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neilparker62 said:Does this solution mean anything ?
neilparker62 said:I thought the solution might be of the form c * e^(jwt) rather than sin(wt).
neilparker62 said:But the frequency looks interesting - very plainly it is ridiculously low for (say) an object in a gravitational field.
pliu123123 said:Einstein always emphasized that the notation [itex]μ=\frac{m}{\sqrt{1-\frac{v^{2}}{c^{2}}}}[/itex] is physically meaningless.
pliu123123 said:it would be more natural to describe a "m" using different reference frame parametrized by [itex]γ=\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}[/itex] to conserve physical laws.(with m not sticked with γ )
pliu123123 said:Moreover, in relativity, to deal with acceleration, we need to use curved space-time structure to replace the "force" concept .
PeterDonis said:First of all, this would not be a different "reference frame"; it would be a different convention for what the symbol ##m## means.
Second, you can't "conserve physical laws" by adopting this definition for ##m##; some of the laws still have to change form from their Newtonian versions (I assume what you mean by "conserve physical laws" is "all the laws look exactly the same as their Newtonian versions").
We don't do this to deal with acceleration; we do it to deal with gravity--more precisely, with *tidal* gravity.
Newton's Second Law states that the force applied on an object is directly proportional to its mass and acceleration. In the context of relativity, this law still holds true, but the equations must be modified to account for the effects of time dilation and length contraction.
In Newtonian physics, mass is considered to be a constant value. However, in relativity, mass is relative and can change depending on the observer's frame of reference. This means that the mass in Newton's Second Law must be replaced with the relativistic mass, which takes into account the object's velocity.
No, according to Einstein's theory of relativity, objects with mass cannot travel at the speed of light. As an object approaches the speed of light, its mass increases infinitely and would require an infinite amount of force to accelerate it further. Therefore, Newton's Second Law cannot be applied to objects traveling at the speed of light.
In relativity, momentum is considered to be a conserved quantity, meaning that it cannot be created or destroyed. Newton's Second Law can be rewritten in terms of momentum, where force is equal to the rate of change of momentum. This allows for a more accurate understanding of the effects of velocity and mass on an object's motion.
No, Newton's Second Law only applies to objects in inertial frames of reference. In the context of relativity, gravity is explained by Einstein's theory of general relativity, which states that massive objects cause a curvature in space-time, resulting in the force of gravity.