# Tag Info

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OK, I can not show the math, but anything you try to fit inside the box, will itself be curved/stretched/contracted along with the space. Therefore, you should not be able to fit more stuff inside one box as compared to the other of the same size. Even saying same size involves space and its curving. So, even your box will be curved as there is nothing that ...

-1

This can be visualized like bending a sheet of paper. The surface area of the sheet never changes but its configuration in a 3-D space changes. Analogous to this, bending a 3D space will and should show no change in volume but a change in configuration in a 4 Dimensional space coordinate system. (wiggling a jelly doesn't change its volume)

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Within the Schwarzschild metric, the volume does change. It is the rectangle formed by the radial dimension and time which is invariant: The dilating effect of the Schwarzschild metric $$\mathrm ds^2 = -\left(1 - \frac{2GM}{c^2 r}\right) c^2 ~\mathrm dt^2 + \frac{1}{1 - \frac{2GM}{c^2 r} }~\mathrm dr^2 + r^2 (\mathrm d\theta^2 + \sin^2 \theta~\mathrm d\... 1 How can we look into the past? Light has a fixed velocity of almost 300.000 meters per second. Sunlight takes about 8 minutes to reach us. So we see the sun always 8 minutes ago. As the other answer says, stars are much further away and it takes light that much longer to reach us. How do we know how far away the stars are? There are various methods that ... 1 Stars are very far away. So light takes a while to get from stars to you. The light arriving now shows you what the stars looked like when the light left. It is like getting a letter from a far away friend. The letter took a few days to arrive. It has news from a few days ago. -2 You go outside at night and you look at the sky. That's the universe and that's the past streaming in on you. With your own eyes, of course, you can't see much farther than approx. 2.5 million years back - the Andromeda galaxy is easily seen, even though it's not as pretty as in astrophotographs: https://en.wikipedia.org/wiki/Andromeda_Galaxy. What you will ... 1 Yes, curved spacetime does change the volume of space. When space is curved by mass it is stretched more in some dimensions than others. Picture a balloon being stretched or squeezed--the volume changes. 2 I can answer some of it, and in such a way that it has invariant general relativistic meaning. However, not a general answer. You do have to, and can, treat curvature and some measures of volume invariantly. There are two questions. 1)Does negative/positive curvatures have more volume, that some (in some sense) equivalent spacetime with no curvature? And 2)... 15 In a question like this you need to ask what does the volume change relative to. So it's a little bit ambiguous. However, the answer to your question is "yes" in the following restricted sense. Imagine having a "swarm" of test objects, with mass so small that their effect on the spacetime around them is negligible. Assume that they are in freefall, i.e. ... 0 The speed of light is invariable but the number or ratio of the frames of reference are variable as determined by the amount of gravity, the result of which is gravitational lensing. 0 No, the age of the universe doesn't depend on the observer. What depends on the observer is the "perceived" time that has passed since the Big Bang. What you are asking is if the conformal time and the age of the universe are the same and the answer is negative as you can see in that link. 3 We don't believe this is possible. The justification for this belief is nothing less and nothing more than experimental observation. We have never observed a process where an effect comes before its cause, so we simply reason inductively to establish a postulate that the preferred order of events in physical processes is always the same, for any observer. ... 1 Given a few plausible assumptions about the universe its spacetime geometry is described by a solution to the Einstein equations called the FLRW metric. If we know the densities of various types of matter/energy present, e.g. photons/matter/dark energy/anything else, then we can calculate how the expansion of the universe varies with time. Generally ... 0 This is not what I, and I would posit most physicists, understand as a physical treatment of what general covariance is in physics. General covariance is that the equations look the same in any coordinate frame - any meaning that the transformations can be any function. The only limitation is that the functions be differentiable, maybe n or infinite times (... 2 A 3D cube with pacman topology is translationally invariant and not rotationally invariant. A space like this is a possible (but unlikely) flat space part of a cosmological spacetime 3 The development of general relativity has led to a lot of misconceptions about the significance of general covariance. It turns out that general covariance is a manifestation of a choice to represent a theory in terms of an underlying differentiable manifold. Basically, if you define a theory in terms of the geometric structures native to a differentiable ... 6 I can offer up something similar to this, which is an isomorphism between something called the Tsirelson bound and the spacetime metric. This is not exactly the emergence of spacetime from quantum mechanics, but it does illustrate how spacetime could be seen as quantum mechanics in diguise. Suppose we have four operators A_1, A_2, B_1, B_2 such that:$$ ...

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The time dilation factor with respect to an observer at infinity is $$\sqrt{1-\frac{\text{2 G M}}{\text{c}^2\text{ r}}}$$ so if we plug in G=1, c=1, r=10 and M=+1 we get the clocks running slower by a factor of 0.8944 if they are in a distance of 10GM/c² from the center of the positive mass. If we change the sign of M to M=-1 we get a time dilation factor ...

