# Tag Info

34

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 ...

17

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

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 ...

14

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.

12

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 E = m\, c^2\, \frac{1}{\sqrt{1-v^2/c^2}} \approx mc^2 + \frac{1}{2} m v^2 + ...

8

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 ...

7

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 ...

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 ...

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 ...

4

No, they are not the same. If we use a quantum field theory to describe gravity then we get a theory with the graviton as a gauge boson propagating in a flat spacetime. We expect this theory to be an effective theory that is useful only where spacetime is not highly curved. So gravitons are (probably) not a fundamental description of how gravity works, and ...

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. ...

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 ...

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?

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 ...

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

Suppose Andromeda is at rest relative to earth. You are on earth, holding your ruler, which just touches Andromeda. Now you instantly start traveling toward Andromeda at a high speed. Your ruler, of course, travels with you, still pointing toward Andromeda. Your journey just began an instant ago, so neither you nor your ruler has yet moved appreciably. ...

2

Yes, you're quite correct that in the example you describe Andromeda can be moving faster than the speed of light. But that's perfectly in accord with special relativity. It's just that the rule that nothing can move faster than the speed of light is true only for unaccelerated motion. Although beginners are (usually) taught special relativity using ...

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 ...

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

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 ...

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 ...

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 ...

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. ...

1

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 ...

1

Just to complement John Rennie's answer, one can always perform a Lorentz transformation to a coordinate system such as the particle is at rest for a given time. It's called instantaneous rest frame (IRF). This frame changes point to point, unless the particle's velocity is constant. In such a frame, we have $ds^2 = -c^2d\tau^2,$ where $\tau$ is the ...

1

The high speed of travel causes both time dilation and space contraction, so the numbers add up from both frames of reference. For the astronaut traveling at near lightspeed, the space between him and Andromeda is contracted; at a very high speed, Andromeda would appear to be only 25ly from the Milky Way, but since the astronaut is traveling slower than ...

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 ...

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 ...

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

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 ...

Only top voted, non community-wiki answers of a minimum length are eligible