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Yes to the first question, no to the second, but there will be motion, as they are drawn together, if I understand you correctly. The two point masses (let's assume they are Earth mass, but in theory any amount of mass will do), are drawn towards each other by Newton's law of gravity, that is the force pulling them together is proportional to the product of ...


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One of the lessons of relativity is that we are free to choose any coordinates to describe the geometry of spacetime, though obviously some coordinates make more physical sense than others. In the case of a Schwarzschild black hole we choose a set of polar coordinates $(t, r, \theta, \phi)$ called the Schwarzschild coordinates. The singularity at the centre ...


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There are lots of things an EmDrive could 'push against' - some as yet unknown or ill understood field for instance (dark matter, dark energy, something else). It could also couple to the gravity field - in which case it would be pushing on space itself. The coupling to gravity would be miraculously strong though, so that's not likely. The main problem ...


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Most surely the em drive is just miving its center of mass during the small intervall they measure something. To clarify... i am guessing is an inteligent scam or honest mistake. If you reorganise the inside of a wagon you generate "thrust" for the small intervals needed to move the center of mass. The EMdrive experiment only detects temporary thrust, not ...


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No, we can't say that. The vacuum of space cannot carry momentum. "Pushing against space itself" is just a roundabout way to say "pushing against nothing at all", or in other words "violating conservation of momentum".


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The math in that article is based in Cartesian space. Note specifically figure 4, where a portion of a Cartesian plane is pinched in at one side to show the supposed warping due to gravity. Using the shown transformation, she concludes that space is compressed near a black hole rather than stretched. The diagrams after that along with the process ...


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Charged versus rotating black holes as different kinds of wormholes There are no wormholes Timaeus. And no time travel either. There is no magic. Sorry. I've heard that a maximally extended charged black hole can be a traversable wormhole to the same universe And I've heard that when you die you go to heaven. Only I know that my fable isn't ...


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It just means the Schwarzschild coordinate system is faulty at the horizon because it assigns the same coordinates $(t,r,\theta, \phi)$=$(\infty,2m,\theta,\phi)$ to multiple events that are actually distinct events. If you look at the Kruskal-Szekeres coordinate system you can pick an event on the horizon and then draw the past light cone and those are ...


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Time is defined as the change we experience. Which is things being different in two different places in time. Which is annoyingly circular. Why can't we freely move back and forth in time like spatial dimensions? Because then it wouldn't conform to our idea of time. It's perfectly plausible though, to have another kind of being who perceives one of our ...


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Perhaps it's more illuminating to look at the whole thing in a spacetime diagram. we have the earth frame with coordinates $(t,x)$, and its trajectory through spacetime is the blue line. The trajectory of the spaceship is the red one. Straight worldlines are inertial frames of reference, curved or non-straight worldlines are non-inertial frames of ...


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The axis of simultaneity, or in other words, the set of events which are simultaneous as measured in the rest frame of the ship, does indeed change suddenly when we turn back. This is because it depends on your reference frame. There isn't a single inertial frame that stays with the ship for the whole journey; you can either accept that the frame is ...


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I can't make a lot of your question, but I will try to address it point by point. I think maybe a clearer way of you thinking about looking into a telescope and observing events that perhaps happened a long time ago is thinking about the more precise physics. You are observing light that was emitted by this event a long time ago and has only reached your ...


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Is there anything else than spacetime? There's space and energy and fields and waves, but there is no actual spacetime. It isn't what space is, instead it's an abstract thing. See Ben Crowell's answer here. Objects don't move through spacetime. Objects move through space. The Earth is surrounded by space, not spacetime. Light waves move through space, ...


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Time such a pesky pest To leave it alone will be the best Cause its sure not to let you rest Until your thoughts explode in chest. What you say cannot be refuted. But speed of light alone cannot define it But you are accepting the notion of space , then of course space and motion will together be able to define time. Similarly c can be thought of as a ...


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In a certain narrow sense, I think the answer to your question is believed by most physicists to be an emphatic no. That is, if by curvature you mean the fourth rank, valence $\left(\begin{array}{c}1\\3\end{array}\right)$ tensor $\mathbf{Riemann}$ that appears (through its contracted rank 2 covariant version the Ricci tensor) in the Einstein field equations. ...


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Newtonian mechanics, with no upper limit on velocities, is perfectly consistent and has no problem talking about time.


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Why isn't time just a function of the speed of light being finite In a way it is. If the speed of light was infinite, everything would happen at once. And it doesn't. But more generally I think it's better to say time is a function of motion. The mechanism of a clock is called a movement. A clock doesn't literally measure the flow of time like it's some ...


