# Tag Info

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Motion is not caused by slowdown of clocks in a gravitational field. Whoever said that is wrong. Here is a video to show how curved spacetime affects motion. https://www.youtube.com/watch?v=DdC0QN6f3G4

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The "total spacetime velocity" refers to the four-velocity (c, 0, 0 , 0) where even though the object is still in space, it is moving through time. The spacetime coordinates are given by (ct, x, y, z) differentiating which we get the four velocity, and since the object is at the same pt. in space, the four-velocity is c. & 3. Let us take the spherically ...

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The problem is that no "intuitive" explanation can capture what gravity is actually about, because if it could, then general relativity should itself be intuitive. The rubber-sheet analogy is in my view not a totally misleading analogy for what it wants to show (namely that masses curve spacetime), but it tackles the wrong problem - the main problem being ...

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Yes. I think Randall Munroe put it perfectly in this comic: The rubber sheet analogy does not tell you much about actual gravity.

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Well, I suppose we could add time as a 4th. However, apart from that there is no experimental evidence whatsoever for more than 3 spacial dimensions. String Theory and its friends remain theories with negligible experimental evidence in their favor.

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I might be wrong but I interpret your question as : if actual measurements of physical events are extended in both space (such as a macroscopic clock), and time, why do we interpret them as happening instantaneously and located at a single point in space?. In this sense, an event is an idealization that is exact only in the limit when it can be thought of ...

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When you talk about a point in space, you're talking about a specific set of $(x, y, z)$ coordinates. Of course there's no use to talking about a point in space unless something is happening there, e.g. $(0, 6, 0)$ is the cannonball's starting location". An event is the same idea in $3+1D$ spacetime- it's a specific set of $(t, x, y, z)$ coordinates. ...

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I can't say that I have ever seen any attempts at simulating non-causal spacetimes (the closest I've seen is the simulation of fields upon such spacetimes). A few non-causal spacetimes do admit a time slicing, by the way, although by definition not all of these slices are achronal. Just solving it like any other PDE might be an avenue worth exploring, but ...

1

No. Photons do not experience the passage of time, as they are traveling at the speed of light. Remember when they discovered that neutrinos must have mass? Originally it was thought that neutrinos traveled at the speed of light, but then it was discovered that neutrinos change their flavors over time, which means that time must pass for neutrinos, which ...

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The principles of space time homogeneity and isotropy are dependent of one another. The reason of dependency of one another refers to the region of space time of being homogenous. Homogeneity in space time results from being symmetric, and what causes space time to be symmetrical is simply the Laws of Nature. Hence our space time, or the shell we are living ...

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All of your questions have no good answer at this point in time. All of them are being researched by physicists, cosmologists, and theorists. We don't even know whether our universe is the only universe or whether what lies beyond the visible universe is just more space like the kind we can see. Our best theories of space and time (Einstein's General ...

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I don't know the "formal" proof, but here is my proof: Time dilation and length contractions are given to us by the Lorentz transformations by: t’ = t/(1-v2/C2)1/2  and d’ = d/(1-v2/C2)1/2 (in other words “same” or proportional to each other) where: t = distance/length traveled through the T dimension in observers own frame of ...

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What you have done here is a Galilean transform, that is a non-relativistic transformation. Take your final result (which is quite correct): $$t' = \frac{\sqrt{\beta^2 + \alpha^2}}{\sqrt{\eta^2 + \mu^2}} \tag{1}$$ We know that the vertical velocity is $\eta$, so the vertical distance moved in our time $t$ is given by: $$\beta = \eta t$$ We also know ...

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No, the straight beam will not magically turn into a curved beam. I suspect you have a slightly confused idea of what the curvature of spacetime means physically. Basically it means that a freely moving body will appear to accelerate relative to some distant observer. Conversely if we want stop the body from accelerating then we have to apply a force (i.e. ...

1

There's a very real phenomenon called 'Gravitational Lensing', in which light is bent from its original trajectory by a massive enough cluster of matter (which curves the space-time around it). Moreover, it's bent by a different amount than predicted by a simply application of Newtonian ideas, as kindly pointed out by Rob Jeffries. Is this evidence enough? ...

