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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 ...


2

OK, I'll give this a shot, cause . . . why not. The article you quoted covers a lot of ground - perhaps too much ground. And I'm not sure the quote of Matt Strassler is fair because he's answering a very specific question and while the source is given, it's not mentioned that it's a specific question that he's answering. but, lets jump to this part: ...


1

Let embrace your attitude here. If the atom is 'empty', all that we have is charge and mass. By Newton's third law we have that this 'empty' with charge and mass need to absorb energy and momentum too. Now we have an empty space with charge and mass that absorb momentum and energy. Furthermore, this empty are allowed to move through space, because is ...


1

I feel like it is correct to call gravity a force. As you know, there are several models for how the universe works. The Newtonian model. The relativistic model. The quantum-mechanical model. Within certain different boundaries of scale, these each work very well at predicting things that will happen. However the language or terminology of each ...


28

There are two parts to your question. First, why can we see things "46 billion light years away" if the Universe is only about 13.8 billion years old? Because the Universe is expanding. How far does a photon travel in 13.8 billion years in an expanding Universe? It depends on the rate of expansion. I'll give a simplified example to illustrate the point: ...


2

There is quite a nice description of this area in the Wikipedia article on the shape of the universe. As well as the torus possible shapes include the Poincaré dodecahedral space and the Picard horn. Googling will find you lots of stuff about the duodecahedral shape, and despite its potential for causing sniggers there is quite a bit on Picard's horn as ...


2

No, because of the large scale. Doing things like this only seems instantaneous. The speed of a push on this object is actually the speed of sound in the object.


1

Because near matter spacetime isn't expanding, and if it isn't expanding it can't be stretching the matter. The expansion of spacetime is a prediction of general relativity for the special case of a matter distribution that is homogenous and isotropic. If we feed in this condition we find that the geometry of spacetime is described by an equation called the ...


0

General relativity deals with equivalence classes of maps. If you take one map of space-time, put it through a continuously differential equation, and alter the metric accordingly, you get an equivalent map. You can't talk about one or the other being right. They're equivalent. Either they're both right or they're both wrong. To be fair, that's just a ...


3

To expand a bit on the others' answers, a couple of ways to visualize/understand the difference between intrinsic and extrinsic curvature: Intrinsic curvature, as the name suggests, only deals with stuff that lies inside a surface/space/manifold etc. (I will use the term manifold) If your lines, triangles, etc. don't work the same way as they do in ...


0

Is a black hole a 3D hole? I think so. Some people will say it isn't really a hole, but I think it is. That's because I think the "frozen star" interpretation is the one that's right. You can see a mention of that in Kevin Brown's article The Formation and Growth of Black Holes. He doesn't favour it, many people don't know about it, and others maybe hate ...


3

A black hole is a 4D object, but that's because all objects are 4D as they live in a four dimensional spacetime - three spatial dimensions and one time dimension. However what I suspect you're asking is whether there has to be an extra spatial dimension for space to bend in, making five dimensions in all. If so, then the answer is that no there is no extra ...


1

Our model for spacetime is that of a manifold, which is the mathematical term for something that looks like $\mathbb{R}^n$ in any zoomed-in patch, and where all these patches are stitched together in a sensible way. On our manifold we have $n$ coordinates -- real numbers that describe each point and vary smoothly from point to point. We also add to our ...


1

OK, let's take you questions one by one. Theoretically, the answer is yes. If you manage to observe the people on the planet from an area not in the vicinity of any significant mass, you would see the people moving much slower, clocks running slower, etc. Although the speed of light is a constant in a vacuum, the frequency of the light will be different ...


1

Over the real numbers, any non-degenerate quadratic form is determined (up to a change of basis) by its signature, which consists entirely of $1$s and $-1$s.


1

Is it possible to travel ONLY through Time and not Space? Well, in a sense, we can't help but travel through time, but in the way that I think you mean, one way to do it is to hover just above the event horizon of a black hole - preferably a super-massive one so the tidal effects wouldn't be a problem. Park a spaceship at 1/10th of 1% greater ...


3

The problem with your question is that velocity is relative so there is no absolute way to say whether something is travelling through space or not. Any observer can set up some time and space coordinate system $(t, x, y, z)$ to measure positions of spacetime points. The observer can then use these coordinates to measure changes in position with time i.e. ...


