# 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.

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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: $$T' = T/\gamma, \quad \gamma = ... 53 Due to momentum being conserved, when you accelerate yourself forwards relative to the plane, the tangential force you're applying to the floor will accelerate the rest of the plane backwards. Since the plane has a lot more mass than you, its velocity will not change by very much. Thus, an inertial observer who was initially at rest with respect to the ... 53 Key point in your quote is: "from protons reference frame". In the reference frame, travelling at a relativistic speed, length contraction is experienced. All the lengths in the direction of travel of the particle are contracted by Lorentz factor:$$ l'=\frac{l}{\gamma} \gamma = \frac{1}{\sqrt{1- \frac{v^2}{c^2}}}$$So  \gamma = ... 50 Imagine two donut-shaped spaceships meeting in deep space. Further, suppose that when a passenger in ship A looks out the window, they see ship B rotating clockwise. That means that when a passenger in B looks out the window, they see ship A rotating clockwise as well (hold up your two hands and try it!). From pure kinematics, we can't say "ship A is ... 44 It's not a mechanism so much as a misconception of the nature of space (and its relationship to time): at low velocities, everything looks linear and Euclidean so we assume it is, but in reality it is not (as can be determined by appropriate experiments). It's kind of like asking by what mechanism you can reach something to your west by traveling east: if ... 36 Kinetic energy is not invariant under Galilean transformations. To see this consider the following: In the rest frame of the plane you apply a force F of 100N for one second to accelerate yourself to 1 m/s. During this time you move a distance d of 0.5m so the work done is:$$ W = Fd = 100 \times 0.5 = 50\,\text{J} $$This of course is equal to your ... 30 No. Relative to Earth your bus will have (almost) zero length, so moving from back to the front of the bus will contribute nothing to your speed relative to Earth. 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 ... 25 Yes, kinetic energy is a relative quantity. As you might guess, this means that when you're using energy conservation, you have to stay within a single frame of reference; all that energy conservation tells you is that the amount of energy as measured in any one frame stays the same over time. You can't meaningfully compare the amount of energy measured in ... 24 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 ... 24 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 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 ... 20 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 ... 18 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 ...

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

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 ...

15

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 ...

14

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 ...

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.

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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 ...

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

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 ...

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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 ...

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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 ...

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Relativity makes time relative (what a surprise! :)). It makes a difference, whether we look at the particle from "outside", or if we travel along with the same speed. So viewed from outside the particle is a normal fast particle, and need some hundreds of thousands of years for the milky way. The "oh-my-god"-ity does nothing here, it makes it only a few ...

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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. ...

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