I’m having trouble understanding the brouhaha regarding Mach’s principle. I’ve Googled around and read a few pages on sites concerning this. I am confused regarding some of the notions presented in an empty or near empty universe.
One site has an example concerning an airplane in a fog. Flying above the Earth the passengers can sense acceleration from the pseudo-forces arising in their frame of reference. The airplane is then taken out to an empty universe. The author says that there is some disagreement among current scientific belief whether or not the passengers would be able to sense some acceleration of the aircraft, since there would be nothing else in the universe to which they could compare their motion.
My explanation would be that they compare their motion to whatever it was that they pushed on. In order to have an acceleration you need more than one object and the force between them mediated by whatever agency you like; virtual particles or magic sky pixies.
In a single massive point-object universe the question of acceleration and inertia is meaningless. Assign any value you like to the object because it doesn’t matter: You can’t measure motion anyway.
As I think to myself as I write this I have a question as I jump to a two massive point-object universe. Since there is only one measure in this universe (namely the distance between the objects) is there any way of differentiating between a collision with a force momentum exchange and merely a close pass? Seems to me on first thought that they’re equivalent. Is this where the problem arises?
And with a three objects…
Help! I feel like I fell into the deep end of the physics pool and there’s no lifeguard around.
Consider rotation. If you spin a wheel-shaped space station, you can produce artificial gravity for the occupants. The question then becomes, would this work if the space station were the only thing in the Universe?
If the airplane were in an otherwise empty universe and it accelerated, the passengers would be comparing their motion to that of the airplane. Just like in a car – the car accelerates and the bodies lag behind; you feel the difference. What you feel has no relation to the road, trees or buildings around you.
The only way that wouldn’t work is if you could contrive a way for all particles in all parts of the plane and all occupants and parts to be accelerated at the same rate & time. That would have to include all parts of the gyroscopes and accelerometer sensors as well, of course.
First, a historical context: Remember that Mach was working before Einstein’s work on relativity, so if you want to understand the historical relevance of Mach’s work to physics you have to understand that it put new emphasis on defining reference frames, something that is of course very important in Einsteinian relativity.
The question Mach was considering was, in modern terms, basically whether there was an absolute reference frame in the universe independent of the matter it contains: Is there a difference between moving an object in one direction and moving the universe in the other?
Chronos’ example is one of the common formulations of Mach’s questions. In Newtonian mechanics, we would immediately say that inertia will cause the same centrifugal effects; the distant bodies in the universe don’t seem to exert any substantial effects and can be ignored. But Mach was trying to explicitly call this assumption into question. Why must the effect be the same? If inertia is, somehow, a property of an object relative to the universe as a whole, then the rotation of the universe-space-station won’t cause centrifugal effects.
This is of course a hard question to answer empirically :). But general relativity does predict “frame-dragging effects” around rapidly-spinning masses, which is consistent with Mach’s principle and not with Newtonian gravity.