0

The reason it's thought of as expansion of space rather than just things moving farther apart through space is that the math of general relativity describes it that way, and GR has been well-supported by experiments so far. GR is all about curvature of spacetime, and curvature of anything can be determined by how we measure distances. A lot of the math in ...


0

To make the math work. Ever since Einstein determined that time is actually another dimension, Physicists have used that notion to expand the conception of the Universe to include added (by not sensible) dimensions to get their math and theories to work. Of particular note is Witten's unification of string theories which "only" required the addition of yet ...


5

Is time an illusion? No. I think it's best to think of it as something like heat. You know what heat is, especially if you put your hand on a stove: szzz aaargh! Heat is definitely not some illusion. However it is an "emergent property". Think about the kinetic theory of gases. The temperature of a hot gas is something like a measure of the average kinetic ...


0

I used to wonder how spacetime curvature could cause you to start moving when you weren't moving already. I got the idea that the path you followed could be bent by the curvature of spacetime, but what if you start out standing still? (Standing still relative to a particular massive body, that is.) If you understand all the other answers that have been ...


0

No, you don't have to re-introduce the luminiferous aether (or aether of any sort) in order to make space/time and General Relativity sensible. You do not have to postulate any sort of spatial filling or philosophical substratum in order to keep General Relativity logical and experimentally intact. It would be helpful for you to conceptualize space/time as ...


1

You are absolutely correct that three-dimensional sections of space-time do not satisfy Euclidean geometry -- they are not flat. However, they are almost flat. On room-sized scales the curvature is very small indeed. I don't know the exact context where you read that "tridimensional space sections of space time continuum (whatever its number of dimensions) ...


0

You've mostly only stumbled upon one fact with your list of paradoxes: a lot of the things presented in the movie Interstellar are not parts of a physical theory. This includes: "The bulk", whatever that's supposed to mean, and especially Arms reaching through "the bulk" (???) True back-in-time communication/time travel, "Tessaracts" (the word "tessaract" ...


5

This is a commonly considered idea, of which one variant is the "Hubble bubble". Anything that happens outside of the visible universe, is, after all, in principle unknowable to us.


2

The latest data is from the Planck satellite, and you can find the results in this 15MB PDF. The matter and dark energy densities are; $$\begin{align} \Omega_M &= 0.315 \pm 0.017 \\ \Omega\Lambda &= 0.686 \pm 0.020 \end{align}$$ So we get a total density of $\Omega = 1.001 \pm 0.026$. So within the 2.6% experimental error spacetime is flat.


-1

there is NO curvature of spacetime. To prove this claim we will first assume that there IS curvature of spacetime. From that we derive the following: spacetime must have properties. The truth of the matter is that spacetime does not have properties. Therefore, our initial assumption was invalid, i.e. opposite must be true: there is no curvature of spacetime. ...


0

Notice that one of the observers has to stop and turn back in order to compare watches and hence feel an acceleration. Thus they are not symmetrical in this sense. That's why the observer, who experiences the acceleration would be younger. As Feynman puts this fact in his famous lectures: This [twin paradox] is called a “paradox” only by the people who ...


-1

Special relativity is define has either points A or B being motionless to a third point, even if neither observer at point A or B can define that third point. Only after comparing stopwatches will the observers know which of them was at relative rest and which of them was in relative motion to the third point. Can't define absolute rest...but the classic ...


0

Is this really possible? No. Or does Hawking's mechanism protect this system from a causality violation, destroying the CTCs in it? No. Hawking's chronology protection conjecture is redundant because time travel is science fiction, because there is no forward travel through time, and no backward travel through time, because there is no motion through ...


1

Everything about special relativity is contained in the Minkowski metric. That single equation contains everything you need to know about SR. There are no end of questions in this site demonstrating how various things can be calculated from the metric. Re your comments above: note that it is an assumption that $ds^2$ is an invariant, and that the metric ...


0

Answer: by combining a black hole and a white hole Both black holes and white holes contracts the space-time but the difference is that one can only go inside a black hole whereas one can only exit a white hole So when you combine a black hole and white hole, we get a a black hole which we can enter and then we exit at a white hole at some other location ...


