transformations. Conventionally there are said to be separate electric and magnetic fields that are the same when viewed from different frames. In which case these same fields should have the same effects for all values of v.

Where am I going wrong?

#### HallsofIvy

You first go wrong in saying "magnetic and electric fields as being the same in each reference frame". Given a frame in which there exit either a magnetic field or electric field or both, there exist other frames in which there is only a magnetic field, in which there is only an electric field, and other frames in which there are both of different strengths.

#### Pmb

PHF Hall of Fame
You first go wrong in saying "magnetic and electric fields as being the same in each reference frame". Given a frame in which there exit either a magnetic field or electric field or both, there exist other frames in which there is only a magnetic field, in which there is only an electric field, and other frames in which there are both of different strengths.
If there is an EM wave in S moving in the direction of the x-axis then in what frame is there no magnetic field? In which frame is there no magnetic field.

If a magnet has an electric charge in its rest frame S then in which frame is the electric or magnetic field zero?

#### AndrewS

You first go wrong in saying "magnetic and electric fields as being the same in each reference frame".
It should help if you read my reply on the other thread, but I’ll summarise here the reasons why I think the electric and magnetic fields are simple superpositions in all frames.

1 Forces do not act at right angles to their fields. No demonstrably real force does this.

2 Any demonstrably real force acts between points, it does not go round in closed loops.

3 If energy flows in a perpendicular magnetic field it cannot do work in the direction of the electric field. Energy has mass, so if it simply turns through a right angle then momentum would not be conserved.

4 An asymmetry in charge behaviour is not a valid scientific hypothesis. How is it possible to prove whether the asymmetry is clockwise or anticlockwise?

5 By abandoning this assumption of asymmetric rotation we end up with a beautifully simple, and symmetrical, rule: like currents attract and opposite currents repel. Students can stop wasting their time pondering how their fingers should point in different directions.

6 I can find no experimental evidence to support the needless assumption that the universe needs two different fields and directions to mediate forces between charges.

7 Perhaps it is a human weakness to try to simplify one’s understanding of the world by uniting things. If so it’s a weakness I share with physicists. They like to unite the forces and they wish to find a grand unified theory – something which will continue to elude them while they cling to irrational beliefs.

#### tomh4040

To Oz93666, I would say that currents do indeed attract or repel. Here is the reason :- Magnets attract/repel only (with some notable exceptions) ferrous metals. Pass a current through a copper wire parallel to another copper wire which has current flow in the same direction (use separate batteries so there is no physical interaction), and there is an attractive force between the wires.
When current flows in opposite directions in the wires there is a repulsive force between the wires.

#### AndrewS

Many thanks Pmb for responding, but I don’t understand the point you are making.

I’ve seen physics sources saying that the acceleration from a magnetic field in one frame is identical to the acceleration from an electric field in another frame. This is when viewing the same acceleration event that arises from a neutral conductor. But I haven’t yet seen how this works for charges that are just in a vacuum.

My question wasn’t about EM waves. Please can you just explain where I’m going wrong with the simple analysis I have presented.

#### HallsofIvy

What do you mean by "demonstrably real"?

#### AndrewS

An interesting question, but not one I would want to spend much time on. We might get bogged down in a philosophical debate about the nature of reality.

In general I suppose I would say a force is demonstrably real if we have good reason to believe it exists. Ideally we can identify a physical agency that links a cause with an effect, in some cases we cannot and so we have to use our judgement based on the properties of forces where a physical agent can be demonstrated.

For example, a fluid force is mediated by identifiable air or water molecules etc. This is certainly a demonstrably real force. It can be represented by a vector along the line linking the cause with the effect. We can also see that energy is dissipated in the same direction.

No physical agency may be apparent in the case of gravity, but we are still able to describe it as a real force. It too can be represented by a vector and has a potential energy gradient along the vector. If someone said that the force of gravity involved two forces, one that acts in the direction of the force and another that goes round in endless perpendicular loops, then it would not be sensible to say the second force was demonstrably real. This is because it does not share the properties of real forces.

Whether or not we ascribe a physical agent to the electric force, such as photons moving between charges, the electric force is at least as real as gravity. In contrast the traditional magnetic “lines of force” do not share these properties. We cannot even say which way these “forces” acts, let alone measure any forces or energy gradients along them.

#### Woody

I vaguely remember a thread from some time ago which followed a similar course,

As I recall, the essential conclusion was that it is improper to refer to either Electrical or Magnetic fields!

It should always be an ElectroMagnetic field.

So called Electric and Magnetic fields are actually different views of the same beast (the ElectroMagnetic field).

#### AndrewS

Sounds pretty good to me.