102

It sounds like your confusion is coming from taking paraphrasing such as "everything is relative" too literally. Furthermore, this isn't really accurate. So let me try presenting this a different way: Nature doesn't care how we label points in space-time. Coordinates do not automatically have some real "physical" meaning. Let's instead focus on what doesn't ...


82

Voyager $1$ is headed away from the Sun at around $17$ km per second at an angle to the ecliptic of around $35$º. The orbital velocity of the Earth is $29.8$ km per second, and multiplying by $\cos 35$º to get the component of the velocity in Voyager's direction gives a shade over $24$ km per second. So at the point in its orbit where Earth is moving ...


54

Within the context of Newtonian mechanics, there's a simple answer: velocities are not absolute, but differences in velocities are. So you can state that acceleration occurs unambiguously. In special relativity, this is a bit more complicated because of relativistic velocity addition, but all observers can unambiguously compute a "proper" acceleration for ...


49

According to classical physics: no. It is impossible to tell how fast something is moving from a snapshot. According to special relativity: yes. If we choose a frame of reference where one of the balls is at rest then only that ball will look normal. The other ball is moving in this frame so it will be length contracted. If its rest length is $L$ then its ...


42

Speed doesn't kill us, but acceleration does. When astronauts go into space at launch and when fighter pilots turn very tight turns at high speed they experience 'high g forces' - their bodies are accelerated very fast as they accelerate and gain speed to go into space or as the direction of their speed changes. One of the problems with this is that for ...


40

Speed of light is actually a pretty special case compared to how we typically think of speed (as far as I understand it). Movement is always relative to some frame of reference. In the case of a single isolated object, it's hard to really think about how you could have any frame of reference without at least a second object to measure the speed relative to....


39

I'm not going to really touch what one could mean by "multiple realities", but I think this can still be useful. Let's say we are facing each other. I see a building to my left. You see a building to your right. Does this mean there are two different buildings? Let's say I then point to the right, and you say I pointed to the left. Did we just create two ...


35

There are two separate questions there. The easiest one to answer is how we measure the velocity 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 ...


32

First: Maxwell's equations predict that the speed of light is absolute. The whole motivation for the special theory of relativity is to reconcile this with the notion that all motion is relative. In other words, you're worried about exactly the same thing that troubled Einstein. You just haven't understood how he solved it. The key to your confusion is ...


29

If we could take a snapshot of both tennis balls, would there be any evidence that could suggest that one is moving and the other one is still? We can't. Problem solved. Well, almost problem solved. So in reality, we can take shorter and shorter exposures. I can take a 1 second exposure of the scene, where the moving tennis ball will be heavily blurred ...


27

What keeps a bicycle up is a variety of things, but it all comes down to the front wheel, which can move left/right. The bike is always out of balance, and if it starts to fall to the left you unconsciously turn to the left, which moves the point of support (the wheel on the surface) to the left, which arrests the fall and may start the bike falling to the ...


25

A rocket's thrusters function by ejecting reaction mass (exhaust). You can measure the movement of the rocket by its distance from its reaction mass. The rocket moves relative to its reactant. You can say the rocket didn't move, but not because it can't be measured. The center of mass of a rocket-reactant system* never goes anywhere—not even in our universe*...


24

"A state of rest" is a relative term. Relative means - measured in comparison to the things around it. When you sit in a train and sip from a cup of coffee, you can do so because the cup is still relative to you even though both of you might be hurtling through the countryside at 200 km/h. For most experiments, objects can be considered "at rest" if they ...


24

When launching into a low Earth orbit only your velocity relative to the Earth matters, as seen from the not-rotating reference frame of the Earth. Your velocity relative to the sun does not matter, because once you are in the orbit your velocity vector relative to the Earth will oscillate between pointing towards and away from the velocity vector of the ...


22

The fly does not slam into the windshield because at smaller scales of size, air effectively becomes much more viscous and halts its motion. A fly using a jet pack in a vacuum-filled car would slam into the windshield, however. Viscosity is a fascinating issue in terms of scale. Paramecia, for example, effectively must drill their way through water, not ...


