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STAii
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From this link http://jnaudin.free.fr/lifters/lorentz/index.htm
Is it true ?
Is it true ?
No. They assume that the electric field propagates instantaneously, while the magnetic field does not. Which is false .Originally posted by STAii
Is it true ?
Originally posted by STAii
From this link http://jnaudin.free.fr/lifters/lorentz/index.htm
Is it true ?
In a system involving moving charges, the forces between charges predicted by the Biot-Savart law may indeed violate both forms of the action and reaction law.*
*(footnote) If two charges are moving uniformly with parallel velocity vectors that are not perpendicular to the line joining the charges, then the net mutual forces are equal and opposite but do not lie along the vector between the charges. Consider, further, two charges moving (instantaneously) so as to "cross the T." i.e. one charge moving directly at the other, which in turn is moving at right angles to the first. Then the second charge exerts a nonvanishing magnetic force on the first, without experiencing any magnetic reaction force at that instant.
Biot-Savart is for stationary currents - not single moving particles. Because there's nothing 'stationary' when you have a single moving particle. There's no such thing as a 'magnetic field of a single moving particle'. Each particle is affected only by the Lorentz-transformed Coulomb field of the other one, and since Lorentz-transformation is symmetrical, so is the interaction. Don't be fooled...Originally posted by pmb
the forces between charges predicted by the Biot-Savart law ...
Originally posted by arcnets
Biot-Savart is for stationary currents - not single moving particles.
There's no such thing as a 'magnetic field of a single moving particle'.
Each particle is affected only by the Lorentz-transformed Coulomb field of the other one, and since Lorentz-transformation is symmetrical, so is the interaction. Don't be fooled...
The missing momentum is, of course, in the field. I.e. the EM field has momentum so that the total momentum of Fields + Particles is constant.It is worth pointing out that one of Newton's basic assertions about forces between bodies - the equality of action and reaction - has almost no place in relativistic mechanics. It must essentially be a statement about about force acting on two bodies, as a result of the mutual interaction, *at a given instant.* And, because of the relativity of simultaneity, this phrase has no unique meaning unless the points at which the forces are applied are separated by a neglegible distance. [...] What the relativistic analysis does do, however, is to compel us to conclude that, according to measurements in a given inertial frame, the forces of action and reaction are in general *not* equal and opposite, and so the total momentum of the interacting particles is no conserved instant by instant.
Originally posted by arcnets
pmb,
I admit I didn't put enough thought into this. I'll check - just don't have the time now, hang on please.
Originally posted by pmb
The missing momentum is, of course, in the field. I.e. the EM field has momentum so that the total momentum of Fields + Particles is constant.
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Originally posted by Creator
Thanks for the quotes, Pete. I could have used them last year when on another forum I received a lot of flak for stating that... to adopt relativity one has to be willing to give up the concept of Newton's 3rd law.
J.L. Naquin's site (given in the 1st post) has an excellent graphic which illustrates precisely the point made in your referenece in Goldstein's footnote, which show how when two charges approach each other with orthagonal trajectries, one avoids the magnetic reaction force - at least temporarily.
Which brings us to the next point, which he only briefly mentioned, and you brought up succintly.
So you therefore would say that the 'missing' momentum remains in the field? Or would you say the field produces a back reaction on the source particle - thus no real asymmetry?
Creator
Originally posted by Hurkyl
There's a problem with equation 1 on your page. mk is not a constant with respect to t; as time changes, particke k's velocity may change, which will thus change particle k's relativistic mass. Thus, you cannot, in general, perform the last step in equation 1.
Originally posted by Hurkyl
lol I read the whole thing twice, and never noticed the text up there before the diagram!
Originally posted by pmb
People hate it when you disagree with them and will refuse to give up their old ideas. He shakes at the notion that light has mass
In the first I've never considered a photon as something being "pure energy." The notion of anything being pure energy makes no sense to me.Originally posted by jeff
The idea you seem to "hate" giving up is that it's wrong to view massless particles as pure energy.
According to Einstein, a photon of frequency v has energy hv, and thus (as he came to realize several years later) a finite mass hv/c^2 and a finite momentum hv/c.
I'm pretty sure that Rindler would tell you that you're twisting his view about the efficacy of using the term "relativistic mass" into something he never intended or agrees with.
I'm pretty sure that Rindler would tell you that you're twisting his view about the efficacy of using the term "relativistic mass" into something he never intended or agrees with.
Originally posted by Hurkyl
Incidentally, just because the sum of the momenta of two or more photons may have mass does not mean each individual photon has mass.
Originally posted by selfAdjoint
In fact the energy of just one photon, if high enough, can be used to create a new particle and antiparticle. The photon ceases to exist in this pair production
Am I misunderstanding or does that sentence translate into: 'if we ignore some of the forces, the forces are imbalanced'?Note : To be in agreement with Newton's 3rd law, it would be necessary to take into account the moments of the magnetic and electric fields.
Originally posted by russ_watters
From the article: Am I misunderstanding or does that sentence translate into: 'if we ignore some of the forces, the forces are imbalanced'?
The scientific principle of "Action does not equal reaction" is a concept in physics known as the principle of non-reciprocity, which states that the forces acting on two objects do not necessarily have equal magnitudes and opposite directions. This is in contrast to the commonly known law of motion, "For every action, there is an equal and opposite reaction."
This principle differs from the law of motion because it allows for the possibility that the forces acting on two objects may not be equal and opposite. This means that the acceleration of each object may not be the same, and therefore, the resulting motion will not be equivalent.
One example of this principle can be seen in the motion of a rocket. The rocket exerts a force on the gas it expels, causing it to accelerate in one direction. However, the gas exerts a smaller force on the rocket in the opposite direction, resulting in the rocket's overall motion. Another example is when a person jumps off a boat. The person exerts a force on the boat, causing it to move in the opposite direction, but the boat's movement is much smaller due to its larger mass.
This principle is essential in the design and function of objects and machines, such as engines and rockets. It allows engineers to create more efficient and effective designs by understanding the unequal and non-reciprocal forces at play. For example, rocket engines are designed with directed nozzles to maximize the force exerted in one direction and minimize the force in the opposite direction.
While this principle applies to many situations in the physical world, there are also instances where the forces acting on two objects may be equal and opposite. The law of motion is still a fundamental principle in physics, and the principle of non-reciprocity is an extension of it. Therefore, both principles are necessary to fully understand and explain the motion of objects in the physical world.