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Yash, Imagine S is the Sun sending two photons, P1 and P2, and the object O is represented by two asteroids, O1 and O2 - equidistant from S and moving in the same direction at the same velocity (c/2), and one moving towards the Sun and one away from it. So you are right that the speed of light is the same in all frames of reference. However, the distance ...


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You can define energy in an accelerating frame, and you do it every day. The surface of the earth is an accelerating frame. Sometimes you say a frame is close enough to inertial and just treat like it is inertial even though it isn't inertial and hope for the best. Other times you just have to sit down and learn how to do physics in a noninertial frame. ...


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Imagine sitting on an airplane and playing with a laser pointer. As you fire the laser beam upward perpendicular to the motion of the plane you see it go straight up to the ceiling. The same would be true on a spaceship from the point of view of its passengers. As for the people watching this happen on Earth, they will see you fire the photon at an angle ...


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So a train passenger has synchronized two clocks at both ends of the train. Then you, a person standing on a platform, synchronize two other clocks at both ends of the train. Let's say the two clocks at the front of the train read the same time. Now the difference of the clocks at the rear of the train is the synchronization "error". It's your ...


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I think you are imagining the earth as one giant rigid inertial frame and that creates problems. Let's look at the atmosphere, a giant doldrum over the pole to make it simple. What keeps the air up there a certain height. Well there is a stronger pressure from the air below it than from the air above it. Newtonian gravity would say the air stays at rest ...


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The whole problem is really about knowing what the words mean. An event is a time and a place together as single object. For instance the event where a light sends its first, last, or only pulse. Or the event where a beam or particle touches something and bounces. Anything you can describe with a time and place together is an event. And different people ...


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I was confused by this too -- pop descriptions of the equivalence principle don't mention the problem where the gravitational field points in different directions in different places. It is true that gravity is equivalent to acceleration, and that as a result, if you are freely falling, you feel like you're in an inertial frame. But this frame is only ...


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The Earth's gravitational field extends inward from all of space to the Earth's surface, with it's origin at the center of the Earth. The Earth's gravitational field is characteristic of space-time that has been "curved" by a massive object. If you stand on the ground and let go of a ball, it falls away from you at the acceleration of 9.8 m/sec^2. ...


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As you know, dealing with "simultaneous" events in relativity is tricky. If I think two things happen at the same time, you may not. However, it is guaranteed that if if I think two things happen at the same time and the same place, you will agree. That's because these two things are just the same spacetime point. In your frame, we have the simultaneous (in ...


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To add to David Hammen's answer on the question: When numerically integrating this, together with Euler's equation of rotation, is there a way to ensure that the determinant of $R$ remains equal to one (otherwise $\vec{x}(t)$ will also be scaled)? Method 1 Dumb But Effective Naïve Multiplication Whilst you are getting up to speed with more ...


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Do I need to use the angular velocity vector in the rotating or inertial reference frame for this? Yes. You can do it either way. I start with the expression that relates the time derivative of a vector quantity $\boldsymbol u$ in the inertial and rotating frames: $$\left(\frac {d\boldsymbol u}{dt}\right)_I = \left(\frac {d\boldsymbol u}{dt}\right)_R ...


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The math is almost trivial for someone beyond algebra 1. Write the kinetic energy of each particle as $p_n^2/2m_n$. Then converse momentum and kinetic energy in the center-of-momentum. You will see that the magnitude of the momentum each particle does not change.


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Are tidal effects from the Sun and/or Moon taken into account in GPS systems? On calculating the orbits of the satellites, yes. The satellites orbit high enough that accurately modeling the orbits of the satellites mandates accounting for third body perturbations from the Moon, the Sun, and the planets. The orbits of the satellites are calculated from ...


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Isn't a physical frame of reference useless for calculating speed? There aren't really any physical frames of reference. You can't step outside and point up to the clear night sky and say "Look, there's a reference frame". You can point to the Moon and the stars, but they are what they are. You can use them in your reference frame, but that reference ...


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Velocity and speed of a body are measured with respect to another body (see other answer). This is the only possible definition. The "actual" speed respect to the "empty space" is not well defined instead. And this is because we are not moving inside an "empty space" or an "aether" which fills the universe. To grasp the concept think about how you will ...


