The first time someone explained the  to me (referring to  -not spacetime) they drew a picture of a  and used the analogy of starships traveling through subspace at warp speed.   When ships are traveling at warp, are they traveling through  in the fourth dimension?
114781
Triggered by a  I was wondering what actually would happen to a ship (e.g. the Enterprise-D NCC-1701) that collides with a stationary object such as a) another ship of a similar configuration or b) a gigantic structure like a moon or even a planet.  We know the deflector is supposed to keep interstellar dust (not to be confused with ordinary dust, which is a different thing) from ripping large holes in the ship.  At first, one thinks "Obvious. ." But does it really? Would the deflector manage to actually deflect both masses? If not, where is the threshold of what a deflector can handle? Would the ship maybe tunnel right through the object, because of wibbly-wobbly space wobblification by the warp field? It does do some weird things to the space right in front and behind the vessel.  Important remark: We cannot approach this with what we know about physics at all. For all intents and purposes, both ships must measure the other ship travelling faster than light, resulting in it having infinite (or rather undefined) mass and by extension momentum. If we start with that reasoning any ship jumping to warp would suck in the entire universe (it takes a moment, but think about it). So, obviously we cannot apply our intuition (even our relativistic intuition) here.
20172
In the middle of , the crew of the Enterprise-D is flying on a rescue mission toward Bersallis III, to save a Federation outpost from an impending fire-storm.  Upon reaching Bersallis III’s system, the ship drops out of warp. During senior officers meeting Riker states that it will take another hour to reach Bersallis III, so LaForge's team will have another two hours for a rescue transportation. When Riker tells this, we can clearly see, through windows behind him, that the ship is indeed travelling on conventional engines.  Why? Wouldn't it be more efficient in terms of rescue mission, to fly in warp until reaching the planet and not to waste another hour of precious time travelling?
46734
I have been studying causality (specifically why there is no such thing as a simultaneous instant of time across all observers) recently and I keep hearing references to the Andromeda paradox. Can anyone tell me what it is and how it is resolved?  I've tried reading what  says about it, but I could really use someone's explanation.  Edit Ok, after reading the related question, now I'd like to know does this imply there is some sort of privileged reference frame, in which there exists absolute velocity and absolute time? I ask because the answer for the other question seemed to indicate that the actions seem to be at different points of simultaneity but that in fact the person not moving is getting it right. But this seems strange to me because if we accelerated our galaxy to a different speed, we would still perceive our stationary observer as being right even though they'd see something different than before the acceleration.  So who is right? In what frame can we be sure that our present is Andromeda's present?
66800
There is a problem with my logic and I cannot seem to point out where. There's a rocket ship travelling at close-to-c speed v without any acceleration (hypothetically), and there is an observer AA with a clock A on Earth, and there's another observer on the rocket BB with a clock B and these two clocks were initially in sync when the rocket was at rest with a FoR (frame of reference) attached to Earth. Now, this rocket's moving and AA tells us that B is running slower than A by a factor of$$ \gamma = 1 /(1-v^2/c^2)^{1/2} $$ $$ t_A/t_B = \gamma $$ where v is the relative 1d- velocity between the two i.e the earth and the rocket! That would mean the time elapsed on A is greater than that on B but this will happen only in the FoR of AA? So $t_B$ in this equation must be the time on B as observed by AA? Is this correct? What do the terms mean in the equations? If the symmetry holds and BB doesn't accelerate, then BB could say that $$ t_B/t_A = \gamma $$ right? where $t_B$ and $t_A$ are the times on B and A with respect to FoR of BB? But I was solving this problem and I took the earth FoR of A, but the prof took the rocket FoR of B? Like how will I know which FoR to solve the problem from? It'd greatly help if the terms in all the above equations were laid down neatly! DO we even need these FoRs?? Because in all the solved problems the prof is't specifying any and is using random ones! Please help!!!! This is the question where I messed up. The first rocket bound for Alpha Centauri leaves Earth at a velocity (3/5)c. To commemorate the ten year anniversary of the launch, the nations of Earth hold a grand celebration in which they shoot a powerful laser, shaped like a peace sign, toward the ship.  According to Earth clocks, how long after the launch (of the rocket) does the rocket crew first see the celebratory laser light?  This must be 25 years. My reasoning is: If v = 3c/5 10v + vt = ct where t is time taken by the light to reach the rocket from Earth as calculated from Earth.. and I solved that for t. and added 10 years to that because the time starts at the launch of the rocket!  According to clocks on the rocket, how long after the launch does the rocket crew first see the celebratory laser light?  This is 20 years. Here, I say: If it takes 25 years as observed by clocks on earth for the laser to reach the rocket, what should be the corresponding time as seen on a clock on the rocket? Using the formula: 25 = $\gamma$t where $\gamma$= 5/4 solved for t!  According to the rocket crew, how many years had elapsed on the rocket's clocks when the nations of Earth held the celebration? That is, based on the rocket crews' post-processing to determine when the events responsible for their observations took place, how many years have passed on the rocket's clocks when the nations of Earth hold the celebration?  For this, I did the following: 10 years on earth = T years on rocket ship where T must be lesser than 10 as observed from Earth FoR! Therefore, T= 4(10)/5 years = 8 years! But, prof says, 10 years on Earth = T years in rocket ship where T must be GREATER than 10 as observed from the rocket FoR??? Therefore, T = 10(5/4) years = 12.5 years!! What does this question actually want?
