On Apr 8, 5:58 am, Timo Nieminen <t...@physics.uq.edu.au> wrote:



On Mon, 7 Apr 2008, Darwin123 wrote:
On Apr 7, 8:37 pm, Timo Nieminen <t...@physics.uq.edu.au> wrote:
On Mon, 7 Apr 2008, Darwin123 wrote:
On Apr 7, 4:41 pm, "Timo A. Nieminen" <t...@physics.uq.edu.au> wrote:
On Mon, 7 Apr 2008, ram.rac...@gmail.com wrote:

Rather, one would use Maxwell's equations (etc) to obtain the same result
as Newton's laws (see further below), in an appropriate limit.

    Key qualifier: In the appropriate limit. Maxwell's equations are
still considered more accurate than Newton's Laws. There is no way to
extract a force law consistent with both Maxwell's equations and
Newton's Laws at the same time. As a special limit, sure.

Sure there's a way. See, e.g., Jackson pp 105-108. Once you have the
canonical energy-momentum tensor, you know what the momentum and energy
density of the field is (assuming one can identify the integrands in the
relevant conservation laws with the density of the conserved quantities)..
Maxwell's equations tell you how the energy and momentum moves from one
place to another in the field, the Lorentz force tells you the forces
involved in the interaction with matter, and, given that the force
exterted by the field is indeed equal to the rate of loss of momentum of
the field, how can this _not_ be consistent with Newton's laws? Of
course, not consistent with Newton's definition of momentum.

--
Timo Nieminen - Home page:http://www.physics.uq.edu.au/people/nieminen/
E-prints:http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits:http://www.users.bigpond.com/timo_nieminen/spirits.html

I'm pretty confused Timo. So how do I calculate the electric force on
a particle, if that force is carried by a finite-speed field?

Ram.

On Mon, 7 Apr 2008, ram.rac...@gmail.com wrote:
The reason I was confused over this is because of the conservation of
momentum. Assume you're right, and the third law doesn't hold. Observe
this. Momentum is conserved in Special Relativity. Momentum remains a
constant. Force is the change of momentum over time. Therefore, the
total force must always be zero. But that would mean that for every 2-
body system, Newton's third law WILL hold. So how do you explain that?

Newton's 3 laws of motion can be summarised as "momentum is conserved",
with a definition of force thrown in for good measure. Sounds nicely
compatible with special relativity (given some care in what the derivative
in the rate of change of momentum in the definition of force is taken
w.r.t.).

What is incompatible between Newton and SR are: (a) Newton's definition of
mass, as the quantity of matter, vs SR magnitude of the energy-momentum
4-vector, (b) Newton's definition of momentum, and (c) if you include it
as part of Newtonian dynamics, Newton's law of universal gravitation.

In SR, there are no separated 2-body systems with forces. If the 2 bodies
are separated, and there is a force acting between them, it's mediated by
a field, and this field can transport energy and momentum. For 2-body
systems where the bodies only interact when in contact, Newton's 3rd will
be fine. For separated 2-body+field systems, it'll work too, if you assume
that you can exert a force on a field, defined by Newton's 2nd.

--
Timo Nieminen - Home page:http://www.physics.uq.edu.au/people/nieminen/
E-prints:http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits:http://www.users.bigpond.com/timo_nieminen/spirits.html

On Mon, 7 Apr 2008, Darwin123 wrote:
On Apr 7, 8:37 pm, Timo Nieminen <t...@physics.uq.edu.au> wrote:
On Mon, 7 Apr 2008, Darwin123 wrote:
On Apr 7, 4:41 pm, "Timo A. Nieminen" <t...@physics.uq.edu.au> wrote:
On Mon, 7 Apr 2008, ram.rac...@gmail.com wrote:

Rather, one would use Maxwell's equations (etc) to obtain the same result
as Newton's laws (see further below), in an appropriate limit.

Key qualifier: In the appropriate limit. Maxwell's equations are
still considered more accurate than Newton's Laws. There is no way to
extract a force law consistent with both Maxwell's equations and
Newton's Laws at the same time. As a special limit, sure.

