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I really need a detailed explanation to understand this topic thoroughly, so if someone could help me on this, I would be more than grateful.

Thanks

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I really need a detailed explanation to understand this topic thoroughly, so if someone could help me on this, I would be more than grateful.

Thanks

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Borg

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Vanadium 50

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The laws are low velocity approximations. At higher and higher velocities, the laws get worse and worse.. My question is that why do the laws of Sir Isaac Newton no longer apply to objects at the speed of light? Is it the formulae that are causing the problem or the laws?

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Do they? Galilean transformation fails at the speed of light, but Newton's laws of motion (in their original form) still apply. If it makes sense to use forces for photons is another question.My question is that why do the laws of Sir Isaac Newton no longer apply to objects at the speed of light?

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mfb

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We just happen to live in a universe where Newtonian physics is not exact. It is perfectly possible to imagine a world where the laws are exact at all speeds (particle physics and some other fields would get problems , but let's ignore the microscopic part here), but experiments show we do not live in such a world.My question is that why do the laws of Sir Isaac Newton no longer apply to objects at the speed of light? Is it the formulae that are causing the problem or the laws?

Acceleration is not parallel to force in general. How does that agree with Newtonian physics?but Newton's laws of motion (in their original form) still apply.

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With replacement of Galilei transformation by Lorentz transformation Newton's "quantity of matter" becomes velocity dependent. In the result acceleration is no longer parallel to force.Acceleration is not parallel to force in general. How does that agree with Newtonian physics?

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Chet

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mfb

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A velocity-dependent scalar mass is not sufficient, you would need some sort of "vector mass". And I think that is beyond Newton's equation of motion. Even the Lorentz transformations on their own are beyond Newton's physics.With replacement of Galilei transformation by Lorentz transformation Newton's "quantity of matter" becomes velocity dependent. In the result acceleration is no longer parallel to force.

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The velocity-dependent scalar massA velocity-dependent scalar mass is not sufficient, you would need some sort of "vector mass".

[itex]m = \frac{{m_0 }}{{\sqrt {1 - \frac{{v^2 }}{{c^2 }}} }}[/itex]

results in

[itex]a = \left( {\frac{F}{{m_0 }} - v \cdot \frac{{v \cdot F}}{{m_0 \cdot c^2 }}} \right) \cdot \sqrt {1 - \frac{{v^2 }}{{c^2 }}}[/itex]

There is no need for some sort of "vector mass".

Of course it is. That's why I limited my statement to Newton's laws of motion.Even the Lorentz transformations on their own are beyond Newton's physics.

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mfb

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Okay, if you add those extra terms - I would not call this "Newton's laws of motion" any more.[itex]a = \left( {\frac{F}{{m_0 }} - v \cdot \frac{{v \cdot F}}{{m_0 \cdot c^2 }}} \right) \cdot \sqrt {1 - \frac{{v^2 }}{{c^2 }}}[/itex]

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mfb

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Compared to a=F/m?There are no extra terms.

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You've rolled it into the second term in the pre-factor.There is no need for some sort of "vector mass".

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Which second term of which pre-factor?You've rolled it into the second term in the pre-factor.

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The part with the dot product. That makes it directional.

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Are you confusing the equation for acceleration with the equation for quantity of matter (we better do not use the term mass at this place)? The latter does not contain such a part.The part with the dot product. That makes it directional.

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Chestermiller

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Chet

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Newton made a few assumptions about nature that turned out to be incorrect. For example, Newton's conception of time in the definitions given in theMy question is that why do the laws of Sir Isaac Newton no longer apply to objects at the speed of light? Is it the formulae that are causing the problem or the laws?

So... to answer the question. It is the axiomatic assumptions that are 'causing the problems'

As others have said, Newton's laws are still applicable in SR if you change the definition of force and momentum to be their four-vector definitions. However, in my limited experience with SR I've noticed that the concept of force (in the Newtonian sense) is not very convenient simply because of how messy this would get when applying the Lorentz transformations. The form of the laws look the same when using four-vectors (which is probably one of the reasons that four-momentum was defined the way it was!), but I would argue that this isn't really

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Chestermiller

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I used to feel the same way, thinking that the 4-force was just a contrived entity, designed specifically to recover Newton's 2nd law within the framework of SR. However, that feeling was dispelled when I saw the dazzling development in MTW in which they derived the equation for the 4-force acting on a stationary or moving charge within an electric and/or magnetic field and showing that it was described, independent of ma, by the magnitude of the charge times the contraction of the Faraday tensor with the 4-velocity vector. Did you not have the same response when you studied this?As others have said, Newton's laws are still applicable in SR if you change the definition of force and momentum to be their four-vector definitions. However, in my limited experience with SR I've noticed that the concept of force (in the Newtonian sense) is not very convenient simply because of how messy this would get when applying the Lorentz transformations. The form of the laws look the same when using four-vectors (which is probably one of the reasons that four-momentum was defined the way it was!), but I would argue that this isn't reallyNewton'slaws anymore.

Chet

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Cool. I have not seen that derivation. I'll have to check it out.

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I felt this way for a short time too. For me the four-force concept became clear when I started thinking about it as just a measure of the deviation of a particle's path from geodesic motion. Forces are defined that way too in Newtonian mechanics after all, as a measure of deviation from inertial motion.I used to feel the same way, thinking that the 4-force was just a contrived entity, designed specifically to recover Newton's 2nd law within the framework of SR. However, that feeling was dispelled when I saw the dazzling development in MTW in which they derived the equation for the 4-force acting on a stationary or moving charge within an electric and/or magnetic field and showing that it was described, independent of ma, by the magnitude of the charge times the contraction of the Faraday tensor with the 4-velocity vector. Did you not have the same response when you studied this?

Chet

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Chestermiller

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That would apply more to acceleration than to force.I felt this way for a short time too. For me the four-force concept became clear when I started thinking about it as just a measure of the deviation of a particle's path from geodesic motion. Forces are defined that way too in Newtonian mechanics after all, as a measure of deviation from inertial motion.

Chet

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yes, you're right, I will have to elaborate more on that thought.That would apply more to acceleration than to force.

Chet

If there's acceleration then we have force, but that alone cant account for the whole thing since different particles deviate from inertial motion differently when they interact with the same fields.

But still forces are a measure of how particles deviate from inertial motion,

I guess it is safe to say that force is a measure of how much a particle's motion is not inertial, once you take into account the dynamical parameters of the particle, what do you think?

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