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16

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. ...


16

Does the discovery of a photon and development of quantum electrodynamics make Maxwellian electrodynamics redundant? Not a bit. Each physical theory has its domain of applicability. Electrodynamics successfully describes the macro phenomena of electricity and magnetism which are very much obscured when you look at them from the point of view of QED. ...


4

If the graviton is detected and its cross section and other properties and interactions are measured well find out something about quantum gravity and maybe even how to unify gravity and the other forces. As @CuriousOne says we are pretty far from discovering it, nobody is looking for it, and we don't have any way of even coming within 10 orders of magnitude ...


4

In a quantum world, all oscillations are quantized (if they are truly periodic, not just approximately periodic). For example, oscillations of a solid are quantized and the quanta are called phonons. That doesn't mean that the model of the solid as a lattice of (quantum) atoms is wrong, or even that it's an approximation with a limited domain of validity. On ...


3

Newton would not say that an individual standing on the Earth represents an inertial frame of reference. An inertial frame is one in which Newton first law applies i.e. an object moves in a straight line at constant speed. Since the observer dropping the apple observers the apple to accelerate that observer's frame is non-inertial. However you are correct, ...


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 ...


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)...


2

I can answer to the first part of your question. A metric with harmonic coefficients is for example the FLRW metric for an universe with positive curvature. In this case the metric takes the form ($c=1$): $$ds^2 = dt^2 - a^2(t) \left(dr^2 + \frac{1}{\sqrt{k}} \sin(r\sqrt{k}) d\Omega^2 \right)$$


2

According to the fuzzball proposal in string theory, black hole are actually horizonless and regular solutions. For some systems in five dimensions made with bound states of intersecting branes this has been already proved directly in supergravity: there are solutions without horizons and singularities, with the same asymptotic charges (Mass, Angular ...


2

At best things are pretty speculative. Cumrun Vafa has proposed that black holes have condensates of tachyons. In some sense you can understand this without much complexity. The Schwarzschild metric has a physical singularity that is a spatial surface. The Penrose conformal diagram for the Schwarzschild metric illustrates this The bosonic string has two ...


2

Since you mention the following in one of your comments I'm less interested in Einsteins historical struggles and would love a more modern perspective on how to get to this insight. I hereby unashamedly ignore history, and offer instead a quick plausibility argument. Let's start with the equivalence principle which, loosely speaking, says that a (...


2

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

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.


1

To add to Ocelo7's answer, the transverse part is, as I have seen it used by e.g. Ellis, used to refer to components that are orthogonal to a future-pointing and geodesic null vector field spanning the past light cones of a particular world line -- the central observer (e.g. our world line). They are defined on parts of spacetime that is observeable by the ...


1

Take the covariant derivative of the equation $X^aX_a=-1$. The RHS becomes zero so we have $$2X_a\nabla_b X^a=0\implies X^aB_{ab}=0.$$ The other equation, $X^bB_{ab}=0$, is the geodesic equation, so it doesn't hold for just any $X^a$. Let's consider the situation at some point $p\in M$. Then $X^a$ is a prime candidate for the timelike basis vector of $T_pM$....


1

Certain condensed matter systems show emergent behavior that is similar to general relativity: see this for example. Also, in fluid mechanics, sound waves can become trapped behind an "event horizon" called an acoustic black hole. Finally, the Einstein field equations are essentially the only possible classical equations of motion for a massless spin-two ...


1

General relativity is a theory of gravity; as such, it makes predictions about gravity. However, general relativity does make predictions about time and physical entities such as black holes. Some of the predictions general relativity did make: Gravitational waves exist (proved by LIGO last year) Black holes exist Light bends (proved in 1919 by an ...


1

A 2013 paper by Shtanov and Sahni (already mentioned by Ben Crowell in the comments) says that the modes grow exponentially in conformal coordinates, and Barrow et al overlooked the fact that the conformal time changes very little during and after inflation. A 2014 preprint by Tsagas, one of the authors of the original paper, cites Shtanov and Sahni and ...


1

The Einstein equations which describe general relativity do not make a difference between waves propagating forward in time and waves propagating backwards in time. Just as the Maxwell equations, which describe electromagnetism, allow both solutions for waves propagating forward in time as well as for waves propagating backwards in time. However, for an ...


1

Gravitational waves are on the same footing as electromagnetic waves - they are lightlike processes, propagating with speed of light c. For all fundamental problems concerning time, we may not forget to have a look at the corresponding proper time. The proper time of lightlike processes is zero, their spacetime interval is empty. Observers are synchronizing ...


1

I was laying awake last night thinking about this very question, there may be a way to test this by looking for a specific type of signal in something like the LIGO. This type of signal would precede the actual event that created the signal (a binary merging event 2ly away would arrive 2 years prior to the actual event occurring) and the data should be "...



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