Here I state and try to answer three variations of the twin paradox 1) &quot;Classical&quot; problem, no acceleration, no turn around Consider the case where there's a stationary planet, and a moving spaceship moving at close to the speed of light, starting at the left going right at constant velocity. Now imagine at some instant, two beings spawn on earth and in the spaceship. They are both aged 0 at that point. Now as the spaceship continues, both frames remain inertial. Which twin is older at any given point? According to one of the answers here (the 4th answer down to be exact): , there is no solution to this paradox. Either A or B will be older depending on who you ask (person A or B or anyone else).  Is this problem reasonable and is the &quot;solution&quot; correct?  2) Normal problem, no acceleration, yes turn around Everyone knows this one; the paradox is resolved because the person traveling changes direction. . Been there, done that. 3) Weird problem, no acceleration, no turn around, curved universe? Now I was thinking, &quot;what if I combine the two?&quot;. Imagine the earth is like an asteroids game, or it's a sphere/torus. Going in a certain direction for long enough means that I eventually end up where I started. Consider the case I stated in (1), where two beings aged 0 appear on the earth and on the spaceship. The spaceship proceeds to go at a constant velocity to the right, never changing direction, never under any gravitational field, but due to the nature of the universe they are in, the spaceship twin ends up reaching the earth again. Now at this point, who is older? The solution for (2) won't work because there's no turning point, right? In the link I provided:  You do this by just putting a sheet above the one you started with (or to the side, if moving in that direction). Nothing wrong with that, and no edges to worry about crossing. The trick is though, when the traveler gets to this new point, you yell &quot;surprise&quot; and identify the new point with the point in the original sheet using the symmetry of the torus. So the poor sap thinks they're getting away from their twin, only for you to change the nice new spot they picked out for themselves to the place they started from. It's a mathematical sleight-of-hand, but it is the easiest way to see exactly who is younger in the Twin Paradox on the torus.  And my question that I don't feel like the other question sufficiently addresses:  A specification question: I don't quite see how this particular &quot;mathematical sleight of hand&quot; makes it so that the moving twin is aging less. Sorry if I'm being slow, but could anyone explain that part more thoroughly? I still don't see how even in an inertial constant-velocity frames one twin is aging slower.  Feel free to tell me that this problem is nonsensical and stupid--I'm a complete noob so there is a high chance that I have no idea what I'm talking about (please tell me if that's the case)
123195
I'm reading about the twin paradox in special relativity - if there are two identical twins, one of whom who sets off in a high speed rocket to a planet, and then heads back, will find the twin who remained on Earth to have aged comparatively more due to time dilation. However, from the perspective of the travelling twin, it was the Earth that was moving and so the Earth twin should be the younger one. The 'paradox' can be resolved by realising that the travelling twin does not remain in an inertial frame for all time, since he has to turn around at the planet and hence accelerate.   Now, there are three possible curvatures the universe could have - positive, negative, or flat. As far as I'm aware, we're quite sure it's flat. However, if it was positive, does this mean that the travelling twin, if he travelled long enough, would loop back to Earth eventually? And therefore he would be able to return to Earth without having changed inertial reference frame, and then we would actually have a paradox?  I'm thinking perhaps that travelling through curved space itself constitutes acceleration, since in a way you're changing direction? In which case the travelling twin wouldn't remain in an inertial reference frame and we could solve the 'paradox' as before?
7159
There is a relativistic paradox I was introduced by a friend in Ithaca (Courtenay Footman). It involves a vehicle travelling over a ravine relativistically, so it's in the general family of ladder paradoxes. There are many ways to phrase it, but here's a simple one.   A three-car train with each car of length $L$ is travelling over a bridge across a ravine. (Assume that the couplings between cars are stiff: this train does not bend.) Unfortunately, some evil genius has precisely removed a length $6L$ of the track. The train however is relativistic, travelling at a speed such that $\gamma \approx 12$.  In the reference frame of the ground, the train should appear to be 1/24th the size of the gap, which suggests that it will fall a little and should crash into the bridge opposite. But in the reference frame of the train, each car of the train is at least twice as long as the gap and aside from the very front wheel and the very back wheel, which need to be supported by rigidity, everything is constantly well-supported. This suggests that the train makes it. Who is right?  I vaguely remember that as an undergraduate knowing only a little relativity, I trusted the train's perspective because it's at rest in that perspective, and Courtenay said that this was ultimately correct after a lot of details got resolved. But I do not remember all of these details such that I could work it out for myself. So I'm looking for some discussion that's a little more well-sourced or authoritative.  What is this paradox called, and what literature has addressed the issue?
25466
I sent this problem to Presh Talwalkar who suggested me to send it to this site. I tried many things but was not able to find the correct solution.   I made various segments trying to get an equilateral triangle similar to the Russian triangle problem, but no success.  I also tried to flip the triangle UFO over side NO but again no success.   I tried to find like triangles, but not enough.  Could you please give me a hint?   Thanks, R. de Souza
104656
So, according to Einstein's theory of general relativity, gravity is not a force instead it is a consequence of objects with mass deforming spacetime, right? And so, according to him, there is no difference between standing on a platform accelerating upwards at 9.81 m/s^2 and standing on Earth, right? But, there is a difference. At least, I think it's a valid difference. If you drop two apples from a high altitude on Earth, not only will they accelerate downwards at 9.81m/s^2 but they will also slightly move towards each other because the Earth is a sphere and gravity acts radially inwards pulling the two apples closer to each other. But if you drop the apples from the same height above the accelerating platform, the apples will only appear to accelerate downwards at 9.81 m/s^2 but will not move towards each other like they would on Earth. Why is this true? Is this even a valid difference? If it isn't, why isn't it?
