New answers tagged

0

I'd just like to emphasize the point - touched on in several of the other answers - that the core of the "paradox" here is our natural, nonrelativistic tendency to implicitly assume a universal time. Such an assumption indeed is contradicted because, if true, the well orderedness of time intervals would be blatantly contradicted by the situation where both ...


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 ...


0

The situation is symmetrical, so both will see the other one* undergo time dilation. This seems contradicting at first sight, but if any of them turned around for a meetup, they would undergo acceleration and thus change in which inertial frame of reference they are stationary in. This will result in a "speed-up" of time for the accelerating spaceship.


0

Yes and no. Coordinate acceleration doesn't need to be relative, but proper acceleration is always invariant.


-2

Consider a positively charged particle, if it comes in upward motion its velocity increases as a result its mass decreases(according to conservation of momentum i.e. m1v1=m2v2), as mass decreases its number of atoms decrease i.e. equal number of protons and electrons are decreasing which reside in an atom.thus the charge on the particle is unaffected by its ...


3

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 ...


0

According to Special Relativity, an event can be affected by all the events in its past light cone and All the information one can get is the information from his/her past light cone. Now if one needs to predict something about an event then to be entirely sure, he/she needs the information of the events in the past light cone of the event to be predicted. ...


0

Lower index is a tool to map upper index to a real number (W dot V for example). So to define a lower index, you need g(v,w)v (with one slot waiting for w to fill in order to spit out the dot product. So you can think g(v,w) as a tool to make two vectors dot with each other. Now you have v available, if you encounter a w later g(v,w)v is a tool to map w to ...


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 ...


4

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 ...


-1

The speed of light in a material is expressed in this equation: $$ c = {\frac{1}{\sqrt{\mu_{0} \mu_{r} \epsilon_{r} \epsilon_{0}}}} $$ With regards to sound, the pressure waves really depend on the bulk modulus of the material as a factor or the wave equation. $$ Y_{m} = \frac{\frac{F}{A}}{\frac{x}{\triangle x}} $$ which is characteristic of pressure ...


1

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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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 ...


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 ...


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....


0

The question is a bit weird because from that distance, the photons would take so long to come back, I am not even sure a whole species could survive long enough to see one photon come back. You have to realize that even for the Sun, as relatively close as it is, photons take on average 8min 20sec to arrive. So you're always seeing the Sun as it was over ...


0

Take 1 To see clearer, let's simplify. Your system is completely equivalent to 2 observers (posts of a ball) moving in an accelerating frame (falling down). This is basically the setup of Bell's spaceship paradox and you should read about that. We will make an assumption of homogeneous gravitational field, so the acceleration is constant - but we have to do ...


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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 ...


0

If you're going to give that many significant numbers, you might as well learn by heart that $c=299 792 458 m/s$ But no, for many reasons. 1) Your clock is too heavy, it will collapse in on itself, even when outside of the pull of the earth. 2) The clock will tear itself apart, try stopping something that heavy, that fast in a fine system like a clock. $\...


1

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 ...


0

The bottom line is that space and mass do interact with one another. Otherwise, they would not tell one another "how to curve" and "how to move". Therefore a moving (or rotating) mass and space will interact slightly differently. The interaction will drag with rotating mass. It may or may not be detectable depending upon the mass & speed of rotation and ...


1

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 ...


0

Universe is expanding because the space itself is expanding. The expansion is not due to acceleration of the bodies with respect to space. Therefore, the bodies are getting away from others with the expanding space, not due to their own acceleration. So, their speed with respect to space is not changing and so, the mass approaching infinity does not apply. ...


0

I find this question quite confusing myself, because it is over-simplified. There is a lot which is not explained. I presume that 0eV corresponds to a free (unbound) electron and the other levels correspond to the possible bound electron energies. What I find confusing is that there is no indication of how far up the electron energy levels are filled. ...


0

When a fast electron is fired at an atom, it can collide with an electron in the atom and some of the KE of the fast electron is transfered to the atomic electron. The fast electron keeps the rest of its KE and continues moving away from the atom after the collision. The atomic electron uses this gained energy to move to a higher energy level. The electron ...


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 ...


1

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 ...


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 ...


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 ...


1

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 ...



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