Understanding Lorentz Equations and the Solution to Maxwell's Equations Variance

[dak246]

I'm reading how the Lorentz equations allow for relativistic transformation that can include Maxwell's equations but I'm a bit confused on how it solves the problem of Maxwell's equations being variant under a Galilean transformation. The example I'm looking at says that if you are moving away from an infinitely long wire and point charge, and use yourself as the frame of reference, then you would see the wire and point charge system moving away from you and you'd have to consider the magnetic field that would arise, which you wouldn't consider if you were looking at the system from its own frame of refrence. Can someone explain how the Lorentz equations solves this problem, because I can't figure it out. Thanks.

 

[Daverz]

Found this on the web:

http://physics.weber.edu/schroeder/mrr/MRRhandout.pdf#search="charge wire lorentz transformation"

I not quite sure, or don't remember, why the usual discussion uses the model of negative and positive charges moving in opposite directions instead of something closer to what's actually going on in a wire.

 

[DaveC426913]

"simple relativity question"

Hee! Put that in the bin along with

"jumbo shrimp"
"military intelligence"
"deafening silence"
"original copy"

 

[clj4]

I'm reading how the Lorentz equations allow for relativistic transformation that can include Maxwell's equations but I'm a bit confused on how it solves the problem of Maxwell's equations being variant under a Galilean transformation. The example I'm looking at says that if you are moving away from an infinitely long wire and point charge, and use yourself as the frame of reference, then you would see the wire and point charge system moving away from you and you'd have to consider the magnetic field that would arise, which you wouldn't consider if you were looking at the system from its own frame of refrence. Can someone explain how the Lorentz equations solves this problem, because I can't figure it out. Thanks.

This question is so old that many people may have forgotten the answer to it. The answer lies in a 1904 Lorentz paper in which he:

1. starts by pointing out that the Maxwell equations do not conserve form when passing from one inertial frame to another one UNDER the Galilei transforms

2. continues by proposing another set of transforms (the ones that were given his name much later by Poincare) that solve the problem.

The paper can be found in a book that also contains the Einstein 1905 paper.

I'll give you the exact name of the book in a few hours. "Original copy" , ha,ha,ha.

The book is "The Principle of Relativity"
The article is : Electromagnetic Phenomena in a System Moving with any Velocity Less than that of Light" by Lorentz.

 

[dak246]

This question is so old that many people may have forgotten the answer to it. The answer lies in a 1904 Lorentz paper in which he:

1. starts by pointing out that the Maxwell equations do not conserve form when passing from one inertial frame to another one UNDER the Galilei transforms

2. continues by proposing another set of transforms (the ones that were given his name much later by Poincare) that solve the problem.

The paper can be found in a book that also contains the Einstein 1905 paper.

I'll give you the exact name of the book in a few hours. "Original copy" , ha,ha,ha.

Is it "The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity" ?

I thought I understood the answer to this question in terms of the speed of light being constant regardless of the sources motion and therein the failure of the classical transformation, but now considering the example regarding the magnetic field I can't understand how the Lorentz equations compensate mathematically. Is this is a matter of logic in some way, i.e. when a reference frame moves relative to the wire and an observer in this frame then sees the wire moving, he simply ignores its apparent motion?

 

[pervect]

I'm not positive I understand your question. You do realize that the total force on a point charge, the four force, transforms covariantly according to the Lorentz transform, don't you? I believe this was mentioned recently in another thread.

The description of the force, i.e. describing what parts of the force are due to "electric" fields and what parts are due to "magnetic" fields, changes, but the total force itself is Lorentz covariant.

The manifestly covariant description of forces in special relativity is the "four force".

 

[dak246]

I'm not positive I understand your question. You do realize that the total force on a point charge, the four force, transforms covariantly according to the Lorentz transform, don't you? I believe this was mentioned recently in another thread.

The description of the force, i.e. describing what parts of the force are due to "electric" fields and what parts are due to "magnetic" fields, changes, but the total force itself is Lorentz covariant.

