[pensador (OP)]

Can Special Relativity be derived from Newtonian mechanics? 

https://futurism.com/newtonian-physics-vs-special-realtivity

[Bored chemist]

No.
because they contradict eachother

[Colin2B]

Can Special Relativity be derived from Newtonian mechanics? 

To add to what @Bored chemist said, Newtonian mechanics does not contain any theory of electromagnetism which is key to special relativity.

[yor_on]

No Newtonian mechanics came from a belief, that the world could be counted at.
Hup does not give you that

It might give you 'statistics'
But that's the long run

It does not include yourself.

[pensador (OP)]

I was thinking in terms of light clocks in a moving reference frame. ie The photon moves further and so ticks slower for a stationary observer. This could be modelled using newtons equations of motion.

How would special relativity give a different answer in this case to a Newtonian explanation of the same thing. Both are modelling the exact same light clock. Both are limited by the speed of light, are they not?

[pensador (OP)]

No Newtonian mechanics came from a belief, that the world could be counted at.
Hup does not give you that

It might give you 'statistics'
But that's the long run

It does not include yourself.

Does the HUP limit the speed of light to c via quantum foam. ?

How is the HUP related to special relativity or Newton mechanics ?

[Bored chemist]

If I start with a 1 Kg rock and apply 1 newton to it then it will accelerate at 1m/s/s.
Per Newton it will accelerate forever.
Per Einstein it will accelerate less as time goes on, because there's a limit at C.

[yor_on]

Beautiful BC :)

As for a quantum foam? Under Planck scale?
Your guess is as good as mine.

Scaling it up 'c' will be a limit though.

[yor_on]

I don't expect Newton to have known about 'HUP', I read someone say that everything has its season. What it might me think is that even though you stand upon someones shoulders gaining new ideas, it also might be read as time have passed on.

[evan_au]

The photon moves further and so ticks slower for a stationary observer.

Perhaps you are thinking that Newton could have discovered the Doppler effect long before Doppler: the frequency of light shifts towards the red when you are moving away from an object.

But this depends on understanding light as a wave - and Newton came down on the side of the debate that said "light is a particle".

See: https://en.wikipedia.org/wiki/Corpuscular_theory_of_light#Isaac_Newton

Now we understand that light has characteristics of both a wave and a particle, so we can apply Doppler shift to light (such as in Police radar).

But this is a long way from understanding that:
- Light has a specific speed (in a vacuum): would not have been known until Maxwell's equations of electromagnetism
- Every observer sees light with this speed (in their own lab)
- This paradox is related to time dilation of observers moving relative to each other
- The existence of this paradox would not have been understood before the Michelson-Morley experiment
See: https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment#Most_famous_%22failed%22_experiment

[pensador (OP)]

If I start with a 1 Kg rock and apply 1 newton to it then it will accelerate at 1m/s/s.
Per Newton it will accelerate forever.
Per Einstein it will accelerate less as time goes on, because there's a limit at C.

Am I correct in thinking acceleration is to do with general relativity and not special relativity? Special relativity deals with none accelerating objects does it not.

Using simple algebra and tracing the path of a photon between two moving mirrors, will result in time dilation for an observer in a stationary reference frame. Assuming of course that light is fixed at c for the observer and someone moving with the mirrors.

Would Newton have assumed that light speeded up for the observer, so that the clocks would still tick at the same rate, for the observer and for someone moving with the mirrors?

[pensador (OP)]

Perhaps you are thinking that Newton could have discovered the Doppler effect long before Doppler: the frequency of light shifts towards the red when you are moving away from an object.But this depends on understanding light as a wave - and Newton came down on the side of the debate that said "light is a particle".

Both Newton and Einstein viewed photons as particles.

How does viewing light as a wave affect a photons movement between two moving none accelerated mirrors?

I understand special relativity has been inccorporated into quantum field theory and QED. But Special relativity does not need Quantum field theory. What am I missing in what way does special relativity include waves and quantum theory?

[Halc]

Am I correct in thinking acceleration is to do with general relativity and not special relativity? Special relativity deals with none accelerating objects does it not.

Special relativity deals with acceleration just fine.  General relativity introduce the equivalence principle with allowed the properties of gravitational fields to be (locally) described in terms of accelerating reference frames.
Newton's equations did not cap speed of mass at c.  F=ma.  If you continue to apply force to an object, the acceleration will continue up to any beyond c.  With SR, acceleration (not proper acceleration) drops off and that same force just drives up m after a while.  They do this in particle accelerators where getting a particle to near light speed is easy, but then they just add mass to the thing until up to the limits of the magnetic field to hold it in its path.

Using simple algebra and tracing the path of a photon between two moving mirrors, will result in time dilation for an observer in a stationary reference frame.

Reference frames are not stationary.  Things are stationary relative to them.
That said, I see what you are getting at.  Newton probably wouldn't consider the light device to be a clock since without knowing its speed, there is no way to tell how far the light needs to travel.  Not like there is any real light clock anyway.  How would you get it to work?  You can't measure a photon going between mirrors, counting cycles.  A photon can be measured but once.

[pensador (OP)]

They do this in particle accelerators where getting a particle to near light speed is easy, but then they just add mass to the thing until up to the limits of the magnetic field to hold it in its path.

How is this explained, is it that does the particle shrinks to the observers, and Its inertia and or wavefunction frequency, increases. 

[geordief]

They do this in particle accelerators where getting a particle to near light speed is easy, but then they just add mass to the thing until up to the limits of the magnetic field to hold it in its path.

