Anyone who's flown on a plane knows that once the aircraft reaching its cruising speed (roughly constant) and altitude, for the most part, you can walk around the cabin just as you would if you were on the ground. Your leg muscles apply force in the same way as if you were walking on the ground. You need to do nothing special to account for the fact that you are moving 600+ miles per hour relative to the Earth. If the aircraft is accelerating, changing altitude or speed, whether by turbulence or intent, you must expend more effort, but accelerated frames are a topic for another time.
Similarly, any child knows that if the car (or van) is traveling at a constant speed on straight and level highway, you can toss your ball up from your lap and it will fall back to your lap, same as if you were sitting in a chair at home, even though the van you are in might be moving 50+ miles per hour relative to the Earth. You get a similar experience traveling on a train or subway.
The reason for this is that Newton's Laws are the same in inertial reference frames. Inertial frames are defined as non-accelerating, or moving at a constant velocity. A consequence of this fact is that Newton's Laws DO NOT DISTINGUISH ANY PREFERRED INERTIAL FRAME.
Why is this?
By Newton's Second Law (wikipedia):
F = m*a
where 'F' is the applied force, 'm' is the mass of the object to which the force is being applied, and 'a' is the acceleration, or rate of change of velocity, 'v' (velocity is the rate of change of position). Mathematically, these are written using derivative (wikipedia) notation:
a = dv/dt = d^2x/dt^2
and the acceleration is the second derivative of position, x, with respect to time.
If the force, 'F', and mass, 'm', are constants, the most general solutions to this equation is, for some future time, t>0, for velocity, v:
v = dx/dt = B + (F/m)*t
and for position, x:
x = A + B*t + (1/2)*(F/m)*t^2
where 'A' & 'B' are called 'arbitrary constants' in the mathematical sense. In practice, these constants are determined from initial conditions (wikipedia) of the system under consideration. Beyond that, these constants are truly arbitrary - you can choose them with any origin, or zero point, that is convenient for your problem - the corner of your house, the center of the city, the center of the Earth, the center of Mars, or even the center of the Galaxy, or the center of a galaxy a million light-years away.
Note that the variable 'B' represents a velocity, so in addition to Newton's Laws being the same regardless of your POSITION in space, the laws also do not require a favored VELOCITY in space.
Note that if F = 0, the equation reduces to the spatial component of the Galilean transformation (wikipedia):
x = A + B*t
This equation solves the problem in one spatial dimension, but you can expand the case to three-dimensions by writing similar equations for the y and z directions, which are perpendicular to the x-direction, and each other.
Engineering Implications
Newton's Laws, and their invariant properties under coordinate transformations, have been experimentally tested for over three hundred years and have huge practical implications. They get tested with the construction of probably every mechanical device.
The most important of these practical applications is that in inertial frames, we can build devices that will work exactly the same if they are moved (accelerated) to another inertial frame. We can test a rover robot on the surface of the Earth, then transport it to Mars, and the forces required for it to move are fundamentally the same (adjusting for the different surface gravity, ground texture, etc.) - the torque driving the wheels moving it forward does not need to consider that the rover is on a planet moving many kilometers per second relative to the Earth. Similarly, thrusters adjusting the course of spacecraft moving very fast in the distant solar system (wikipedia: New Horizons) impart the same accelerations to the satellite as if it were in Earth orbit.
If the Earth were physically preferred reference frame, as claimed by Geocentrists, we would expect these principles to function differently when moving relative to the Earth, or at great distance from the Earth. The fact that these devices function according to the same physical laws we've discovered on the Earth is evidence that the Earth is NOT a physically preferred reference frame. A scientist on Mars will derive the exact same physical laws as a scientist on the Earth.
If Geocentrists want to claim that certain devices work in these other remote locations because we've designed them to work that way, the statement carries with it the implied assumption that somehow human technology violates the laws of physics. That is utter nonsense. The technological progress human society has enjoyed over the past three hundred years is an outgrowth of our ability to understand those physical laws and work within their constraints.
Additional References:
Frames of Reference and Newton’s Laws
by Michael Fowler
2 comments:
Tom - If the Earth were physically preferred reference frame, as claimed by Geocentrists, we would expect these principles to function differently when moving relative to the Earth, or at great distance from the Earth.