The manifestly covariant description of forces in special relativity is the "four force".

That is basically my question in a nutshell. I understand that the total force will be the same, but I'm having trouble figuring out how the Lorentz equations allow for this while Galilean equations do not.

 

[Hans de Vries]

Found this on the web:

http://physics.weber.edu/schroeder/mrr/MRRhandout.pdf#search="charge wire lorentz transformation"

I not quite sure, or don't remember, why the usual discussion uses the model of negative and positive charges moving in opposite directions instead of something closer to what's actually going on in a wire.

Unfortunately, This is again the erroneous "split-wire" argument for the
derivation of magnetism as a relativistic side-effect of electro-statics.The figure at the right shows how the positive-charge-part of the wire
becomes longer as the negative-charge-part of the wire... This does not
happen. The wire doesn't split. Imagine for example a semiconductor
where the electrons don't hop from one free position to another but end
up hopping to arbitrary positions in the middle...

It's the Coulomb fields of the electrons and ions moving relative to the
test-charge which become Lorentz contracted and therefore cause an
imbalance in the forces felt from the positive and negative charges
resulting in a non-zero force acting on the moving test charge.Regards, Hans.

 

[pervect]

That is basically my question in a nutshell. I understand that the total force will be the same, but I'm having trouble figuring out how the Lorentz equations allow for this while Galilean equations do not.

Probably you need to revist in depth how the electric and magnetic fields actually transform.

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

writes this down, there is a more detailed explanation as well at u of fla

You start here:
http://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_11.pdf

then visit _12, _13, _14, etc...

This was recently discussed in another thread here on PF, too...

 

[clj4]

Is it "The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity" ?

I thought I understood the answer to this question in terms of the speed of light being constant regardless of the sources motion and therein the failure of the classical transformation, but now considering the example regarding the magnetic field I can't understand how the Lorentz equations compensate mathematically. Is this is a matter of logic in some way, i.e. when a reference frame moves relative to the wire and an observer in this frame then sees the wire moving, he simply ignores its apparent motion?

You got the right book. Now read the Lorentz paper I quoted.
Electromagnetic Phenomena in a System Moving with any Velocity Less than that of Light

 

[dak246]

Probably you need to revist in depth how the electric and magnetic fields actually transform.

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

writes this down, there is a more detailed explanation as well at u of fla

You start here:
http://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_11.pdf

then visit _12, _13, _14, etc...

This was recently discussed in another thread here on PF, too...

Thanks for the links. I'm just starting out with courses in quantum physics and relativity so I have a long way to go, but the book we're using seems to leave out some rigor and detail at certain points that I think I need to grasp a firm understanding before moving on, so I'm trying to fill in the holes.

 

[pervect]

Thanks for the links. I'm just starting out with courses in quantum physics and relativity so I have a long way to go, but the book we're using seems to leave out some rigor and detail at certain points that I think I need to grasp a firm understanding before moving on, so I'm trying to fill in the holes.

As far as textbooks go, I rather like Griffiths "Introduction to Electrodynamics" https://www.amazon.com/gp/product/013805326X/?tag=pfamazon01-20

He discusses this issue in some depth (i.e. how general electromagnetic fields transform under the Loretnz boost). You'll probably be able to get most of it from the web if you look hard enough, but if you can get a hold of Griffiths from the library, it might be helpful.

 

[Daverz]

Unfortunately, This is again the erroneous "split-wire" argument for the
derivation of magnetism as a relativistic side-effect of electro-statics.

Thanks for your comments; I always thought this derivation was a bit dodgy.
Do you know of a source for a more realistic derivation?

 

[RandallB]

The example I'm looking at says that if you are moving away from an infinitely long wire and point charge, and use yourself as the frame of reference, then you would see the wire and point charge system moving away from you and you'd have to consider the magnetic field that would arise, which you wouldn't consider if you were looking at the system from its own frame of refrence. Can someone explain how the Lorentz equations solves this problem, because I can't figure it out. Thanks.