Sure there's a way. See, e.g., Jackson pp 105-108. Once you have the
canonical energy-momentum tensor, you know what the momentum and energy
density of the field is (assuming one can identify the integrands in the
relevant conservation laws with the density of the conserved quantities).
Maxwell's equations tell you how the energy and momentum moves from one
place to another in the field, the Lorentz force tells you the forces
involved in the interaction with matter, and, given that the force
exterted by the field is indeed equal to the rate of loss of momentum of
the field, how can this _not_ be consistent with Newton's laws? Of
course, not consistent with Newton's definition of momentum.

Maybe thats the problem. Newton did not define momentum

On Apr 6, 5:40 pm, "Androcles" <Headmas...@Hogwarts.physics> wrote:
--
This message is brought to you by Androcles
http://www.androcles01.pwp.blueyonder.co.uk/
"Robert J. Kolker" <bobkol...@comcast.net> wrote in messagenews:pPqdnTx62_sicWXanZ2dnUVZ_oWdnZ2d@comcast.com...| Darwin123 wrote:

Newton and Maxwell's
equations are technically in contradiction.

Maxwell's equations and Newton's Laws are in logical
contradiction. Newton's Laws were stated in the present tense as
though forces are instantaneous, but in actuality forces propagate at
a finite speed. I think this contradiction preceded special
relativity. I suspect that this contradiction lead to relativity.
Special relativity started as a means of modifying Newton's Laws so
that there is no logical contradiction.

Newton's Laws are not Lorentz Invariant. Therefore they are wrong.


Newton's Laws are not Lorentz Invariant. Therefore they are right, crank.

The Lorentz relations D = epsilon_0 E, B = mu_0 H for the
electromagnetic field in free space in vacuuo are both Lorentz
invariant and right -- and quite obviously so, since that´s, in large
measure, how where the name "Lorentz invariance" came from in the
first place! Therefore, you're wrong for saying "therefore", since
this serves as a counter-example of something that is Lorentz-
invariant and yet not wrong.

On Tue, 8 Apr 2008, ram.rac...@gmail.com wrote:
On Apr 8, 5:58 am, Timo Nieminen <t...@physics.uq.edu.au> wrote:
On Mon, 7 Apr 2008, Darwin123 wrote:
On Apr 7, 8:37 pm, Timo Nieminen <t...@physics.uq.edu.au> wrote:

Rather, one would use Maxwell's equations (etc) to obtain the same result
as Newton's laws (see further below), in an appropriate limit.

    Key qualifier: In the appropriate limit. Maxwell's equations are
still considered more accurate than Newton's Laws. There is no way to
extract a force law consistent with both Maxwell's equations and
Newton's Laws at the same time. As a special limit, sure.

Sure there's a way. See, e.g., Jackson pp 105-108. Once you have the
canonical energy-momentum tensor, you know what the momentum and energy
density of the field is (assuming one can identify the integrands in the
relevant conservation laws with the density of the conserved quantities).
Maxwell's equations tell you how the energy and momentum moves from one
place to another in the field, the Lorentz force tells you the forces
involved in the interaction with matter, and, given that the force
exterted by the field is indeed equal to the rate of loss of momentum of
the field, how can this _not_ be consistent with Newton's laws? Of
course, not consistent with Newton's definition of momentum.

I'm pretty confused Timo. So how do I calculate the electric force on
a particle, if that force is carried by a finite-speed field?

Calculate the electric (+magnetic) field via the Maxwell equations (or, if
you have a couple of charged particles, perhaps the Heaviside-Feynman
equations or the Lienard-Wiechert potentials).

Then you have two choices. Firstly, use the Lorentz force to give you the
force due to the field from the other particles/external fields. Add
radiation reaction as needed.

Alternatively, you can calculate the rate at which the charged particle of
interest is changing the momentum of the field, by integrating the
momentum flux through a surface surrounding the particle. There's an
immediate problem if you try to do this for a point electron, so better
stick with a classical electron of finite radius.

