So there's general relativity and Einstein's field equations that tell us "mass(or equivalently energy) warps space-time, and the warping tells mass how to move", but I'm still having trouble understanding how space (a thing I conceive to be 'empty' or nothingness) can be 'warped'.  After researching books, on-line articles, and this stack exchange itself I can't seem to find any descriptions or discussions that don't immediately resort to jumping into GR and its mathematics to provide a more physical intuitive understanding of what it means to for space to be warped.  Is it space, this empty thing, that's getting warped. Or rather is it some field (Higgs field?) that exists around matter that's getting warped?  Although this question appears similar to  , it's asking if it's empty space that's being warped by matter or rather a field in space that's being warped (the Higgs Field?). The other question and all 10 answers addressing it do not address fields vs. empty space - What's really getting warped?
13561
I understand that people explain (in layman's terms at least) that the presence of mass "warps" space-time geometry, and this causes gravity. I have also of course heard the analogy of a blanket or trampoline bending under an object, which causes other objects to come together, but I always thought this was a hopelessly circular explanation because the blanket only bends because of "real" gravity pulling the object down and then pulling the other objects down the sloped blanket. In other words, to me, it seems that curved space wouldn't have any actual effect on objects unless there's already another force present.   So how is curved space-time itself actually capable of exerting a force (without some source of a fourth-dimensional force)?  I apologize for my ignorance in advance, and a purely mathematical explanation will probably go over my head, but if it's required I'll do my best to understand.
2038
I have looked at other questions on this site (e.g. "why does space expansion affect matter") but can't find the answer I am looking for.  So here is my question: One often hears talk of space expanding when we talk about the speed of galaxies relative to ours. Why, if space is expanding, does matter not also expand? If a circle is drawn on balloon (2d plane), and the balloon expands, then the circle also expands. If matter is an object with 3 spatial dimensions, then when those 3 dimensions expand, so should the object.  If that was the case, we wouldn't see the universe as expanding at all, because we would be expanding (spatially) with it.  I have a few potential answers for this, which raise their own problems:   Fundamental particles are 'point sized' objects. They cannot expand because they do not have spatial dimension to begin with. The problem with this is that while the particles would not expand, the space between them would, leading to a point where the 3 non-gravity forces would no longer hold matter together due to distance Fundamental particles are curled up in additional dimensions a la string theory. These dimensions are not expanding. Same problems as 1, with the added problem of being a bit unsatisfying. The answer seems to be (from Marek in the previous question) that the gravitational force is so much weaker than the other forces that large (macro) objects move apart, but small (micro) objects stay together. However, this simple explanation seems to imply that expansion of space is a 'force' that can be overcome by a greater one. That doesn't sound right to me.
91829
Layman here,  Stumbling through some physics stack posts and started reading the Wikipedia for the . In it, it states     The very earliest universe was so hot, or energetic, that initially no   matter particles existed or could exist except perhaps fleetingly, and   the forces we see around us today were believed to be merged into one   unified force. Space-time itself expanded during an inflationary epoch   due to the immensity of the energies involved. Gradually the immense   energies cooled – still to a temperature inconceivably hot compared to   any we see around us now, but sufficiently to allow forces to   gradually undergo symmetry breaking, a kind of repeated condensation   from one status quo to another, leading finally to the separation of   the strong force from the electroweak force and the first particles.   Where is the "immense energy" going to when it is "cooled"? Is there now no "immense energy"?
104460
I've heard the Higgs mechanism explained as analogous to the reason that a photon acts like it has mass in a superconducting field. However, that's not too helpful if I don't understand the latter. Why does this occur, and how?
12176
Whenever I read about the curvature of spacetime as an explanation for gravity, I see pictures of a sheet (spacetime) with various masses indenting the sheet to form &quot;gravity wells.&quot; Objects which are gravitationally attracted are said to roll down the curved sheet of spacetime into the gravity well. This is troubling to me, because, in order for objects on the locally slanted spacetime sheet to accelerate, gravity must be assumed. Therefore I ask; does the explanation of gravity as the curvature of spacetime assume gravity? If yes, what is the point of the theory? If No, what am I missing?
