# Tag Info

## Hot answers tagged reference-frame

54

It travels forwards instead of backwards in an accelerating car for the same reason that a helium balloon travels upwards instead of downwards under the influence of gravity. Why is that? In an accelerating car, for all intents and purposes the acceleration can be considered a change in the amount and direction of gravity, from pointing straight down to ...

38

When your car accelerates forward, the air inside moves back relative to the car. This creates a slightly high pressure in the rear of the vehicle and a low pressure up front. Since helium is lighter than air, it moves away from the region of high pressure. A similar balloon filled with $CO_2$ would move back, since it is heavier than the surrounding air

23

An observer with zero comoving velocity (i.e. zero peculiar velocity). Such an observer can be defined at every point in space. They will all see the same Universe, and the Universe will look the same in all directions ("isotropic"). Note that here I'm talking about an "idealized" Universe described by the FLRW metric: $$\mathrm{d}s^2 = ... 18 The effective gravity inside the ISS is very close to zero, because the station is in free fall. The effective gravity is a combination of gravity and acceleration. If you're standing on the surface of the Earth, you feel gravity (1g, 9.8 m/s2) because you're not in free fall. Your feet press down against the ground, and the ground presses up against your ... 17 Calculating the effect of acceleration in special relativity is straightforward, but I suspect the algebra is a bit much at high school level. See John Baez's article on the Relativistic Rocket for a summary, or see Chapter 6 of Gravitation by Misner, Thorne and Wheeler for a more detailed analysis. When you're first introduced to SR you tend to be told ... 16 The view of most physicists is that asking "How can it be that the speed of light is constant?" is similar to asking "How can it be that things don't always go in the direction of the force on them?" or "How can it be that quantum-mechanical predictions involve probability?" The usual answer is that these things simply are. There is no deeper, more ... 16 Fun question. Here's my "me-too" answer. Suppose the car has just emerged from a river, so there's a lot of water in it, and the balloon is tied to the floor. Then you drive away. The air in the car is just like a bunch of water :) 14 Ok, here is my (hopefully rigorous) demonstration of the origin of these forces here, from first principles. I've tried to be pretty clear what's happening with the maths. Bear with me, it's a bit lengthy! Angular velocity vector Let us start with the principal equation defining angular velocity in three dimensions,$$\dot{\vec{r}} = \vec{\omega} \times ...

14

The alien doesn't really see our future. He's still seeing our past, but a more recent past than he did before. Assuming that the alien is 100 light years away when he starts cycling then he is seeing what happened to us 100 years ago. If he "cycled" fast enough (i.e. at an appreciable percentage of the speed of light) so that he was now only 50 light ...

13

This web page provides a good explanation: http://www.thebigview.com/spacetime/spacetime.html To oversimplify the explanation, you have to understand the curvature of space time around a black hole. The basic principle is that because of the curvature of spacetime around a black hole, the amount of "distance" a beam of light has to cover is greater near a ...

12

This is just a footnote to Crazy Buddy's answer (which is correct! :-): Length contraction is a real phenomenon, and indeed the RHIC observes this every day because the nuclei are moving so fast that the collision is between two disks not two spheres. However to see something you need to have light emitted from the object reach your eye, and the light from ...

11

"Relativity" is actually a misleading word that Einstein didn't like. It doesn't mean "every vantage point is equivalent and it's all relative". It really means only inertial, non-accelerating vantage points are equivalent. You could think of it as, prior to relativity, people believed that there was an absolute position/speed to the universe. Special ...

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Short answer: no. Explanation: Many introductory text books talk about "rest mass" and "relativistic mass" and say that the "rest mass" is the mass measured in the particles rest frame. That's not wrong, you can do physics in that point of view, but that is not how people talk about and define mass anymore. In the modern view each particle has one and ...

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In relativistic mechanics, there is a conserved quantity, relativistic momentum: $\vec p = \gamma m \vec v$ $\gamma = \dfrac{1}{\sqrt{1-\frac{v^2}{c^2}}}$ where m is the invariant mass or less precisely, the rest mass. Now, one interpretation is to identify $\gamma m$ as the relativistic mass, a speed dependent mass. But this is actually unnatural as it ...

