29 votes

Time is the only dimension that has an arrow, and the only dimension which contributes an opposite sign to the metric. Is that just a coincidence?

Minkowski spacetime is a mathematical model constructed to capture aspects of the phenomena we observe. It is a product of the human imagination, like all of our models of physics. The observed fact ...
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  • 4,038
15 votes

How do gravitational waves propagate?

There are a few misconceptions in the question. I'll try to address them in order of abstraction. Waves don't propagate only on surfaces I believe you are thinking of waves as surface waves, such as ...
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12 votes

"Moving" clocks

It's better to consider time dilation and length contraction to be the results of the relativity of simultaneity rather than the cause of it. You might find it useful to consider purely spatial ...
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  • 18.8k
12 votes

Is space — as opposed to space-time — curved by a gravitating mass?

Let's suppose you are an observer and you have a clock to measure time and rulers to measure distance. You construct a coordinate system by placing yourself at the origin and using your clock and ...
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10 votes
Accepted

Using time dilation to find universal frame of reference

I'm afraid your idea won't work. Time dilation is symmetrical. Suppose your frame of reference and mine are moving inertially relativity to each other. A clock in your frame will seem dilated relative ...
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  • 18.8k
7 votes

Why is proper time equated to $ds$?

Generally speaking, the line element can be written as $$ds^2=g_{\mu\nu}(x)dx^{\mu}dx^{\nu},$$ where $g_{\mu\nu}(x)$ are the metric components at the point $(x^0,x^1,x^2,x^3)$. For example, working in ...
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  • 546
6 votes

"Moving" clocks

Here's a position-vs-time graph (time running upwards) [a.k.a. a spacetime diagram] that can help you visualize what is going on. The "rotated graph paper" helps us visualize the tickmarks ...
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  • 8,677
6 votes

How do gravitational waves propagate?

Spacetime isn't supposed to be a surface, it is solid It sounds like the idea you were trying for is that space is 3 dimensional, not a 2 dimensional surface. You are right. Spacetime includes time, ...
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  • 26.9k
6 votes
Accepted

Is space — as opposed to space-time — curved by a gravitating mass?

A few facts: In a 4-dimensional manifold such as spacetime you can pick any timelike direction and call it time in the vicinity of any given event. Directions orthogonal to this will then make up '...
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4 votes

Why are distances to event horizons linear with mass when gravitational effects fall off as $1/r^2$?

Forget black holes, just think about Newtonian physics. The escape speed from some radius around a spherically symmetric mass is just where the sum of the kinetic and potential energy is zero. This ...
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  • 111k
4 votes

Do Two IDENTICAL Bodies Cancel-out Each-other's Gravity?

"Do two identical bodies cancel out each other's gravity?" In general, no. According to Newton's law of universal gravitation the two bodies will attract each other with a force that is ...
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  • 33.9k
4 votes

Using time dilation to find universal frame of reference

Axis Omega asked: "can a frame of reference in which time runs the fastest (there is the least amount of dilation) be found in which to compare to the rest of the universe?" That is the ...
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  • 7,737
4 votes

Amateur question. But could you fix a hole in space-time?

General relativity is a theory of gravity. There is a very common picture of gravity as a distortion in a rubber sheet. The Sun sits on the sheet, causing a depression. The Earth rolls around in the ...
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  • 26.9k
4 votes

Why is spacetime in special relativity hyperbolic?

No, spacetime is not 4 dimensional Euclidean in Galilean relativity; it's 3+1 dimensional, where the time dimension is completely separate from the spatial dimensions and does not mix with them at all....
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  • 6,129
3 votes

Time is the only dimension that has an arrow, and the only dimension which contributes an opposite sign to the metric. Is that just a coincidence?

It is not a coincidence, I think, for the following reason. First, this question is not just a question about a manifold; it is a question about a manifold and a matter-content together. Considered as ...
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3 votes

Is it theoretically possible to create a 'time bubble', where inside the bubble time will stop or at least slow down radically?

