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 ...


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 ...


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 ...


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 ...


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

Relax, take a deep breath :-) to me it seems that you do not realise that Alice and Bob have two different times. That is, what Alice calls time, Bob calls a mixture of space and time. So, If you draw a single chart showing all the events in space and time on one page, then draw Alice's time you will find it has a different direction on the chart from Bob's ...


11

It is about the frame of reference, in the frame of reference of the tennis ball pushed by the astronaut, it could be considered as standing still and the other ball, the astronaut, and everything else as moving. For the frame of reference of the other ball it could be considered as standing still, and the first ball as moving. If you were with either one, ...


10

Cylinders Don't Exist If I show you a picture of two round objects and tell you that one is a sphere and the other is a cylinder you are looking at head-on, how can you tell whether I am telling the truth or lying? You can't, and therefore, I conclude that there is no difference between spheres and cylinders, because we lack the proper evidence for their ...


8

how speed can be a constant It's not, it depends on selected reference frame. The only exception is light speed in vacuum, which in any reference frame is $c$. But what if the Earth itself now starts moving? Now the distance is still changing, but how the individual speeds be calculated? In a pre-relativity times there was a Galilean speed addition rule ...


6

Turning my comment into an answer ... The velocity can be non-zero because velocity is represented by a vector, so the vector changes when the direction changes, even if the magnitude ("speed" in this case) remains constant. For example, consider the case of two objects in circular orbits around the barycenter. If I am riding on top of one of them ...


5

A hot air balloon floats immersed in the air, similar to the way a fish might float immersed in the ocean. The fish doesn't see the seafloor below it zoom off at 1000 miles per hour because it is inside the ocean which is rotating with the Earth. Similarly, a hot air balloon rests inside the atmosphere which is rotating with the Earth. The ocean and the ...


5

The thing you're missing is that if the elevator is travelling uniformly at some velocity $v$, the coin starts with that same velocity. So taking our SUVAT equation - in the case where the elevator isn't moving, you have: $$\tfrac12 g t_1^2 = h$$ and when it is, $H$ is clearly equal to $v t_2$ so: $$v t_2 + \tfrac12 g t_2^2 = h + H = h + v t_2$$ $\...


5

As others have pointed out, the impact of velocity on apparent time is really small on this scale. We can show the reason, however, if instead of a bouncing ball taking 1 second, we make the problem as follows: Person A shoots a photon at light speed at a mirror on the floor 1.5 meters down. In his reference frame, the photon travels a total of 3 meters ...


4

why can't we define absolute rest as the inertial frame at which time is running the fastest? We cannot define absolute rest in that manner because it is not unique. In Abe’s reference frame Abe’s time runs the fastest and Bob, Cam, and Don’s times all run slower. But in Bob’s frame Bob’s time runs he fastest and Abe, Cam, and Don’s times all run slower. ...


4

From the Principia, Newton writes the first law as: Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus illud a viribus impressis cogitur statum suum mutare. or, "Law I: Every body perseveres in a state of being at rest or of moving uniformly straight forward except insofar as it is compelled to change ...


4

There is no such law, because it isn't true. It isn't even remotely true. Probably the most extreme counter example would be the earth itself, which hurtles around the sun at about 67,000 mph. I'd like to see your bee do this! (without riding on the back of the Earth, of course!) And, of course, bees do not travel faster than birds. Bees travel about ...


4

Your definition is incorrect. The coefficient of restitution, $e$, is not defined as you stated. Let $u_1$, $u_2$, $v_1$, and $v_2$ be the initial and final velocities of objects $a$ and $b$ respectively. The way to correctly remember the coefficient of restitution is defined as the velocity of separation divided by the velocity of approach. Alternatively, ...


3

The sign/direction of the relative velocity between the two frames matters when transforming coordinates, velocities, momenta, energies, forces, etc. The length contraction and time dilation factor $\gamma$ depends only on $v^2$ so the sign/direction of $\vec v$ doesn’t matter for them. The relative velocity between the frames is really a vector, but often ...


3

Apple's and Earth's accelerations are with respect to which observer (or which reference frame)? In any inertial frame, you will measure the same acceleration of the Earth and the same acceleration of the apple. One example is the one in which the Earth is initially at rest (neglecting the Earth's motion about the sun, etc). Another could be the frame in ...


3

You are limiting your snapshot to a 3D picture. If you took a 2D snapshot, it would be impossible to tell how deep your tennis "balls" are (in addition to being unable to tell their motion). So, take a 4D "snapshot", and all'll be fine.


3

Your question assumes one ball is moving and the other is still. That assumption is meaningless without specifying a frame of reference. All motion is relative. To each of the balls it would appear that the other was moving. The 'evidence' that they are moving includes the fact that they would appear smaller to each other, and that their separation was ...


3

You are given the velocity of the boat with respect to the water. You are also given the movement of water with respect to the ground. You don't assume that the water affects all boat paths equally. If you are told the velocity of the boat with respect to the water, you know how much the water affects the movement of the boat, because you are already ...


3

The earth's gravity attracts the apple with a force of $mg$ where $m$ is the mass of the apple and $g$ is the acceleration due to gravity, which may be considered a constant and equal to 9.81 $\frac{m}{s^2}$ if the separation is not too great. Newton's third law essentially states that every action has an equal and opposite reaction. So the apple exerts an ...


3

Motion is relative but acceleration is absolute. You can know if you are being accelerated without any reference to the outside world. You will feel it in your internal organs and if you carry out an experiment you will observe pseudo forces, even if you don't look outside your space ship. If a body A feels none of these effects and sees that another body B ...


3

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? What you are missing is that distance and time themselves are not constant. Both distance and time depend in part on the velocity of the observer. You are on Earth, and ...


3

It isn't a question of distance from the Earth. It is just a question of relative velocity. For example if you were next to a geostationary satellite in a geostationary orbit then you would not observe the rotation of the Earth; the Earth would still appear to be stationary to you. On the flip side, if you were to (somehow) hover $1\,\rm m$ above the ...


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