37220
The  basically boils down to: "surprise your enemy by jumping right next to him and unload all your cannons". However, Trek canon makes a bit more of a technological fuss about how it works.  Seeing that the Star Wars universe also has FTL travel, I wondered if:   the Picard Maneuver would be technically possible in SW and  if there are any references (probably by a different name) in the SW universe.
104002
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?
123837
In the TNG episode "", we are treated to the following line of dialogue...three times.       "Captain's Log, Stardate 45652.1. The Enterprise has entered an area of space known as the Typhon Expanse. We are the first Starfleet vessel to chart this unexplored region."    This strongly suggests that no Starfleet ship has ever actually been into this part of space.    Yet the very end of the episode shows that a Starfleet ship WAS in this section of space, Specifically the USS Bozeman, years ago. Proven when it emerged from a temporal loop just in front of the Enterprise.    How do we account for this inconsistency - saying that the Typhon Expanse has never been charted, and yet there clearly being a federation ship already in the Typhon Expanse?
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Hyperspace travel is a norm in Star Wars universe. Even small ships have that capability and without this capability galactic-scale economy isn't possible.  My educated estimates say that at any point of time at least billions of ships are in hyperspace across the galaxy. Now, talk about economic hubs like Coruscant during Clone Wars Era. The number of ships arriving here should be enormous. Millions in an hour? If one person small ship can have warping capability, then the number can exceed even billions in a peak hour. You can go shopping on a neighbor planet five times a day or you can live on a cheap planet even if you have a job on Coruscant (there are public transport cabs featured in Rebels TV show in case you aren't rich enough to have own ship).  Now, the famous quote:     "Traveling through hyperspace ain't like dusting crops, boy! Without precise calculations we could fly right through a star or bounce too close to a supernova, and that'd end your trip real quick, wouldn't it?"   That's fine. Calculations prevent you from hitting a star, supernova or planet which are already on map, but how does a ship avoid hitting another ship? Provided that number of ships arriving near a planet is that much high, the probability of two ships jumping to the same co-ordinate can't be zero. In fact, the probability should be very very high.  Is there a central body which controls the traffic by coordinating the hyperspace calculations of different ships? This seems unlikely because everyone seems to go anywhere they want while maintaining the destination privacy (there are countless examples). Or, is there really a traffic control body and those who travel privately actually gamble? Is there any other protocol if not traffic control body?  Has the canon ever addressed it? What about Legends?
37464
Could someone judge my (stoner) hypothesis that the speed of light has changed over time -- i.e. as the universe has expanded in volume light has slowed down, perhaps going so far as back to the big bang when it was infinitely fast and there was no time because everything happened at once etc. Thinking that the speed at which information can propagate through the universe is linked to the size of it seems intuitive to me. My question -- is there an easy disproof of this? Would Einstein have to be wrong? Does it violate anything supposedly more fundamental such as quantum or string theories? Do any current experiments invalidate it? If not can you show me in any case why you think its unlikely.   Edit 8/24  I'm accepting Mark M.'s answer but will post this here because there is a character limit on comments  @Mark M thanks, good answer but as someone who has only read some popular physics, and should leave this to the experts, I'm still muddled in my personal theory. I don't see why you should need two units to measure the speed of light. The thing I have a hard time wrapping my head around is the relation of time and distance. They seem like they could fundamentally be the same thing. If you say time is measured fundamentally by the vibration of so and so quantum object in space... why can't we just measure that vibration distance as the constant... I'll repeat myself to try to be clear... there is a certain minimum distance that particles have to go to interact with each other... if it wasn't vibrating there wouldn't be time,its what creates the illusion of time...so instead of talking about speed or c as distance/time.... can't we simply talk about that distance a quantum object vibrates....I'll lead up to my point.....perhaps there can need be only one constant here, and that is the physical size of the universe. a tiny metal tuning fork doesn't appear to be vibrating at all but if you blew it up to the size of the empire state building the metal rods would move from window to window. perhaps as our universe expanded in size the length of that minimum vibration (perhaps infinite at point zero) would have expanded, and therefore created the illusion of time and the speed of light, which, as the universe expands, will continue slowing down. perhaps we are like a big balloon and we have been blown up and all the fields/particles-without-size are vibrating more and more in that space.. am i missing something obvious here?
