# Tag Info

## Hot answers tagged machs-principle

43

The principle is surprisingly simple. Suppose you are holding an object and you let go of it. What happens to that object? If the object just floats next to you without moving then you are in an inertial frame. If the object accelerates away from you then you are in a non-inertial frame. Where general relativity comes in is that in GR inertial frames can be ...

33

Velocity is relative. There is no special reference frame that would be "at rest". But acceleration is not and was never claimed to be. Reference frames in free fall are special and reference frames that are accelerating relative to the ones in free fall contain inertial forces (circular motion involves acceleration towards the centre; the corresponding ...

28

What you're basically asking about is Mach's principle. You might want to read the presentation of an example like this in Einstein's paper "The foundation of the general theory of relativity," which can be found in translation online. According to general relativity, the answer to your question is yes, there would be a centrifugal force. However, there are ...

27

This is a longstanding problem in physics and has not been wholly solved to anyone's satisfaction. It's not just rotational motion, any motion is subject to this concern. Very basically, what is "motion" for a singular object in its own universe? Mach was one of the first to really explore this issue. He spoke of masses in deep space and wondered if they ...

25

Because the Earth is rotating on it-self, it is not an inertial referential, which means that there are additional fictitious forces acting on objects at rest in the frame of reference. For a spinning referential, the fictitious force is called the Coriolis force, which is responsable of many phenomena such as Foucault pendulum.

20

This is indeed a Big Question; you have essentially stumbled into Mach's principle. For an even more bewildering version: suppose that in that bit of intergalactic space, you have two spherical objects, which are rotating relative to each other about their separation axis, with the distant stars stationary with respect to object 1. Our current ...

19

Scientifically, there's no reason to expect rotational velocity to be relative. To see why, think about linear velocity first. Historically, we start with Aristotelian physics, which states that linear velocity is not relative; objects have a preferred rest frame. Then we get Galilean physics, where linear velocity is relative. Why do these theories say ...

18

Using Mach's 1893 definition of Mach's principle condemns the discussion to irrelevance. It's like posting on physics.SE with a question titled "How is the emission spectrum of hydrogen determined?," but then saying in the body of the question that we want an answer written in terms of the aether and Newtonian mechanics. In the 1960's and 70's, there was a ...

18

The problem is that to determine the distribution of mass in the universe you need to choose a coordinate system that you're going to be using for measuring the positions of all those masses. The trouble is that you are free to choose whatever coordinate system you want to make this measurement. There is no absolute coordinate system for measuring the mass ...

16

While we may not be able to define a universal rest frame (Galilean invariance), we can still tell when frames are non-inertial. A spinning frame of reference is non-inertial, and thus there are non-inertial forces that arise, which we have ascribed to being "fictitious," which means that they are not fundamental, but rather a poor choice of reference. If we ...

12

I like John Rennie's answer, but I'd like to add something. From the point of view of general relativity alone, and equations of motion, his answer is complete. From the point of view of large-scale cosmology, there is something to add. It turns out that the distribution of matter in the universe is rather simple on the largest scales, in that the evidence ...

11

Special relativity deals with "inertial" or "non-accelerating" frames. Physics in inertial frames are equivalent independent of their velocity and the velocity of inertial frames are relative. You are free to assume any inertial frame is stationary and all other frames are moving relative to it. Rotating frames are not inertial, they are accelerating ...

11

Galilean relativity is Galileo's observation that the laws of physics are the same in all reference frames. Specifically, he noted that if a scientist and his laboratory move at constant speed in an unvarying straight path, the scientist will have no way of knowing his reference frame is in motion. In other words, unaccelerated motion of an object has ...

10

In general relativity, angular motion actually does have some "relativity" to it as well. When you're in close proximity to a spinning object, you'll actually be dragged along with it. This is known as the Lense-Thirring effect, or just "frame-dragging". The most dramatic example is the ergosphere of a spinning black hole, a region where no object can remain ...

10

Your question will eventually lead you to Mach's Principle. It is an old, yet unsolved question, that still remains at the stage of "philosophical idea". I understand that your question is equivalent to "What would be found if we could measure all effects on the pendulum with infinite accuracy?", what if even the tiniest contributions could be registered? (...

10

Newton's idea of absolute space simply appeared as an answer to the following question: What is an inertial system? Saying that an inertial system is one with constant velocity relative to another inertial system of course does not answer the question. To avoid such logical weakness in Newton's first law one has, at some point, to assume that there is a ...

10

If you are talking about the rotation of the body around its Centre Of Mass, it could be detected, because different parts of the body will have different acceleration and, therefore, there will be internal forces, which could be measured, at least, theoretically. If you are talking about the rotation of the body relative to some remote mass due to its ...

7

The development of general relativity has led to a lot of misconceptions about the significance of general covariance. It turns out that general covariance is a manifestation of a choice to represent a theory in terms of an underlying differentiable manifold. Basically, if you define a theory in terms of the geometric structures native to a differentiable ...

7

In Thermodynamic equilibrium, the pressure will be the same throughout the whole can. If there was a region with higher pressure, this high pressure would immediately cause a motion in the gas. So the pressure is the same everywere. The author you cited emphasizes that the pressure can uniformly stress the wall. The property that is not uniformly ...

7

How did you start rotating and how do you know in the first place that you are? :) I'd image you start alone, but to rotate you have to accelarate for which you have you create thrust that will emit particles in the other direction what in turn means you are no longer alone...

7

In General Relativity, there is no background to spacetime and so there is no absolute reference frame. However, in Special Relativity (SR) there IS a background from which accelerations are absolute. So, Special Relativity is precisely the arena you describe - a space void of matter so that we ignore gravity. There's a nice discussion here. What ...

6

There is a substantial literature on this positivist point of view. The key to looking it up is "Mach's principle". Wikipedia has a page on it and the Stanford Encyclopedia of Philosophy discusses the question amongst other issues on a page on "Early Philosophical Interpretations of General Relativity". If you want to go to the opera on the question the SEP ...

6

Imagine a point mass attached to ends of six identical springs of relaxed length $L$. The springs are oriented in co-linear pairs, with these pairs mutually perpendicular to the other pairs, i.e., they form an $(x,y,z)$ coordinate system. Attach the other ends to the walls of a cube of dimension $2L$. If the mass remains in the center of the cube, the cube ...

6

Assuming that Classical Electrodynamics (Maxwell's Equations) holds, the answer is that the inertial observer would see the radiation while the non-inertial observer would NOT. The question you are asking is basically the following paradox: https://en.wikipedia.org/wiki/Paradox_of_a_charge_in_a_gravitational_field This paradox has been analyzed and ...

6

The internal pressure in the can is resisted by the walls in two different ways: (1) by stretching the wall and (2) by bending it. A typical beverage is made of material that is as thin as possible (to save weight and cost), and therefore its stiffness in bending is very small compared with the stretching. The ratio of the two stiffness values can be of the ...

6

This section of MTW is not really a coherent argument, it's more like an outline of a research program. They were writing during the 1960's (finished writing in 1970-71). They say, "Much must still be done to spell out the physics behind these equations and to see this physics in action." They were anticipating that these theoretical investigations would be ...

6

The basic definition is, that physics has to be the same in every inertial frame (Classical Mechanics). As one gets fictitious forces in accelerated frames (e.g. Centrifugal, Coriolis force), these frames are not inertial. But if the forces in phenomena you want to observe are way bigger than the fictitious forces, you may approximate your frame (on the ...

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