27873
I was reading  and these paragraphs got me wondering...     Before I list the replies, here is some background. The Higgs mechanism describes an invisible field that, it is argued, split one   force into two soon after the birth of the universe. Specifically, it   divided an ancient "electroweak" force into the electromagnetic and   weak forces we see at work today. The latter is seen in some   radioactive decay processes, and is involved in creating sunshine.      The Higgs field splits the electroweak force by giving mass to the   particles that carry the weak force (the W &amp; Z bosons) and leaving the   particle that carries the electromagnetic force (the photon) massless.   The Higgs boson is the quantum particle associated with the Higgs   field.   What I'm wondering is... can anyone hazard a guess as to the possibility at some point in the future of humans being able to manipulate the Higgs mechanism so as to give photons some kind of mass? I'm thinking they obviously couldn't go at the speed of light anymore, so could we make 'slow light'?
12800
As I'm reading about GR a lot lately, I was wondering: how do gravitons (if they exist ofc) impact the general relativity?  Since in GR, when we look at particles moving in space-time, we are only looking from geometric point of view so to say. Since gravity is represented with curvature of space-time via Einstein equations, we don't say gravity is a force that influences on bodies, gravity is just curvature affecting the bodies.  So if there is a graviton (gravitons) which would be mediators of gravity as a force within or not within the Standard Model, how would this be reconciled with the view of gravity as a curvature of space and time?  I would guess that this kinda question was asked by some scientists and answered, but I never really read anything on it. I don't even remember seeing gravitons mentioned in standard books about GR.  Are there any explanations about it?
2102
So I have learned in class that light can get red-shifted as it travels through space. As I understand it, space itself expands and stretches out the wavelength of the light. This results in the light having a lower frequency which equates to lowering its energy.  My question is, where does the energy of the light go? Energy must go somewhere!   Does the energy the light had before go into the mechanism that's expanding the space? I'm imagining that light is being stretched out when its being red-shifted. So would this mean that the energy is still there and that it is just spread out over more space?
2538
I'm looking for a rather intuitive explanation (or some references) of the difference between the metric of a curved space-time and the metric of non-inertial frames.  Consider an inertial reference frame (RF) with coordinates $\bar x^\mu$, in flat spacetime $\eta_{\mu \nu}$ (Minkowski metric).   If I have well understood, on one hand, I can go to an accelerated RF by change of coordinates $x^\mu(\bar x)$. The metric is given by: $$\tag{1}g_{\mu \nu}(x) = \frac{\partial \bar x^{\alpha}}{\partial x^{\mu}} \frac{\partial \bar x^{\beta}}{\partial x^{\nu}} \eta_{\alpha \beta}$$ On the other hand, I know that a curved space-time with metric $q_{\mu \nu}$ cannot be transformed to Minkowski $\eta_{\mu \nu}$ by coordinate transformation. In other words there does NOT exist any coordinate $x^\mu(\bar x)$ such that (in the whole coordinate patch): $$\tag{2}q_{\mu \nu}(x) = \frac{\partial \bar x^{\alpha}}{\partial x^{\mu}} \frac{\partial \bar x^{\beta}}{\partial x^{\nu}} \eta_{\alpha \beta}\qquad \leftarrow \text{(does not exists in curved space)}$$   So far, everything is more or less ok... But my question is:    What is the difference between $q_{\mu \nu}$ and $g_{\mu \nu}$? I mean, in both cases a particle would "feel" some fictitious forces (in which I include the weight force due to the equivalence principle).  What physical situation can $q_{\mu \nu}$ describe and $g_{\mu \nu}$ cannot?   I additionally know that by change of coordinates $q_{\mu \nu}$ is locally Minkowski. But still, I can't see clearly the difference.
67975
Is there a physical reason why not to think that instead of space expanding, all physical constants and parameters are shrinking (including of course the instruments we use to measure the constants) and space is static, or is it a case of Occam's razor?
59564
I get the curvature tensor in General Relativity, it is “just” math. Does space-time REALLY curves as a tangible thing, or is Einstein proposing a mathematical abstraction?  More naively, please allow, is space-time a real physical “something” like a “new ether”? If yes, does anyone have any idea what is it made off?
104117
We always hear how gravity bends space-time; why shouldn't velocity?  Consider a spaceship traveling through space at a reasonable fraction of the speed of light. If this spaceship, according to special relativity, gains mass as a factor of y as it approaches c, then its gravitational field should increase in strength as well. Hence, space-time should warp.  Note: Changes in space-time, gravity and mass should only be measureable by an outside observer with a different velocity. Those inside of the ship moving with it would not be able to measure the change in these properties.
