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-4

The Universe actually has 10 dimensions, 3 of space, Sx,y,z, 3 of time, Te,ƒ,i, 3 scalar dimensions, the quantum, human and cosmological scale and the 10 whole dimension that wraps them all.


1

As said in the comments, you need to use Einstein's equations (no cosmological constant for simplicity): $$R_{\mu\nu} - \frac12 R g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$$ Your energy goes into the energy-momentum tensor $T_{\mu\nu}$; in particular, there is a formula which you can use to find the energy-momentum tensor of an electromagnetic field. The ...


0

Since spacetime is four-dimensional, stars, planets, rocks, and people are four-dimensional. In spacetime, a star is not a ball in the middle of a dimple; it is more like a rope going from the past to the future, with the planets like strings spiraling around it. A boulder that is initially at rest is a string that starts out pointing "straight into the ...


0

You can walk halfway around a block two ways - east then north, or north then east. In flat space either path takes you to the same place. This does not happen in curved space. The surface of the Earth is gently curved, but you can see it if you use a big enough block. On a globe start at the equator. Go east 1/4 of the way around the world. Turn right ...


0

This started out as a comment on Ernie's answer, but I like it enough to put it here on its own. Lots of people have heard of the "rubber sheet" analogy: you imagine (or see with your eyes; it's a common demo to build) some masses sitting on a piece of spandex. The large masses make deep indentations in the spandex, and the small masses make shallow ...


3

Imagine space-time as a flat sheet of elastic fabric. Put a grapefruit on it, and it will sag and form a depression around the grapefruit. Now try to roll a marble straight across the fabric. If it passes near the grapefruit, it will start rolling into the depression. If the marble is rolling fast enough, it will begin to circle the grapefruit before ...


1

http://www.einstein-online.info/spotlights/light_deflection Tell them about how a light ray from a distant star is deflected as it passes through curved space near the sun, making the star look as though it has moved position. The above link should give you the details of how, without curved space, the light ray is predicted to be half the angular ...


0

In classical mechanics, we often deal with three vectors and their inner products, that is: $a \cdot b = a^1b^1 + a^2b^2 + a^3b^3$ (note the superscripts above are not exponents, but indices) Really, this is a specific kind of inner product, and one which only holds true in a flat, 3-dimensional space where all inner products are positive-definite. There ...


1

In geometric algebra, higher dimensional geometry is built from a set of vectors. The geometric multiplication (Product = object x subject) used to perform this is essentially 'extrusion' that sweeps one space (object) into higher dimensions using a vector (subject). A requirement is that the subject vector have a novel (relative to the object) component. ...


1

Usually, when I encounter infinity in my classes or in my work, I define infinity relative to something--that is, it's usually something that is very, very large that, for all intensive purposes, is the usual mathematical notion of infinity. Empirically, I don't think we have ever come to witness true infinity. Of course, some theories predict infinities. ...


2

Assuming you found a way and managed to accelerate above light speed without disintegrating, and went to the edge of the universe... I'm confident you can't go faster than light, but when it comes to the edge of the universe, I'm also confident that nobody knows any answers. However people say they do and state categorically that there is no edge. For ...


0

Light speed travel is impossible, so you are asking what happens to a system when we totally ignore the system. Aside from that, the universe probably does not have an edge. The observable universe does have an edge, but you can never reach it. This is because when you move, the the edge of your observable universe moves with you.


67

Short answer: nobody knows, but the Planck length is more numerology than physics at this point Long answer: Suppose you are a theoretical physicist. Your work doesn't involve units, just math--you never use the fact that $c = 3 \times 10^8 m/s$, but you probably have $c$ pop up in a few different places. Since you never work with actual physical ...


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None of the above. Though there are many speculations about the significance of the Planck length, none is proven in any currently accepted theory. It is expected, though, that quantum gravity effects become definitely non-neglegible at the energy/distance scale set by the Planck length, so it provides a heuristic scale at which we should not expect our ...


1

I'll answer to 1 Maxwell equations are already relativistic, but - in a flat spacetime. You can write Maxwell equations for a general metric $ g_{\mu \nu} $ (The original Maxwell equations are formulated for a flat spacetime - $ g_{\mu \nu} = \eta _{\mu \nu}$ ). One way this can be done is by the following algorithm: Transform coordinates to a local ...


0

What is the exact meaning of homogeneity in cosmology? Conifold and Milad have adequately explained the distinction between homogeneous and isotropic, so I'll answer on a different tack: See the Einstein digital papers where he said 'empty' space in its physical relation is neither homogeneous nor isotropic. A gravitational field is a place where space is ...


