# Tag Info

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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 ...

24

I am wondering whether is it taken as a postulate or a proven phenomenon that c is constant irrespective of observer's speed? Either one. Both. Einstein took it as a postulate in his 1905 paper on special relativity. From it, he proved various things about space and time. The frame-independence of $c$ is also experimentally supported. This is what the ...

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You cannot tell moving with constant speed apart from standing still. This is the principle of Galilean relativity.

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Because in the frame of reference that is co-rotating, the object doesn't move, and therefore it has no kinetic energy in that frame, which is the frame in which most problems involving objects on earth are looked at. Note that kinetic energy is evidently not a frame-invariant quantity, but it is not required to be.

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The fundamental postulate of special relativity, indeed of Galilean relativity, is that there is no experiment that determine the state of motion of any inertial frame relative to the outside world unless the measurement uses data gleaned from outside the frame. Read Galileo's wonderful and very famous allegory of Salviati's Ship for a poetic and rock ...

15

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 ...

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As an abstract spherical-chickens-in-a-vacuum-type question, then no, basic relativity says not. But that isn't much fun. .. First up, what do you mean by speed? If you mean speed along surface of earth then you have a chance. Since the earth is curved you are always accelerating, and you could measure the drop in g as you speed up. So long as you don't ...

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An observer is a timelike worldline with 4-velocity $u^{\mu}$ and an orthonormal basis $e_{\hat{\alpha}}$ with $e_{\hat{0}} = u$ such that $e_{\hat{\alpha}}$ is transported along the worldline under some transport law e.g. Lie transport, Fermi transport, or parallel transport. Physically the Lorentz frame represents a local set of three orthogonal meter ...

8

Ultimately, what's special about angular momentum is this: Look up in the sky. A certain set of physical laws pertain in that direction. Look to the north. A certain set of physical laws pertain in that direction. Look to the west. A certain set of physical laws pertain in that direction. Those physical laws: They're the same in all directions. There's ...

8

I physically understand it as the momentum of an object rotating around something given a certain position. However, I can't give a physical explanation to the formula. Why do we multiply the linear momentum by the position? Why does the angular momentum is a function of the position? Angular momentum $L = mv * r$ (This is a late answer, but I ...

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 ...

6

The answer depends on what the symbols mean. The question does not make it clear how the symbols are defined. The most confusing quantity is $\omega_2$. How is this defined? Is it the angular velocity of the disc relative to the fixed lab axes or relative to the axle about which it is rotating (where this axle itself will be rotating at $\omega_1$)? Also ...

5

Acceleration does not kill us any more than speed. If your head and feet do not move at the same velocity long enough, whatever the cause, you are in trouble. Velocity does not kill us when the whole body has the same velocity. Similarly, I doubt acceleration kills us when all parts of the body accelerate, but without having to transmit forces. It is said ...

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Here's a simple demonstration: Consider flat space (i.e. Minkowski), viewed in a rotating frame (in e.g. cylindrical coordinates one just replaces $\phi$ by $\phi'=\phi+\omega t$). One can calculate (without too much trouble) that, in these coordinates, a spatial line element can be expressed in terms of the canonical cylindrical coordinates as $$... 5 The exact quantities of kinetic energy (like momentum) depend on your choice of a reference frame. Don't get too worried though; regardless of your choice of a reference frame, you will find that energy (and likewise momentum) is conserved within the reference frame. Therefore, two observers may not agree on the kinetic energy or momentum of an object, but ... 4 Consider something like a door. A piece of wood with a hinge on one edge. Maybe it is one meter tall and three meters long. Now say that you're trying to hold the door in place, at the position half a meter from the hinge, while someone else throws a baseball at the other side of the door. If the baseball hits the hinge, you don't have to push at all. If ... 4 In an inertial frame the only force that causes a particle to move in a circular motion is the centripetal force. The reason that a particle does not "fall" into the center is because it has some tangential velocity, so it moves away from the center tangentially as it is falling towards it. The relationship between the centripetal acceleration and tangential ... 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 By your assumptions, the train will always be stationary. Light will always take time \frac{L}{c} to traverse the distance simply because c is a constant. Additionally, even if your train was moving at c, it would still not matter because you are still at zero velocity with respect to the coach. Relativistic measurements would come into picture if you ... 4 Update and note: In the answer below, I do assume the OP and reader are aware of the Galilean relativity of motion but wonder why the invariance of the speed of light cannot be used to find an absolute rest frame. If this isn't he case, then Rod Vance's excellent answer is more appropriate. I switch on the torch and measure the amount of time it takes ... 4 The basic idea of general relativity is that a freely moving object follows a path through spacetime called a geodesic. By freely moving I mean the object experiences no force i.e. if you were that object you would be weightless just as if you were floating in space. In flat spacetime geodesics are straight lines i.e. a freely moving object moves in a ... 4 speed is a relative concept. We are fairly still relative to the air around us. like we all being sitting in a car with closed windows moving with a constant speed. In the void space, where nothing exists, speed can never hurt anything. But when an asteroid enters the atmosphere, it has high speed relative to the air, and gets burnt. 4 By using orthogonal optical resonators, laboratory tests concerning verifying the isotropy of c have come a long way. As quoted from http://journals.aps.org/prd/abstract/10.1103/PhysRevD.80.105011 "An analysis of data recorded over the course of one year sets a limit on an anisotropy of the speed of light of \Delta c/c \sim 10^{-17}. This constitutes the ... 3 It's intuitive that while accelerating in a locally constant gravitational field, there is no perception of acceleration, since the body accelerates uniformly. The reason you can't perceive it is not that it's uniform, the reason is that there's nothing to compare with. If there's something to compare with, then you can see the difference. For instance, ... 3 The theory of relativity tells us what is the answer to this question. See Wikipedia, as John Rennie recommends, http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_case:_parallel_velocities If in the formula$$v_{rel} = \frac{v_1 + v_2}{1 + v_1 v_2/c^2} you set $v_1 = v_2 = 0.9 \, c$, you get $v_{rel} = 1.8/1.81$, i.e. slightly less than ...

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What is the formal definition of an observer in special relativity? I have seen a few: The actual coordinate system. The collection of synchronised clocks that cover the coordinate system. A well reasoned person in the system. But what is the actual definition? In #3, what is missing is that the observer's state of motion, i.e., ...

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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", ...

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Actually special relativity states that all inertial reference frames are equivalent, so there is no such thing as absolute speed. You can't ask "What is my speed", this question is just not well formed. You can ask: "What is my speed in reference to this object", and in fact all "real life" examples of asking "What is my speed" actually have some implied ...

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There are several ways to describe a particle's motion. For example, in 2 dimensions, you could use cartesian $x,y$ coordinates or polar $r,\varphi$ coordinates. To each coordinate, we can associate a 'quantity of motion' or 'generalized momentum'. If a given coordinate corresponds to a symmetry of the system, the corresponding quantity is conserved by ...

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