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Seemingly equivalent linear form of the Sagnac effect

This is a derivative of [the question regarding the Sagnac effect][1]. Judging from the metric $ds^2=-dt^2+(rd\phi)^2$ for a constant $r$ for this question, it should be no different from that on a ...
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Seemingly equivalent linear form of the Sagnac effect

As for $t_1-t_2$, the difference between the linear and circular cases is that in the linear case, you can arrange for two unprimed clocks that are a distance $2πr$ apart in the lab (primed) frame to ...
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I can't wrap my head around the idea of matter interacting with spacetime. How is the interaction taking place?

Answering this question with accuracy requires an understanding of matter and gravity that do not currently exist in physics. It appears to me that matter comprises trapped harmonic vibratory energy (...

Does dark matter have mass?

Dark matter must have mass because it is defined that way. To quote Wiki: In standard cosmological calculations, matter means any constituent of the universe whose energy density scales with the ...
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Is it possible to express various nonlinear motions as straight lines in transformed spacetime?

Case 3 Case 3 is actually way more simpler as it seems to be hard. We can solve it in 2 steps: Determine the trajectory of the particle. Do the neccessary transformations for this trajectory. The ...
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If we consider the spacetime of the universe to be four-dimensional, does the Big Bang lie in its center?

Some other answers say the universe isn't embedded in a background space, but I think that misses the point; the universe doesn't have to be embedded in anything for this idea to make sense. If the ...
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Accepted

If we consider the spacetime of the universe to be four-dimensional, does the Big Bang lie in its center?

There are two important points in here. The first was raised in a previous answer (and I'll comment on it also), but there is another nuance. The Big Bang is not a point in spacetime Yeah, that's ...
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If we consider the spacetime of the universe to be four-dimensional, does the Big Bang lie in its center?

Differential topology allows us to describe a 4 dimensional (3spatial+1temporal) space expanding without needing to embed it in a higher dimensional space. The balloon is a common metaphor for an ...
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Is there a location in the universe with the minimum rate of time dilation?

This question actually has more of a "physiological" answer than of a "scientific" answer. The notion of dime dilation is frame-dependent. Let's say you are a moving observer. You can consider ...
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1 vote

Does quantum entanglement arise from perpendicular time vectors?

First, what you are proposing as a “perpendicular” time axis is a new dimension, making 5 rather than the traditional 4. Considering how well general relativity does with four (and not five), that’s a ...
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If gravity is not a force, what makes massive objects spheroid?

Gravity es not a force, but there are more forces in the game, contact forces. As in the Newtonian view, in the relativistic view the particles forming the body are being diverted from its inertial ...
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Is a stationary spacetime automatically globally hyperbolic?

No. I will give a different example. Consider the cylinder with metric $$ds^2 = d\rho^2 - \rho^2 dt^2.$$ This is static, but not globally hyperbolic (it has closed timelike curves).
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1 vote

Does time arising from entropy agree with GR?

General relativity doesn't tell you, in principle, what is the direction of time. This is something you add in by hand. In fact, some spacetimes don't even admit a choice of time-orientation. When a ...
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Are non-point spacetime events partially ordered?

There is a well-developed theory of the causal structure of spacetime in general relativity. This is discussed in detail in the books by Wald (General Relativity) and Hawking and Ellis (The Large ...
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Approximation of solution for Laplace's equation in 5d (Kaluza-Klein)

You can build an intuition using basic electrostatics. Instead of thinking in terms of periodised space, imagine instead that you have real charges spaced by $2\pi R$ along a direction. As $R\to0$, if ...
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If gravity is not a force, what makes massive objects spheroid?

I don't want to be redundant of other answers, which are all very good, but instead want to focus on the premise - that "gravity isn't a force". This is like saying "bowling isn't a ...
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Sagnac effect viewed in the rotating frame

The animated GIF below illustrates a fundamental property of the Sagnac effect. The grey dots represent circumnavigating clocks. It can be clocks that are on Earth, co-rotating with the Earth, or it ...
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Sagnac effect viewed in the rotating frame

However, if viewed from the frame fixed to and rotating together with the emitter/detector, since the speed of light should be the same in both directions, the light signals in both directions should ...
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Sagnac effect viewed in the rotating frame

from the frame fixed to and rotating together with the emitter/detector, since the speed of light should be the same in both directions The speed of light is not usually isotropic in a non inertial ...
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1 vote

If gravity is not a force, what makes massive objects spheroid?

