Consider the twins paradox with a slight variation:  Twins A and B are in separate space ships both capable of going at the speed of light instantly (i.e. without any acceleration). Both ships are stationary relative to each other in intergalactic space facing in opposite directions. They synchronize their clocks.  Then Twin A sees ship B zooms off to the "right" at the speed of light, and ship B travels a round trip of 8 years. Twin A sees ship B recede away from him at the speed of light (in fact, ship A just disappears).  When ship B returns, Twin B's clock will show he has been gone 8 years. But from Twin B's perspective, it's ship A that zooms off to the "left" at the speed of light, does an 8 light year round trip, and according to Twin A's clock, he has also been gone 8 years.  So they both would agree that one has been away from the other 8 years, and both have aged the same amount of time.  It would seem clocks do not actually run slower as they move closer to the speed of light. So is time dilatation just an illusion?
5507
It is said that we can verify time dilation by flying a very accurate clock on a fast jet or spaceship and prove that it registers less time than the clocks on earth. However, the clocks on earth would be moving relative to the clock on the spaceship, and since time always dilates and never goes faster regardless of the direction of relative motion,  the clocks on earth should register less time than the clock on the spaceship.  Is this true? Whenever there is a fast-moving object such as a rocket do all clocks on earth really become slow?  If the rocket with the clock landed after moving at relativistic speed, would its clock and the earth's clock again show the same time since during its travel both appeared slow to each other?  Or is all this just an illusion, ie. the clocks just appear to be slow to each other but in actually run at normal speed, and neither is behind when the rocket actually lands?
51414
Many texts about STR time dilation use as an example thought experiment with  The conclusion of this experiment is: In a frame moving relative to the clock, they will appear to be running more slowly. As I understand it, this is just a visual effect, it doesn't mean that processes in the system with clocks are affected by someone observing it from moving frame. I can't imagine any other interpretation of this, cause this would result in all sorts of paradoxes, like what if there are 3 clocks oriented: parallel, perpendicular and at 45 degree relative to direction of moving frame. If you visualise light path from moving frame perspective like it is done in wiki link above, and do analogical interpretation, this would imply that some of the 3 clocks in same frame are running slower and some are faster, depending on orientation.   According to the same wiki page this time dilations are not just visual effect and do change behavior of objects, here is a quote from 2nd paragraph:     Such time dilation has been repeatedly demonstrated, for instance by small disparities in a pair of atomic clocks after one of them is sent on a space trip, or by clocks on the Space Shuttle running slightly slower than reference clocks on Earth, or clocks on GPS and Galileo satellites running slightly faster.   So if we continue our analogy, we can take 4 pairs of atomic clocks, and send 3 of them on a space trip oriented differently, we would get different time results on them.  We can even continue this absurd, and remind "twins paradox", and conclude that the one that was perpendicular to moving frame would become older....
35295
There are two kinds of time dilation:   One because the other clock moves fast relative to me (special relativity). Another one because the other clock is in a stronger gravitational field (general relativity), or accelerating rapidly (equivalence principle).   So are these two effects are totally independent? Is it possible to derive the general relativity case from the special relativity case?
92554
Suppose two twins are put asleep.  One is put in a rocket ship and accelerated to 90 percent of the speed of light.  They are then both awakened, after which  they both train their telescope on each each other.  They both start dancing.  Will the twin in the rocket ship and the twin on the ground both see the other dancing at the appropriate rhythm; or will the twin in the rocket ship see the other twin dancing at a too fast rhythm and the twin on the ground see the other twin dancing in slow motion.
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?
91372
I just want to first say that I'm aware I am asking a question due to my own confusion and ignorance and not because of anything to do with special relativity. I hope that's alright.   What I'm confused about is whether two beams of light moving in opposite directions away from eachother, have a relative speed of $c$, or $2c$.   The thing is, we can always say it's $c$, but then when we look at the relative distance travelled for the time elapsed, the result is $2c$.   Can anyone explain what is going on?   Response to Alfred Centauri 22/08/2016   I question your reasoning for two reasons. Firstly to photons moving in opposite directions was one of Einstein's examples of the counter-intuitive implications. So what you're saying wasn't around then, and Einstein himself was misconceived. In fact you can find instances opposite direction light beam as recently as 10 years ago. Phillip Green in his popular science book uses that very example in his introduction. So the question is whether this is a formal adjustment to SR, backed by a publication and a reasonable consensus. Is it?   The second reason is to do with your reasoning. You say it is not a legitimate measurement because there is no inertial frame in which one or the other photon is at rest.  That at-rest criteria as you define the constraints, is equally applicable to two beams coming toward eachother. In fact almost every problem setup has no way to assume that one of the two frames is stationary. The way it's handled, I believe, is mathematically by the simple addition of the equal and opposite motion. This is also implicit in the Laplace transforms, I think.  The reason this can be done, I think, is because all inertial frames are assumed to be equilvant....they are part of a global reference frame.   A further matter derives from the fact the relative motion of two frames can be represented as tangential and radial components. If what you are saying is correct, then one of the two components cannot be measured in almost all cases.   I definitely want to make clear I am a novice in the theory, and you probably are not. It's possible this is all misconception, except for the historic part of my response which can easily be confirmed. Please do let me know if you can as I am trying to learn and need my mistakes corrected, especially the long running ones.
