# Tag Info

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I agree. Light can not exist in 2D spacetime as well as a $\vec{B}$ component that has to be perpendicular to $\vec{E}$. Also, the Gauss law requires $$E \propto \frac{q}{r^{D-1}}$$ where D is the number of spatial dimensions. Therefore it is absent in 2D. However, 2D or 3D spacetimes still can have the speed of light and Lorentz invariance! $$ds^2= - c^2 ... 2 The mistake in your question is in the second sentence, where you say that the relative velocity of light is 3+2 km/s. The whole point about relativity is that the velocity of light is the same relative to everyone. So if it is 3km/s relative to the train it is 3km/s relative to someone on the ground too, even though the train is traveling at 2km/s relative ... 0 Are they proportional? Yes. And is time dilation with a specific speed-mass equal to the time dilation with a stationary mass (like a planet). It's not clear what you're saying here. If so, can we say that it is mass alone, and not speed, that causes time dilation? No, increase in relativistic mass doesn't cause time dilation, they are both caused ... 0 If so, can we say that it is mass alone, and not speed, that causes time dilation? Speed, esp., the speed of light, is an apriori definition in relativity according to which some relativistic results such as time dilation or mass increase are defined. Therefore, you cannot infer the posterior mass increase prior to the anterior speed. 1 Relativists no longer use the relativistic mass convention: http://physics.stackexchange.com/a/133395/4552 But yes, if you're using that convention, then the factor in both cases is \gamma. And is time dilation with a specific speed-mass equal to the time dilation with a stationary mass (like a planet). If so, can we say that it is mass alone, and not ... 1 Reflection happens when light encounters a boundary between two media. It is a result of the light being absorbed and re-emitted, the direction being due to interference between the incident light and the outgoing. Gravity bends the space through which light travels, but it doesn't absorb and re-emit light, so it can't create reflection in the usual sense of ... 2 Light follow geodesic in spacetime geometry. If we consider a photon propagating in gravity only then the notion of refraction and reflection do not make any sense. Bending of light doesn't mean refraction. Still if you choose to call it, light going around a spacetime singularity and bending back to the observer can be called reflection. 2 I see, though, that this breaks down at the pole θ=0, because all points with θ=0 are identical. But is this a problem? Yes, it is a problem, because if you omit the poles from a sphere, then it has the topology of a cylinder, not a sphere. There is a theorem in differential geometry called the Myers theorem. This is a theorem in Riemannian geometry (not ... 2 No, homogeneity does not implies that the expansion is uniform. Homogeneous expansion could be anisotropic which would lead to different changes in length depending on orientation. A simple example to demonstrate this is the Kasner metric which is homogeneous but anisotropic. For a (3+1) spacetime this metric could be written in the following form:$$ ds^...

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One could define "Komar-like" quantities for spacetimes which admit Killing vector fields, in general. But, whether they make sense is another question. It is known that there is no well-defined notion for the mass in asymptotically de Sitter spacetime since in such spacetimes the Killing vector of time translational symmetries is spacelike at future null ...

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The universe was not transparent to light until about 380,000 years after the Big Bang, because it was a hot ionized plasma. However, hypothetically, if a photon existed shortly after the Big Bang and happened to hit nothing ever, no matter how unlikely, then it would still be traveling in space. Of course, this photon would be dramatically reshifted and ...

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According to Marco's answer and comments, I tried some numbers playing with http://www.trell.org/div/minkowski.html, and now I can answer my own question. We have two events, event $A$ in $x=x'=0$ ; $t=t'=0$ and event $B:$ $x=11$ and $t=7.5$ with $v=0.8$ ($t' = -2.1666$, $x'=8.333$) Lorentz transformation gives you the distances regarding each observer, ...

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No, the difference in time simply reflects the fact that the clocks of the two observers are out of synch with each other. A good way to understand this is to imagine that the speed of light is, say, one foot per second. Now imagine the classic set-up of a 100ft long railway carriage on a platform. All along the platform are people waiting to see the train ...

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It is called effective quantization of gravity: In general the way singularities are treated in present day physics modelling is by using quantum mechanics, which always introduces an indeterminacy due to the the probabilistic nature of quantum mechanics. The coulomb 1/r potential is only used within the quantum mechanical equations but no test charge can ...

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If your embedding of the hypersurface is given by a level-set function $F$, the normal vector to that hypersurface is given by the exterior derivative of that level-set function, ie $$n = dF$$ Any vector tangent to your surface will be obtained by a path entirely within $\Sigma$. For a path $\gamma \in \Sigma$, the tangent ...

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One of the things I like the most about this question is the other insights we can infer from the possible answers. We are taught that mass warps spacetime, and the curvature of spacetime around mass explains gravity — but the exact manner by which this happens is still unclear. Curvature is also a seemingly arbitrary term, we cannot definitively say if the ...