JM – This is a non sequitur statement. Why? Geocentrists claim the earth is a preferred reference frame for it alone is stationary in the universe. This does not mean the earth is a preferred reference frame in relation to the force of gravity as you insist it does.
Tom - The fact that these devices function according to the same physical laws we've discovered on the Earth is evidence that the Earth is NOT a physically preferred reference frame. A scientist on Mars will derive the exact same physical laws as a scientist on the Earth.
JM – These same physical laws are merely assumptions, geometry and maths. Those same assumptions and maths are used at other parts of the universe, then fine. Does this mean geocentrism is invalidated because a theory can assume no preferred reference frame? Definitely not, simply because the geocentric preferred reference frame is preferred in reference to the rest of the universe and not preferred in reference to another local reference frame. This means that according to geocentrism we should see the large scale structure of the universe centered on the earth. This is exactly what we see with the CMB quadropoles and octopoles and the axis of evil, which show the earth is at the center of the universe. We also see this with the large scale structure of the galaxies and other light sources that are focused in on the earth and located around the earth in concentric spheres. We also see this with the functioning of the lunar laser ranging experiment that is only satisfactorily explained by a stationary earth (relativity special pleads a deformation in the moon retro-reflector that causes the laser to trace out a triangular path back to the earth!!). I also note the lack of moon light aberration, which indicates the earth is stationary relative to the moon. Finally, Airy’s failure to detect the earths motion is also clear evidence for a preferred reference frame.
Tom merely assumes that mass attraction and inertia as defined within Newtonian mechanics holds true always an everywhere and as Newtonian mechanics does not require a preferred reference frame, then when technology has some success on another planet, then this is supposedly evidence that the earth is not a preferred reference frame. But if we examine the ‘m’ in the F=ma equation we see ‘m’ is really not known as a cause within Newtonian mechanics at all. It is merely special pleaded to be a magic cause within all physical bodies. Also if we understand inertia not being caused by the motion of the body, but by a local aether flow around and with the body, then the Newtonian equations are merely convenient equations that approximate reality. As such, any special claims that such a model clearly indicates the earth is not a preferred reference frame, is to over estimate the power of the theory and ignore all the counter evidence against the geocentric preferred reference frame claim.
Tom - If Geocentrists want to claim that certain devices work in these other remote locations because we've designed them to work that way, the statement carries with it the implied assumption that somehow human technology violates the laws of physics.
JM – This statement does not establish its initial claim concerning what geocentrists claim. The statement is also a non sequitur, for to claim devices have been designed without a preferred reference frame, does not mean the non preferred reference frame universe really exists. All it means is that technology can be designed with local, non preferred reference frames, using a model that makes assumptions about inertia and mass attraction. The technology is then used on another planet, where the same assumptions are used and the technology seems to work well. So all Tom can conclude is a model can approximate the real in a local reference frame that produces some good results using local forces and local mass attraction.
Geocentrists can do the same thing. We can claim the earth is the preferred reference frame with respect to the rest of the universe due to the large scale structure of the universe being structured around the earth. We can then approximate the forces and value of mass of an object and use Newtonian mechanics in a local frame. This does not remove, nor contradict the geo claim of the earth as a stationary object within the universe, for the earth can be used mathematically as an absolute reference frame and as a local reference frame. For mathematically the numbers work out the same.
Tom - That is utter nonsense. The technological progress human society has enjoyed over the past three hundred years is an outgrowth of our ability to understand those physical laws and work within their constraints.
JM – This is merely a claim made by Tom, based upon a false premise. Geocentrists can mathematically (according to Newton’s equations) use the earth as a preferred reference frame with respect to the rest of the universe, or as a local reference frame. When we see the large scale structure of the universe and several experiments that demonstrate the earth is stationary, we conclude that experimentally the earth is stationary. We can also use Newtonian mechanics is a local frame, knowing that gravity and inertial are really caused by earther flow and not mass attraction and the motion of a body.
Even so, in Toms examples of constant velocity of say the plane, this assumes the body on then plane can act as though the plane is stationary. Just like Newtonians assume the earth is stationary when they make their technology. Just like geocentrists assume the earth is stationary the same way the Newtonians do.
JM
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