The two should give the same answer, due to conservation of momentum.
There have been some recent papers showing from first principles that the
two methods are in agreement for EM forces exterted on dielectric objects
(aimed at verifying methods of calculation used, e.g., for applications
such as optical tweezers).

Essentially, Maxwell + Lorentz force gives you a very complicated force
law that you can plug into Newton's laws to find the acceleration of an
object. It's a force law for the interaction between particle and field,
not between 2 particles, but viewing the field as an extended
(non-rigid) object that can have momentum and transport momentum
internally, it's just another force law like, e.g., Newton's law of
universal gravitation, Hooke's law, buoyancy forces, etc.

Note that we can't say that the _field_ has a speed - the field occupies
all space. Changes in the field propagate with some speed (c in free
space).

--
Timo Nieminen - Home page:http://www.physics.uq.edu.au/people/nieminen/
E-prints:http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits:http://www.users.bigpond.com/timo_nieminen/spirits.html

On Apr 7, 10:58 pm, Timo Nieminen <t...@physics.uq.edu.au> wrote:
On Mon, 7 Apr 2008, Darwin123 wrote:
On Apr 7, 8:37 pm, Timo Nieminen <t...@physics.uq.edu.au> wrote:
On Mon, 7 Apr 2008, Darwin123 wrote:
On Apr 7, 4:41 pm, "Timo A. Nieminen" <t...@physics.uq.edu.au> wrote:
On Mon, 7 Apr 2008, ram.rac...@gmail.com wrote:

Rather, one would use Maxwell's equations (etc) to obtain the same result
as Newton's laws (see further below), in an appropriate limit.

Key qualifier: In the appropriate limit. Maxwell's equations are
still considered more accurate than Newton's Laws. There is no way to
extract a force law consistent with both Maxwell's equations and
Newton's Laws at the same time. As a special limit, sure.

Sure there's a way. See, e.g., Jackson pp 105-108. Once you have the
canonical energy-momentum tensor, you know what the momentum and energy
density of the field is (assuming one can identify the integrands in the
relevant conservation laws with the density of the conserved quantities).
Maxwell's equations tell you how the energy and momentum moves from one
place to another in the field, the Lorentz force tells you the forces
involved in the interaction with matter, and, given that the force
exterted by the field is indeed equal to the rate of loss of momentum of
the field, how can this _not_ be consistent with Newton's laws? Of
course, not consistent with Newton's definition of momentum.

Maybe thats the problem. Newton did not define momentum
explicitly.

He certainly did not come up with "conservation of
momentum." Conservation of momentum can be derived from Newton's Laws
assuming all the mass is contained by "bodies," and that the force is
is invariant with respect to displacement.

I think it was Leibnitz who
actually came up with conservation of momentum independent of Newton
and his third law.

Both Newton and Leibnitz considered only "bodies," they did not
consider fields. Therefore, the only defition of momentum they could
come up with, if any, was:
p=mv
where p is the momentum, m is the mass and v is the velocity. However,
this formula obviously can't be applied to a field because the field
is moving. The velocity v is undefined.

Einstein once said that he was trying to resolve the
contradictions created by the existence of radiation pressure. Someone
may well ask what contradictions are in the existence of radiation
pressure. Einstein described a thought experiment that showed clearly
that heat energy, as in the motion of molecules, makes an object more
massive. His analysis presumed that light exerts a pressure, which was
well know at that time. His point was that if radiation exerts a
pressure, than the electromagnetic field has to have inertial mass.

The questions and insults were addressed toward Einstein before
1905. The claim was made that Einstein SHOULD NOT have accepted the
formula for kinetic energy because it was purely empirical.
[cut]
I was merely trying to clarify for any lurkers here my
understanding of the historical development of science. I am using the
troll as a sounding board. Yes, it is a vanity thing.

On Apr 8, 10:49 pm, "Timo A. Nieminen" <t...@physics.uq.edu.au> wrote:
a particle, if that force is carried by a finite-speed field?

Calculate the electric (+magnetic) field via the Maxwell equations (or, if
you have a couple of charged particles, perhaps the Heaviside-Feynman
equations or the Lienard-Wiechert potentials).