11

Everything moves in geodesics, unless acted on by a non-inertial force. Ok. Everything moves in geodesics This just means it takes a path in spacetime, with this path satisfying the geodesic equation: $$\frac{\mbox d^2x^\rho}{\mbox ... 11 It acts precisely like water in a cup. Or, more specifically, like the air in the cup. Since the helium is a much lower density than the nitrogen and other gasses in your car, it can be visualized like an air bubble in a bottle. The container for the helium(the balloon) has negligible mass. When you accelerate forward, the water in a bottle will move ... 10 You have successfully discovered that the kinetic energy depends on the reference frame. That is actually true. What is amazing, however, is that the fact that kinetic energy is conserved is NOT reference frame-dependent. So, when you balance your conservation of energy equation in the two frames, you'll find different numbers for the total energy, but ... 10 Your question is a natural one to ask, but it has no answer. It is a bit like asking by what mechanism the angles of a triangle always wind up adding to 180 degrees (in Euclidean geometry). There is no mechanism for that - no one is going around checking all the triangles to make sure their angles add up right. It is just a logical consequence of the theory ... 9 Centrifugal force is a particular example of a fictitious force. It is introduced so that Newton's second law holds in a rotating reference frame. Newton's second law says$$F = ma$$This means that whenever we find an object accelerating (speeding up, slowing down, turning, or some combination), we can look around and find a physical reason why this ... 9 The real force at work is centripetal force, or a force pushing inwards. Imagine you have a bucket on a string, and you swing that around in a circle: As you swing the bucket, it travels in a circle. The red line shows the path the bucket takes. In order to make it swing like this, you have to apply a constant force on the rope -- this is the green arrow ... 9 Because spacetime includes both multiple points in space and multiple moments in time, you have to think of a particle as a line (or a 1D curve) through spacetime, not a point. The line is called the world line. It's made up of all the (x,t) points at which the particle exists: in other words, if you, as an external observer, measure the particle's ... 9 The sphere is contracted in the horizontal axis and perceived as an ellipsoid. This is what we believe about length contraction and this happens only, when we take Einstein's simultaneity into account. But, the stationary observer would see the sphere appearing as the sphere always (i.e) the circular outline would still be there at any velocity relative to ... 9 Fermat's principle is a bit more complicated than what you state: it says that in travelling from A to B, light will go along the paths that will minimize the time taken to get there - and these may or may not be straight lines. (See e.g. Wikipedia.) That said, the gravitational lensing of light does not operate quite like that. Since it is in vacuum, ... 9 Firstly you need to understand Newton's law's. basically the second law. Concisely second law is :"whenever we apply a force on an object this force changes object's velocity's magnitude if it is in the same direction as that of the direction of motion and changes the direction of motion if the applied force is not in the direction of motion." When an ... 8 In actual fact, the relative speed rule does not apply, ever. The relativistically correct speed addition rule is the following:$$s=\frac{v+u}{1+\frac{vu}{c^2}} When $\frac{vu}{c^2}$ is close to zero (in other words when the velocities invloved are much less than the speed of light, then the correct formula reduces to the Galilean version $s=u+v$. ...

8

John Norton at Pitt relates the story quite nicely. In Einstein's own words: After ten years of reflection such a principle resulted from a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with a velocity c (velocity of light in a vacuum), I should observe such a beam of light as a spatially oscillatory ...

8

You can't travel at the speed of light. So it's a meaningless question. The reason some people will say that time freezes at the speed of light is that it's possible to take two points on any path going through spacetime at less than the speed of light and calculate the amount of time that a particle would experience as it travels between those points along ...

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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 ...

8

Both are right. Any moving clock is slower than a clock at rest, from the perspective of the frame at rest. Maybe this simplified freehand graphic (apologies for its lack of precision) helps to see that both A and B feel the same about each other's time dilation: Let's say that the red axis represents A and its proper time measured in minutes (first ...

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