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30

Those objects are orbiting closely to SgrA${}^{*}$, certainly, but they are not orbiting closely enough to exhibit significant time dilation effects. In particular, consider the Schwarzschild spacetime. The inner most stable circular orbit around the central obect is at $r = 6M$, three Schwarzschild radii away. This makes the time dilation factor: ...


9

Your question has an answer which applies to physics in its entirety. Whenever we try to explain something in Physics; we come up with a model/hypothesis to explain a particular phenomenon. Then the model/hypothesis is extensively tested for inconsistencies and when people are satisfied that the models/hypothesis is correct, these become Laws. Now, we ...


6

It's important to state exactly what one means by "aether" when saying that aether theories are discredited. Specifically, the notion of medium that one can in principle detect one's motion relative to is what has been ruled out by experiment. Mediums such as water for acoustic waves fall into this category: the acoustic wave equation changes its form when ...


5

If I'm interpreting your post correctly, you may be misunderstanding time dilation. Time dilation will not cause the stars to seem to move more slowly. The apparent velocity of a star in your frame of reference is the apparent velocity, and relativity will not change it. What time dilation would change is the apparent rate at which a clock moving with the ...


5

It was the first to fit the observations (e.g. the anomalous precession of Mercury), while having no free parameters to "adjust". The only parameter is the gravitational constant, which was already known with high precision in 1916. Its every prediction since either has been confirmed or is consistent with observations without any massaging. It has ...


5

We don't really have a good perspective on what a photon "feels" or, indeed, anything about what its universe would look like. We're massive objects; even the idea of "we must travel at the speed of light because we're massless" makes little sense to us. But we can talk, if you like, about what the world looks like as you travel faster and faster: it's just ...


4

Let me try to break down the question into several parts, in the context of seeking a gravity theory that satisfies an action principle. That is, we are looking for a Lagrangian density that describes the theory. First, the equivalence principle tells us that the gravitational field must couple universally to matter. Second, the theory has to be (at least) ...


3

Charge, giving rise to EM fields (or any other kind of field, really) does create spacetime curvature. See for instance the difference between the Schwarzschild metric and the Reissner-Nordström metric.


3

One way to define spacelike separation in special relativity is that any two events are spacelike separated if and only if there exists a reference frame in which the two events have the same time coordinate. So yes, if $x^0 = y^0$ the separation is spacelike. Alternatively you can work from the definition where two events are spacelike separated if (and ...


2

We need to clarify what we mean by dimensions of a mechanical system. They refer, in the standard terminology, to the number of different degrees of freedom we need to describe the kinematics of a point particle (in this case). To this extend, given any reference frame $S$, an event in the space-time is identified by its position $(x,y,z)$ and the time $t$ ...


2

The metric tensor is unrelated to the topology of spacetime, as it does not actually qualify as a metric in the topological sense : it is not positive definite, nor does it apply to spacetime points (at least not directly : you can always find the length between two spacetime points by integrating the tangent vector of the path between them). The topology of ...


1

One of the basic principles in relativity is that spacetime always looks locally flat. By this I mean that if you restrict your observations to a small region surrounding you the curvature becomes negligable. You can make the effects of curvature arbitrarily small by making the region you consider arbitrarily small. The point of this is that for your clock ...


1

The Chronology Protection Conjecture is an entire bundle of rough theorems, counterexamples and conjectures. Hawking's original paper on the topic hinges on two main arguments : That compactly generated closed timelike curves (aka "a time machine", roughly) will violate the energy conditions. That a Cauchy horizon (the part of spacetime where the time ...


1

It is helpful to look at another simpler classical field theory, electromagnetism. Electromagnetism has equations for how electromagnetic fields change in time, they are fairly simple compared to general relativity, namely $$\frac{\partial \vec E}{\partial t}=\frac{1}{\mu_0\epsilon_0}\vec \nabla \times \vec B, \text{ and }\frac{\partial \vec B}{\partial ...


1

Einstein didn't actually get rid of the aether. He said the luminiferous aether was redundant when he was doing special relativity in 1905. But later when he was doing general relativity, he described space as an aether. See his 1920 Leyden Address. He said this: "Recapitulating, we may say that according to the general theory of relativity space is endowed ...


1

I think Gennaro covered, this, I'll give a layman's explanation. In spacetime there are four general dimensions, three of space and one of time. Why is it that other dimensioned qualities seem to be rarely considered as part of spacetime? For example, why isn't speed part of spacetime, forming a five-dimension spacetime-speed manifold? Objects in ...


1

The reason why the commutation relations between a field and its conjugate at equal times are of the form $$ \left[\phi(t,\textbf{x}),\pi(t,\textbf{y})\right]=i\hbar\,\delta^{(3)}(\textbf{x}-\textbf{y}) $$ is only to mirror and copy the canonical hamiltonian commutation relations $[q_i,p_j]=i\hbar\,\delta_{ij}$. No causality is involved, rather it is somehow ...


1

When you ask "how curved is spacetime?" there isn't a simple answer because curvature is a complicated property and can't be described with a simple number. However a good way to get a feel for the curvature of spacetime is to measure the acceleration of a freely moving body. By this I mean if you were stationary with respect to the Sun, and you dropped an ...


1

In Minkowski spacetime, the spacetime interval of lightlike movements is zero. That means, from the (hypothetical) point of view of a massless particle such as a photon, it does not even exist one Planck time. At a proper time zero, any wavelength becomes meaningless, even if the physical process is the same that we observe. For the answer you have to take ...


1

If you and your friends took some helicopters to the north pole and went up and then took off in different directions and flew at the same altitude you would feel like you were being bent towards each other, but yet as you all started to approach the south pole you would notice that you were all moving a way from other at first, you were all moving parallel ...



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