86645
OK...before everyone blasts this with references to the relativistic invariance of the physical laws, time dilation, etc let me add some context. Also, I am an amateur with an interest in physics, so I don't know the details of the physics. However, I have read enough about the cosmological principle and cosmic time to develop this "confusion" .  Based on evidence gathered to-date, it appears that the universe is both , as evidenced by observations and the . This principle, when combined with the FLRW metric, allows space-time to be divided into non-intersecting slices and therefore establish a "cosmic time."   Now, the existance of such a time in no way suggests that it is the "right" time or a true "now", hence violating relativity -- although some presentist philosophers (e.g., W.L. Craig) have tried to make this argument, but it is not generally accepted in philosophical circles.  However, this leaves me confused about an apparent disconnect between relativity and the cosmological principle:  Isotropy only holds if we are at rest relative to the cosmic microwave background radiation (universal rest frame), o/w anisotropy is present - yet each reference frame is supposed to allow equally valid observations. How can these two be reconciled when most reference frames would lead us to conclude that the universe is NOT isotropic?  It seems that only by appealing to the idea of being at rest relative to "universal rest frame" can we explain away any discrepancies from isotropy as due to "peculiar motion". However, doesn't this give this "universal rest frame" and its associated time an empirically privileged status, even though physical laws work just fine in every reference frame?   For example (pardon any abuse of astronomy): if look off in some part of space and see only quasars, and then in another part of space and see only brown dwarfs, but I measure both as apparently the same distance from me, then can I conclude that we are in motion, since otherwise we would have an empirical contradiction (kind of like finding dinosaur and human remains in the same strata)?  Any help on where I am going wrong would be helpful. Intuitively, I don't think there should be a way to establish absolute ordering between space-like separated events, but the above reasoning suggests otherwise.
58833
Can you resolve this paradox: Time and space are supposed to be treated symmetrically in SR, yet time dilates while length contracts. I've been working on this for weeks, and I can't resolve it.  The mirror experiment shows that time and space both expand for the moving observer, in contradiction to the results one derives from the LT, yet a well-known text, Eisberg's Fundamentals of Modern Physics (pp. 20-21) incorrectly concludes the usual asymmetrical results from that, by changing the definition of time dilation! He defines it as meaning that time measured in the moving frame is longer, when tau is actually well-known to be shorter. Time dilation refers to the mover's time UNITS LOOKING longer to the stationary observer because the total number of time units is FEWER, the opposite situation from the mirror experiment.
2344
The paradox in the  is that the situation appears symmetrical so each twin should think the other has aged less, which is of course impossible.  There are a thousand explanations out there for why this doesn't happen, but they all end up saying something vague like it's because one twin is accelerating or you need general relativity to understand it.  Please will someone give a simple and definitive explanation for why both twins agree on which twin is younger when they meet for the second time?
119732
is a video game created by the MIT Game Lab which allows users to experience what it would be like if the speed of light was closer to normal walking/running speeds and thus experience relativistic effects in an otherwise familiar environment.  From the site:     A Slower Speed of Light is a first-person game prototype in which players navigate a 3D space while picking up orbs that reduce the speed of light ... [allowing] the speed of light in the game to approach the player’s own maximum walking speed. Visual effects of special relativity gradually become apparent to the player [as more orbs are collected]... These effects, rendered in realtime to vertex accuracy, include the Doppler effect (red- and blue-shifting of visible light, and the shifting of infrared and ultraviolet light into the visible spectrum); the searchlight effect (increased brightness in the direction of travel); time dilation (differences in the perceived passage of time from the player and the outside world); Lorentz transformation (warping of space at near-light speeds); and the runtime effect (the ability to see objects as they were in the past, due to the travel time of light).   When I play the game and collect enough orbs for relativistic effects to really start becoming significant something happens that I didn't expect: as I accelerated towards objects they appeared to move further away from me (despite length contraction definitely being taken into effect, since I was able to get to those objects faster over a given distance than had I not collected any orbs).  Luboš Motl in  says that this is due to:     the shrinking of transverse directions if you're moving forward (or their expansion if you move backwards) which makes object look "further" (optically smaller) if you're moving forward. Because of this shrinking, you may effectively see "behind your head". You also see things how they looked like some time ago.   Based on my understanding of the Lorentz transformations the directions transverse to one's motion aren't effected ($y'=y$ and $z'=z$ if all motion is in the $x$ direction).  So, what exactly causes this effect that I see in the game and Luboš Motl explains?  Am I misunderstanding the Lorentz transformations?
97250
My question has a few parts concerning the speed of light in general relativity.  Firstly, time changes in response to gravity and speed. Therefore, as gravity effects time in an area of space, should the speed of light "change?" When I say "change" I understand that light's speed is finite but wouldn't the length of second change and then change light's speed in meters per second?  Secondly, does the speed of light actually change with gravity? Time stops at the speed of light but does that mean light cannot experience time? Can light experience slower time while travelling through warped space time?
