171–180 of 451 posts
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And at the same time, in your new frame of reference, you're still moving at exactly c through the time and 0 through space. But your time axis is no longer parallel with the time axis of the rest of the world.
Axes being parallel by whose point of view?
My enlightening moment about general relativity: apples do not fall on the ground, instead, the earth is inflating, and the inflation of the earth is accelerating at 9.8 m/s^2. Eventually, the ground catches the apple. Of course, you are going to tell me that the earth is not inflating, obviously, because it is still the same size after so many years. But here is the trick: the earth is inflating at the same rate as…
How would spacetime know to contract right to the center of earth?!
Because both terms of the equation affect one another, solving it is complicated but here, the result is that spacetime contracts to the center of the earth.
Veritasium recently posted an excellent video on the subject: https://youtu.be/XRr1kaXKBsU
Another good video to visualize GR is this by ScienceClic: https://www.youtube.com/watch?v=wrwgIjBUYVc
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Curvature due to gravity depends entirely on mass. No mass = no spacetime curvature. In this case, the mass of the Earth is causing the curvature.
Slight correction: curvature depends on the stress-energy tensor, of which energy is a component. A more energetic particle of the same mass will have a very slightly higher gravitational attraction.
I've seen this explained elsewhere, and it does look very cool when displayed this way. But perhaps someone with more background can explain to a lay person -- what even is a force? Why does the existence of a transformation that makes movement under a supposed force actually follow a straight line mean it's not really a force? For the other forces (e.g. electromagnetism) can we say that there's _no way_ to exhibit a…
The effect of a spacetime transformation isn't just to redefine straight lines along which particles move. It means measurements (e.g. lengths, areas, time intervals) are different depending on where you are in the spacetime. The are forces don't come with these "extra" effects - an EM field doesn't stretch and contract space. However, there are a lot of parallels between electromagnetism and relativity! Quite often…
Would not an electron and a positron trace out an identical line/parabola? Would that mean electromagnetism is not a force either? What is the difference between the two that makes one a force and one not a force?
The indicator that gravity is special is the fact that 'inertial mass' and 'gravitational mass' are the same thing.
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Off topic, but in reality, the trajectory of a ball thrown on Earth is not a parabola, but an ellipse [1]: > under the laws of gravity, a parabola is an impossible shape for an object that's gravitationally bound to the Earth. The math simply doesn't work out. If we could design a precise enough experiment, we'd measure that projectiles on Earth make tiny deviations from the predicted parabolic path we all derived in…
It's a parabola in a uniform gravity field, an ellipse in a circular gravity field coming from a point mass. So if you want to be really pedantic, it's never an ellipse because the Earth is not a point mass. It would be equivalent to a point mass if the Earth were a perfect sphere of uniform density, but it isn't. In reality it's a potato like mass blob that's approximated by what geodesists call the "geoid". So in o…
In relativity, there is no such thing as a "uniform gravity field", if by that you mean a field where the "acceleration due to gravity" is the same everywhere. The closest you can come is the "gravity field" inside a rocket accelerating in a straight line in empty space, where the acceleration felt by the crew is constant. That kind of "gravity field" has an "acceleration due to gravity" that decreases linearly with height.
I heard an interesting question at one point: "how come, when you throw a ball up on Earth, the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola?" I'll answer this question as I understand it, but I only took four lectures of General Relativity before I gave it up in favour of computability and logic, so if there is a more intuitive and/or less wrong an…
Your answer is basically the one given in an early chapter of Misner, Thorne, and Wheeler, which is one of the classic General Relativity textbooks.
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Spherical mass can be replaced with a point mass. Earth however is not spherical (biggest deviation is polar flattening). And even then, Einstein's model, unlike Newton's, says it's not an ellipse even for a point mass. So, moral of the story - we have to be not too pedantic.
> Spherical mass can be replaced with a point mass I'm not a physicist, but that doesn't sound right. One example is that if you are inside of the sphere, at least some of the mass will be pulling you away from the point at its center. I think what you mean is that a point mass closely approximates a spherical mass, but the degree to which that is true becomes less and less the closer you get to the center. I don't t…
If the mass is spherically symmetric, this will not be the case; all of the Newtonian forces from the masses further away from the center than you are will cancel out. This is called the "shell theorem", and it turns out to hold even in General Relativity.
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It's a parabola in a uniform gravity field, an ellipse in a circular gravity field coming from a point mass. So if you want to be really pedantic, it's never an ellipse because the Earth is not a point mass. It would be equivalent to a point mass if the Earth were a perfect sphere of uniform density, but it isn't. In reality it's a potato like mass blob that's approximated by what geodesists call the "geoid". So in o…
> it's never an ellipse because the Earth is not a point mass. At least classically, a sphere is indistinguishable (gravitationally) from a point mass while you're outside it. The earth is pretty sphere-ish, locally speaking.