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If we say that the spaceship and earth are very close to each other, let us then imagine that the spaceship, right as it passes by earth, shoots a photon out at $45^{\circ}$ from its direction of travel. The simplest way to attack this problem will be with the transformation of velocities in the x-direction. From our known information, we can determine ...

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Why is it important to incorporate both electric and magnetic forces into one single expression? Because the Lorentz force is "due to electromagnetic fields". I know people talk about electric fields and magnetic fields, but see Wikipedia: "Over time, it was realized that the electric and magnetic fields are better thought of as two parts of a greater whole ...

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Well, you could treat them separatedly, via two equations, say $$\mathbf{F}_\text{elec}=q\mathbf{E}$$ $$\mathbf{F}_\text{mag}=q\mathbf{v}\times\mathbf{B}$$ but since Newton's second law holds, in presence of an electric field and a magnetic field, the total force will be the sum of both, that is, the Lorentz force. I would say is just as simply as that.

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David Z, excellent answer - You comment that "... it does require that space defines some sort of absolute rotational reference frame". I believe that the existence of the reference frame is provable - In a nutshell - The proof is based on the relationship between angular velocity and the centripetal force it produces. It assumes that the same angular ...

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Although the most common answer to questions like that is "relative to what?", there are possible side-effects. If I recall correctly, the earth's velocity relative to the cosmic background radiation is on the order of a mere 600km/s. If we were to be travelling arbitrarily close to the speed of light as compared to our current motion, part of this ...

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I drew the spacetime diagrams for you. On the l.h.s. you may see two simultaneous events in the unprimed (x,t) frame. The axes of a frame going in the positive direction (the primed frame) should be drawn into the unprimed as I have done it. You can find the new space coordinates by drawing a straight line parallel to the new time axis through the event. ...

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The observer sees you travel from A to B - a distance that, in his frame of reference, is greater than one light year. He sees that you take more than a year. He concludes you are traveling at less than the speed of light. You, traveling so fast, "see" a much shorter distance (this is the concept of length contraction) $L' = L_0/\gamma$ where $\gamma = ... 0 In the original paradox, there are two events of note: the front of the train exits the tunnel, and the rear of the train enters the tunnel. Call these events A and B, respectively. Because these two events are spacelike separated, the two observers (tunnel-based and train-based can disagree on the order in which they occurred. According to the tunnel ... 1 The Lorentz transformations are used to transform between different inertial frames. For example if you and I are in relative motion then the Lorentz transformations convert the positions of spacetime points in my rest frame to the positions of spacetime points in your rest frame. However anything travelling at the speed of light has no rest frame, so the ... 1 the forward land delegate IS approaching the light and the backwardland delegate IS moving away from it Are they? Or are the delegates sitting perfectly still, and the Earth spinning quickly beneath them? Of course we have a convention that the Earth is stationary and the train moves across it, but we also know that the Earth is not stationary - it ... 2 Simply put, relativistic speeds cause for events previously thought of as simultaneous to no longer be simultaneous if the velocity of the reference frame of the event changes relative to the defined observer. The best way to wrap your head around this is to pictorially trace what is happening in space time. The case you describe is v>0 Think of v in ... 0 When 1686 Newton writes "Principia...", the inertial frame concept does not exist yet. However, we can find in it Corollary IV (introducing the center of mass CM concept for any interacting body set), Corollary V (Galileo's Principle of Relativity, applied to any limited body set with CM at any uniform velocity), and the today almost forgot Corollary VI (a ... -1 If the speed of light is constant no matter the speed of the source Actually, the speed of light isn't constant. It varies with gravitational potential, see Einstein talking about that here. However in gravity-free space the speed of light is constant. In addition you measure it to be constant regardless of your motion through space. That's because of the ... 0 It does not matter what your velocity is relative to a photon - the photon will always move at a fixed speed from your point of view. This is the 2nd postulate of special relativity - the speed of light in a vacuum has the same value (it's invariant) for all non-accelerating observers (in a medium of uniform density, the speed would be different from its ... 0 Einstein's postulate is that the relative speed between the observer and the source does not affect the speed the observer sees the photon moving, as long as the observer isn't accelerating, that is. This basically means there is no such thing as absolute 0 speed. Speed of light is your new and only constant friend. 0 Now, when reading about Special Relativity, some books says that prior to Einstein there was one "principle of relativity" that could be stated as follows: The laws of Mechanics are invariant in every inertial reference frame That is not the best formulation, since constancy of laws is already assumed implicitly. What is meant by the ... 0 I asked someone who studied physics this question and was told that the following is a definition: A reference frame in which a mass point thrown from the same point in three different (non co-planar) directions follows rectilinear paths each time it is thrown is called an inertial frame. 4 Imagine a point mass attached to ends of six identical springs of relaxed length$L$. The springs are oriented in co-linear pairs, with these pairs mutually perpendicular to the other pairs, i.e., they form an$(x,y,z)$coordinate system. Attach the other ends to the walls of a cube of dimension$2L$. If the mass remains in the center of the cube, the cube ... 3 An inertial frame of reference is one that is not accelerating. A frame that is accelerating with respect to another inertial frame is a non-inertial frame of reference. An inertial frame moves with steady velocity in respect to other inertial frames, such that an observer within the frame can not detect any movement of the frame, unless she looks outside ... 5 There are a certain number of known forces, so you could start by ruling each one out by experiment. Otherwise the so-called fictitious forces - the centrifugal force and the Coriolis effect - have the characteristic that they provide the same acceleration to all objects, regardless of their mass. As you know, in classical mechanics$a = F/m$so forces will ... 10 Draw a spacetime diagram. Really, there is no better way to solve relativity problems. In the above, the nail has worldlines$1$(back) and$2$(front), while the hole's worldlines are$3$(front) and$4$(back). Let's agree that the origin$\mathcal{O}$of the coordinates is the event of the front of the nail just entering the hole, i.e. the intersection ... 23 Imagine a slightly different scenario: two pilots, Alice, and Bob, are in their spaceships. They move towards a tunnel of length$L$at a velocity$v$, and remain a distance$l'\$ apart. Alice is closest to the tunnel and thus enters first, approaching a wall at the end of the length of the tunnel. Just as Bob enters he decelerates, coming quickly to a halt ...

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This is a variation of the pole and the barn paradox, and is also known as the bug and the rivet paradox, see Rod Nave's hyperphysics: The final line of this article is "the paradox is not resolved". Some people will say the paradox is resolved via consideration of simultaneity, but I don't think it is. Another variation of the theme is when you and I are ...

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The bug lives! Since BOTH the hole and the nail will change length in the moving coordinate system and their proportions Ln/Lh will be constant, if you pick a third coordinate system that is moving at half the speed of the nail. In this system both the hole and the nail are moving at the same speed in opposite directions.

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The bug will die: What does cause the nail deceleration? it's the base of the nail hitting the outside of the hole. In the best case scenario for the bug the tip of nail stops as soon as it gets the information (the shock wave from the abrupt deceleration). This will travel across the nail no faster than the speed of light. So let's assume the best case ...

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What is the question that Mach tried to address in his principle? Mach's principle isn't as clear as people suggest, but IMHO what it tries to address is inertia. Resistance to change-in-motion. I mean, we know how to detect the inertial and non-inertial frames (by Newton’s law). I "root for relativity", but I have to say this: an inertial frame isn't ...

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