Tag Info

Hot answers tagged

28

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 ...


26

There are two separate questions there. The easiest one to answer is how we measure the vleocity of the Earth, Milky Way etc, because we measure it relative to the cosmic microwave background (or CMB). If you measure the CMB in all directions and find it's the same in all directions then you are stationary in comoving coordinates. However if you find the ...


10

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 ...


9

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 ...


8

On the quantum level, force is not acceleration. The concept of "fictitious force" makes no sense on a QFT level, because forces are interactions between quantum states, not the classical forces you might imagine. Quantum forces are not vector fields in space. The notion of "fictitious force" would mean that, e.g., the strong force is something influencing ...


8

The classical theory of electrodynamics can indeed be written as a geometrical theory in a similar way to general relativity. As it happens there is a question and answer addressing just this, but it's in the Maths SE: Electrodynamics in general spacetime. Classical electrodynamics is an example of a class of theories called classical Yang-Mills gauge ...


8

There are a number of different frames of references. For the velocities of celestial objects we use: (i) The geocentric frame: This is a velocity measured with respect to the Earth's centre. Obviously this is quite useful for artificial satellites, but also for things like meteors. (ii) The heliocentric frame: this is the velocity as seen from the centre ...


5

General covariance applies only to freely falling observers -- once you invoke non-gravitational forces, like the inward pressure of the wall, the observer is no longer freely falling.


4

is it possible to consider also the other fundamental forces [...] to be fictitious forces like gravity in the framework of general relativity? No, because the equivalence principle only holds for gravity. If we want a final unification of all fundamental forces, hasn't this feature of gravity to become a feature of the other forces as well? The ...


4

Careful with comments like "when he receives it"--simultaneity is relative, different frames will disagree about which reading on your clock happens "at the same time" that he receives the pulse. If he is 10 light years away in the frame where you were initially at rest, and you wait 10 years after sending the signal to fire your rockets, then you fire your ...


3

The site rules forbid us from giving the answers to homework problems, but this problem illustrates a fundamental issue in relativity so I think it's worth some general comments. Incidentally you may be interested to read the Wikipedia article on the ladder/barn paradox, though in it's efforts to be comprehensive I think the article gets a bit confusing. ...


3

The Coriolis force $\vec F_{\text{coriolis}} = -2m \, \vec \omega \times \vec v$ only depends on velocity. The centrifugal force $\vec F_{\text{centrifugal}} = -m \, \vec \omega \times (\vec \omega \times \vec r)$ only depends on position. Finally, if the object is not rotating uniformly ($\dot {\vec \omega} \ne 0$), then yet another fictitious force comes ...


3

Are Lorentz transformations more adequate representations of motion, than the more intuitive velocities? Yes. The non-associativity that bothers you simply arises because there is no group of three dimensional boosts. Confined to one dimension, boosts form a rather lovely one parameter subgroup of the Lorentz group $SO^+(1,3)$. So everything "works", ...


3

If the occupants of the space station were not aware of its design and could not look out a window then there is no way to tell if it is rotating or they are near a earth size planet that causes the gravity. Orbiting around another space station will causes a sensation of gravity, and it seems you are contradicting yourself. If there is any rotational ...


3

Easy way to distinguish between gravity and rotating space station: Throw a ball straight up in the air. If it comes straight down, gravity. If it moves away from you (behind your tangential velocity), it's a rotating space station.


2

My guess would be that $\mathbb E^n$ denotes Euclidean space. In addition to having geometric structure (angles and distances) and motions (rotations, translations, reflections) - not all of it terribly useful in the 1-dimensional case - it is an affine space. Affine spaces have no notion of distinguished origin or zero point. We can use a vector space like ...


2

Your first sentence is not true. There is a whole family of freefall frames that are co-incident at any spacetime event. They correspond to different "initial velocities" as they diverge from that event: in geometric language, their origins follow the many different geodesics defined by different tangent vectors of the tangent space at that spacetime event, ...