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Time is a physical quantity which cannot be defined, just like mass and length. They happen to be the fundamentals of our knowledge regarding understanding of nature. Nobody in this world can define time. Moreover, c ,that is, the speed of light in vacuum is used to define the unit of time second. This is because speed of light in vacuum has been observed ...


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We have never seen a singularity before so we aren't sure what happens. We can't therefore even be sure they actually form, maybe he theories we use to predict their formation start to break down before they form. But if they did form we have no idea what they do the instant after they form because the theory that predicted them actually breaks when they ...


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Due to gravitational time dilation, for an observer of the planet, the frequency of electromagnetic radiation would be slower. Visible light emitted from the planet would appear as infrared or micro-waves. The amplitude of the radiation would not change. Since frequency decreases while amplitude remains constant, the radiometer would receive less ...


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Imagine a 1d space and a little vector in it that can change its location but not its length. It can't continuously change in a way that turns it around. If that vector was the momentum this says in 1d you can't continuously change you direction without your momentum being zero. A similar thing happens in relativity. A massive object has a location in 4d ...


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Yes. However it is much better to recognize events as locations in a 4d spacetime and that a clock ticks based on how distance is measured on this 4d spacetime between two events. So you being born is one event. And your first birthday is another event and you can imagine the xy plane as showing where you are and time being the z axis showing when it ...


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The mathematics of general relativity is clear and unambiguous. The trouble comes when you try and describe what is going on it non-mathematical terms, because there is no precise way to do it. Kip Thorne is attempting to talk about black holes in non-mathematical terms, and he is adopting a different perspective from (probably) most of us. That doesn't mean ...


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You are approaching the question from the wrong end. The expansion of the universe is described by a particular solution to Einstein's equation called the FLRW metric. To derive this metric we have to make some assumptions, and the key assumptions are that the universe is isotropic and homogeneous i.e. that it is the same everywhere. So the universe being ...


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Expansion of space is allowed by General Relativity. Which has made quite specific predictions that passed. So it seems valid to have solutions with an expanding space on the table (and leave it to observation to exclude them or to favor them). And there are two different situations where it comes up. A cosmological context where the expansion is the ...


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Yes. You can make a model where you have coordinates $t, x,y,z$ where for any $x,y,z$ the universe looks the same. The metric ends up looking e.g. like $$ds^2=dt^2-(a(t))^2(dx^2+dy^2+dz^2)$$ and you can move your $x,y,z$ to have any value and everything looks the same (those things do loom different for different cues of $t$). You end up with the densities ...


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You are not travelling faster than light in the sense that if you send some light to your destination it gets there before you do. It can be faster than light in the sense that if space is isotropically and homogeneously distributed with energy and such then there is an obvious global frame and distance in the global frame between two points can decrease ...


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How do we know the speed of light is constant and spacetime dilates rather than vice versa? We know that the speed of light is not constant. I'm afraid it's a popscience myth that the speed of light is constant. See Irwin Shapiro talking about it here: Some conspiracy nut was telling me that Einstein was BS and there's a giant conspiracy that he's ...


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You might be confusing some issues. In special relativity, space and time do not stretch or compress. It really comes down to measurements with clocks and rulers made by people that are moving uniformly with respect to each other. One option that is consistent with observations for SR is that there is one family whose clocks and rulers are right and ...


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Marek didn't really make a mistake, but you did. But Marek might have been unclear by jumping over some steps. So first let's clarify. The metric gives the differential squared interval $ds^2=-dt^2+dx^2$ from which you can get the differential proper time $d\tau=\sqrt{dt^2-dx^2}.$ So for the blue straight line you have $\tau$=$\int ...


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It is an analogy, as a 4 dimensional equivalent would be hard to draw, and if it was 3 dimensional, you couldn't see what's inside!


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Light cannot exist without spacetime. Every light ray has one place of emission and one place of absorption. You might agree that between both places there must be a spatial distance, otherwise there would be no light ray and no transport of momentum. Light in vacuum (v=c) is associating this spatial interval with a zero spacetime interval, because it is a ...


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String theories quantize gravity and aim to a model of a unified theory with the other three interactions which are well described by the standard model for elementary particles. In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String ...


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To complement Ernie's description of the experimental evidence (and some of the theoretical evidence) that gravity must ultimately be 'quantum' in nature there are additional theoretical arguments that gravity waves (which as Ernie said are distinctly prediced by general relativity, even though we haven't observed them yet) must correspond to some ...


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General relativity predicts gravity waves. If subatomic particles deliver the full menu of gravitational effects, they should should agree with the equivalence principle, an important corollary of gravity. Here it is in Einstein's own words: "...the law of the equality of the inertial and gravitational mass is equivalent to the assertion that the ...