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When physicists use the word velocity it has a precise definition that is meaningful and unambiguous. If I measure the displacement from me to you then the result is a vector i.e. it tells me how far apart we are and in what direction you are. The velocity tells me how this vector is changing in time. The point is that I can do this for any pair of objects: ...


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The relevant part of the book is the section titled Motion through Spacetime in chapter 2. I'll copy the paragraph, but it's a bit long so feel free to skip over it: Einstein proclaimed that all objects in the universe are always traveling through spacetime at one fixed speed—that of light. This is a strange idea; we are used to the notion that objects ...


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Everywhere in the observerable universe is affected by gravity and since you can't escape it, that means it is always pulling on you. So every objecct in every place will be moving relative to everything else, so an absolute state of rest is impossible. If you could edit your post to quote the part of the book where he says "stationary", you will probably ...


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You are correct time does stop at $c$ speed of light, however we (planet) did not place a timer inside the light but are measuring it from outside so time for us passes normally and nothing weird happens and nothing is frozen. As a result we simply are measuring the gap of time from the 1 point to another point whilst a object (light) goes to it so as ...


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No they will not cancel each other as both of them act on two different bodies.


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You are going in the right direction: Since on a different latitude the pendulum will be rotating with earth, it will change the rotation due to the coriolis force. As the pendulum being at a pole is an extreme case, so is the position at the equator: Here there's no reason for the rotation Foucault's pendulum is famous for. An intuitive guess would ...


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The thing is, in relativity you cannot have a reference frame "chasing" a photon. You'll get singularities if you try to view the world from a photon's perspective. A photon cannot move like you and you cannot move like a photon. As a photon, travelling along a light-like world line, experiences no proper time it's proper velocity is simply undefined. ...


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Light travels at the speed $c$ this speed is finite and with out using any relativity we can calculate the time it takes for something travelling at this speed to reach us: $\text{time} = \frac{\text{Distance}}{\text{speed}}$ or $ t= \frac{d}{c} = \text{8 minutes}$ in this case. For a person travelling very close to the speed of light with velocity $v$ from ...


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I'd like to add a few words to Domagoj Pandža's excellent answer. He makes this statement: "....Intuition and perception (or the lack of there of) can be a big problem when you're trying to comprehend the implications of special/general relativity ...." I think Domagoj's answer is excellent, but I disagree a little with this statement. Actually almost ...


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You release a ball in space. Measure its distance every 1s or C second. if you find $S(t)-S(t+c) $ is not constant , where c is a constant. then you are in a Non inertial system


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Inertial frame of reference is such that free bodies move with constant velocity. If you detect free body accelerating, the frame is not inertial.


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You ask: If this is the case, then can we say that "acceleration" or changed frames of reference are not required to resolve the twin paradox? and you say: they can be viewed as they are both in inertial frames of reference from each other's perspective The answer is that acceleration is required to resolve the twin paradox and the two observers ...


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This is a good (and notoriously difficult) question. I'm going to follow the explanation given by Crispino, Higuchi, and Matsas in their review 0710.5373, but you should be aware there are different answers out there and also there is no (uncontroversial) experimental test of this effect. Having said all of that, the basic picture I have (and is given in ...


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So, just to recap the Twin Paradox, it is a variation of the paradoxes of relative motion of reference frames Alice and Bob, created by the statement "Alice sees Bob's clocks moving slowly, but Bob also sees Alice's clocks moving slowly." The simplest such paradox, in my opinion, is "what if Alice calls Bob up and they talk on the phone? One of them surely ...


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So, here's the deal. "Time is relative" means a lot of different things to a lot of different people. In order to make a solid step forward, Einstein and company basically needed to clarify what they were trying to say. What they were trying to say looks something like this: "if you see a train passing by you, you're going to see things happen in slightly ...


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If you think about it, time as we know it does not actually exist/flow - it is our mental manifestations of the world around us that we think of as time. For example, what we see is not actually there as we view it. The object sends us light-waves (only a small portion possibily of what the object really is), our eyes then have to decode the light waves and ...



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