-1

"My question wasn't intended to challenge the standard interpretation, since I don't know nearly enough physics to do so. I'm just a curious sort. It was honestly an attempt to ascertain if there exist good theoretical reasons why it can't be curved spacetime, since that seems a logical possibility based on my laymen's knowledge, given the lack of any DM ...


3

Not quite likely, simply because of these experimental facts: a.) Distant Gravitational lensed: We observed the following picture, and it can't be by luck for galaxies to arrange themselves like that. One strong suggestion is there is something big (therefore it can't be black hole) and massive between. b.) Gravitational rotational curve: Classical ...


-9

Dark matter is not a clump of stuff traveling along with the matter. Matter moves through and displaces the mass which fills 'empty' space. The Milky Way is moving through and displacing the mass that fills 'empty' space. The Milky Way's halo is the state of displacement of the mass that fills 'empty' space. The state of displacement of the mass that ...


3

This would contradict general relativity. Because there are no static solutions of the einstein equation with localized curvature not being caused by some mass distribution.


0

The simplified answer for this is that gravity basically means that you are in elevator which is accelerating: even if you are standing on the ground. So if you take that constant gravity field is pretty much the same as a constant acceleration, then if a beam of light bends downward in an accelerating elevator, it must bend downward if it is in an constant ...


2

In the two-dimensional rubber sheet visualization, it is wrong to think that things fall towards the massive object because they are "rolling down the hill" of the curved spacetime. There is no perpendicular gravity pulling things down into the well. What happens is that you are moving along your world line at a constant velocity, "into the future at one ...


0

Yes, photons are affected by those curves. They also curve space-time due to something called a stress-energy tensor. Remember that the energy of a photon is given by $$E = hf$$, so photons do have energy. This energy lets them be affected by gravity.


1

It's more sensible to talk about spacetime curvature than spatial curvature as the latter depends on how you foliate spacetime. For example de Sitter spacetime is not flat, but it can be foliated in ways that gives you flat spatial slices and in ways that give you curved spatial slices. One way of seeing that gravity can never be described as purely spatial ...


1

Yes. Space and time are both technically a single entity. The curvature of space-time is actually pretty famous.


0

Your entity is pretty close to the conception of the modern conception of the quantum field in its ground (lowest energy) state. Space and time are not voids of "nothing", but are made of the quantum fields. What conscious beings mean when they say "things happen" in the World is that they are observing interactions between the handful of quantum fields that ...


0

First the obligatory comment that the Big Bang didn't happen at a point. Put behind you all those representations of the Big Bang as an explosion, which are so beloved of TV documentaries. Now on to your question: far more than 90% of the volume of (the known) universe is vacuous. The average density of matter is around 1 hydrogen atom per cubic metre while ...


0

If it is admissible the question and answer to 'How old is the universe ?' then we can not drop the absolute time notion. I can elaborate on other ways but one reason is enough to justify my answer.


0

How can we justify dropping the absolute time hypothesis? By simply looking at what clocks do. A clock doesn't actually "measure the flow of time". It isn't some cosmic gas meter. The passage of time is just a figure of speech. A clock clocks up some kind of regular cyclical local motion and displays a cumulative result that we call the time. Time is a ...


-2

Yes! The center of the universe is the one place where time is "correct". That is, not influenced by extraneous gravitational fields. So by 'correct' I mean where time is running faster (or no slower) than anywhere else. It is left as an exercise to the reader how this location might be found.


0

It is not just absolute time that is being thrown out the window, it is also absolute rest and absolute motion being tossed as well. But to start, it must be understood that Time is a dimension. It is 1 dimension of the 4 dimensional structure known as Space-Time. If you are moving across the dimension of time, then time passes by. If however, you were able ...


0

Regular matter and energy, through, gravity tends to slow the expansion. I do not know of any theory that treats it or any other "retarding" force as friction. However there is evidence that another stuff in the universe, different from regular matter and energy (called dark energy) is actually accelerating the expansion, rather than slowing it (also, ...


1

Gravity is the retarding force. I don't think that non-conservative forces are customarily considered.


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 ...



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