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The $s$-orbital is spherically symmetric and thus its angular momentum should not generate any sort of gravitational waves. According to your theory, atoms should never be able to excite out of an s-orbital. That's experimentally wrong. If the $s$-orbital is not spherically symmetric (contrary to what experiments show), but involves a classical particle ...


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Calculus works in two senses and fails in a third one: as a mathematical theory, it is well-founded, independently of Newton and Leibniz invention. For operations with space and velocity, it also works, because these quantities are not even discrete in usual quantum mechanics, and the only argument can come if you go "atomistic"; then it must be substituted ...


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Even though calculus was invented in order to study a physics problem, it is a mathematical tool that is very general, that also describes discrete situations. But if I am not mistaken a fundamental principle of the quantum world is that things can only take on disjointed, discrete values You are confusing necessary and sufficient. It is sufficient to ...


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Remember that $ds^2$ is calculated using the Minkowski metric. As @ACuriousMind is saying, you need to understand what a metric means. A metric is basically a prescription for how distances are measured in the space. So, for example, a metric for a sphere would be useful for finding the distance between two points on Earth given their lattitudes and ...


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Assume you have a set $F\subset \mathcal M$ called a future set which is the chronological future of some set $S\subset \mathcal M$, ie., $F=I^+[S].$ Where $\mathcal M$ is your spacetime. Similarly, assume you have a past set $P=I^-[S']$ for some $S'\subset\mathcal M$. So that we are clear, $F=I^+[S]$ means that $F$ is exactly those events $f$ where there ...


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A Minkowski diagram is showing by its light cone that null geodesics are linking different points in spacetime. In your example, the space interval is 1, but the spacetime interval is 0. The null geodesic of a photon includes a point of emission and a point of absorption, each one is a different point in spacetime. The spacetime interval of two points on ...


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I have heard three theories for how space-time is shaped, flat, sphere-like, or saddle-like. Flat is the most likely, as all our measurements implies that space time has curvature close to 0. Inflation makes it so that a sphere like or saddle like spacetime evolves into a sphere like or saddle like spacetime that has a curvature very very close to zero. ...


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Is it plausible for spacetime to be shaped something like a torus? I can't give a factual answer, so I will give an opinion. People have proposed that space or spacetime has a toroidal topology. This goes back to the old asteroids game, and there's plenty of papers on the arXiv. But there's nothing actually plausible about these proposals. There's no ...


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If you measure that it takes an apple 2 days to rot, then you note that another apple (which happens to be colder) takes 3 days to rot, you could either conclude that time has slowed down, or that the rotting of an apple does not make a very reliable clock. I conclude the latter. A cold apple and a hot apple are both experiencing the same passage of ...


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OP is looking for the vacuum solutions to the Einstein field equations. Including only the cosmological constant $\Lambda$, the EFE become the Lambdavacuum field equations, $$ R_{\mu\nu}=\left(\frac12R-\Lambda\right)g_{\mu\nu}\tag{1} $$ with $R_{\mu\nu}$ the Ricci curvature tensor and $R$ the Ricci scalar. Solutions to this depend on the sign/value of ...


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Solutions to $G_{\mu\nu}=0$ are called vacuum solutions in GR, it follows mathematically that this happens if and only if the Ricci tensor vanishes, i.e. the solutions are exactly the Ricci flat Lorentzian manifolds. In most known explicit examples only some region is Ricci flat (e.g. around Schwarzschild or Kerr black holes), but some global vacuum ...


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The Einstein Field equations are $G_{\mu\nu}=8\pi GT_{\mu\nu}$. An empty universe would be one where $T_{\mu\nu}=0$ The Einstein field equations would than read $G_{\mu\nu}=R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=0$. The 00 term of this (for an FLRW metric) is $\left(\frac{\dot{a}}{a}\right)^2=\frac{8\pi G}{3}\rho-\frac{\kappa}{a^2}$. You say that you want ...


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If you're asking whether there can be more than one time dimension, that's hard to answer. It's unclear how to reformulate physics to accommodate more than one time dimension in any field, except for maybe special relativity. In special relativity, time is "just like" a space dimension, except it has a minus sign in the metric. As a result, you can easily ...


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It's quite common to use time to parameterise an equation. For example suppose you have a particle moving in a circle (or radius $r$). One way of describing its motion would be to say the trajectory describing its motion is: $$ x^2 + y^2 = r^2 \tag{1} $$ but an alternative description would be to use the pair of equations: $$\begin{align} x &= ...


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It's the same question but now we've specialized on length contraction. Right on. Why we can say what we're saying You can work this out from Lorentz transforms if you want, but Lorentz invariants let you simply write it down: a particle has an invariant 4-velocity $\gamma~[c, \vec v]$ and we can form the inner product of this with the local 4-positions ...



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