86189
Imagine a space ship orbiting the sun at near relativistic speeds, when compared to Earth (say from the reference frame of the sun) there would be x amount of time dilation.  This would mean people on the ship could live for 100's of Earth years.  My question is what would happen if a second ship flew directly away from the Sun and back (ignoring acceleration) at the same speed the orbiting ship is travelling, would the time dilation for the ship that travels in a straight line be the same as that moving in a circle?  The reason I ask is that I was imagining a scenario where intergalactic travel is possible as time dilation means even a journey of light years only ages the crew a fraction of that time, with space stations orbiting certain star systems at similar speeds so that people that don't work on ships can live a similar length of time. I understand that time dilation is all linked to a certain reference frame but working with a reference frame of the sun what would the time dilation be for the different objects taking different paths but at the same speed relative to the sun? If the ship docked back with the space station would they both say the same amount of time had passed?
76615
I am by no means an expert in this field, however something puzzles me about the speed of light and the relativity of time and space (space-time).  Is is universally acknowledged that the speed of light (299,792,458 m/s) is the universal speed limit, and that nothing can travel faster than light? That is a measurement based on a man-made interpretation of time (hours, minutes and seconds etc. are man made...there is nothing natural dictating how long a second should be).   For instance, according to Einstein, time and space bend around the physical matter of the universe, so for example, time near or on the surface of a "super massive black hole" should be drastically slower, relative to that of earth. Lets say for example that for every second that passes on the black hole, 10 seconds pass on earth, so essentially time on the surface of the black hole is 10 times slower than the time on earth.  Given the example above, is the speed of light at the surface of the black hole still 299,792,458 m/s, or is it 299,792,458,0 m/s?
22168
How does light travel, does this not contradict the idea that going the speed of light stops time? Because if going the speed of light stops time and light goes the speed of light shouldn't it be dark?
15302
My understanding of Special and General Relativity comes from books which attempt to explain them to non-experts in these fields.   Let A and B be observers, which at some time t(0), are together at some location P fixed to the earth's surface. A and B are provided with "clocks", which at time t(0), are identical lumps of the same radioactive element-that has a very long half-life. A and A's "clock" remain fixed to the earth's surface. B and B's "clock" leave A and stay together, but eventually return to A after some interval of time T (as measured by A's "clock"). If, during this time T, B's velocity relative to A is sufficiently close to the velocity of light or B remains close to a sufficiently massive body, it seems that time can "pass more slowly" for B than for A. So that when B rejoins A, B's "clock" will contain more of the radioactive element than A's "clock"   My question is: Are there any scenarios that B together with B"s "clock" can undergo (during the time T) which will cause time to "pass more quickly" for B than for A? So that when B rejoins A, B's "clock" will contain less of the radioactive element than A's "clock". If there are no such scenarios, is there any fact or law in Relativity theory which rules them out?
31538
I understand that time is relative for all but as I understand it, time flows at a slower rate for objects that are either moving faster or objects that are near larger masses than for those that are slower or further from mass.  So, the illustrative example I always see is that if I were to leave earth and fly around at near light speed for a while or go into orbit around a black hole the time I experience would be substantially shorter than for those I left behind at home on earth and I'd come back to find that I've only aged however long I felt I was gone by my own clock but that on Earth substantially more time would have elapsed.  Following through on this model, the stars in orbit around the black hole at the center of the Milky Way are aging much much slower (relative to us), right?  So does it not follow that the center of the galaxy is some appreciable (I have no idea how to go about putting this in an equation so will avoid guessing at the difference) amount "younger" than the stuff further away from the center?   If this is not true, could someone please explain why not, and if it is true, can someone please point me to where I can calculate the age of the center of the galaxy :-)  And to be clear... what I'm asking is... if there was an atomic clock that appeared at the center of the galaxy when the center was first formed, and we brought it through a worm hole to earth today - how much time would have elapsed on that clock vs. the age we recon the galaxy currently is? (13.2 billion years)
83673
I think one catch in Twin Paradox was about the big acceleration that can turn back the traveling twin from light speed outward bound, to become light speed inward bound.  What if there is strictly no acceleration?   Peter is on a space ship, traveling 99% of light speed.  He is exactly 20 years old.   Michael is on Earth (or a planet similar to Earth, but with a radius so small that any centripetal acceleration is negligible... or consider him standing just on a piece of concrete in space with an oxygen supply) Michael is also exactly 20 years old. According to time dilation, Peter's clock in the spaceship is slower than Michael's clock. According to time dilation, Michael's clock on Earth is slower than Peter's clock.  (since motion is relative, if we consider Peter to be stationary, and Michael is traveling) Peter's spaceship is traveling towards Michael. After 30 years on Earth, Peter's spaceship went past Michael's face, so Peter and Michael are 1 cm apart, face to face and eye to eye. Now, would Peter see Michael quite older than him, and also, Michael sees Peter quite older than him?