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0

If you want a direct, physical measurement of curvature, here's a plan that would take lots of money and decades, possibly centuries to set up. Perfect for physics! What you need are three satellites equipped with lasers, light detectors, precision aiming capabilities, and radio communication. These three satellites are launched into space and position ...


3

Following Synge's description of a "five-point curvature detector" 1 and its generalization (e.g. as indicated in [2]), the curvature of five participants ($A$, $B$, $N$, $P$, $Q$) who were and remained (chrono-geometrically) rigid to each other (i.e. finding constant ping duration ratios) is measured as the real number value $\kappa_5$ for which the ...


2

There are measurable effects of the space-time curvature due to a star - the precession of the perihelion of Mercury and the bending of light as it passes near the sun, for instance. Indeed these were the first effects of GR to be experimentally confirmed. There are even measurable effects of the space-time curvature due to the Earth: the redshifting of ...


11

Measuring Curvature Curvature can be quantified by many tensors, and their various contractions give rise to a plethora of scalars describing curvature. In general relativity the most common are, Riemann curvature tensor, $R^{a}_{bcd}$ which measures to what extent the metric is not isometric to flat Euclidean space. In another manner, it measures the ...


0

At very high velocity, time is dilated with respect to an observer. The speed of light remains constant but since the distance that the light must travel increases, the time that it takes for it to travel from say a point A to a point B is longer than if it were stationary relative to the observer.


2

Spacetime curvature is mathematically equivalent to the presence of so-called geodesical deviation of timelike geodesics. In other words there are freely falling bodies starting from points close to each other and with similar velocities which measure a nonvanishing relative acceleration. This is the most direct physical meaning of a nonvanishig Riemann ...


1

"Space curvature" refers to the geometry of a spatial-slice of space-time, with a constant time coordinate (so the slice has no time dimension). "Space curvature" is what the common rubber-sheet-analogy refers to, mimicking Flamm's paraboloid, which represents the geometry of a spatial slice through the Schwarzschild metric: ...


1

The above data is the is the anisotropy of temperature of the Cosmic Microwave Background (CMB) as measured by NASA U2 airplanes in the 1970s. The anisotropy is due to the redshift and blueshift of the Earth moving 300 kilometers per second or 1,080,000 kilometers per hour relative to the frame of the CMB, in the direction of the + at the center of the ...


1

1 - It is false! If $E = mc^{2}$ is true only for an object that isn’t moving, the mass never changes (is a "Lorentz invariant"). 2 - Can you rephrase it, please? 3 - Energy and mass are not at all the same thing; an object’s energy can change when its motion changes, but its mass remains the same. 4 - In Special Relativity, time can be variable, its ...


0

Your suspicions are correct: It is wrong! At least as it is written presently. Let us start form the embedding of manifold $$\imath_t : F_t \ni p \mapsto p \in M\:.$$ It induces and embedding of corresponding tangent bundles: $$T\imath_t : TF_t \ni (p,v) \mapsto (p, d\imath_t (v)) \in TM$$ The latter can only preserve the vectors tangent to $F_t$ seen ...


0

No. Due to the phenomenon of space expanding, the light from a point 10 light years away will actually take more than 10 years to get here. Therefore, you will actually see the object as it was much longer than 10 years ago. So if the star exploded as a nebula 10 light years away right now, you would see it not after 10 years, but a little after 10 years. ...


4

I don't think there's an a priori reason, but there's certainly a good a posteriori empirical one: if you make two long, straight parallel things, they neither meet nor diverge away from one another. It was presumably this empirical fact that led Euclid to introduce his parallel postulate, although he probably wouldn't have seen it as empirical. Moreover, ...


1

The limit of non euclidean geometries, as the radius goes large, is euclidean. It's like relativity. Unless you have fancy equipment or fast things, the euclidean newtonian model does quite fine. If you model space on hyperbolic geometry, with a curvature the same size of the earth, the observable universe would fit inside a sphere of radius 432000 miles. ...


2

In the absence of evidence to the contrary we tend to assume the simplest possible description for physical systems. Suppose the spatial scalar curvature had the non-zero value $S$. Immediately we have the question: why is it $S$ and not $S + 0.001$ or $S - 0.001$ or any other value. There must be some mechanism for making the curvature exactly $S$ and that ...