Sure you can! You will need: One (1) large spherical shell of ordinary matter It can be shown that inside a spherical shell like this, the amount of time $\tau$ experienced by an observer at rest ...
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3 votes

Can gravity exist without time?

It depends what you mean by 'exist without time', and also whether we're talking about our Universe or a different hypothetical one. I've given two possible answers below, but you can clarify which ...
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  • 3,058
2 votes

"Moving" clocks

I'd take it from the invariant interval (in the $i^{th}$) frame: $$ \Delta s^2 = (c\Delta t_i)^2 - (\Delta x_i)^2 $$ doesn't depend on $i$. So in a frame where $\Delta t_i=0$, that is, two distant ...
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  • 23.2k
2 votes

Characterizing compactness of the Alexandrov topology in a spacetime

Consider a 2D Minkowski spacetime and identify two constant time surfaces $S_T\equiv S_{-T}$ for some $T>0$. Remove the lines $t=0$, $x\geq 1$ and $t=0$, $x\leq -1$ from the obtained cylinder. The ...
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2 votes

Time is the only dimension that has an arrow, and the only dimension which contributes an opposite sign to the metric. Is that just a coincidence?

Remember that the metric signature was discovered in the context of electrodynamics. It is related to the propagation of light and thus, so to speak, a "local" property of space-time. ...
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  • 926
2 votes

Is space — as opposed to space-time — curved by a gravitating mass?

"Can we relatively freely rotate our 4 dimensional coordinate system for the universe's spacetime such that what was space before (time fixed, say at zero) is rotated "into" the time ...
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2 votes
Accepted

Is energy only the change in spacetime of an object with respect to an observer?

It is fact that there is only kinetic energy that is eligible to do some work. Even the, EM energies are the kinetic energy of quantum particles such as photons. This is simply incorrect, and ...
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  • 65.6k
2 votes

After I travelled north one lightsecond and then stop, is a clock I carried along one second behind a clock I left behind?

It will depend what speed you are travelling at. However, dealing purely with time dilation effects from special relativity, if it takes you $\tau$ amount of time to travel a certain distance as ...
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  • 624
2 votes

Why is spacetime in special relativity hyperbolic?

related: Is spacetime in special relativity hyperbolic? ANS: The spacetime in special relativity is not hyperbolic (is not a [curved] hyperbolic geometry). Similarly, the geometry of Euclidean space ...
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  • 8,677
2 votes
Accepted

Equivalent of the geodesic equation for fields

Maxwell's equations (albeit in curved spacetime). The geodesic equation is, in some sense, just the equations of motion you get for a massive point-particle coupled to the gravitational field. The ...
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2 votes

Penrose conformal diagram of Morris-Thorne wormhole

Making a Penrose conformal diagram of a Morris-Thorne wormhole is challenging since the fundamental properties of such a spacetime can't really be represented in two dimensions (there isn't any two ...
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  • 14.4k
1 vote

Why is proper time equated to $ds$?

In general, the separation between two events contains a spatial component and a time component. If the separation is time like, the time is large and the distance is small. You can travel between the ...
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  • 26.9k
1 vote

Could the curvature of spacetime, as in general relativity, result from the interaction of quantum fields?

Is it possible that the curvature of spacetime, as in general relativity, results from the interaction of those quantum fields with the fields of quantum matter? I find this phrasing a little weird, ...
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1 vote

Could the curvature of spacetime, as in general relativity, result from the interaction of quantum fields?

I'm gonna write a pretty quick and not much detailed answer, but to give you a quick idea. The first taught thing to quantize gravity is actually, that its quantum field behaves as a spin 2 particle ...
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  • 551
1 vote

Is the space-part of a four-vector temporally connected to the time-part and vice-versa?

Can we say that it's the time part that's involved in defining the space part and the space part in defining the time part? A displacement 4-vector has a time-component that has nothing to do with ...
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  • 8,677

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