40

Contrary to the other answers, I will point out that gravitational lensing due to planets in the solar system is a significant and measurable effect. The measured positions of stars, as seen from a point in the solar system near the Earth are altered by the gravitational deflection due to the fields of the Sun and then, in order of decreasing effect, Earth ...


20

So can light travel at an infinite speed, or not? No, it cannot. First, Lanza’s claim is based on a self contradiction, and literally anything can be proven from a self-contradiction. The colloquial idea of a “photon’s experience” is based on the mathematical idea of the inertial frame of the photon. Such a frame would require light to both be at rest (...


15

The deflection angle for a light ray that is just grazing the surface of a planet or star (so the maximum observable deflection) is $\displaystyle \theta = 2 \left( \frac {v_e} {c} \right)^2$ where $\theta$ is in radians, $v_e$ is the escape velocity of the planet or star and $c$ is the speed of light (see this Wikipedia article). For a planet, $\frac {v_e}{...


14

This is a common confusion thinking that there is such thing as a "real" amount of time. Time literally runs slower. The brain will think that an hour has passed, and an hour will have passed at that location. Saying "in reality 7 years passed" is incorrect. "7 years passed on Earth" would be correct.


10

There are four different curvature tensors at play here. The complete information about the curvature is encoded into the Riemann tensor $R^{\sigma}_{\;\mu \tau \nu}$, and the other three tensors are all derived from it. The Ricci tensor is a contraction $$ R_{\mu \nu} = R^{\sigma}_{\;\mu \sigma \nu} = g^{\sigma \tau} R_{\sigma \mu \tau \nu}. $$ The Ricci ...


9

If one could travel at lightspeed, one would find oneself everywhere in the universe at once. This indeed is what a photon of light must experience if it were sentient. Well, this is badly worded to the point of being completely misleading. What is true is, that special relativity describes two effects: Length contraction and time dilation. From the point ...


9

First, intrinsic curvature and extrinsic curvature are not the same. When you bend a piece of paper, e.g. into a cylinder, it gains extrinsic curvature, but geometry on the paper is not changed (angles in a triangle, circumference of a circle etc) so it does not gain intrinsic curvature. It may be possible to mathematically embed spacetime into higher ...


7

It is true: $$G_{\mu\nu} = 0$$ at, say, the space station...yet it doesn't just sit there, does it? Look at Maxwell's equation: $$ {\bf \nabla \cdot E} = \rho/\epsilon_0 $$ we could just as well say "charge tell the electric field how to diverge, and the electric field tells charge how to move" (to paraphrase J. A. Wheeler), but a zero divergence ...


7

The Big Bang theory does not in itself need to focus on the distinction between matter and radiation. And the Big Bang theory is not a statement about origins in the philosophical sense. Rather it is a statement about the nature of the evolution of the universe from very early times. It holds that that evolution is one in which an initially hot dense state ...


6

There is no link. The dimension of the Hilbert space is determined by the number of possible outcomes of experiments measuring commuting observables. Thus, for a single spin-1/2 system, where the number of outcomes is $2$, the dimension of the Hilbert space is $2$ and it is known one cannot expresse the spin angular momentum operators in terms of spatial ...


6

The only possible answer that can be given here is that those gridlines are not an accurate representation of spacetime curvature. It's unfortunate, because we would all love to have a graphical way of understanding general relativity, but it's true. Therefore, it doesn't really make sense to draw conclusions based on it. The -time part in spacetime ...


6

A flat spacetime has a zero Riemann tensor, while a Ricci flat spacetime has a zero Ricci tensor. The Ricci tensor is a contraction of the Riemann tensor, and it is possible for the Ricci tensor to be zero when the Riemann tensor is not. An obvious example of this is the Schwarzschild geometry that describes a static black hole. In this geometry the Ricci ...


6

The Big Bang started from a singularity -- which is to say not a physical singularity, which would be an oxymoron. A singularity means a point at which we have no mathematically valid description of physics. General relativity implies nothing at a singularity, except that we need a more comprehensive theory to say what happened. Going back as far as we can, ...