21

A red or blue shift is created when the light source is moving relative to the detector. In your thought experiment, you emit light and you receive it, so there is no red or blue shift. For your idea to work, light must be emitted not by you, but by the universe equally in all directions. Such emission is known as Cosmic Microwave Background. By measuring ...


20

It all comes down to the fact that we are moving too. How can the bird drop down and catch the worm, if the earth and the worm are moving so quickly. It can because the tree, the bird, and the air are moving at the same speed, cancelling out. If we launch a spacecraft from Mars to the earth, the spacecraft is zooming around the sun at the same speed Mars ...


20

By the principle of relativity, you will not fall over – assuming that you know how to use the bike and you won't be deliberately "confused". The principle says that the laws of physics have the same form in all inertial frames that are moving by a constant velocity relatively to each other. The reference frame associated with the moving sidewalk is as good ...


20

how can we say a rocket accelerates in empty space ? According to third Newton law, body in a rocket will experience pseudo-force with direction opposite to that of rocket acceleration. That is - rocket acceleration will induce body weight which can be observed / measured : It's much like water "feels" centrifugal force. What you actually will not be able ...


19

The speed of light is the same in every direction; specifically, $c=299,792,458$ m/s. This fact was proven by Michelson and Morley in 1887, when they measured the speed of light very precisely using the Michelson-Morley interferometer. They proved more than that, though: the speed of light is not only independent of direction, it is also independent of the ...


17

Charge density $\rho$ and current density $\vec{J}$ form a Lorentz four-vector $(c\rho, \vec{J})$ that transforms under a Lorentz transformation just like $(ct, \vec{r})$ does. For example, if two frames are in relative motion in the $z$-direction, with the primed frame having velocity $v\hat{\mathbf{z}}$ relative to the unprimed frame, then the ...


16

Let me first go through this without friction or air drag. You say $v_y$ along the $x$-axis and the train moves with $v_x$ along the $z$-axis. This is a little inconsistent. I will use the velocities, but not your description of the axes. So the train moves in the $x$-direction, the ball is thrown into the $y$-direction and it the $z$-direction is up-down. ...


16

Why should a high velocity kill you? The danger comes from acceleration, not velocity. Where you are in an airplane with a constant (but high) velocity, you feel nothing because the atmosphere of the plane is moving at the same velocity as you are, and because there is no net force or acceleration applied to you. However, acceleration is like a force for ...


16

This is a simple but important point. While the speed of light is invariant among all inertial observers, the direction of light is not. Let's show this explicitly. Let's say that light is propagating in the negative$-y$ direction w.r.t. observer $\mathcal{O}_1$ who is standing still. Now, consider an observer $\mathcal{O}_2$ running at a uniform speed $v$ ...


16

My question is: If speed is not an entity in itself, but only dependent on other constant factors, how can the speed of anything (let alone light) be a constant? Am I completely missing something here? The question you are really asking is which is the more fundamental, speed or distance? Think about the distances in space. How are we to measure them ...


15

How can kinetic energy be proportional to the square of velocity, when velocity is relative? Without reading the rest of your question, I must first reply that one has nothing to do with the other. Kinetic energy is frame dependent, just as velocity is. Momentum is proportional to velocity and is frame dependent too, just as velocity is. Now, looking ...


13

It is counter intuitive, this question or variants of it get asked a lot. Surely if you're travelling towards a beam of light it will appear to be travelling faster? The answer is it won't, every inertial observer measures the speed of light to be exactly $c$, regardless of their velocity. It is for this reason that the Galilean transformations break down ...


12

The space bicycle paradox (also known as "The Shadoks go to space" or "How to walk in space") I think this is a cute question. Though the style is a bit awkward regarding frames and speed, it is presented as an interesting paradox. In a nutshell the question is the following (simplifying details): If I am driving a spaceship, inertial frame invariance ...


12

By my reckoning, if all speed is relative, then no mater how fast you go light should always race away from you at the same apparent speed. I.e. there should be no speed limit. If an invariant speed $c$ exists, then if an entity has speed $c$ relative to an inertial reference frame (IRF), the entity has speed $c$ relative to all IRFs. That's what it ...


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