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There is no %100 proof in science; at least not for good science. It's always a question of being the most accurate / descriptive / useful theory. For example, Newtonian gravity is 'true' to the extent that it is very effective in a huge diversity of situations. General Relativity (GR) includes all of the accuracies of Newtonian Gravity, and then also ...

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Time is not like space. It is a coordinate, as the space coordinates, but that doesn't mean it is the same. Read Ben Crowell's answer here. Entropy is stochastic, it doesn't have to increase monotonously. The very low current universe entropy can make the illusion that it always does, but there is still a very low probability that it decreases for a short ...

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I found the Weinberg passage, but to quote it I need to do it in an answer (too long). So here it goes. We have seen in this chapter that the nonvanishing of the tensor $R_{\lambda \mu \nu \kappa}$ is the true expression of the presence of a gravitational field. We also saw in Chapter 1 that Gauss was led to introduce the Gaussian curvature $K = -R/2$ as ...

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Gravitational waves do cause fluctuations in clock rate. However, a gravitational wave as strong as you request would very strongly self-gravitate. It might even collapse into a black hole. By comparison, this is the level of time dilation one would experience hovering above a black hole at a distance about 1% of its radius.

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Yes, the statement is correct. One proof I am familiar with was given by V.Fock (of Fock states, etc) in his book "Theory of Space, Time, and Gravitation". See Chap.1, Sec.8 therein (pg.20, bottom). In modern notation the idea is as follows: In inertial frame $S$ parametrize straight lines as ($x_0 = ct$) $$x_i = \xi_i + \beta_i s, \;\;\; i=0,1,2,3$$ ...

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I have finally got a answer from a professor Ulf Danielsson. http://katalog.uu.se/empinfo?languageId=1&id=N94-1558_2&q=Ulf+Danielsson He say that time fluctuate around the time of the position where the gravitational wave pass. So now the question remain. Can the general relativity theory mathematically describe a gravitational wave that make the ...

3

Comments to the question (v1): In Newtonian mechanics with Newtonian gravity, a body can have orbital angular momentum wrt. a reference frame. A non-point-mass can also have spin angular momentum. Bodies can exchange angular momentum via tidal forces. In GR, it possible to assign angular momentum to certain space-time regions (such as e.g. the Kerr ...

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The black axes give the frame of the meter stick. The black vertical axis is the worldline of the left end of the stick and the parallel black line is the worldline of the right end of the stick. Your condition 1) says that the spatial distance from A to B, measured in the black frame, is shorter than the spatial distance from A to B, measured in the ...

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First of all, the universe is not infinite. There is enough reason to disprove an infinite universe model. In such a case, the universe can have a beginning. Reasons to why the universe simply cannot be infinite are as old as the time of Isaac Newton. The problem is gravity. In an infinite universe, the total gravity of the mass it contains would be infinite ...

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Alice makes the observation of her choice. Bob makes the observation of his choice. The pair of observations has an outcome with probability distribution determined by the initial joint state of the two particles. The spacetime locations of the two observations, and the states of motion of the observers (relative to each other or anything else) have ...

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No. The Uncertainty Principle has to do with the act of measuring. Basically, you cannot simultaneously measure both position and momentum to an arbitrary degree of accuracy. The more accurately you meausre one, the less accurate your measurement of the other becomes. The uncertainty in momentum , as far as I know, won't result from your not knowing when ...

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Let's suppress some dimensions to simplify: $$\Delta s^2 = -(c\Delta t)^2 + \Delta x^2$$ This quantity $$\Delta s^2$$ is preserved by changes of reference frame, just as in Galilean physics the quantity $$\Delta r^2 = \Delta x^2 + \Delta y^2$$ is preserved by rotations. Notice it is also the equation of a hyperbola. Thus, the effect of a frame shift is ...

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While I can't speak to the specific example listed, or the particular meaning of the $S$ term, there are examples of spacetimes that agree up until the singularity. First consider a spacetime that is topologically $\mathbb R^4$ with time being the radial coordinate and then for each time you get a three sphere where you then adjust the scale factor in the ...

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As ACuriousMind stated in his comment, light also follows geodesics. For a Lorentz-metric, such as the metric of spacetime in GR, $g_{ab}$, a tangent vector $X^a$ is spacelike if $g_{ab}X^aX^b>0$, timelike, if $g_{ab}X^aX^b<0$ and lightlike or null, if $g_{ab}X^aX^b=0$ (assuming $(-+++)$ signature, if opposite signature is used, then these signs are ...