Can it be argued that the force applied in a particle accelerator has its own speed of propagation and that it would for this reason be unreasonable for the particle to be accelerated to a speed higher than that of the speed of the force itself?

If true ,would that observation have any theoretical consequences?

[Halc]

How is this explained, is it that does the particle shrinks to the observers, and Its inertia and or wavefunction frequency, increases.

Newton has no explanaion.  He'd say that a continued force would give it more kinetic energy (correct) and so the v must be going up (it is accelerating indefinitely, wrong).  E = ½MV², so V can get highter than c.  You could outrun light just like you could theoretically accelerate past sound.  Neither had been demonstrated in Newton's time.

Anyway, SR says a (acceleration in F=ma) approaches zero as v approaches c, so kinetic energy must be gained by an increase of mass.  You called it inertia.  Same thing.

[Halc]

Can it be argued that the force applied in a particle accelerator has its own speed of propagation and that it would for this reason be unreasonable for the particle to be accelerated to a speed higher than that of the speed of the force itself?

If true ,would that observation have any theoretical consequences?

That would imply that as a particle approached c, the force on it would decrease, which would be measurable in the drop in reaction magnitude.  The recoil of a railgun would approach zero if the projectile is already going fast.

The force is applied via a field set up along the entire length of the accelerator, so is is not an issue of trying to keep up. The particle isn't pushed from some endpoint like it is in a chemical gun or a light sail, both of which would nevertheless have recoil even without a projectile since it uses mass to convey force to the projectile whether it is there or not.  Fire a cannon without a ball and it still has some recoil due to the accelerating powder, but not nearly as much as with the ball.

[geordief]

which would be measurable in the drop in reaction magnitude. 

How would that be measurable. Isn't the acceleration (change in speed) the only measurable effect?

The force is applied via a field set up along the entire length of the accelerator, so is is not an issue of trying to keep up. The particle isn't pushed from some endpoint like it is in a chemical gun or a light sail, both of which would nevertheless have recoil even without a projectile since it uses mass to convey force to the projectile whether it is there or not.  Fire a cannon without a ball and it still has some recoil due to the accelerating powder, but not nearly as much as with the ball. 

Yes ,I appreciate that the force is applied equally at every point along the trajectory (no one point of emanation) ,but does this force  still always have a (same) speed of propagation at every point regardless?

If this force propagates at c  how could it propel any object to a faster speed?

Am I right to imagine that the speed of propagation of force is actually a valid concept?( ordinary physical waves in a medium  do apply a force that applies an acceleration as a function of their speed of propagation;would  the same hold for em waves?)

I apologize if I am showing my ignorance ;-)

[Halc]

which would be measurable in the drop in reaction magnitude.

How would that be measurable. Isn't the acceleration (change in speed) the only measurable effect?

One can measure force, no?  Most of the force applied by a cyclotron (as opposed to a linear accelerator) is used to bend the fast moving particle into a circular path.  That goes up as the the particles gains mass even though the increase in speed (not the same as acceleration) drops to near zero.

Yes ,I appreciate that the force is applied equally at every point along the trajectory (no one point of emanation) ,but does this force  still always have a (same) speed of propagation at every point regardless?

A force is a field, not something that needs to propagate. Gravity has no propagation speed for instance.  A change in the field does need to propagate, so that is indeed confined to light speed, just like gravity waves.
I don't know enough about particle accelerators to say if the field needs to change and thus need an awareness of the particle location or an awareness of the focus of the beam. I suspect not on the former at least, even though a mag-lev train certainly involves such awareness of the projectile as it passes, possibly only for energy efficiency and levitation purposes.

If this force propagates at c  how could it propel any object to a faster speed?

Oh, you're asking about the Newton thing.
Did Newton have any idea that EM force was a field or that light speed was relevant at all here?  Why not use gravity?  Throw a rock at nearly light speed into a star and the gravity (which is a field, but Newton might not have known that) would boost it over c.  The gravity would hardly need to 'keep up' since the rock is not moving away from the star.
Newton did have a crude speed of light figure available to him.  It was first measured when Newton was about age 35.

Am I right to imagine that the speed of propagation of force is actually a valid concept?

A change in a field needs to propagate, but the field itself isn't something that has a velocity.  Again, Newton likely wouldn't have worded things that way.

( ordinary physical waves in a medium  do apply a force that applies an acceleration as a function of their speed of propagation;would  the same hold for em waves?)

I'm trying to figure out a case where waves do that.  In general, a bit of flotsam on the water tends to go nowhere as waves pass, but a surfer can ride a wave if he can stay consistently on one side of it, and propel himself to considerably higher speeds than the speed of the wave.  Similarly, a sailboat can move faster than the wind.
A field is more like a hill and less like a wave.  I can accelerate as I roll down a hill and don't need to worry about the speed of the medium as I do so.

I apologize if I am showing my ignorance ;-)

Don't think there is ignorance here.  We're trying to posit what Newton might have concluded for these question given the state of science at the time.  We know he suspected light speed to frame dependent, so the conclusions drawn from it being otherwise were unavailable to him.  The universe appeared more or less static.  There are other stars, and they have a bit of relative motion, but nothing anywhere appeared to be going particularly fast.  The idea of galaxies (or any large structure held together with mutual gravity) was unknown at the time, let alone the fact that they recede from each other, which wasn't even known to Einstein at first.  So the model of the universe was just sort of a soup of stars wandering here and there.

[geordief]

I think I might have been a little off topic .I have just started a new thread on this subject.

Hope it goes well.