I’m sorry maybe I missing something but why would applying Maxwell's equations here create a problem at all?
If you’re only considering the distant wire stretched perpendicular to your travel and a stationary point charge near it or on it as a system with no other charges or magnetic fields, any complete Lorentz transformation would still show wire and point charge to hold fixed relative positions.
If however you are using any magnet and/or point charge moving with you; then you would detect an EM effect from that system moving away from you – but that system would also see the same thing due to your magnet and/or point charge moving away from them.

So why does your problem think you would see something any differently than the system you observing would see from there view? I don’t see a problem or conflict for Lorentz equations to solve.

 

[dak246]

I’m sorry maybe I missing something but why would applying Maxwell's equations here create a problem at all?
If you’re only considering the distant wire stretched perpendicular to your travel and a stationary point charge near it or on it as a system with no other charges or magnetic fields, any complete Lorentz transformation would still show wire and point charge to hold fixed relative positions.
If however you are using any magnet and/or point charge moving with you; then you would detect an EM effect from that system moving away from you – but that system would also see the same thing due to your magnet and/or point charge moving away from them.

So why does your problem think you would see something any differently than the system you observing would see from there view? I don’t see a problem or conflict for Lorentz equations to solve.

Its the example given in my textbook for why a Galilean transformation won't work with Maxwell's equations. I realize that a Lorentz transformation would resolve this problem (which the book suggests without explanation), I'm just not sure precisely how.

 

[RandallB]

Its the example given in my textbook for why a Galilean transformation won't work with Maxwell's equations. I realize that a Lorentz transformation would resolve this problem (which the book suggests without explanation), I'm just not sure precisely how.

And the problem, error, or paradox the Galilean transformation gave was what excactly?

 

[dak246]

And the problem, error, or paradox the Galilean transformation gave was what excactly?

Because the equations for the electromagnetic force acting on the point charge near the wire will have different forms in the two frames of reference, and therefore wouldn't be invariant under a Galilean transformation.

 

[RandallB]

Because the equations for the electromagnetic force acting on the point charge near the wire will have different forms in the two frames of reference, and therefore wouldn't be invariant under a Galilean transformation.

As I said before the nearby stationary Galiaean observer using Maxwell will see zero magnetic affect on the stationary charge near the stationary wire. How and what difference will you moving at any high speed v, away from (or towards) this group of three as a Galiaean observer using Maxwell going to see anything different than zero as well?
Where is there a difference or error?
As far as I can tell Maxwell’s EM does not depend on or need Classical, Lorentz, or Relativity.

 

[dak246]

As I said before the nearby stationary Galiaean observer using Maxwell will see zero magnetic affect on the stationary charge near the stationary wire. How and what difference will you moving at any high speed v, away from (or towards) this group of three as a Galiaean observer using Maxwell going to see anything different than zero as well?
Where is there a difference or error?
As far as I can tell Maxwell’s EM does not depend on or need Classical, Lorentz, or Relativity.

This is exactly what I can't figure out. The book specifically says that different forms for the equation of the force will arise in the different frames due to the apparent motion of the system that a moving observer would see in their frame. I can't see how the Lorentz equations would solve this problem even if it was a problem (as you suggest it isn't). Thats why I'm confused. Heres a quote straight from the book: "It follows that the Galilean transformation of coordinates between intertial frames cannot be correct, but must be replaced with a new coordinate transformation whose application preserves the invariance of the laws of electromagnetism." And from here the Lorentz transformation is introduced.

 

[RandallB]

straight from the book: "It follows that the Galilean transformation of coordinates between intertial frames cannot be correct, but must be replaced ... "

I take the book as just plain WRONG.
Just say it is wrong without show the error doesn’t say much for the book.
I think even Einstein commented on being impressed with Maxwell as his EM worked in all theories.
Sorry I don't have a ref: for that; may have seen it in "Einstein's Heroes".