Timo - Assume I have two charged bodies. How do I know the force
between them? I mean, I can calculate the field that one body creates
at the location of the second body, but I need to remember that when
that field was created, the first body might have been somewhere else
entirely! So how do I calculate what it should be?

On Tue, 8 Apr 2008, Darwin123 wrote:
On Apr 7, 10:58 pm, Timo Nieminen <t...@physics.uq.edu.au> wrote:
On Mon, 7 Apr 2008, Darwin123 wrote:
On Apr 7, 8:37 pm, Timo Nieminen <t...@physics.uq.edu.au> wrote:
On Mon, 7 Apr 2008, Darwin123 wrote:
On Apr 7, 4:41 pm, "Timo A. Nieminen" <t...@physics.uq.edu.au> wrote:
On Mon, 7 Apr 2008, ram.rac...@gmail.com wrote:

Rather, one would use Maxwell's equations (etc) to obtain the same result
as Newton's laws (see further below), in an appropriate limit.

Key qualifier: In the appropriate limit. Maxwell's equations are
still considered more accurate than Newton's Laws. There is no way to
extract a force law consistent with both Maxwell's equations and
Newton's Laws at the same time. As a special limit, sure.

Sure there's a way. See, e.g., Jackson pp 105-108. Once you have the
canonical energy-momentum tensor, you know what the momentum and energy
density of the field is (assuming one can identify the integrands in the
relevant conservation laws with the density of the conserved quantities).
Maxwell's equations tell you how the energy and momentum moves from one
place to another in the field, the Lorentz force tells you the forces
involved in the interaction with matter, and, given that the force
exterted by the field is indeed equal to the rate of loss of momentum of
the field, how can this _not_ be consistent with Newton's laws? Of
course, not consistent with Newton's definition of momentum.

Maybe thats the problem. Newton did not define momentum
explicitly.

He did. First, he defined mass, then "quantity of motion" (the usual
English translation, but it's what we call momentum) as m*v.

He certainly did not come up with "conservation of
momentum." Conservation of momentum can be derived from Newton's Laws
assuming all the mass is contained by "bodies," and that the force is
is invariant with respect to displacement.

Why is this least one needed?
According to Noether's theorem, which applies to both classical

I don't recall an explicit statement of the conservation of momentum in
Principia.
Neither do I. That is my point. Einsteinian relativity is a

I think it was Leibnitz who
actually came up with conservation of momentum independent of Newton
and his third law.

I've read very little of Leibniz, but iirc, an important contribution of
his was the recognition of "vis viva", mv^2, as an important quantity in
dynamics, and at least some of argument with Newton/Newtonians was
concerning the relative important of momentum and his almost-KE.

The Leibniz-Clarke (Clarke might have been Newton-by-proxy?)
correspondence might be a good place to look for an early explicit
statement of such conservation laws.
I agree. I may have overextended myself here. I know Leibnitz

Einstein once said that he was trying to resolve the
contradictions created by the existence of radiation pressure. Someone
may well ask what contradictions are in the existence of radiation
pressure. Einstein described a thought experiment that showed clearly
that heat energy, as in the motion of molecules, makes an object more
massive. His analysis presumed that light exerts a pressure, which was
well know at that time. His point was that if radiation exerts a
pressure, than the electromagnetic field has to have inertial mass.

... or, in other language, simply that it must have momentum.
However, the momentum is not in the form p=mv. Not without making

The classic treatment of the transport of energy by fields (in the general
sense, so including stresses in elastic bodies etc) and the associated
momentum was by N. A. Umov, c. 1874, but little known outside Russia. The
essential result is that the momentum flux p is related to the power P by
p=P/v, where v is the speed of energy transport.
That looks artificial to me. Not that I am putting down Umov. Do

SR provides a neat unification of this result with the transport of energy
and momentum by moving bodies.
Yes. Very neat.

Hmm - I didn't read the troll-end of the thread (and I don't see much
point doing so).
Good for you. I just wanted to have a conversation with someone

Hello,

Does Newton's third law, that says that every force has an equal and
opposite counter force, still applies in Special Relativity?

