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0

If you mean by "our universe" the matter in spacetime we are able to reach and observe then you are right. The universe will become more and more finite for us unless someone will invent a "warp drive" or "wormhole" (currently the probability for it is very low). According to research you have ca. 100bn years time before all others galaxies will be gone ...


2

Galaxies are not moving away from us, it is the space between us and the galaxies (and everything, in general) that is continually expanding. This is allowed to happen faster than the speed of light, because no object actually crosses the light speed barrier in the process. So consequentially, the universe has no size constraint like the one you've stated.


1

I'll give this a shot. I think I follow what you're asking. I'm thinking of the to-be-fissioned-away material as a mass traveling at the speed of light in some sense, In a sense that's true, but it's probobly good to keep in mind that time isn't a dimension quite like the other 3 and traveling through time isn't exactly moving, so in a sense it's ...


2

Let us take a uranium nucleus being hit by a neutron .At the rest mass system of the two bodies there is an invariant mass m described by E=m*c^2. The CM system, seen as an excited U236 in the diagram below, is not moving in three dimensions nor in any other dimensions, velocity needs a dx/dt. An induced fission reaction. A neutron is absorbed by a ...


0

E=mc2 applies equally to ordinary chemical bombs, except there is less "m" turned into "E", by around a factor of a million.


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Must every point in spacetime remain attached to its current neighbours? Basically yes, this captures the spirit of allowable deformations. Some background: If you want to measure distances between points, this is very much in the realm of mathematical analysis. However, it is sometimes useful to be able to discuss "closeness" in a looser (but still ...


2

In short, usually I see people saying that Galilean Relativity is bound to one certain structure of spacetime where space is relative and time is absolute. What really is the relation between such structure and the principle stated? Another possibility is that the implication is the other way around: absolute time implies Galilean Relativity. But I also ...


3

You need to be careful about comparing the curvature of spacetime to the deformation of a block of jelly. In particular, in general relativity time is curved as well as space, and this is impossible to represent with the jelly model. In fact it's just about impossible to give a really good description of spacetime curvature to anyone who doesn't have at ...


5

To a first approximation the spacetime curvature around the Sun is indeed spherically symmetric. I say to a first approximation because the masses of the planets (particularly Jupiter) also produce curvature and this breaks the spherical symmetry. However let's ignore this for now because I don't think it's relevant to your question. If I understand you ...


0

the quantity $ds^2 = g_{\mu,\nu} \ dx^\mu \ dx^\nu $ is a measure for distance on a manifold. It is indeed invariant under coordinate transformations, since $g_{\mu,\nu}$ transforms like $$ \tilde{g}_{\mu,\nu} = \frac{\partial x^\alpha}{\partial \tilde{x}^\mu} \frac{\partial x^\beta}{\partial \tilde{x}^\nu} \ g_{\alpha,\beta} $$ and $dx^\mu$ transforms like ...


0

Based on the comments from @ACuriousMind, the question itself is poorly formed. To calculate an interval between two events on a general manifold, one needs both a metric and a connection. Using the process of parallel transport, one moves one of the points next to the other. Then one can subtract the two points. The metric at that point is then used to ...


0

I feel that in general there is a lot of confusion around what black holes are and what they do. in reality, it only gets very different from other objects such as stars very close to or inside the event horizon; in most circumstances it is simply a heavy object. therefore objects would simply orbit around it like any other massive object, as long as the ...


3

In the comments you mention Susskind's use of a metaphor involving water flow 7 minutes into this video, but this shouldn't be understood in terms of spacetime behaving fundamentally differently around a black hole as opposed to any other gravitating body. Rather, I suspect Susskind is just referring to the analysis of a black hole in a particular type of ...


0

Similar to, but perhaps more repeatable on-demand than Quadmaster's answer: After you see the supernova, just look at a black hole somewhere "to the side" (not along the line between the supernova and you) and compensate for the distortion. A black hole, like a lens, bends light traveling near enough to be affected by its gravity (in our case, we want it ...


3

What I think this means is if you observe a supernova that's at just the right distance away while the Earth is traveling away from the event during its orbit then wait half a year for when the Earth is traveling in the opposite direction, you'll sweep another slice of space from spacetime that also contains the supernova event. This is a great way of ...


2

Yes, the source of the gravitational field in general relativity is the stress-energy tensor The $00$ component is the total energy density


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One supernova has been observed 4 times, over the course of 20 years! This didn't involve the Earth's orbit. Instead, the supernova's light took 4 different routes from its source to Earth, the routes bending due to the gravity of galaxy clusters between the supernova and Earth. Because the lengths of these paths varied by up to 20 lightyears, the light ...