1

The situation you are describing is very similar to (but not exactly like) a Schwarzschild-de Sitter universe. That is a spacetime that is flat, infinite in size, expanding with a cosmological constant, and contains a massive body (such as a black hole). The metric for such a spacetime is: ...


0

A model i used to explain it is this. It is particularly true of non-euclidean geometry. All space is curved. Curvature is a measure of circumference per angle. Straight lines divide the circumference. A large mass would cause space near it to become more negatively curved, which would create more circumference in the direction towards it. Gravity can ...


1

May I suggest that your premise that "Space isn't moving so as to push or rotate matter" is the source of your problem in appreciating the General Relativity explanation of gravity. The GR perspective is that the very fabric of space is accelerating from outers space towards the centre of the earth. A freely falling object feels no force. It has not moved ...


2

Let $M$ be a manifold, let $V$ be a finite-dimensional vector space, and let $\Omega$ be a sample space (in the sense of probability). For each point $p\in M$, let $X(p):\Omega\to V$ be a random variable. A mapping $T_V:V\to V$ is called a target space transformation and a mapping $T_M:M\to M$ is called a space transformation (or spacetime transformation ...


0

There is a central point, the point that is the opposite to the expansion of the sphere. We can't see it, but I would assume that in a similar way to how when large stars go supernova they leave behind a black hole, and how there are black holes in the middle of galaxies, there would probably be a black hole in the centre. We would never see it, because ...


0

This is similar to the idea that if the universe was infinite in size and infinitely old, the sky would be as bright as the sun, since every point in the sky would end on a star, somewhere in the infinite universe. Since this is not the case, it led people to conclude that the universe is either finite in size or age. Similarly, even if the universe was ...


0

is not the time that B observes the signal, it is merely the time which the event takes place in the reference frame at which B is at rest. But that's what observe means in SR. From the Wikipedia article "Observer (special relativity)": Physicists use the term "observer" as shorthand for a specific reference frame from which a set of ...


1

Space itself was once concentrated in an infinitesimally small point. During the Bang of the Big Bang all distances between points got bigger. If you try to measure the expansion of the universe from any point you will draw the conclusion that the expansion started from that point. It seems that the expansion happened everywhere, and nowhere at the same ...


-1

Regarding question 1, Inflation was offered as a theory to explain why the universe seems more or less the same and has the same cosmic background radiation in all directions today. A multiverse can be suggested from a multiplicity of theoretical positions. One could say there could be an infinite number, etc. One can argue, for example, given our small ...


0

Other than noting that galaxies are moving away from us, we have no frame of reference in order to state how the universe is expanding. We would need to be out side the universe in order to get a description.


0

I am not sure that being in 3+1-D is a privilege. Actually, all the troubles with Feynmann integrals come from 4D. Secondly, the QFT is integrable only in 2+1-D. From the mathematical point of view, the 4D differentiable manifolds are most problematic. On contrary, I also heard that if the space is not 3D then the signal cannot be transmitted, but at the ...


2

As I understand it, the space is not actually moving, but expanding; Which means that objects in this space are "moving apart". Now, "moving apart" has not much to do with the physical term of moving. Essentially, one does not move space because that makes no sense; Not because it is impossible. (Or, more poetically: It is not even impossible to move ...


0

by definition, any object is stationary relative to itself, regardless of any other frame. from the perspective of that object, no dilation exists, and time is experienced at it's full normal rate rather than a fractional amount as relative to another objects perspective. the rate of time doesn't increase to infinity, but rather can decrease by a fractional ...


6

The time used in describing the evolution of the universe is comoving time. This is the time that would be measured by a freely moving observer on their wristwatch (assuming the high temperatures didn't melt both the observer and the wristwatch :-). Time is not a simple thing to define in general relativity, however we can always unambiguously define proper ...


19

This is a common point of confusion, not only with regards to inflation, but any time an expanding universe comes up... The "cosmic speed limit" as you call it says that no particle or signal can move through spacetime faster than the speed of light. Spacetime is a very specifically defined thing, described with a coordinate system. There is no restriction, ...



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