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Physics at this point in time has arrived to the standard model of particle physics as the basis of all observations in the quantum mechanical frame. As all classical observations emerge from the underlying quantum frame ( except this is a hypothesis for the case of effective quantization of gravity) macroscopic states also follow the rules of the underlying ...

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This question is debated at length by those who are interested in the philosophy of time. The fact that so many philosophers of time can hold so many conflicting opinions about it (some of those opinions being at odds with physical fact) suggests that it is not one that is open to an easy or testable answer. Some take the view that things (mass, energy etc)...

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That is an interesting question, and to answer it we need to deconstruct most of the notions used to ask it. First point: spacetime is a four-dimensional mathematical object which encompasses both space and time, so nothing moves through spacetime (motion is how position changes along time), and similarly nothing can be said as being persistent or not in ...

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A black hole is a four dimensional hyperspherical object tucked away from our view in thee dimensional space. So basically, from our point of view its not one but zero dimensional. Here's my best analogy: take a circle (which is a sphere in three dimensions) and draw it on a sheet of plastic. Then turn the sheet on its side and now the circle is a one ...

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Yes, all lengths are multiples of the Planck length. All lengths are also multiples of the meter and the mile and the parsec. The Planck length is just another unit length and all lengths may be expressed as some multiple of any unit length. The Planck scale is expected to be the scale at which quantum gravity is expected to become important. That does not ...

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In general relativity, we can't in general define a spacetime interval between two given events. You would also have to specify the path along which the metric was to be integrated. You can say you want a geodesic path, but in general that doesn't uniquely determine the path. Normally we would describe this relationship in terms of light cones. We would say ...

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The fourth dimension is time. It isn’t “out in space”; it’s everywhere and you are moving through it right now. Four-dimensional spacetime is curved in a four-dimensional way, but it isn’t really like a two-dimensional fabric; that’s just a popsci metaphor. So there no fabric to tilt around Uranus, but there is curved spacetime around Uranus. Except for a ...

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I suggest learning the basics of conformal field theory before diving into string theory. To illustrate where holomorphicity comes in, let's consider the free bosonic string (the simplest example of a CFT). One starts with the worldsheet embedding $\phi(z,\overline{z}): \mathbb{C}P^1 \to \mathbb{C}$ and derives the equations of motion $\partial_{\overline{z}}... 0 My understanding of the clock postulate is that observations of (not by) the two clocks reveals no difference between the clock of the NIO and the one of the CMIO. The NIOs acceleration affects how he sees other clocks. His own clock is unaffected. Clocks in the direction of his acceleration appear to him to be running faster, those in the opposite ... 2 As has been discussed already, the term infinity is ambiguous and needs clarification to give a proper answer. No, the CMB does not rule out an infinity of the spacial nature of the universe. Space can be infinite ›although‹ we see the CMB in all directions in the same strength and with the overall same features. Space itself isn't involved in the ... 0 Layman answer: Three dimensions are not enough to describe things that vary in time. Mathematically, you need a fourth dimension. You can 'measure' that fourth dimension with a clock. It is analogous to: Two dimensions are not enough to describe how things like birds move. You need a third dimension. You can 'measure' that third dimension with an altimeter.... 0 Another way to look at it--We actually only "See" in two dimensions. Each of our eyes only has the ability to process xy coordinates, not z (A one-eyed person has no depth perception). Our brain diffs the two 2d images from our eyes to give us a good guess at a z coordinate (Since it's not true 3d perception our brain can be tricked here, hence illusions! ... 0 Time runs relatively slower near a planet than in outer space. Does this mean that there is less energy near the planet? There is less energy if you consider the minus sign of the gravitational potential energy, however, its magnitude (absolute value) is much. Is there a relationship between energy and the speed of time? Yes,$E=h\nu=h/T$. If so, ... 0 Two positively charged plates are pushed closer together using a constant force F that moves the plates distance d. Energy used is: E=F*d. Then the system of two plates is accelerated to speed 0.87c at which speed the Lorentz factor, or time dilation factor, is 2. The repulsive force between the plates is now F/2, in the frame where the plates move, we can ... 0 I'm going to be pedantic here and nitpick your wording because I hear this quite often, and it seems to confuse people. Time is not THE fourth dimension. Time (in at least some models) is A dimension, which may or may not correspond to the fourth dimension in any given context. If we're talking about three spatial dimensions, then we add time as a ... 0 Pick any massive object in the world, like a football ball, or whatever you want. Now, think what was this object's history: which position$x$has it had throughout its existence? Now, you can tag each point in this object's history with the time you read on the world's clock, or better, any clock you have with you, at the moment you saw the object in some ... 0 No! There is a straightforward extension of 3D geometry to higher dimensions, where all the normal Euclidean axioms apply. This is the world where we draw tesseracts and spinning toruses as shown in other answers. This is what you are most likely referring to when you say "the mathematical 4th dimension". In this Euclidean 4-dimensional space, all of the ... 0 The analogy of a sheet bending with a ball on it is just popsci physics. In mainstream physics, spacetime is the collection of events that happen at certain places at certain times, but spacetime itself does not have a fabric that would stretch like a sheet (at least not like in that example with the ball). In GR we use the expression, spacetime curvature, ... 0 If you look closely, it seems to be a very good fit. You didn't look closely, though – you only calculated one parameter from your model. If you calculate more, you'll find that the rest of them don't fit. if one assumes the radius of the hypersphere is 13,820 Million Light-Years [...] one gets 70.75 km/s/Mpc That value is just 1/(13820 million years) ... 1 More generally, if the wave equation$\Box y=0$is satisfied for a scalar field $$\mathbb{R}^{n+1}~\ni~ (\vec{x},t)\quad \stackrel{y}{\mapsto} \quad y(\vec{x},t) ~\in~ \mathbb{R},$$ with spacetime$\mathbb{R}^{n+1}$as domain, and with a 1-dimensional target space$\mathbb{R}$, we speak of the wave equation in$n+1$-dimensional spacetime, or equivalently, ... 0 The 1D wave equation is called like that because it has only one independent space variable,$x$. That's it. The 2D equation has two variables, etc. You are correct that an oscillating rope sweeps out a 2-dimensional plane; in fact, by moving one end in a circle instead of up and down, you can make it occupy a 3D region. But the equation doesn't care about ... 0 Looking at the answers, it's exactly what I experience when I ask questions about general relativity: or too abstract, or too simple. There seems to be no way inbetween :-( 2 IMHO, it depends on the context. Minkowski's geometry of space-time is not Euclidean. So while spacetime is a type of mathematical 4 dimension geometry, not all mathematical 4 dimension geometries have time as the 4th dimension. In fact, math (and engineering and finance) has no issues dealing with n-space, where n is as big as needed. Here is a ... 11 Essentially, the dimension of a space is the number of numbers you need to specify a point in it. The Earth's surface is two-dimensional, because you need to specify longitude and latitude. The set of possible electromagnetic field values is six-dimensional, because you need to specify$E_x$,$E_y$,$E_z$,$B_x$,$B_y$, and$B_z$. The set of possible$...