0

Speed itself... is a type of "negative and/or anti length" and "negative and/or anti time" dimension and/or probable "quantum" projection of "either/or". By formula, the amount of time used to transverse a distance is reduced by speed. As speed increases, the amount of time used decreases... and/or the length is, by first observer, shortened. In order to ...

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Relativistic mass will not increase the gravitational pull, the gravitational force depends on the rest mass of an object.

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You need to accelerate and slow down the flywheel. In order for the system to be self contained, the energy has to come from within your device, The total energy of the device does not change with the accelerating flywheel since the energy has to come from something else in the device.

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A higher speed does not equal a higher mass. This is something commonly taught to beginning students of relativity as an explanation of relativistic momentum because it is easy to understand (but does lead to misconceptions). Also, momentum must be transferred to slow down the flywheel.

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Theoretically speaking, of course, if your true linear speed with respect to the true center of the universe was zero, you would be experiencing true time. Even on Earth, who's movement is what we base our time (e.i. seconds, days, years, etc) off of, we theoretically would be experiencing time dilation based on Lorentz, assuming that at a true zero ...

0

I think the fact that point in question is separated in a spacelike way for the two observers does not address the argument put forward by the paradox, as it explicitly states that the two observers are comparing their accounts in the distant future, after it would be possible for the invading fleet to arrive and affect them. Penrose states it as: "In fact ...

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Questions like this are complicated because you have to be clear what you mean by time. The simplest definition is that time is what is shown on a clock, so if I was holding some hypothetical clock that had been reset to zero at the Big Bang my clock would currently be showing 13.799 billion years i.e. the age of the universe. The question then becomes what ...

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One thing you have to note is that speed is relative, Clock A would see clock B moving from A's point of reference, and B would see A moving in B's reference, so you shouldn't be using the word "stationary" in this context. Both the clocks would see the other clock tick slower, B would see A's future only if it returns back to A, this makes it obvious to A ...

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Let me answer my question. By the definition of conformal flatness, $\nabla_a\Omega|_{i^0}=0$, where $\Omega$ is the conformal factor, and $i^0$ is the spatial infinity. So the spatial infinity is singular, and I think that is the reason people think spatial infinity is a point.

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This is true for galaxies beyond the cosmologic horizon. BTW they are not moving at that speed: their apparent speed seen from our place is such. Quite like the fact that the far galaxies we see close to the horizon seems both very young (which they aren't "in real life"), very red-shifted (while their emitted colors are indeed normal) and living very ...

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have a read through Did the Big Bang happen at a point? as this provides important background. If, as you say, you are considering only a simply connected universe, so it isn't finite due to its topology, then the assumption we make when solving Einstein's equations is that the universe is the same everywhere - the technical terms are isotropic and ...

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Let's assume that they go with the speed $v$ wrt their earthy friends. So for them (now onwards 'they' refere to spaceship crew unless otherwise mentioned) the initial distance is $l_0 \sqrt{1-v^2/c^2}$ and the planet is coming towards them at the speed of $v$ . Where $l_0$ is 8 light years. Now in their frame the planet takes 8 years to reach them. ...

0

However, if the universe is infinite and unbounded and uniformly populated, there is no empty volume for the galaxies to move into. Therefore logic dictates that the space between galaxies must be expanding. Your premise is faulty. Just because something is infinite doesn't mean it can't expand. For example, although it's intuitively obvious that the ...

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The world lines exists independent of the frame you choose. That is, Minkowski space-time is an affine space (like the euclidean space $\mathbb E^n$, not to be confused with $\mathbb R^n$) where there are no frames. Here you can "draw" world lines, and doesn't matter that there is none inertial frames yet. Then, when you select the frame you are actually ...

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Time dilation: linear or exponential or other? Other $$\Delta t' = \gamma\Delta t = \frac{\Delta t}{\sqrt{1 - \frac {v^2}{c^2}}}$$ Lorentz factor $\gamma$ as a function of speed (in natural units where $c=1$) - Image by Zayani CC BY-SA 3.0

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