2

A photon cannot be said to have its own inertial reference frame, because inertial reference are defined to be a family of coordinate systems that satisfy the two fundamental postulates of SR, one of which is that light moves at c in all frames. You could construct a coordinate system where the photon was at rest, but since this coordinate system wouldn't be ...


2

Look in Wikipedia http://en.wikipedia.org/wiki/Coriolis_effect. For understanding intuitively the Coriolis force effect, assume an object moving according to a static (inertial) frame of reference, in the plane perpendicular to the rotation axis, and along the radius, In the rotating frame, see the animation in Wikipedia, the Coriolis force imposes an ...


2

I see what you're trying to ask. Let me try to rephrase it: Does an observer at the bottom of a massive gravity well perceive that the clocks of actors outside of the gravity well move faster? The answer is yes, but the intensity depends on the depth of the gravitational well. For anyplace far away from exotic things like event horizons and perhaps neutron ...


2

The discussion is mostly semantic. They are both calculated relative to a point, in the case of the torque the point has the additional meaning that if you put an axle trough the point, the object will start to rotatte around it if the net torque is not zero. It happens also that the torque will be the same if you chose any other point along the axis ...


2

Let's do some math, shall we? Let's call $t$ the time as measured from Earth, and let's say your engine is running with acceleration $a$ for $0 \le t \le T$. The proper time, that is, the time as measured by a clock on a ship, is given by $\tau = \int_0^T \sqrt{1-v^2/c^2}\ dt$, where $v$ is the velocity as measured from Earth. Newton's second law for ...


2

Speed is a distance (separation between two well defined points in space) traveled over a time. The speed of Earth you quote is the orbital velocity. We know how far away the Sun is and we know the shape of the orbit, so we know how far the Earth travels relative to the Sun (distance) per year (time). Likewise the speed of the Milky Way is also given ...


1

The only outright requirement is that you compute all the angular momenta in your problem around the same center (modulo applying the parallel axis theorem to break the angular momentum of extended bodies into of-and-around the CoM parts). So you can freely chose any single point to use Now, as with most such "free" choices in physics there are generally ...


1

I was doing a question about if a train fits in a tunnel. Did the question assignment include a specific consistent definition of what's meant there by "to fit", in the first place? Presumably, in the setup which is typically considered, the ends of the tunnel (say participants $A$ and $B$) are supposed to be at rest to each other, the ends of the ...


1

You say: But for the observer on the planet, since the total angular momentum of the star about its axis is zero it should remain zero. But the observer on the planet does not occupy an inertial frame. An observer in a rotating frame measures fictitious forces. So there is no reason why angular momentum should be conserved.


1

As pointed out you can't travel at the speed of light but you can look at the limits we are tending towards as we approach it. So, if I were to travel in a spacecraft at the speed of light, would I freeze and stop moving? From the perspective of a stationary observer if your spacecraft was traveling at close to the speed of light, time on the ...


1

How to understand non-associative composition of velocities in STR? Special relativity introduces a weirdness about how your axes can be related to other observers' axes: if your axes are aligned with observer A's axes and theirs are aligned with observer B then special relativity (i.e. the Lorentz transformations) say that B's axes will be rotated with ...


1

Have a look at my answer to Time Dilation Effects from simply being on a spinning planet orbiting a star in a rotating galaxy in an expanding universe.. Compared to an observer far from the Earth, time at the Earth's surface runs more slowly by a factor of 0.9999999993. Over a 70 year lifespan this makes a difference of about 1.5 seconds. So the man in ...


1

There are two types of time dilation: dilation caused by being near a large body, and dilation caused by traveling very fast relative to another observer. Relativistic time dilation plays a bigger role for astronauts aboard a space station similar to the ISS. Even though velocity and gravity produce opposite time dilation, in this scenario, time dilation due ...



Only top voted, non community-wiki answers of a minimum length are eligible