The reason I'm confused over this is that according to the force
equations for electro-magnetic force, it seems that this law doesn't
hold. But on the other hand, since there is still a conservation of
momentum in special relativity, and force is just the change of
momentum, it makes sense that the total force should always remain
zero, so that the momentum will not change.

So what is the right answer? Does Newton's third law hold in Special
Relativity?

On Apr 7, 4:41 pm, "Timo A. Nieminen" <t...@physics.uq.edu.au> wrote:



On Mon, 7 Apr 2008, ram.rac...@gmail.com wrote:
The reason I was confused over this is because of the conservation of
momentum. Assume you're right, and the third law doesn't hold. Observe
this. Momentum is conserved in Special Relativity. Momentum remains a
constant. Force is the change of momentum over time. Therefore, the
total force must always be zero. But that would mean that for every 2-
body system, Newton's third law WILL hold. So how do you explain that?

Newton's 3 laws of motion can be summarised as "momentum is conserved",
with a definition of force thrown in for good measure. Sounds nicely
compatible with special relativity (given some care in what the derivative
in the rate of change of momentum in the definition of force is taken
w.r.t.).

What is incompatible between Newton and SR are: (a) Newton's definition of
mass, as the quantity of matter, vs SR magnitude of the energy-momentum
4-vector, (b) Newton's definition of momentum, and (c) if you include it
as part of Newtonian dynamics, Newton's law of universal gravitation.

In SR, there are no separated 2-body systems with forces. If the 2 bodies
are separated, and there is a force acting between them, it's mediated by
a field, and this field can transport energy and momentum. For 2-body
systems where the bodies only interact when in contact, Newton's 3rd will
be fine. For separated 2-body+field systems, it'll work too, if you assume
that you can exert a force on a field, defined by Newton's 2nd.

    I don't think a field, or even a little piece of a field, can be
thought of as a body in the Principia sense.

On Apr 8, 5:58 am, Timo Nieminen <t...@physics.uq.edu.au> wrote:





On Mon, 7 Apr 2008, Darwin123 wrote:
On Apr 7, 8:37 pm, Timo Nieminen <t...@physics.uq.edu.au> wrote:
On Mon, 7 Apr 2008, Darwin123 wrote:
On Apr 7, 4:41 pm, "Timo A. Nieminen" <t...@physics.uq.edu.au> wrote:
On Mon, 7 Apr 2008, ram.rac...@gmail.com wrote:

Rather, one would use Maxwell's equations (etc) to obtain the same result
as Newton's laws (see further below), in an appropriate limit.

    Key qualifier: In the appropriate limit. Maxwell's equations are
still considered more accurate than Newton's Laws. There is no way to
extract a force law consistent with both Maxwell's equations and
Newton's Laws at the same time. As a special limit, sure.

Sure there's a way. See, e.g., Jackson pp 105-108. Once you have the
canonical energy-momentum tensor, you know what the momentum and energy
density of the field is (assuming one can identify the integrands in the
relevant conservation laws with the density of the conserved quantities)..
Maxwell's equations tell you how the energy and momentum moves from one
place to another in the field, the Lorentz force tells you the forces
involved in the interaction with matter, and, given that the force
exterted by the field is indeed equal to the rate of loss of momentum of
the field, how can this _not_ be consistent with Newton's laws? Of
course, not consistent with Newton's definition of momentum.

--
Timo Nieminen - Home page:http://www.physics.uq.edu.au/people/nieminen/
E-prints:http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits:http://www.users.bigpond.com/timo_nieminen/spirits.html

I'm pretty confused Timo. So how do I calculate the electric force on
a particle, if that force is carried by a finite-speed field?

On Apr 7, 3:08 am, Darwin123 <drosen0...@yahoo.com> wrote:



On Apr 6, 11:29 am, "Robert J. Kolker" <bobkol...@comcast.net> wrote:

Darwin123 wrote:

Newton and Maxwell's

equations are technically in contradiction.

