Understanding Mach's principle: What does it answer?

What is the question that Mach tried to address in his principle? I mean, we know how to detect the inertial and non-inertial frames (by Newton’s law). Once this is understood we also see that due to the acceleration of a non-inertial frame pseudo forces appear. Since there is no privileged inertial frame the acceleration of a non-inertial frame is quite unique i.e., one and the same with respect to every inertial frame. Right? So what extra does the Mach’s principle try to answer? I’m a little confused.

EDIT : I have read that Newtonian theory doesn't attempt to answer the question that what is the physical origin of pseudo forces but Mach's principle does (see "Introducing Einstein's Relativity" by Ray D'Inverno). I thought this is due to the acceleration of the frame itself. I think what Mach meant is that local inertial frames are determined by global mass distribution in the universe. And if that mass distribution changes then the local inertial frame changes to a non-inertial one and gives rise to pseudo forces. I don't know but this is the impression I have. I may be totally wrong.

Next I also wanted to ask is it really essential to understand Mach's principle or Newton's bucket experiment to understand general relativity? Is the idea/definition of frames based on Newton's law insufficient to understand frames in general relativity?

• You are not the only one who is confused. I would say so were Mach and all who followed in his footsteps. Because local physics doesn't depend on whether your lab has windows or not (that's an experiment we can do by opening and closing shutters), I would suggest to simply ignore all Mach-like attempts to nail down inertial frames by non-local observations. – CuriousOne May 4 '15 at 6:21
• The idea is that space and time does not exist "by itself" (empty of matter), but inherits some inertial structure thanks to the existence of matter interacting. Mach's principle is therefore part of relational physics. For Mach, inertiality is related to the whole "lattice" of interactions between physical objects. That is, one could "shift" all physical objects interacting with any quantity (say, some linear acceleration) without changing whole physics. – sure May 9 '15 at 13:03
• If inertia is related to all the masses in the universe, what would happen to it in a black hole , after the event horizon ? do black holes show having more or less inertia ? – user46925 Jun 4 '15 at 20:53

What is the question that Mach tried to address in his principle?

Mach's principle isn't as clear as people suggest, but IMHO what it tries to address is inertia. Resistance to change-in-motion.

I mean, we know how to detect the inertial and non-inertial frames (by Newton’s law).

I "root for relativity", but I have to say this: an inertial frame isn't some actual thing that has an objective existence. The universe exists, you exist, the Earth exists. But an inertial reference frame is little more than a steady state of motion, and a non-inertial frame is little more than a changing state of motion.

Once this is understood we also see that due to the acceleration of a non-inertial frame pseudo forces appear.

Since there is no privileged inertial frame the acceleration of a non-inertial frame is quite unique i.e., one and the same with respect to every inertial frame. Right?

There is a privileged frame of sorts, which is the CMB rest frame, see this question. It isn't an absolute frame in the strict sense, but you can use it to gauge your motion with respect to the universe, and the universe is as absolute as it gets.

So what extra does the Mach’s principle try to answer? I’m a little confused.

Like CuriousOne said, you're right to be confused. Because Mach's principle is contradicted by E=mc². Inertia doesn't depend on distant rotating stars, it depends on local physics here and now. A photon has energy E=hf and momentum p=hf/c. These are two measures of resistance to change-in-motion for a wave travelling linearly through space at c. You divide by c to go from one to the other. Then remember the wave nature of matter: when you trap that wave in a mirror-box, it increases the inertia of the system. Because mass is a measure of energy-content, like Einstein said, and you divide by c again to say how much mass there is. But all it really is, is resistance to change-in-motion for a wave going round and round at c. Open the box, and it's a radiating body that loses mass. That radiation "conveys inertia between the emitting and absorbing bodies". Catch it in another mirror-box, and you increase the mass of that system. Having said all that, check out this article where Mark Hadley says large-scale rotation could be the cause of CP violation. It isn't quite Mach's principle as we normally understand it, but it relates to what's in the Wikipedia article, and IMHO is very interesting.

• One way to look at it is that an "inertial frame" is an operational definition. It's a frame in which "physics looks simple". In that sense the CMB rest frame is no better or worse than any other frame in which "physics looks simple". Indeed, local physics stays simple in the elevator to the singularity, no matter how distorted the long distance universe gets on that ride. That's a gift of nature that we shouldn't pass up easily, although I can understand why some people (Mach included?) may wish for global order in this place... even though local order is the best we are being offered. – CuriousOne May 4 '15 at 12:16
• IMHO it's always simple, oh CuriousOne. But IMHO it isn't always what you think. – John Duffield May 4 '15 at 15:34

Actually, Mach's Principle is not much applied to linear motion, but rather to rotational motion. Consider that, for linear motion, there is no such thing as a privileged frame of reference. In general, there is no way to tell (in a sealed box) whether the box is stationary or moving with a constant velocity.

This is not true of a rotating box. Detecting centrifugal (or centripetal, if you will) forces is easy. Just separate two bodies by a string and measure the tension on the string.

So, the question Mach's Principle addressed is: How is it that we can detect rotation? Why aren't the two descriptions, "the object is rotating while the fixed stars are not"/"the object is stationary while the fixed stars are rotating around it" equivalent?

• "This is not true of a rotating box. Detecting centrifugal (or centripetal, if you will) forces is easy. Just separate two bodies by a string and measure the tension on the string." Wouldn't we experience the same exact centrifugal force if you rotate all the universe but the box? Also it brings to mind spin, though spin is detectable from the lab's frame reference. – 0x90 Jan 26 '20 at 20:31

Your definition of Mach's principle is as good as any other.

Their are many definitions : https://en.wikipedia.org/wiki/Mach%27s_principle#targetText=Mach's%20principle%20says%20that%20this,to%20the%20local%20inertial%20frame.&targetText=A%20very%20general%20statement%20of,scale%20structure%20of%20the%20universe%22.

But the important idea they are all grasping for is the same. When we learn about reference frames we very quickly learn that a universe exactly like ours, but with everything moving an extra 10 meters per second to the left, is identical to our universe. The absolute motion of everything together would not be observable and thus "moving to this universe" is just a reference frame shift (change in notation), not a change in physics.

Once we get used to that idea it starts to strike people as odd that the same is NOT true for rotational motion. A universe exactly like ours but rotating at some angular velocity about some chosen axis would look and behave very differently from our universe. The Galaxies many light years away from the axis of rotation would be thrown away from this axis by very powerful centrifugal forces. In a plane (orthogonal to the axis of rotation) the universe would expand far faster.

Mach's principle (roughly all definitions of it) is the idea that everything rotating together should be un-observable (just like linear motion), and that we need to fix our understanding of the laws of physics so that our theories predict this.

PS. Sorry for resurrecting a very old thread.