1

Here is a short summary inspired by Barbara Ryden: Homogeneity: No preferred location Isotropic: No preferred direction And here are some examples to clarify things: Example of homogeneous but not isotropic: A forest, it looks the same no matter where you are, but trees make the vertical direction distinct. Example of Isotropic but not homogeneous: When ...


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Homogeneity in cosmology means uniformity from point to point, not only in composition or content, but in geometry as well. An empty space with a singularity is still non-homogeneous. Isotropy at every point does imply homogeneity, but we are not in a position to observe the universe from every point. Mathematically, isotropy at any two distinct points ...


1

Background The shock front -- the steepened, discontinuity in pressure, speed, density, and temperature (and magnetic fields if it's a magnetized plasma) -- is ahead of its driver, which is usually called a piston. The region between is typically called the sheath (unfortunately, I couldn't find a quick article on sheaths for neutral gases). An example of ...


0

They are not simultaneous, but in most areas we can treat the margin of error as negligible. Therefore, they are approximately simultaneous.


2

First, as has been said in the comments, this has nothing to do with General Relativity per se and can be perfectly explained within Newtonian gravity. The answer is yes, depending on what you mean by weight, since, after all, the building will pull you to the side. Weight is a force and forces are vectors; in this case, your weight will be longer and ...


1

I drew the spacetime diagrams for you. On the l.h.s. you may see two simultaneous events in the unprimed (x,t) frame. The axes of a frame going in the positive direction (the primed frame) should be drawn into the unprimed as I have done it. You can find the new space coordinates by drawing a straight line parallel to the new time axis through the event. ...


5

Everyone who has been interested in modern science has heard explanations (certainly simplifications) of general relativity, mostly that space is curved. I'm afraid that those explanations that say space is curved are misleading. See Baez: "Similarly, in general relativity gravity is not really a 'force', but just a manifestation of the curvature of ...


0

"Straight lines" in curved space are geodesics. But the geodesics that define particle paths are in the pseudo-Riemannian manifold of space-time, they are not geodesics in space! As a planets path is not closed in space-time (but some kind of spiral), massive bodies do not induce loops in the topology of the space-time. (Actually the loop is not even closed ...


20

Calling orbits loops is a dangerous line of thinking. Objects that are not under the influence of other forces follow geodesics, which are the curved space equivalent of straight lines. And, while it's tempting to say that the orbit of a planet is effectively a loop in spacetime, let me try to convince you why such a simplification should be avoided. Yes, ...


16

No. A loop has to start and end at the same point. In GR that means it has to start and end at the same spacetime point i.e. the same point in time as well as the same point in space. Such loops are called closed timelike curves, and with the exception of some obviously non-physical geometries they do not exist.


2

I was thinking how, since an object in our universe can move from one position to another, it must have passed through all the positions between those two positions. (I am thinking it moved it a straight line) This must mean that in actuality there are only so many positions between those two points doesn't it? There must be some maximum accuracy to ...


0

There are objects in the universe yet to be discovered as shown by constant new discoveries of new types of planets under conditions that were previously considered impossible. (Diamond Planet, Fire Ice Planet) I believe this works the same way with objects in motion as well. If the Big Bang theory is correct, and our current interpretation of how physics ...


1

If the light was emitted after the recombination, it can't have traveled over 13.7 billion years. The EGS-zs8-1 galaxy is located 13.1 billion light years away , which is close to the maximum for a plausible picture. More details on the wiki http://en.wikipedia.org/wiki/EGS-zs8-1 . If the light is not absorbed by an obstacle, it will probably travel to the ...


0

I have made some videos of the twin paradox from the traveller's point of view (i.e. first person) here. I'll post the channel notes here to add a bit of substance, I would appreciate feedback and corrections. The twin "paradox" (in quotes because it is NOT a real paradox!) is a valuable learning tool for Special Relativity: ...


4

A few quick clarifications: a particle cannot just annihilate. It disappears when it interacts with something else. The obvious example of this is an electron and positron annihilating to turn into two photons. Also, the total energy of a particle (this applies to electrons, positrons and photons) is given by: $$ E^2 = p^2c^2 + m^2c^4 $$ where $p$ is the ...


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First, something we need to get out of the way: Kinetic energy as $\frac{1}{2} m v^2$ is not a precise formula; it is merely a good approximation for anything that is traveling slowly compared to the speed of light. In fact, more precisely, the energy is \begin{equation} E = m\, c^2\, \frac{1}{\sqrt{1-v^2/c^2}} \approx mc^2 + \frac{1}{2} m v^2 + ...