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The arrow of time is believed to be related to the fact that the universe started in a state of low entropy and is evolving towards a state of larger entropy. The effect of negative mass will not change this. The reason is that any model of negative mass will leave the initial state of the universe as as state of low entropy. A rather uniform distribution of ...

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The geodesic equation is given by, $$\frac{\mathrm d^2}{\mathrm d\tau^2}x^{\mu}+\Gamma^{\mu}_{\lambda\sigma}\frac{\mathrm dx^{\lambda}}{\mathrm d\tau}\frac{\mathrm dx^{\sigma}}{\mathrm d\tau}=0$$ which is a set of 4 equations for $x^{i}$. $\Gamma^{i}_{jk}$ tells us about the curvature of the space time which can be written in ...

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Lower index is a tool to map upper index to a real number (W dot V for example). So to define a lower index, you need g(v,w)v (with one slot waiting for w to fill in order to spit out the dot product. So you can think g(v,w) as a tool to make two vectors dot with each other. Now you have v available, if you encounter a w later g(v,w)v is a tool to map w to ...

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My understanding (which is based somewhat on Jackson's chapter on SR in Classical Elecrodynamics) is that the invariance of the interval is not enough to derive the Lorentz transformations - you also need the second postulate (that the speed of light is constant in all frames). The invariance of the interval follows from the fact that spherical light waves ...

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It depends what you mean by their clocks both being at noon when they're at positions A and B, and their speeds differing by 161,000 miles per second. By the way the question was stated, I'll assume you meant their positions were measured in an outside observer's frame, i.e., at noon in the outside observer's frame ship A is at position A and ship B is at ...

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It is a little different in General Relativity. Let's start with Special Relativity and all the 3 forces of the Standard Model in physics. Then we will talk about gravity and the universe. In The Standard Model spacetime is Minkowski, meaning flat in all 4 dimensions. If it is that way clearly any direction and position is equivalent. That's called ...

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We have to be careful what we mean when we say "moving away". Imagine a grid in which we are at the origin and there are light sources located at each of the grid intersections. If the grid stays as it is while the light sources accelerate away from us, their light will appear to be redshifted. If you set up the accelerations such that everything moves ...

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That is not quite that simple. There is theory and measurements, and it places some constraints. There is more. First, if the universe is infinite now it was infinite at the Big Bang. You can have an infinite universe and have it all in the spacetime at the Big Bang. It does not grow to be infinite, it either is or is not. (Ignoring multiple dimensional ...

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You need to learn to use mathematics to tackle such problems. If you try to do without math using only your intuition then you'll make many hidden assumptions that may not be valid. Physicists who understand some theory well enough can get away with using their intuition, but then that intuition is based on a rigorous mathematical understanding of the theory....

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Infinity is a mathematical concept, as well as the concept of variables describing dimensions. Physics is about observations, either in the laboratory or of the cosmos, which are fitted with mathematical models. It started with the geocentric system, became the heliocentric system and then the realization that the galaxy is composed out of sun like stars, ...

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If "open" means nonpositive spatial curvature (which is the usual meaning), then no. The experimentally measured spatial curvature is consistent with zero, but the error margin includes values on both sides of zero. There's no conflict in the Friedmann equations between accelerating expansion and positive spatial curvature. If "open" means "never ...

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"If inertia is a property of the matter form of mass-energy, and it is a property that allows for the transfer of energy, then why doesn't the energy dissipated in a vacuum, as does applied radiant/free energy" The problem with your logic is that is flawed. It is equivalent to "some fruits are apples; oranges are fruits: why do not oranges taste like ...

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Actually, the explanation as to why rotation of a mass affects the metric in principle is simple. Rotation means there is angular momentum, and angular momentum contributes to the energy-momentum-stress tensor in general relativity. If this was a nonrelativistic rotation we would say that the rotation carries kinetic energy. The rotation contributes as a ...

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The bottom line is that space and mass do interact with one another. Otherwise, they would not tell one another "how to curve" and "how to move". Therefore a moving (or rotating) mass and space will interact slightly differently. The interaction will drag with rotating mass. It may or may not be detectable depending upon the mass & speed of rotation and ...

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The hypersurface at t = 0 as shown in the diagram is not the observers plane of instantaneous, contemporaneous events constituting the present. The speed of light is as instantaneous as anything gets because at the speed of light no time passes. (Therefore the present is relative.)

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I would like to make the argument that time is a force. But I would first like to address some of the items mentioned above. A force does not, by definition, need to have a counterforce as a requisite for existance (F=MA). It exists independently from any counterforce. The "counterforce" is independent and incidental. If you drop a ball, the force of ...