115272
Our high-school teacher told us that the Earth pulls us with some force $F$ and we pull the Earth with the same force $F$. Within Newtonian physics this is true because of , but let’s consider . My mass is small; so I don’t warp space-time much. But Earth’s large mass warps space-time to a far greater extent.  So do I pull Earth with the same force it pulls me? If yes, how?
121981
Like something going at warp hits a planet, star, another ship, moon, satellite, alien, tribble, etc.... Basically, can stuff in subspace (warped stuff) hit stuff in real space (not warp)?  Star Trek: The Voyage Home shows us clearly that entering warp speed within Earth's atmosphere has no adverse consequences for the starship or the environment.  HMS Bounty went through miles of atmosphere, dust, birds, and clouds and nothing entered  to hit her. Enterprise did this again by dropping out of warp in Titan's atmosphere.  which explains some tech used, but now we have to ask if there is even a hazard of collision at warp. Has there ever been a collision in the franchise - any normal object being hit at warp speed? (This obviously doesn't include things traveling at warp together, like photon torpedoes from one ship to another).  Closest example I found: In  Enterprise attempts warp before balancing their warp drives and creates a wormhole instead. They nearly collide with an asteroid which was already inside the wormhole, but neither the ship not the asteroid were traveling at warp.  Compressing Space Real-world (non-canon) attempts to explain ST warp technology rely on compressing space itself in front of the vessel. The image sequence below from Star Trek: Into Darkness (canon) shows Enterprise warping past the USS Vengeance and confirms that Enterprise actually gets smaller (or compresses the space around it). The light on Vengeance shows that at the instant the two ships are side-by-side Enterprise looks like a toy beside it. (Large image needed for detail - sorry):    Thus objects at warp occupy less real space - possibly none at - because , which according to Memory-Alpha is implied to be the medium which FTL travel happens. Normally subspace and real space do not interact. When they do it is called a .  Also, objects inside the warp bubble are not moved by the warp drive:     The observer(spaceship) is still immersed in the interior of the warp bubble and this bubble is carried   out by the spacetime ”stream” at faster than light velocities with the observer at the rest with respect to   its local neighborhoods  (p. 25)   It is my belief that to be consistent with warp bubble physics derived from the Einstein Field Equations in general relativity, the ST interpretation of warp speed travel should not allow collisions between n-space objects and objects within a warp bubble and remove the phenomenon from any plotlines such that warp travel is intrinsically safe for the traveller, but possibly greatly impactful for the normal world outside.  But has it happened?  Points of clarification raised by comments  Deflector Shields: Yes, ships have them. Gene Roddenberry envisioned Navigational Shields which would deflect anything in front of the ship, from a single hydrogen atom to an asteroid (see his notes below).    It's important to note that much of what he had in this guide was changed in final production. In fact, based on this guide we could write an entire episode on a simple deflector sabotage resulting in them hitting a hydrogen atom. Real science calculations tell us that even hitting a photon of light would release incalculable energy.  These notes very much explain the many questions asking why ships don't go to warp inside a solar system. Solar systems are FULL of particles and debris, which would require a great deal of energy to deflect. Interstellar space simply draws less power because the shields work less.
115539
I am doing some research about &quot;time travelling&quot; by shrinking humans to the quantum level. It's something based on the delayed choice quantum experiment, so that we can go back to the past and travel to another parallel universe or to another universe in another timeline. So I just want to make sure if smaller mass changes the way the smaller object experiences time. But do note that I am only 16 so I do wish that it can be simple haha so that I don't end up being more confused.
116784
Physicists have estimated the universe to be flat and infinite, but I can't seem to understand what this actually means. First of all, what do they mean when they say that the universe is infinite,  do they mean that space is unbounded? Or do they mean that the space is currently bounded and is expanding forever (so the bounds are getting further apart) ? And if space is unbounded, how does it expand, how can infinity get larger?  Finally a flat universe could also be bounded if for example it has a toric shape which has zero curvature, could this be a possible shape of the universe?    What also confuses me is that, since the beginning of time, the universe had a very small size, but how did it become infinitely large in a finite amount of time?
18693
In General Relativity Theory, mass can warp spacetime. However, in my view interaction only occurs between pieces of matter. Spacetime is not matter; how can it be affected by matter?