Hot answers tagged time
10
Your question is a natural one to ask, but it has no answer. It is a bit like asking by what mechanism the angles of a triangle always wind up adding to 180 degrees (in Euclidean geometry). There is no mechanism for that - no one is going around checking all the triangles to make sure their angles add up right. It is just a logical consequence of the theory ...
6
Yes, for a circular orbit at about $1.50$ Earth radii, the gravitational and special-relativistic time dilations cancel. GPS is modeled with the static weak-field metric (in units of $c = 1$):
$$-d\tau^2 = -(1+2\Phi)dt^2 + (1-2\Phi)\underbrace{(dx^2+dy^2+dz^2)}_{dS^2},$$
so we can approximate
$$d\tau = ...
2
Block time is not a physical theory. It's a philosophical interpretation. It can't be tested empirically. For these reasons it doesn't really make sense to ask for its status or whether it's accepted. You can poll physicists on whether they like it (there have been polls like this, for example, on the Copenhagen interpretation versus many-worlds), but the ...
2
No, the right ascension of the mean Sun is NOT zero at the vernal equinox. It is in fact nearly identical to the ecliptic longitude of the mean Sun (the difference is due to UT vs ephemeris time), and this is defined such that it coincides with the ecliptic longitude of the apparent Sun when the Earth is at perihelion. So that should be the starting time to ...
2
what exactly does the area under a displacement-time graph denote?
I think it just represents what you said: the area under a displacement-time graph. I can't think of any other use for it. There are two main reasons for this:
Your quantity, let's call it $f(t)$, retains a memory of where the object has been. That's because the area under the graph ...
2
These are not two different effects. They are the same effect as viewed in two different frames of reference. They shouldn't be added. If they were both calculated correctly, they'd be equal to each other.
They are not equal to each other, and that's because the calculation in the rotating frame is effectively assuming the existence of a gravitational ...
2
As far as we can tell (up to energy scales we've measured so far), spacetime is a nice and smooth manifold. It might happen that the smoothness is approximate and spacetime is discrete at a much more microscopic scale, or it could turn out that spacetime is smooth all the way through. Short answer: We don't know.
About the notion of energy quantization: ...
1
There is a relativistic effect, but it's very tiny at that speed (0.24c). In fact, the effect is even smaller, since only the radially most distant particles from the rotation center are traveling with 0.24c. (The speed decreases with 1/r)
See for example this nice plot of relative mass vs. velocity, taken from gutenberg.org
P.S.: I calculated the mass ...
1
For the answer by PMay:
However, both the observer at the center axis and the observer at the perimeter would agree that the circumferance of the perimeter is $2\pi R$.
That is not true for the observer at the perimeter. He/she is moving with an acceleration, and from his/her point of view, space would be distorted, gravitational force, time dilation ...
1
The fact that electrons are identical particles doesn't mean you can't separate one from another and keep track of which is which. They can be told apart according to their positions, energies, and momenta. Say I stick a $\beta^-$ source a foot away from a Geiger counter and I get a click. I know that the electron I detected was 1 ns old (c=1 ft/ns). This ...
1
I don't see this quantity computed very often so I don't think it is that useful, but here is one thing that can be said: If $A$ is the area under the graph and $T$ is the duration of time over which the integral was preformed then $A/T$ is the average displacement from the origin during that interval of time.
1
To add to Mark Eichenlaub's nice answer...
Suppose that in the Euclidean plane, you have two people, $P$ and $P'$, located at the same point (or as near as possible), but they're facing in different directions. Each of them imagines the usual Cartesian coordinate axes, say with $x$-axis to the direction they're facing, which we'll call depth.
Suppose also ...
1
All of our known physical laws including GR (which have so far assumed spacetime to be smooth and quite flat) breakdown at singularities due to the infinite curvature of spacetime. Hence, we say, "One second after the big bang..., An hour after the big bang..., etc." Because, we simply don't know what happened at the instant of big bang. If there were events ...
1
Relativity consists of special relativity (SR) and its generalization general relativity (GR), which includes gravity.
In SR, the history of an object is described by its world-line through spacetime. Every event has future and past light cones, and a material object such as a person's body is limited to "traveling" from the past light cone to the future ...
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