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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, ...


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 ...


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, ...


2

Think of a very thin wire. It is a 3-dimensional object, but for many purposes you can describe it just as a 1-dimensional line or curve. The two remaining dimensions are curled up in a tiny cross section. In a similar way, the speculations (not the slightest experimental hint exists that it should be so) about our world possibly being higher dimensional ...


2

A Penrose diagram of a metric $g_{ab}$ is used to represent the conformal structure of $g_{ab}$. Generally light rays move at $\frac{\pi}{4}$ from the upward vertical and the spacetime considered is spherical symmetric. The metric, $\overline{g_{ab}}$, on the Penrose diagram satisfies: $\overline{g_{ab}}=\Omega^{2} g_{ab}$. This implies that timelike ...


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 ...


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 ...


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 ...


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 ...


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. ...


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

There is no absolute stationary object, an object may only be stationary with regard to an observer. If e.g. the relative velocity of an object is zero in our reference frame, we observe an object which is not moving with regard to our own reference frame. In this case Lorentz factor is 1, that means that there is no time dilation at all.


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 ...



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