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Very simply put, in order to view any event twice, both occasions in absolute real time (ignoring the time the light took to reach you, directly from the event), you would need to outrun the photons, which entails faster-than-light travel. Now, if you're willing to accept less than real time, it is absolutely possible, though it gets less and less practical ...


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You're not going to see the explosion twice, that's pretty much against the rules of SR and reference frames. However, with a lot of fortune, we can actually see the light from the remnant a second time (maybe more). Sorta There are things called light echoes, which is an analog to the common acoustic echoes that we are all familiar with. When this occurs, ...


34

You can't quite look back in time, unless you can outrun a photon. If you think about it, the event being observed is marked by a release of photons forming a sphere like shape. Once you are inside the sphere, you can observe the event. However, once you are inside, the only way to get outside is to go faster than the wave-front of photons. Unless you ...


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"Everyone is born in/at a different space/time" that's irrelevant - what's relevant is your path through space time. So it could be that you are in North America during 2011 and I am in Europe during 2011. "Can I see stars in my light cone that you can never see?" Sure, it's easy to make a trivial example. There's a supernova that lasts for only one ...


-2

The idea that space is expanding is a relation between it's size and time. Time expanding would be a relation between time and time, so it can't???


0

A light cone extends behind (and in front of) a particular point in space-time. So if you want two people to have different light cones, they need to be separated in space or in time. Unfortunately, humans are never going to be very separated in space--any event that enters your light cone will enter mine a few milliseconds later, even if I'm on the other ...


4

It's really an either/or proposition, i.e. either space is expanding or the time experienced by distant objects is dilated, depending on how you view the situation. We choose the former description because it is better. To expand (excuse the pun!) on what I mean, the measurable result of time dilation is red-shift and indeed distant cosmological objects ...


0

You ask Is there more time, longer time or is the time part not affected at all by expansion? First off, Is there more time? I don't know because I dont know exactly what time is? Do you? Did Einstein? No, I think he said he didn't in one of his books? Does anybody? Probably not. Is there longer time is an easier question because I don't think that ...


0

Your whole question relies on the fact that you can define a rest-frame for light. Assuming that the constant c appearing in special relativity is indeed the speed of light, there is no such thing as a rest frame for light. More specifically it is trivial to check that Lorentz factor tends to $\infty$ as you get closer and closer to light speed, hence the ...


1

In a non-accelerated reference frame, a point or a particle cannot be motionless wrt. light, for the reason that busukxuan mentions: All observers will measure the speed of light to the same value, c. But in an accelerated frame, such as an expanding universe, it is possible. For instance, galaxies that are farther away than about 14 billion lightyears, ...


3

from wikipedia "The speed of gravitational waves in the general theory of relativity is equal to the speed of light in vacuum, c." so the time taken to feel the effects of the star is the distance you are from the star divided by the speed of light. so you should feel it at exactly the same time as its light reaches your eyes (20 sec)


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If you allow for light to exist in this universe, then yes, because The meter is the length of that light in a vacuum travels in 1/299792458 of a sec. Measure the time it takes for one beam of light to starting at one photon to reach the other. For the redefining of distance we would need to know the particles mass.


5

The answer above is much more detailed (and better by far) than mine, but I would recommend Penrose's "Road To Reality", pages 200 onwards, specifically the statement that "The quaternionically natural" quadratic form (...) has the incorrect signature for relatively theory. Special relativity depends on a signature of say - + + + (allowing us to express ...


0

General Relativity attempts to give us a way to analyze the universe (or portions of it) as close to fully as it can. With that said, it models time as the fourth dimension and includes it in the description of the universe because time is a dimension as much as the three spatial dimensions are. Time is an independent quantity that is necessary to specify ...


20

There are some problems with using quaternions to describe spacetime. Quaternions have two important properties: (1) they form a four-dimensional vector space; (2) you can multiply quaternions together.[1] The first property is obviously very suggestive, but it's no different from the usual four-vectors that we already use in special relativity. To ...


0

spacelike, timelike and lightlike [...] What, however, is the physical intuition behind? Using "physical" terminology means (foremost, and even exclusively) to refer to distinguishable "participants" (a.k.a. "principal identifiable points", or "material points") where each is (thought as being) capable, at least in principle, of determining with whom ...


