# Tag Info

25

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 ...

16

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 ...

13

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 ...

13

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 ...

9

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 ...

6

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. ...

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

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 ...

5

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} ... 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 ... 5 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 ... 4 When you ask for a "perfect" or "true" inertial reference frame you are asking for something that cannot be answered in physics. Perfection is only possible in mathematics, not physics. So in physics, what can asked is whether or not the reference frame is an inertial to a certain level of accuracy. The surface of the earth is not inertial because of the ... 4 By compression of light you mean the Doppler shift? Then yes you can measure your speed relative to the light source by comparing the Doppler shift in different directions. It's been used for a number of different radio positioning systems - but it only gives you a motion relative to the light sources 4 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 ... 4 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 ... 4 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 ... 4 The speed of light has been measured experimentally to be a certain constant, call that constant$c$. Light waves have been experimentally found to consist of photons...the photo-electric effect, for example. From this, one would naturally deduce that the photons are travelling at the speed of light. But more, the equations for photons have been worked ... 4 In this case, the gravitational force is the centripetal force, i.e. the force which keeps the satellite moving in orbit. As you have correctly surmised, the net force is towards the Earth, and the satellite will accelerate in that direction. What makes you think there is another force "holding the satellite in orbit"? 4 What Sean Carroll refers to is acceleration as indicated by an accelerometer that is right next to the rods, co-moving with the rods. The readout of an accelerometer is a local measurement. That is important in this stipulation about the rigid rods. The demand is not about being unaccelerated with respect to some other object that may be at some distance, ... 4 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 ... 3 They trust the method used by GPS for geodesy, where the claim is they can go down to picosecond and cm accuracy if necessary (for military use). GPS error analysis takes even general relativity into account. In GPS signal propagation (PDF) the systematic errors of a simple GPS setup are given, but the OPERA experiment has more sophisticated use of four ... 3 I believe the equivalent mathematical terminology to an inertial frame is "normal coordinates" at the point$p$. Meaning, in your coordinates the metric at$p$is just the flat Minkowski metric and all the first derivatives of the metric vanish at$p$. Conversely an accelerated frame would be any coordinates that are not normal. 3 Actually the path of the Foucault Pendulum is not "fixed" (even approximately!) to the "fixed" stars. Unless the pendulum is installed at one of the Earth's poles (as someone has done), then the point of suspension is in constant rotation with the Earth itself.$\therefore\$ the pendulum is really not in an intertial frame. Consider a pendulum at the ...

3

Original Newton idea was that $$\vec{F} = m \cdot \vec{a}$$ meaning in inertial frame of reference (net or total) force equals product of mass of body and its acceleration. Indeed, as you mentioned similar expression appears in non-inertial frame of reference $$\vec{F'} = - m \cdot \vec{a'}$$ meaning in non-inertial frame of reference you have to ...

3

The standard test to find out if you are in an inertial frame is to surround yourself with some non-interacting particles e.g. in a sphere. If the shape made up by the particles does not change with time then you are in a (locally at least) inertial frame. Curved space can be detected by either the volume and/or the shape made by the particles changing. ...

2

Yes, the proposition: "the sun moves around the earth" had the earth immobile. This suited the theology of the times which was completely anthropocentric and that is why it prevailed over other theories coming from antiquity, like Aristarchos', who had a heliocentric proposal. The relativity of motion was explored, as Lubos describes, when equations could ...

2

There may be a confusion : it is wrong to say that the Earth is the centre of the Universe, that is, the (unique) point from which the Universe is to be (fundamentally) described (the fact that the Sun turns around the Earth is only a consequence of this) ; what actually matters is that there is no centre of the Universe : there is no such point ; the ...

2

Both Sun and Earth move in circles around their barycenter i.e. centre of mass. The trick is that since Sun is too massive, the center of mass is too close to the sun, actually beneath the surface of the Sun, which makes the motion of Sun negligible. And, we say that Earth moves around the Sun.

2

There's no distinguished stationary platform, such that no others moving with respect to it could claim to be stationary. Another way to put it is, any inertial frame, as far as it's concerned, can claim to be stationary, but nobody on another frame has to agree. "inertial" only means "not accelerating" or "not having a net force acting on it".

2

This is easiest to answer by a rotational analogy. Suppose you don't rotate a block, but shear it. This is not a symmetry--- so the block is under stress. The same is true if you Galilean boost a material instead of Lorentz boosting it. You must have many things filling space-time in order to see what is going on, because if you just look a point observer ...

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