The tendency of (parts of) matter is to follow geodesics (i.e. shortest paths) in the curved space(time) until the internal forces of other matter start pushing back. If there is no force acting upon ...
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Turbulence in flow of spacetime

Spacetime doesn’t flow in general. It has no velocity in general nor does it have viscosity. So the concept of turbulence doesn’t apply in general. There is a “river model” which only applies to ...
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So just because gravity "merely" bends space and isn't "really" a force at a distance - isn't it still a thing at a distance?

This isn’t an action at a distance. The Einstein Field Equation relates the local change in the curvature to the local stress-energy content of matter. So there is no interaction at a distance. Matter ...
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If an area in 2D cannot be curved and finite is the same regarding the space of our pressumed 3D universe?

If a 2D area cannot be curved and finite is the same regarding the 3D space of our universe? Both the premise and the conclusion are incorrect. The sphere, for example, is curved, two-dimensional and ...
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If gravity is not a force, what makes massive objects spheroid?

See Don Lincoln's Is gravity a force?. The answer is yes and no. Physics is a description of the behavior of the universe. There is more than one way to describe it. Classical physics describes it as ...
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If gravity is not a force, what makes massive objects spheroid?

First, even in general relativity (GR), there's nothing wrong with taking a weak-field limit where GR "looks like" Newtonian gravity, and in that limit you can think of gravity just the same ...
• 49.7k

If gravity is not a force, what makes massive objects spheroid?

The basic idea is still the same: the gravitational influence of the parts on each other tends to pull them together. The only difference is that now you don't have a force pulling them together, but ...
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1 vote

Poisson's ratio must be zero from special relativity?

Poisson's ratio is a property of a material and depends on the microstructure of the material. It is a measure of how easy it is to shear the material relative to how easy it is to compress it. But ...
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Poisson's ratio must be zero from special relativity?

No -- length contraction does not correspond to stretching or compression of spacetime, and it especially does not correspond to stretching or compression in response to a force. Length contraction is ...
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I can't wrap my head around the idea of matter interacting with spacetime. How is the interaction taking place?

The first thing is that spacetime might not actually be "nothing". There is a theory called loop quantum gravity (an alternative to string theory) which basically says that space is made up ...
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1 vote

How does gravity act and propagate in a 2+1D universe?—Newtonian versus general relativity

In (2+1)D, it is a geometrical fact that the Weyl tensor vanishes. The Einstein tensor and the Ricci tensor give then all of the independent components of the Riemann tensor, and they are fully ...
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Spacetime and uncertainty principle

Can it be that you know the position of a particle but not the exact time when it was there, and that that gives rise to uncertainty in momentum? If so, wouldn't this be a more elegant way to express ...
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Spacetime and uncertainty principle

I love your question, but you might be thinking of the uncertainty principle incorrectly. The proper form of the uncertainty principle is about the spread in values of independent measurements on an ...
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Time dilation cancelling out with movement in two directions

You are mixing 3 different reference frames here. Time dilation is how a specific observer sees the speed of the clock of another observer moving at v relative to him. If different observers look at a ...
Accepted

How do I interpret the time axis in a diagram with multiple light cones?

The light cones mark the trajectories of light that either originates from an event in spacetime (the future light cone) or arrives at the event (the past light cone). In flat spacetime these are ...
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Why there is a minus in the definition of the Minkowski Spacetime Interval?

It's to force the condition that the speed of light is the same in all inertial reference frames, even those traveling at appreciable fractions of the speed pf light relative to one another. Take the ...
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1 vote

How do I interpret the time axis in a diagram with multiple light cones?

It is probably the spacetime diagram drawn by an "asymptotic observer".
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I can't wrap my head around the idea of matter interacting with spacetime. How is the interaction taking place?

The following is standard contemporary mainstream physics (in contrast to some of the answers so far). General Relativity GR can be expressed in various ways, all mathematically equivalent. The most ...

If a weak light source is attached to a string, and someone swing this light source in circle. It seems that this light source is brighter. Yes or no

Any small constant light source doesn't get brighter when you circle it in the air, unless it is a glowing ember which glows stronger when it is fanned by the air. Thus, as you already have said, if ...
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maximum proper time for a fixed elapsed time

A calculation of this result is given in "Box 1" on p.151 of: "Action: Forcing Energy to Predict Motion," Dwight E. Neuenschwander, Edwin F. Taylor, and Slavomir Tuleja, The ...
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1 vote

What is the manifold topology of a spinning Cosmic String?

I think it is just ordinary Minkowski with a singular spacetime surface (one direction being timelike) at which a spatial wedge is cut out and the sides of the wedge glued back together with a time ...
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1 vote
Accepted

Relativistic force correction factor for time-dilated continuous entities

Not sure time dilation is that important here. Basically, you want to be working with covariant quantities, such as four-momentum. Time-dilation will be taken care of automatically. Now to the ...
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