0

The time dilation (to use the proper term - not distortion) occurs in the frame of reference of the moving object. So only the photon "feels" that time has slowed down. In our reference frame, we simply observe a photon whizzing alone at precisely c. So all our observations that depend on knowing the speed of light remain accurate. Actually, if you consider ...


1

Suppose one person is sitting in a planet A whose 1 hour equals to 6 years of another planet B where another person is sitting. And if they look at each other using a telescope, what will be each others perspective? The first guy A will see the second guy B living a "fast forward" life, while the second guy B will see the first guy A living a "slow motion" ...


-1

The feed would have to be transmitted via electromagnetic signals, so the effects would be the same as if the person in the spaceship was trying to look back at earth normally. It would seem to the spaceman that the time on earth was running slower, and similarly, the video stream would arrive more slowly than if he had just been on earth. It would be like ...


1

I think you have misunderstood the text slightly. In figure 17.7, figure (a) shows a general Newton-Cartan spacetime with random gravitational fields. The trajectories of the freely moving particle worldlines are curves, and there is no global transformation that can simultaneously make them all straight. Figure (b) shows the special case where the ...


0

In the original paradox, there are two events of note: the front of the train exits the tunnel, and the rear of the train enters the tunnel. Call these events A and B, respectively. Because these two events are spacelike separated, the two observers (tunnel-based and train-based can disagree on the order in which they occurred. According to the tunnel ...


0

We were having a conversation with a peer about stupid ways of interpreting theories. Once you understand a few things about gravity and relativity, you understand just how stupid it is. Gravity on a plane in a bidimensional space can be interpreted as the acceleration of spacetime towards an object. Like John Rennie said, spacetime is not a thing. ...


4

Spacetime is not a thing so it can't accelerate. Spacetime is a manifold equipped with a metric. However, in order to describe events in spacetime we construct coordinate systems, and coordinate systems can be accelerating. For example the Gullstrand-Painlevé coordinates describe the geometry around a black hole and they accelerate towards the black hole. ...


2

If I take a plane to the equator, and travel east until I come back to where I started, have I travelled in a curved path or a straight line?


-1

I've been looking for an answer to this question since a week ago. I found a paper which I'm not sure if it's correct or not. Mei Xiaochun proved in his paper that the metric inside a hollow sphere is not flat but almost flat. He proved that if you assume $R$ is zero inside hollow sphere you face problems satisfying boundary conditions. From what I ...


5

The Planck length isn't the smallest possible length, and the Planck time isn't the smallest possible time. As far as we know spacetime is continuous so velocities do not have to be an integral number of Planck lengths divided by an integral number of Planck times. The Planck length is the smallest length that can be measured, but the reason we can't ...


0

I think once you accept that gravity can bend space-time, it is straightforward to accept that light will just follow these curved lines. the real question to me is why can gravity bend space time ? I mean, I fully understand that when considering two mass bearing objects but it is harder to comprehend when we talk about electromagnetic waves...i think if ...


1

Short answer: Yes, spacetime is relative. Einstein's relativity mixes space and time when transforming from one set of coordinates to another, however there is no preferred frame. This is part of the criteria known as Lorentz invariance. If you are given the physical results of an experiment, there is no way to determine which particular inertial frame it ...


2

There is a property of spacetime which is independent of frame of reference. The geometrical properties of the spacetime are described by the metric tensor, $ \eta _{\alpha \beta} =diag({-1,1,1,1})$ is SR (flat spacetime) or more generally $ g_{\alpha \beta} $ (any spacetime) in GR. This tensor specifies the distance between two infinitesimally close ...


2

Using the standard model of cosmology we calculate the Hubble time to obtain an estimate of the age of the universe. Yes, 13.8 billion years. But IMHO there's an issue worth discussing, to do with something John said in another answer: "A distant observer sees falling objects slow as they approach the event horizon and asymptotically approach zero speed at ...


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Strictly speaking the FLRW metric doesn't specify that time starts at the Big Bang. It specifies only that the Big Bang is a singular point so it is impossible to analytically continue a geodesic back in time past the Big Bang. If it helps to make things clearer, exactly the same happens with an object falling into a black hole. A geodesic that crosses the ...


0

Galileo dropped the notion of absolute rest for reasons he described in a dialogue on two world systems; this also meant it wasn't possible to hold onto a notion of absolute motion (the notion was in his time seem as part of Aristotelian Philosophy; though Aristotle himself didn't hold it). Newton then described space and time through his notions of ...



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