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67

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 ...


52

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.


36

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 ...


32

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 ...


18

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 ...


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 ...


15

The right way to think about this is geometry--- but the geometry mixes up space and time. I wrote some answers about this here: Einstein's postulates <==> Minkowski space. (In layman's terms) and here: Help Me Gain an Intuitive Understanding of Lorentz Contraction and if you read these first, you can easily understand the effect. The Lorentz ...


15

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 ...


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

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 ...


11

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 ...


9

To elaborate on Mark M's answer: If you consider an accelerating reference frame with respect to Rindler coordinates (where time is measured by idealized point-particle accelerating clocks, and objects at different locations accelerate at different rates in order to preserve proper lengths in the momentarily comoving reference frames), then light may not ...


9

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. ...


9

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 ...


9

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

Instead of a disc, let's use a ring. Now remember it is a ring I refer to when I tell you to make a measurement. If you sit inside a ring, you aren't moving. Like sitting inside a hula hoop which someone is rotating around you without touching you by applying tangential forces on the hula hoop. Your metre sticks are always in a state of rest w.r.t. you or ...


8

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 ...


7

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 ...


7

At low velocities like this you can ignore special relativity and simply add the two velocities. This is really easy to see if you imagine yourself standing still and the Earth moving under you. Relative to you the gun should fire just like you were standing still. This is called an inertial frame of reference. You see the bullet leave at $400\: ...


7

In at least one history I've read about Einstein's early life -- sorry, I don't recall the name of the book -- the author claimed that even back when Einstein was in Gymnasium (high school), he pondered a simple thought experiment: What would an electromagnetic wave look like if one traveled along beside it at the speed of light? The answer from ...


6

1) You surely feel the pressure when you accelerate. Whether you attribute it to fictitious forces or other forces depends on your choice of the "reference frame" (vantage point). From the viewpoint of your body's reference frame, which is not an inertial frame, there exist fictitious forces (inertia and/or centrifugal and/or Coriolis' force) that are ...


6

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} ...


6

Your argument is actually more or less right, but some of the details are wrong. First you have to realize that Newtonian mechanics and general relativity have different definitions of an inertial frame. According to Newtonian mechanics, the coffee cup sitting on my desk right now defines a (very nearly) inertial frame, but a falling rock is extremely ...


6

The answers that have already been posted are correct, but @kakemonsteret raises a followup question in the comments that's worth addressing: Lets say you are spinning somewhere in outer space, can you know you are spinning, ie can you rule out that the forces you feel are not caused by a mass distribution somewhere ? This question is getting ...


5

Don't worry, you don't need any quantum mechanics or any knowledge about what happens at the subatomic level to understand this phenomenon. Length contraction and time dilation are purely a property of the 4 dimensional space-time continuum that we live in. It has to do with the actual measurements of length and time that can be performed by different ...


5

In a frame of reference attached to the surface of the planet, everything far away (other planets, stars, distant galaxies...) follows a circular (or nearly) path with a period of 24 hours. These paths pose two problems They involve observed accelerations with no obvious forces causing them Any of these bodies more than $24/2\pi$ light hours away are ...


5

David Bar Moshe has given a very complete answer at a high level of sophistication in both math and physics. If that exactly meets the needs of the OP and others who read this page, that's great. I would just like to take a shot at addressing the OP's question in simpler language. GR does not have global frames of reference the way SR does. (When David Bar ...


5

The answer is No, OP's argument(v1) is not enough to derive the Lagrangian for a non-relativistic free particle. It is true that the constant of motion mentioned by OP $$\vec{c}~:=~\frac{\partial L}{\partial \vec{v}}~=~2\vec{v}~\ell^{\prime}$$ does not depend on time $t$. (It is in fact the canonical/conjugate momentum, which in general is different from ...



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