# SR and electric fields

## Main Question or Discussion Point

Probably this has an easy answer but I can't see it just now, according to the principle of relativity we shouldn't be able to tell based on physical experiments if a body is at rest or in a uniform velocity, but in the case of charged objects we seem to be able to differentiate it simply by the fact that at rest produces an electric field as defined by electrostatics formulas and if moving follows electrodynamics and it also has a magnetic field so when in doubt it gives a hint of which object is moving and which in rest, unlike the famous example about looking at the other train by the window and not knowing which is moving or if both are moving.

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tiny-tim
Homework Helper
Hi TrickyDicky!
… we shouldn't be able to tell based on physical experiments if a body is at rest or in a uniform velocity …
Not so.

We should be able to tell if a body is at rest or at a uniform velocity … all we have to do is look at it … if it gets larger (or smaller), then it's moving!

The trick is that we shouldn't be able to tell based on physical experiments if we are at rest or at a uniform velocity.

If we have an electric charge, then no matter how fast we (and the charge) go, we will not be able to detect any magnetic field.

We should be able to tell if a body is at rest or at a uniform velocity … all we have to do is look at it … if it gets larger (or smaller), then it's moving!
Hey, you are not allowed to peek!:tongue:

The trick is that we shouldn't be able to tell based on physical experiments if we are at rest or at a uniform velocity.
If we have an electric charge, then no matter how fast we (and the charge) go, we will not be able to detect any magnetic field.
Sure, I was aware that for the observer the trick wouldn't work referred to its own motion,
and yet there seems to be something odd in the fact that the conditions of the vacuum EM fields change depending on the state of motion of the observer. Maybe it's just a subjective impression.

Hi TrickyDicky!

If we have an electric charge, then no matter how fast we (and the charge) go, we will not be able to detect any magnetic field.
Huh?

There is a magnetic and electric field for a moving charge

Huh?

There is a magnetic and electric field for a moving charge
Yes, but tini-tim is referring to what the observer comoving with the charge detects.

Dale
Mentor
there seems to be something odd in the fact that the conditions of the vacuum EM fields change depending on the state of motion of the observer
More odd than the relativity of simultaneity and time dilation and length contraction? Seems "par for the course" to me.

More odd than the relativity of simultaneity and time dilation and length contraction? Seems "par for the course" to me.
Not more odd, just odd in a different way, as if the vacuum acted as the reference for selecting whether observers are moving or in rest.

Dale
Mentor
Not more odd, just odd in a different way, as if the vacuum acted as the reference for selecting whether observers are moving or in rest.
I think you have a misunderstanding. In what way does the vacuum "act as the reference"?

bcrowell
Staff Emeritus
Gold Member
An observer at rest relative to the charge detects a pure electric field. An observer moving relative to the charge measures a mixture of magnetic and electric fields.

Dale
Mentor
Exactly, the charges "act as the reference", not the vacuum.

tiny-tim
Homework Helper
a reference from a vacuum isn't worth the paper it's written on!

Let's say for the purposes of argument that something can be at rest or can be in motion.

Something charged is in motion at a velocity v, and we are at rest. The object is receding, heading off to the right. We measure the fields from the object in motion and get some values and write them down.

Now we do the same experiment, but the charge is at rest and we are moving with velocity -v. Again, we see the object receding, as we fly off to the left.

As it turns out, we will measure the same fields from the object whether we are moving or the object is moving.

The fields we measure only depend upon the relative motion between us and the object. The results of these measurements cannot tell us which was in motion.

So we might propose that there aren't any experiments that can distinguish between being at rest or being in motion.

Taking a bigger gamble, we could propose that there is no such thing as being at rest, and all uniform motion (moving without a change in velocity) can only be measured in terms the uniform motion of other objects, and this conjecture is special relativity.

I think you have a misunderstanding. In what way does the vacuum "act as the reference"?
An observer at rest relative to the charge detects a pure electric field. An observer moving relative to the charge measures a mixture of magnetic and electric fields.
Exactly, the charges "act as the reference", not the vacuum.
This is all well and I'm sure I have many misunderstandings. My point is a little more subtle, perhaps it's just trivial or wrong, but the electric field is a property of the vacuum, to which the charge reacts, (in fact the whole reason it is a charge is because it lives in a field that tends to neutrality), so how does the vacuum "distinguish" if a charge is a rest or moving wrt an observer if it doesn't act itself as a rest reference? I know it's hard to transfer the point of view from the observer or the charge to the vacuum field but I believe it should be valid to do it, if not please explain why.

tiny-tim
Homework Helper
… the electric field is a property of the vacuum … how does the vacuum "distinguish"

I know it's hard to transfer the point of view from the observer … to the vacuum field …
Stop saying "the vacuum"!

You're using it as another word for "aether" … it doesn't exist!

If you mean space-time, then say so.

Stop saying "the vacuum"!

You're using it as another word for "aether" … it doesn't exist!

If you mean space-time, then say so.
No, I mean the vacuum. If the vacuum doesn't exists please refer me to some citation.
Space-time I would say includes both matter and vacuum.

Dale
Mentor
how does the vacuum "distinguish" if a charge is a rest or moving wrt an observer if it doesn't act itself as a rest reference?
The vacuum makes no such distinction, only the observers do.

For example consider the field immediately outside a uniform ball of charge as measured by two observers, one at rest wrt the ball and one moving wrt the ball. The rest observer will measure a pure electric field while the moving observer will also measure a magnetic field, both at the same point of vacuum. Therefore, the field is not a property of the vacuum since it may have different values at the same point in different frames, and the observer is what makes the distinction.

I know it's hard to transfer the point of view from the observer or the charge to the vacuum field but I believe it should be valid to do it, if not please explain why.
Because there is no physical sense in which the vacuum is at rest or moving in any given frame.

Last edited:
George Jones
Staff Emeritus
Gold Member
No, I mean the vacuum. If the vacuum doesn't exists please refer me to some citation.
So you're saying that the stress-energy tensor of the electric field is either zero or a non-zero constant multiple of the metric? I can give numerous citations for this definition of "vacuum". Stop using non-standard terminology.

So you're saying that the stress-energy tensor of the electric field is either zero or a non-zero constant multiple of the metric?
Show me where I said that or quit confusing things.
At least Dalespam tried and gave an argument.

ghwellsjr
Gold Member
You should read the first paragraph of Einstein's 1905 paper in which he discusses issues around observing a magnetic field and an electrostatic field from different motions.

The point is, if you have two charged bodies separated by a distance and you view them from a frame of reference in which they are both stationary and have been for some time, there will be no magnetic field, only an electrostatic field and you can calculate the forces on the two charges and therefore how they will begin to accelerate if free to do so.

If you view them from a frame of reference that is moving with respect to the two charges and have been for some time, there will be both a magnetic field and an electrostatic field and you must take into account both in order to calculate the forces on the two charges and therefore how they will begin to accelerate if free to do so.

Both frames of reference give a correct viewpoint and allow for correct calculations of what will happen to the charges. But, just like different frames of reference assign different values to the times and locations of events, they also assign different values to the electrostatic and magnetic fields, even to the point of having a value of zero for the magnetic field in one frame of reference and non-zero in another frame of reference.

If you want to read a thorough discussion on this subject, look up volume II of Feynman's Lectures on Physics, section 13-6, called "The relativity of magnetic and electric fields".

JesseM