6

why do we see black holes as [...] Well that's the first issue. We cannot see black holes. Light cannot escape the event horizon, so talking about anything that goes on inside is hypothesis (more or less compatible with available experimental data depending on which theory) or speculation. black holes are just very dense stars which bend space-time like ...


5

The clocks are synched in the platform frame, so can't be synched in the train frame. The story in the platform frame: The light beam takes longer to get to one of the synched clocks than to the other. Therefore it hits one clock when it says 1PM and the other when it says 2PM. The story in the train frame: The light beam hits both clocks at the same time....


5

It is merely a convention. It has no particular importance or significance.


4

You are facing one of the great challenges of science: the belief in the models themselves. We choose to describe science using the language of scientific realism and, indeed you can correctly capture science in that sense. But I find it can cause confusion, especially when an author uses that sort of terminology and then reaches too far. It can be hard ...


4

Ricci flat is not necessarily "truly" flat. Minkowski space has the entire Riemann curvature tensor vanishing, ie, $R_{\mu\nu\rho\sigma}=0$. However, being just Ricci flat is a weaker condition that only requires that the Ricci tensor $R_{\mu\nu}$ vanish. For example, Calabi-Yau manifolds are Ricci flat, but they are certainly not the same as ...


4

The questions, which GR wants to answer are all connected to measurements you can do in spacetime. All you can do is measure distances, angles and time passed. If you cannot measure distance through the 4th spatial dimension, then you do not care how exactly is our spacetime embedded in this higher dimensional spacetime. All you need to know, are distances, ...


4

The effect is proportional to mass and it takes a big galaxy to see it. A big galaxy has typically a mass of $10^{11} $ solar masses so about $3\cdot10^{17} $ Earth masses. The angle of deflection is incredibly small for a planet.


3

In General Relativity, the dimension of spacetime is 4 but there is no such thing as a covariant 4-position. If there were, its covariant divergence would be not be a scalar; you have to take the covariant divergence of a contravariant vector to get a scalar.


3

I think the lines in the drawing describe the tidal deformation of a local cube, which is not the same as a geodesic.


3

If the speed of light was to be infinite, every solid, liquid and gas in the universe would instantaneously turn into super heated plasma soup.If String theory is correct, this would probably cause a tear in the fabric of space-time and could "open up" the universe, exposing it to other universes. Since light has infinite speed,the past and future ...


3

As much as the Earth looks flat it is not, however if you take a really small part of it, you can essentially say that it is flat, same is the case with space-time. On Space-Time, you can define coordinates, which at the given point are flat and follow Minkowskian geometry, but if you start moving away from them, the difference starts to show up. This is ...


3

To get an intuition for the shuttlecock model, imagine a simplified universe with one spatial and one temporal dimensions. Consider this universe is closed, so essentially it is an expanding circle. Imagine the Southern hemisphere of a globe with the South Pole at the bottom. In this illustration, the South Pole represents the Big Bang. At any point passed ...


3

It's simple: there are only two elementary actions that can happen to a photon - it is generated at one point and then it is consumed at another. Its whole life consists of just these two events, two "instants" if you will - the "travel" is really just the delay between those two occurrences with regard to everyone else. Two instants, ...


3

It underlines how the notion of ‘now’ is compromised due to time passing at differing rates in differing frames of reference I think your confusion stems mainly from this. The fact is, that logic is reversed to what you are saying. You cannot compare two clocks before you know what it means for two events to be simultaneous. To say that two clocks tick at ...


3

Really, the coordinate time between two events could be that measured by any observer, not necessarily far away. As you said, for the person who actually passes through both events, their coordinate time happens to be the proper time. For someone who passes through the first event but not the second, we can just apply the hyperbolic rotation of special ...


3

You are right. Spacetime is defined as a Manifold A manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an $n$-dimensional manifold, or $n$-manifold for short, is a topological space with the property that each point has a neighborhood that is homeomorphic to the Euclidean space of dimension $n$. More ...


3

I would like to answer with a quote by Subrahmanyan Chandrasekhar, a Nobel laureate notable for his contributions to the study of black holes: Macroscopic objects, as we see them all around us, are governed by a variety of forces, derived from a variety of approximations to a variety of physical theories. In contrast, the only elements in the construction ...


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