10
votes
Do you always experience the gravitational influence of other mass as you see them in your frame?
Unfortunately the whole premise of your questions is wrong. You seem to be trying to apply Newtonian gravity in a relativistic context, and that just doesn't work. You need general relativity to ...
- 9,611
7
votes
Question on special relativity
With some algebra, we can see eq. 1 and 2 are equivalent,
\begin{align}
&c\Delta t - \sqrt{(\Delta x)^2+(\Delta y)^2+(\Delta z)^2} = 0 \;\;\;\; (1) \\
\Rightarrow\;\;\; &c\Delta t = \sqrt{(\...
- 1,900
7
votes
Accepted
Length Contraction: is $t'$ or $t = 0$?
David Morin is correct. Length in a given frame is defined as the distance between the two ends of an object at the same time in that given frame. So length is a concept that is intrinsically tied to ...
- 103k
4
votes
Accepted
Understanding expansion of the Universe as things flying apart
The scenario: within a matter-dominated universe, you have prepared two particles with initially constant separation.
In this scenario, those two particles will begin to fall toward each other. This ...
- 6,404
4
votes
is $LT$ a Lorentz invariant?
Consulting any text-book on special relativity, you will find the well-known fact that the four-dimensional volume element $d^4x = c \, dt \, dx \, dy \, dz$ is a Lorentz invariant as a consequence of ...
- 6,734
3
votes
Question on special relativity
No, there is no way to get a satisfactory theory using
$$\tag1(c\Delta t)-\sqrt{(\Delta x)^2+(\Delta y)^2+(\Delta z)^2}=(c\Delta t^\prime)-\sqrt{(\Delta x^\prime)^2+(\Delta y^\prime)^2+(\Delta z^\...
- 9,367
3
votes
Do you always experience the gravitational influence of other mass as you see them in your frame?
An easy way to see why this would not work: if you are moving rapidly, aberration makes most of the mass content of the Universe appear to lie in front of you. If gravity were based on apparent ...
- 6,404
3
votes
Does Matter Cause Curvature or Vice-Versa
The actual physics is expressed in math, not words. The equations of general relativity (the Einstein field equations) give a precise relationship between the curvature of spacetime and the stress-...
- 9,611
2
votes
Accepted
Confusion about local Minkowski frames
$x$ and $t$ are just symbols. We like to use the symbol $x$ to refer to the spatial coordinate and the symbol $t$ to refer to the time coordinate. Doing so helps communication with other people as you ...
- 103k
2
votes
Accepted
Confusion about timelike spatial coordinates
For a vector $\bf{V}$, timelike, null and spacelike are defined
\begin{align}
\text{timelike:}&\;\;\;\;\mathbf{V}\cdot\mathbf{V} = g_{\mu\nu}V^\mu V^\nu < 0 \\
\text{null:}&\;\;\;\;\mathbf{...
- 1,900
2
votes
Accepted
When you are in a gravitational field, do object far away get physically closer to you as you get closer to the mass?
This is to answer the latest version of the question, as phrased in the comments:
I should have clarified in the question [...] The only thing that truly matters is clock ticks counted by each ...
- 12.7k
2
votes
What is the problem with this method to measure one-way speed of light?
The first time that you do this experiment, you have six unknowns, the speed along each of the three legs of your triangle ($c_{SO}$, $c_{SM}$, and $c_{MO}$) plus the time take to transit each leg ($...
- 5,097
2
votes
Understanding expansion of the Universe as things flying apart
Can the Universe be pretty much seen just as things flying away from each other [...] ?
Absolutely! This is precisely what expansion means. That nearby particles are moving apart. (Technically, the ...
- 1,148
2
votes
Why would speed of light be directional if spacetime is discrete?
The book cited in the question (contrary to much of the discussion in the comments) is about simulating physics on computers. When you go to a discrete grid and simulate with finite differences ...
- 5,097
2
votes
Does Matter Cause Curvature or Vice-Versa
I am puzzled by the last paragraph--it's been a while since grammar class, but is that subjunctive mood? There is no need to speculate on the density of Earth's core: it's more dense than the planet's ...
- 35.4k
2
votes
What happens if we differentiate spacetime with respect to time?
I think what you're reaching for is the four vector velocity of an object. That is, differentiating it's position with respect to time. You started with a four dimensional vector (position) and ...
- 9,072
2
votes
Do satellites in orbit create Relativity paradoxes?
The satellite is not looking into its own past. It's looking at Jack's present, the clocks in which happen to read a time 1.15 seconds earlier than the clocks on the satellite. As to your second ...
- 1,897
2
votes
Looking for papers that claim that spacetime is emergent
An influential modern classic is the essay Building up spacetime with quantum entanglement by Mark Van Raamsdonk. This is a good starting point to understand the mainstream of thought in this ...
2
votes
Accepted
Is the FRW metric, based on spatial homogeneity and isotropy, rotationally and translationally invariant? If so, how?
Roughly speaking, in addition to Einstein equations, the (spatial) FLRW metric is constructed by assuming that, at fixed time, in the Riemannian manifold defining space:
(a) metric properties are ...
- 73.8k
1
vote
Boundary conditions on transition maps on general relativity
There's nothing fancy going on with transition maps. What a mathematician means by a "transition map", in the setting of general relativity, is nothing more or less than a coordinate change ...
- 289
1
vote
Question on special relativity
Using $\Delta$anything is going to increase confusion.
Relativity is about measuring the same events in different coordinates. So for light propagating a distance $L$, you have 2 events:
Emission (Tx):...
- 35.4k
1
vote
Question on spatiotemporal dimensionality about the contradictions of time being a dimension
There's a lot of misconceptions here. I will try to clear them all up one by one, but first we should review what a dimension is in the mathematical context of analytic geometry. A dimension in this ...
- 1,897
1
vote
Is the FRW metric, based on spatial homogeneity and isotropy, rotationally and translationally invariant? If so, how?
If what you're confused about is why the metric seems to depend on the coordinates and thus might not be translationally or rotationally invariant, look at the Minkowski metric (flat spacetime) in ...
- 689
1
vote
Do you always experience the gravitational influence of other mass as you see them in your frame?
The answer to the question in the title is "No." For a mass moving with constant velocity, the Newtonian approximation for gravity points toward the current position of the mass, not where ...
- 513
1
vote
Does Matter Cause Curvature or Vice-Versa
There are two problems with this idea:
First, you claim that celestial mechanics in your system would be indistinguishable from the celestial mechanics we observe. This is not necessarily true: If you ...
- 1,897
1
vote
Accepted
A few doubts regarding the geometry and representations of spacetime diagrams
The dotted lines are null trajectories. You are correct there is no $T$-dependence in the slope of the light cones. Therefore, the slope of all dotted lines along a vertical (of constant $X$) is the ...
- 1,900
1
vote
Killing tensor in the Kerr metric
The Killing equation is a overdetermined system of PDEs of finite type, as a result, there is a algorithm to compute all Killing tensors for a given metric. See for example arXiv 1704.02074.
- 399
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