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Bob Bee's answer already covers a lot of extra detail, so I just want to give the very concise answer to your specific question. One form of one of the Friedmann equations is: $$H(t) = \sqrt{\frac{8\pi G}{3}\rho(t) - \frac{kc^2}{(a(t))^2}}$$ In a universe with zero global spatial curvature ($k=0$), like ours is thought to be, then the expansion rate $H(t)$ ...

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The oceans , seas , all objects in the earth are already masses added to the earth and objects attracted to it because the total mass earth had already distorted the space time curvature and any object in the vicinity will follow geodesic lines to the center of that mass, which in turn will be thought of gravity forces. This is according to relativity ...

1

As the saying goes, a picture is worth a thousand words. Below is a time-spatial axis diagram of the time and x-axis in two frames. One is at rest relative to the blue, and the other is Lorentz boosted to some velocity. What is the plane of simultaneity is dependent upon the frame that you are on

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Quite clearly the answer to this is that no, it does not. In particular, consider two inertial observers moving (in flat spacetime) relative to one another. We know that neither of these two observers is more privileged than the other: the laws of physics are the same for each of them and so on. Yet they will draw different hypersurfaces of simultenaity ...

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The hypersurface of simultaneity does not represent the present. It is just a plane cut through spacetime. If you changed your own state of motion this would tilt the plane by some angle. So the notion of "now" as the hypersurface of simultaneity would depend on your state of motion, which is of course not meaningful. In fact, the notion of "now" itself is ...

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The problem is that the images that you have seen about spacetime bending depict a two dimensional 'fabric'. Try picturing it in three dimensions and it would be easier to understand. If you are still not able to visualise then see: https://www.dropbox.com/s/h6h5pfe37stxdrv/Photo%2002-06-16%2C%2022%2028%2003.jpg?dl=0

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To answer your question about falling objects to the center instead of straigt think about the following: If you think about the Earth as a whole (rather than just the part you can see around you) and think about how two objects dropped from a height on opposite sides of the planet would behave, then you may be better able to understand the quote. In the ...

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The comment by Walter is on the right track: The "acceleration" does not refer to the fact that recession speed increases with distance, because this is just a consequence of space expanding everywhere. This is why we measure the expansion in km/s per megaparsec. Today, the expansion rate (the Hubble constant) is $H_0 \simeq 70\,\mathrm{km}\,\mathrm{s}^{-1}\,... 1 The FLRW energy equation for the motion of test masses in the universe is $$\left(\frac{\dot a}{a}\right)^2 = \frac{8\pi G\rho}{3}.$$ the scale factor for space is$a$and its time derivative is$\dot a$. I derived this from Newtonian dynamics. The density of mass$\rho$for the case of a quantum vacuum energy level is constant. I now replace this with ... 0 I would argue that the expanding of space cannot and should not be understood adding space into space, nothingness into nothingness. We have no way of observing the space itself as a reason like the one you presented likes. Things seem to get away from us through and the observed mechanism is called redshift, which, in close distances(inside let's say the ... 0 The Standard cosmology model, the$\Lambda$CDM model, rearranged from the Friedmann equations, looks like,$H = H_0 {\sqrt{L_m a^{-3} + L_r a^{-4} + L_{de}}}$This assumes zero curvature space, pretty well measured now (note, not zero spacetime curvature, just the spatial slices). H is the Hubble parameter as function of time, from the Big Bang.$H_0\$...

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The Thorne time machine, a wormhole with one opening accelerated or Lorentz boosted outwards and then conversely brought back, does not permit time travel prior to the Cauchy horizon. This is the point where the time machine is "turned on." This Cauchy horizon has in regions of spacetime prior to its formation a set of curves winding through the wormhole ...

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The claim that energy conservation does not hold in GR is debatable, as any choice of time-like vectorfield will yield such a law via Noether's second theorem (energy conservation in GR was in fact the reason why Noether developed her theorems in the first place). However, these laws are (in Noether's terminology) 'improper', ie given through linear ...

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Dark energy is a form energy that appears to have a constant density in space even as the universe expands. The simplest model for this is a cosmological constant in the gravitational field equations. This model agrees with observations. What dark energy really is or whether this model is correct is beside the point here. My answer assumes this hypothesis. ...

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You sound as though you may have heard of Gullstrand Painlevé co-ordinates, which are a particular system of co-ordinates for labelling spacetime defined by the Schwarzschild metric around a nonspinning, noncharged black hole. The analogy is often made of a "spacetime river" with this depiction; if you stand still with respect to the co-ordinates you are ...

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In the question on dark energy I gave an elementary answer that is reduced to Newtonian mechanics. The Hubble frame has a remarkable property that one can look at local cosmology in a Newtonian fashion. The total energy is set to zero. This does give a result that is commensurate with the Friedmann-Lemaitre-Robertson-Walker theory of the expanding universe. ...

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