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15

No. The derivation of Einstein's $E=mc^2$ is not derivable from the simple Newtonian Mechanical formulae. They are not, a priori, assumed to be true. Einstein starts with his own definition of simultaneity along with the postulates of the principle of relativity and the invariance of the speed of light. From these things we arrive at $E=mc^2$ after ...


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The force between the charges goes to zero. To see this, work in the frame of one of the charges. From its perspective, the other point charge is moving rapidly away, and the field of a moving charge is weaker along the direction of motion, as shown below. One cheap way of seeing this is to pretend the field lines have been "length contracted". For ...


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A boost is "the only other" plausible choice for transformations that mix spacetime co-ordinates, aside from rotations. The two notions in this sense are complementary. See for example: Palash B. Pal, "Nothing but Relativity", Eur. J. Phys. 24, pp315-319,2003 Given certain "reasonable" assumptions about our Universe; roughly The first relativity ...


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This is an excellent question which is much more subtle than it first appears. On a first (or even a second) reading, you seem to answer your own question and then ignore your own answer! What I mean is, you clearly understand that while in an accelerating vehicle you experience a 'jerk' which does not happen with uniform motion, and you also acknowledge ...


3

Time is that which the clock shows. Any one clock. Clocks do not all show the same time but their readings are related to each other and that relation is what the theory describes. In non-relativistic theory any two (perfect) clocks can only differ by a constant time difference but they all progress at the same rate. In relativity any two clocks that are in ...


2

You need to learn to use mathematics to tackle such problems. If you try to do without math using only your intuition then you'll make many hidden assumptions that may not be valid. Physicists who understand some theory well enough can get away with using their intuition, but then that intuition is based on a rigorous mathematical understanding of the theory....


2

The universe is a four dimensional object i.e. to locate any point within it you need four numbers. Most commonly we use a coordinate system $(t, x, y, z)$ and the four numbers give location of the spacetime point in this coordinate system. You ask: But how can this be, if time is relative and dependent on speed of reference frame? and the answer is ...


1

In general, it's more useful to think of special relativity problems in terms of the spacetime interval $\Delta s^2$ than in terms of the question of "who is moving relative to whom." A lot of those explanations (in terms of things like time dilation, length contraction, etc) are very ad-hoc, and are designed to make the idea of the spacetime interval more ...


1

It is a little different in General Relativity. Let's start with Special Relativity and all the 3 forces of the Standard Model in physics. Then we will talk about gravity and the universe. In The Standard Model spacetime is Minkowski, meaning flat in all 4 dimensions. If it is that way clearly any direction and position is equivalent. That's called ...


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The solution to this interesting question has to involve both (a) the distortion of the electric field of point charges when they move close to the speed of light and (b) time (since the longer we wait the further apart the electrons become, so their mutual force becomes smaller). Since the electrons are moving along the same straight line we can reduce ...


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You're confusing concepts, as far as I can tell. Being a "dimension" doesn't imply all values of that dimension (or any of them) are arbitrarily reachable or even exist physically at a given time. It doesn't mean that the intuitive sense of all the baggage a more usual dimension comes with, are applicable to time. It doesn't imply time travel or multiple ...


1

Suppose George and Gracie are moving toward each other, each claiming to be stationary. Their clocks happen to be set so they'll both chime 10PM at the moment they meet. When Gracie's clock chimes 2PM, she says: "I see that George has his clock set to 4PM. He'll be here in 8 hours, with his clock chiming 10PM. That slow clock of his will chime only 6 ...


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Actually, the explanation as to why rotation of a mass affects the metric in principle is simple. Rotation means there is angular momentum, and angular momentum contributes to the energy-momentum-stress tensor in general relativity. If this was a nonrelativistic rotation we would say that the rotation carries kinetic energy. The rotation contributes as a ...


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There is no centre of mass for the universe because it is isotropic and homogeneous. That is every point in the universe is like every other point so there is no one point you can point to and say this is the centre. For more on this see Did the Big Bang happen at a point?. However we can certainly pick any point in the universe as the centre for our ...


1

If I understand you correctly you are concerned that a black hole somehow manages to become less dense than the matter that made it, as if it somehow expands against its own gravity to increase its volume. However a black hole event horizon is not an object - it is just a place in spacetime. Although we can calculate a density by calculating the volume ...


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There is nothing wrong in having something more dense than a black hole, large black holes can have densities less than water. If you put a lot of iron together it might or not become a black hole. An object of any density can be large enough to fall within its own Schwarzschild radius. The larger the black hole the lower the density, so you iron ball will ...



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