# Tag Info

69

The Foucault pendulum is a great experiment which does demonstrate that the Earth is rotating, but it was only introduced in 1851. The Earth had been known to rotate for several centuries before that, probably stimulated by Copernicus and Galileo pushing the heliocentric model of the solar system during the 16th century. A couple of decades before Faucalt's ...

54

Foucault pendulum. I don't know how the ancients did it, but it is surely pure classical mechanics. The animation describes the motion of a Foucault Pendulum at a latitude of 30°N.

52

This is a very good question. Einstein himself, in a 1907 review (available in translation as Am. J. Phys. 45, 512 (1977), e.g. here), and Planck, one year later, assumed the first and second law of thermodynamics to be covariant, and derived from that the following transformation rule for the temperature: $$T' = T/\gamma, \quad \gamma = ... 48 Imagine two donut-shaped spaceships meeting in deep space. Further, suppose that when a passenger in ship A looks out the window, they see ship B rotating clockwise. That means that when a passenger in B looks out the window, they see ship A rotating clockwise as well (hold up your two hands and try it!). From pure kinematics, we can't say "ship A is ... 43 It's not a mechanism so much as a misconception of the nature of space (and its relationship to time): at low velocities, everything looks linear and Euclidean so we assume it is, but in reality it is not (as can be determined by appropriate experiments). It's kind of like asking by what mechanism you can reach something to your west by traveling east: if ... 30 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 ... 23 Imagine a slightly different scenario: two pilots, Alice, and Bob, are in their spaceships. They move towards a tunnel of length L at a velocity v, and remain a distance l' apart. Alice is closest to the tunnel and thus enters first, approaching a wall at the end of the length of the tunnel. Just as Bob enters he decelerates, coming quickly to a halt ... 23 yes, you may describe the motion from any reference frame, including the geocentric one, assuming that you add the appropriate "fictitious" forces (centrifugal, Coriolis, and so on). But the special property of the reference frame associated with the Sun - more precisely, with the barycenter (center of mass) of the Solar System, which is just a solar radius ... 22 There was no problem with electromagnetism. The problem was that Maxwell's equations are invariant under Lorentz transformations but are not invariant under Galileo transformations whereas the equations of classical mechanics can be easily made invariant under Galileo transformations. The question was: how to reconcile both in a universe in which Maxwell's ... 17 I think the Foucault pendulum is the best answer, but for the sake of variety I'll add another very interesting one: the equatorial bulge affecting the figure of the Earth. This is the "pancaking" of the planet due to its rotation. You can measure the geometry of the Earth without leaving its surface, and find that it is bulging in accord with your ... 17 Mach's principle has influenced Einstein but the final formulation of general relativity as of 1916 clearly invalidates Mach's conjecture. According to Mach's principle, motion - including accelerating and rotating one - may only be defined relatively to other objects. That would imply that there can't exist any gravitational waves. However, general ... 16 In physics, it is often implicitly assumed that the Lagrangian L=L(q^i,v^i,t) depends smoothly on the (generalized) positions q^i, velocities v^i, and time t, i.e. that the Lagrangian L is a differentiable function. Let us now assume that the Lagrangian is of the form$$L~=~\ell(v^2),\qquad\qquad v~:=~|\vec{v}|,\qquad\qquad(1) where $\ell$ is ...

15

The fundamental postulate of special relativity, indeed of Galilean relativity, is that there is no experiment that determine the state of motion of any inertial frame relative to the outside world unless the measurement uses data gleaned from outside the frame. Read Galileo's wonderful and very famous allegory of Salviati's Ship for a poetic and rock ...

14

Anything related to the Coriolis effect (some pretty pictures can be found in the link), i.e. even cannons will be (not precisely, rather seem) deflected because of the earth's rotation.

13

An indirect indication that the Earth rotates is the fact that the rotation varies over time. First of all, the orientation of the Earth's axis changes: long-term effects like precession and slow variations in the axial tilt, as well as small short-term variations like nutation. Precession was already known in the Ancient world (Hipparchus, Ptolemy,...) and ...

13

One thing to note is observing something's temperature and thermodynamic notions of temperature aren't exactly the same thing. This is in line with @Mattia 's answer. If a star is receding form you then it will appear cooler because its radiation has been red-shifted. Does this mean that there can be a net flow of heat from us to the star (provided it's ...

13

You certainly could define your origin of coordinates to be the center of the Earth. It would be a little tricky, because this would no longer be an inertial frame of reference, so there would be fictitious forces (or Coriolis forces). That is, your equations of motion would no longer look the same. One reason the standard barycenter frame of reference is ...

13

There's no doubt the solar system is accelerating. The milky way galaxy rotates, and we're quite on the outside. Hence, there's a permanent acceleration vector pointing to the center. However, this is a phenomenally small acceleration. If you'd try to measure it here on earth, you run into all kind of practical problems when you try to isolate it. For ...

12

There are two main reasons it is practical to ignore the pseudo forces due to the rotation of the earth/sun about the galaxy. First, the accelerations are pretty small, and second, they are pretty uniform. The sun moves around galactic center at about 800,000 kilometers per hour, but it takes around 250 million years to complete a single orbit of galactic ...

12

This was going to be a comment on Luboš Motl's answer, but it would be more appropriate as a full answer now. His answer says: Laws of physics can be written more simply for the solar system's center of mass (barycenter) than for a point on Earth (geocentric). Just one thing! One mustn't neglect the non-idealities of the barycenter itself, which has a ...

11

Remarks: In the following explanation 4-dimensional space-times $M$ equipped with a metric of signature (3,1) are considered. There are several Wikipedia pages treating frames (sometimes called tetrads or Vielbeins) in GR. See for example, here, here and here There is a very good introductory chapter on the subject in chapter 5 of these notes by: R. ...

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 ...

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

Back before Copernicus (Or rather, before his view was accepted), we used to think the earth was the center of our solar system. Therefore, if you search for those models, you can find examples such as: This is, of course, based on observations rather than calculations, but it represents the complication of the solution nonetheless. (Image taken from ...

10

Draw a spacetime diagram. Really, there is no better way to solve relativity problems. In the above, the nail has worldlines $1$ (back) and $2$ (front), while the hole's worldlines are $3$ (front) and $4$ (back). Let's agree that the origin $\mathcal{O}$ of the coordinates is the event of the front of the nail just entering the hole, i.e. the intersection ...

10

Dear Nigel, Newton had to postulate an absolute space. In fact, he used his physics insights to support the idea of a "spirit" that is filling the space - a paradigm this greatest scientist and a devoted Christian was as passionate about as about physics itself. The absolute space determined geometry everywhere except that it didn't know about any preferred ...

10

As you say, there's a perfectly sensible operational definition of an inertial frame: it's one in which free particles move with constant velocity. Even in general relativity, it makes sense to talk about inertial frames, but only locally. To be precise, an inertial frame is well-defined only in an infinitesimal neighborhood of a spacetime point, although in ...

9

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? ...

9

I find the phrase "acceleration need not be relative anything" to be awkward, but I can see where it comes from. For the moment restrict our consideration the Galilean relativity (just to keep the math simple). Consider two frames of reference one ($S$) in which the body is at rest and another ($S'$) in which it moves with velocity \$\vec{v'_i} = \vec{u} = u ...

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