2

Spacelike separation means that there exists a reference frame where the two events occur simultaneously, but in different places. Timelike separation means that there exists a reference frame where the two events occur at the same place, but at different times. Lightlike means that, well, light could travel between those points.


2

The flaw in your setup (and you can just say "Zeno's paradox", it's ok) is that you think that the distance between two objects has to be zero for them to "make contact." "Making contact" is largely a matter of electrostatic repulsion between the two objects. At some point, they become close enough that their atoms push apart, and then they can't get any ...


1

Light will always be measured to move at c in a "local inertial frame", see this article on the equivalence principle for a discussion of what that means. If you use a non-inertial coordinate system, there is no requirement that light always moves at constant coordinate speed, so if you don't want to restrict things to inertial frames then the answer to your ...


1

No, the wavelength will grow due to gravity, look up "gravitational red shift"


1

Things are not difficult if you put yourself in the right perspective. "Curvature" is a mathematical concept. Like many mathematical concepts the word may sound like something a taxi driver in London or Jakarta may have heard, but it is really just a "formula". Likewise: "Work" may evoke ideas of money, strikes, unions, customers..., but in physics it is ...


0

I'm guessing you mean Time itself (whatever that is), which converted to a 4 dimensional space-time co-ordinate system used in General Relativity using a simple conversion involving the speed of light and the square root of -1 and, depending on convention, a positive or negative sign change. A popular science book that argues for the complete absense of ...


0

In both special and general relativity, space and time can be seen to warp under extreme conditions. 4-dimensional space-time is a concept which allows to show this in terms of curvature. Near massive objects space-time is curved more causing time to move at a different speed than it does further away from that object. This also allows the motion of objects ...


-1

In GR,we are told that matter tells spacetime how to curve and spacetime tells matter how to move in fact.So the dimension of the spacetime of the universe is four.


0

The simplest way I can describe this is: 1 dimension If you're on a main street and are talking with your friend on the phone, telling them where on that street you are. There are only 2 directions to decide from at any moment, up or down the street. 2 dimensions You're in a city, talking to your friend where to meet you. They are on a different street and ...


1

As I answered to the linked question, it is almost never the case that we write out the field equations in full then work through some procedure to solve them. I think you will struggle to find any reference that does this. Solutions are almost invariably found by exploiting symmetry or using approximations such as the weak field. Have you Googled for the ...


4

No, for several reasons. First, the idea of time "slowing down" is a little bit of a misnomer. If you were traveling at relativistic speeds, you would not perceive the passage of time any differently than you do right now. It's only when you compare your clocks to an observer in another reference frame (let's me, sitting in my living room, at rest with ...


2

Its not possible to stop time but using relativity it can be thought of to be slowed down . Nothing can be faster than the speed of light so its not possible . Even when we near it , energy tends to become infinity .


1

Things will be bigger/smaller/slower with speed as $\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$. Thus, as $v \rightarrow c$, Mass (or energy) goes to infinite, Time goes to zero. But it is only a limit, which is unreachable (at least in the special relativity), because of (1).


1

For example [...] bouncing a photon from [an object] and counting my proper time between firing the photon and receiving it. [...] $L_{[...]} = \frac{c~\tau_{Roundtrip}}{2}$ This would rather be called the "(momentary) chronometric separation" of the "object" under consideration from yourself; or, if you had found equal values of the ping duration ...


0

In both SR and GR time is generally treated as a length by multiplying it by $c$, though we often set $c = 1$ so this isn't immediately obvious. So for example the Minkowski metric is: $$ c^2d\tau^2 = c^2dt^2 - dx^2 - dy^2 - dz^2 $$ and we multiply $dt$ by $c$ to get a quantity $cdt$ that has units of length and can therefore be sensibly added to $dx$ etc. ...


8

Let's separate out some definitions: metric(1): Given a set $X$, a function $d : X \times X \to \mathbb{R}$ such that the following axioms hold for all $x,y,z \in X$: $d(x,y) \geq 0$, $d(x,y) = 0 \Leftrightarrow x = y$, $d(x,y) = d(y,x)$, and $d(x,z) \leq d(x,y) + d(y,z)$. pseudo-metric(1): Given a set $X$, a function $d : X \times X \to \mathbb{R}$ ...


3

Yeah, you've not yet adapted. That's OK. Let me take you through it. In this conventional world of classical physics we have separate notions of distance and time, with the idea that either two events happen at the same time and therefore have an objective distance between them, or two events happen at different times and therefore have an objective time ...



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