Maxwell's equations and Newton's Laws are in logical
contradiction. Newton's Laws were stated in the present tense as
though forces are instantaneous, but in actuality forces propagate at
a finite speed. I think this contradiction preceded special
relativity. I suspect that this contradiction lead to relativity.
Special relativity started as a means of modifying Newton's Laws so
that there is no logical contradiction.

Newton's Laws are not Lorentz Invariant. Therefore they are wrong.

Bob Kolker

I was pointing out WHY Newton's Laws are not consistent with
special relativity. In particular, Newton's Laws are not Lorentz
invariant. However, I don't think this is immediately obvious even to
somebody with a mathematical background. I myself was a little
confused on this point for a while. There is no explicit constraint on
the form of the force laws in Principia. If a force law is Lorentz
invariant, can't one simply use Newtons Laws to calculate the results?
The answer is that there is no Lorentz invariant force law that is
consistent with Newton's Laws.
A nonmathematical way to show that Newton's Laws are not
consistent with special relativity is simply to look carefully at the
sentences in Principia. They are all in present tense. In other words,
only instantaneous forces are allowed in Principia. Therefore, one
can't have a "force field" with a "finite propagation velocity."
The question was at heart historical, although phrased in an
offensive way. I interpreted his question as meaning this, aside from
the jealous attacks on Einstein. The question is, "Why in the days
before Einstein didn't scientists merely modify the force laws
describing the Michaelson Morley experiment in such a way as to
explain the experimental results?"
I conjectured that the reason is that Newton's Laws and Maxwell's
equations are logically inconsistent. I pointed out where the
inconsistency is in Principia. There are several statements made both
by H. A. Lorentz and A. Einstein that pointed me to that conjecture,
but I honestly can't be 100% sure that this is relevant.
I see ad hominum statements as a cry for help. Calling Einstein
stupid is a desperate plea by a scientific illiterate clarification on
a misunderstood point that irritates his or her learning disability. I
try relieve the inner conflict by providing a historical conjecture
that will help him or her make sense of a world that is beyond their
feeble comprehension.

Darwin123, you have not explained the most important part.

The reason I was confused over this is because of the conservation of
momentum. Assume you're right, and the third law doesn't hold. Observe
this. Momentum is conserved in Special Relativity. Momentum remains a
constant. Force is the change of momentum over time. Therefore, the
total force must always be zero. But that would mean that for every 2-
body system, Newton's third law WILL hold. So how do you explain that?

Ram.

On Apr 8, 4:48 pm, "Timo A. Nieminen" <t...@physics.uq.edu.au> wrote:
On Tue, 8 Apr 2008, Darwin123 wrote:

He certainly did not come up with "conservation of
momentum." Conservation of momentum can be derived from Newton's Laws
assuming all the mass is contained by "bodies," and that the force is
is invariant with respect to displacement.

Why is this least one needed?

According to Noether's theorem, which applies to both classical
and quantum mechanical systems, every quantity that is conserved has a
corresponding invariant property from which it can be derived.

Given the laws of optics known in Einsteins time, including both
polarization and radiation pressure, there seems to be no expression
for radiation pressure consistent with the third law of motion. I
think this bothered both Lorentz and Einstein.

His point was that if radiation exerts a
pressure, than the electromagnetic field has to have inertial mass.

... or, in other language, simply that it must have momentum.

However, the momentum is not in the form p=mv. Not without making
up a rather artificial definition of m and v.

Consider two static fields at right angles to each other. A
static electric field and a static magnetic field. Now, calculate the
flux of energy. Fine! Calculate the flux of momentum. Fine! See, they
are both nonzero. However, what exactly is moving with a nonzero
velocity? In other words, where is the body?

The classic treatment of the transport of energy by fields (in the general
sense, so including stresses in elastic bodies etc) and the associated
momentum was by N. A. Umov, c. 1874, but little known outside Russia. The
essential result is that the momentum flux p is related to the power P by
p=P/v, where v is the speed of energy transport.

That looks artificial to me. Not that I am putting down Umov. Do
you see the lengths physicists were going to preserve p=mv?

Not at a distance.

Edward Green wrote:

Not at a distance.

Relativistic momentum is conserved in all collisions.