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In the Asimov short story "Escape!" (part of the Susan Calvin series), Powell and Donovan are set by US Robotics to test a spaceship with a hyperspatial drive.  They, at one point claim they have been on the ship for 5 days, whereas I believe Dr Calvin requests 48 hrs to speak to the Brain. I can't perfectly tell if these two times are coterminate or not, but if there are they only travelled at a fraction of c, not faster than it as might be claimed.  So do they experience relativistic time dilation? Or are they subject to other 'physics'?
902
I've seen many science popularisation documentaries and read few books (obviously not being scientist myself). I am able to process and understand basic ideas behind most of these. However for general relativity there is this one illustration, which is being used over and over (image from Wikipedia):    I always thought that general relativity gives another way how you can describe gravity. However for this illustration to work, there needs to be another force, pulling the object down (referring to a direction in the attached image). If I put two non-moving objects in the image, what force will pull them together?  So where is my understanding incorrect? Or is general relativity not about explaining gravity and just describes how heavy objects bends spacetime (in that case the analogy is being used not correctly in my opinion)?    UPDATE Thank you for the answers and comments. Namely the XKCD comics is a spot on. I understand that the analogy with bent sheet of fabric pretty bad, but it seems that it can be fixed if you don't bent the fabric, but just distort the drawn grid.   Would you be so kind and answer the second part of the question as well - whether general relativity is explaining gravitational force. To me it seems that it is not (bending of spacetime simply can not affect two non-moving objects). However most of the time it is being presented that it does.
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This was explained to me many years ago, by a physics teacher, with the following analogy:  "If someone on the beach wants to reach someone else that is in the water, they will try to travel as much as they can on the beach and as little as possible on the water, because this way they will get there faster."  I'm paraphrasing of course, but this is as accurate as I recall it. This explanation makes no sense to me. Was he telling me the light knows where it is going? It wants to get there faster? It chooses a different direction? (No need to answer these questions, this was just me trying to understand the analogy.)  My attempts to clarify the issue were without success and many years later I still don't know.    Why does light change direction when it travels through glass?
76733
I've always heard people saying, "Faster than light information transfer can't happen because it would violate causality!  Effects can precede their causes!"  However, I'm trying to think of a situation where this would happen.  I'm sure it has something to do with relativity or something like that.  I sort of understand that people going faster perceive time slower.  Can someone help illuminate this for me by showing a scenario where causality is clearly violated due to FTL information transfer?
82924
How much time would it take for a traveler (in traveler's perspective) to reach a star at distance $d$, if it accelerates at 9.8 m/s² (for a comfortable travel)?  I understand that $V = V_0 + a\times t$ and such related high-school physics, and I know there is something called Lorentz transformations that I can grab the formulae from the Internet, but I can't really put the numbers together to get what I want, so I would also like to know how to derive the answer to the question from the basic equations.  Also, it is not quite clear to me the role of the $E = mc^2$ in this travel, specifically: in travellers perspective, can it accelerates at 9.8 m/s² indefinitely, using always a constant energy output? In other words, would the ship's engine "feel" the ship heavier, or the mass increase effect would only be observable from another frame of reference?
12198
I'm a layman, but i watched some intereting videos about big bang on youtube[michio kaku, hawking this kind of things, not some crackpots :)]   I described everything on my picture:     So is there any possibility to see that inner side, for example, by creating wormhole, or entering new dimension? Or i get something wrong, on the way, and my model is totally wrong?  And another question. I heard that even if you would fly a ship across the universe you would eventually end in the place where you started, because we live in a 3d space that is defined on a surface of big sphere. But why a big sphere? Universe might be a big mobius strip, and the same principle of ending at start will apply. Is it possible?  Thanks in advance, and please don't bash me for silly questions. Im just curious, but i don't have any degree in physics. Im also not an english native speaker.
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I am following Carroll's GR book. He explain that it is convention to parameterize geodesics of photons by a parameter $\lambda$ such that  $$p^\mu ~=~ \frac{d x^{\mu}}{d \lambda}.\tag{3.62}$$  But this is the definition of 4-velocity for a massive particle in the case of $\lambda=\tau$ equal to proper time. My question then, is $$u^\mu = p^\mu$$ for all massless particles? I ask because it's well-known that proper time $\tau$ freezes for massless particles.
83695
Space is just open 3D space, right? In Star Trek, ships are always coming from somewhere else: different solar systems, galaxies, etc. However, when they meet, they always seem to be on parallel planes (facing each other).  In some episodes I recall seeing ships that were adrift (and they appeared facing a different trajectory). How can there possibly be some standardized reference plane in space? Do ships just choose to align with each other to be polite? Or perhaps when entering a solar system, the pilot, or navigation system aligns orthogonally with the local orbital axis?