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Yes, time can be treated as a fourth axis- that idea was developed by a German mathematician called Hermann Minkowski not long after Einstein published his theory of special relativity (Minkowski was Einstein's supervisor for a time). Representing time as a fourth axis- along with the usual three spatial axes- is now standard in text books and scientific ...

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So the direct answer is a great NO, because spacetime is something physical which has a deep mathematical meaning. I) Intuitive Idea Intuitively and roughly speaking, spacetime is the "place" of all events, or the set of all events. An event is something that "happens in a time $\tau$ and takes place somewhere". You can grasp the main concept with a simple ...

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We observe phenomena consistent with mass distorting spacetime, and therefore we assume it does. Empirical observation is the ultimate master of all physics. Some of the evidence: https://en.wikipedia.org/wiki/Tests_of_general_relativity The "How does the mass of an object affect space and time", part of your question could mean one of two things. I will ...

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Spacetime has 4 dimensions: 3 spatial and 1 temporal. The temporal (time) dimension is treated slightly different from the spatial dimensions. A 4th spatial dimension is something else, which can easily be modeled mathematically but has not been proven to be relevant in describing the reality we live in.

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Yes, it (time not spacetime) is a mathematical dimension. To describe an event, you need three numbers to define its position, and a fourth number to describe the time at which it occurs. The time dimension works a bit differently than the spatial one when we have to talk about "distances" between events, though. We're used to describing the between two ...

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You're phrasing this in terms of physical travel, but that won't actually work. For example, if you travel 1 billion light years relative to the Milky Way galaxy, which is essentially at rest relative to the Hubble flow, then the universe will have aged at least 1 billion years. Cosmological conditions will have changed by then, e.g., the cosmic microwave ...

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I'll assume that you do a good job of using various clues (the time you see the light, your location when you see it, the direction of the light, and some estimate of the distance to the star) and correctly work out more or less where each explosion took place in spacetime. In this case, no matter where you are, no matter your speed, and no matter anything ...

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“Characteristic radius” is a vague term. For a sphere, it is obviously the radius. For an arbitrary shape with volume $V$, you could take it to be the $R$ satisfying $V=\frac{4}{3}\pi R^3$.

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interesting name, why did you choose it? Anyways, time is shown to be absolute. Time moves at the same speed, that's it. Makes sense right? Since you can't stop time/slow down time and you can't speed up time it makes sense that time always moves at the same speed. Now you go fast, really fast, say at the same speed as time ( or light) as you said. Now ...

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it is different but extremely insignificant.

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