94004
Image Source and Extract:   The simplest version of the problem involves a garage, with a front and back door which are open, and a ladder which, when at rest with respect to the garage, is too long to fit inside. We now move the ladder at a high horizontal velocity through the stationary garage. Because of its high velocity, the ladder undergoes the relativistic effect of length contraction, and becomes significantly shorter. As a result, as the ladder passes through the garage, it is, for a time, completely contained inside it. We could, if we liked, simultaneously close both doors for a brief time, to demonstrate that the ladder fits. So far, this is consistent. The apparent paradox comes when we consider the symmetry of the situation. As an observer moving with the ladder is travelling at constant velocity in the inertial reference frame of the garage, this observer also occupies an inertial frame, where, by the principle of relativity, the same laws of physics apply. From this perspective, it is the ladder which is now stationary, and the garage which is moving with high velocity. It is therefore the garage which is length contracted, and we now conclude that it is far too small to have ever fully contained the ladder as it passed through: the ladder does not fit, and we can't close both doors on either side of the ladder without hitting it. This apparent contradiction is the paradox.   I just read about the ladder/barn paradox and was wondering about the following variation: The barn is equipped with some electronics to measure whether the ladder is completely contained, and will switch on a light (on the barn's roof) if the ladder is inside. Now would an observer on the ladder, looking back at the barn after he's gone through, see the light turn on? I assume he should be able to see the light, which moves quicker than the ladder, if it was turned on. From what I've read in posts here, and on , I would guess that the barn electronics will find the ladder small enough and switch on the light. So the observer on the ladder will be surprised by this, which contradicts his own experience. Is that simply the kind of surprises the observer has to live with (when using such transport :-) or is there some fault in my reasoning?
91613
I'm not familiar with any complicated physics equation, however I do understand some basics. Suppose there is two objects, both of them are moving away from each other in a 3-dimensional space, which they both have the speed of half the speed of light ($c/2$). Relative to the reference frame of object A, object B would be moving away from itself equal to the speed of light.     A          B &lt;-----      -----&gt;   -c/2       c/2   to a 3rd observer    0          c    to A   -c          0    to B   This seems to break the law of "nothing can move faster than the speed of light". I believe that there is some other explanation for this case. I have done some research, and there are quite a few questions on this topic. Take  and  for example. However, they are about adding velocities together, which isn't quite the same as in the case I was describing.   is also similar to my case, however the two objects described are both moving toward the same direction, and I'm not shooting any beam or laser toward the other object.  Most probably in reality there are some extremely complex laws and equations which makes this question more complicated. However, the two objects are not interacting with each other and I'm not trying to "detect" the speed of the other object in the reference frame of A or B. Also none of the objects are moving at a significant fraction of the speed of light relative to the third observer, so special relativity doesn't apply(?) I just could not think of any reason why wouldn't B be moving away from A in the speed faster than light.  A simple explanation would be great.
117580
My questions concerns that classic train paradox, wherein there is a train and a tunnel of equal length, and the train is traveling and some fraction of the speed of light towards the tunnel.  According to the Special Theory of Relativity, an observer outside the tunnel will see the train length contracted (Lorentz Contraction), whereas an observer inside will see the tunnel contracted.   Additionally, suppose that there were doors at the ends of the tunnel and that the observer outside the tunnel closed both doors instantaneously when he/she saw that the train was completely inside the tunnel.  The classic resolution of this paradox invokes the non-simultaneity of events, explaining that the observer in the train sees the far door close first, and then, once the train has begun to exit the tunnel, looks back to see the door at the beginning close. Thus, both observers agree that the train does not touch the door when they are closed for an instant.  Now my questions.  Why is it that the observer on the train sees the far door close first? It seems to me that the information coming from the far door would reach the observer on the train only after the information from the other door is reach.   Under this interpretation, the observer on the train would observe the train getting hit by the doors. What if, by some means, this event can be explained in terms of a stationary observer too? Everyone always concludes that the train remains untouched by the doors, but really the only condition that needs to be met is that both observers must agree. Why can't they both agree that the train was hit?  So, to summarize.   Why is the door that is farther away from the train observed to close first? Why can't the other possible conclusion (both see a hit train) be observed?
82411
I'm talking about this nonsense:   Now, I'm aware that there are problems with the practicalities (or possibilities) of methods involving exotic matter with negative mass, and that kind of thing has been addressed here:   But in this case my question is different and more specific. Sweeping all the other problems of constructing such a beast under the rug, wouldn't this violate causality?  SR says that the simultaneity and relative ordering of events is dependent on the relative motion of the observer, but that no matter how it works out, if event A causes event B, no observer will see B first. One of the many problems with FTL travel (or signals) is that if any information is sent faster than light, there will exist an inertial frame in which the signal arrives before it is sent, a blatant violation of causality. (I think we can all agree, can we not, that the threshold should be extremely high before breaking assumptions that we're in a causal universe?)  So how is any scheme to travel faster than light, even if it may locally satisfy the equations of GR, not a blatant violation causality according to SR?  Is my understanding of GR incomplete and there's something in it that obviates the causality implications of SR? Or am I correct that FTL claims should be dismissed with extreme prejudice on this basis alone? (Pending a serious replicable experiment showing causality to be breakable.)
90871
I've recently been contemplating things like artificial gravity in a rotating space ship (for example, the ) and learning about the Coralis effect and other interesting fictitious forces that appear in rotating reference frames.  It occurred to me that, if you were living on a space station spun for artificial gravity, it might be possible to become weightless in such an environment by travelling fast enough against the spin of the ship. My friend, who I was discussing this with, thinks otherwise, that you would actually be under more g's as you tried to gain the speed to lift off from the inner edge of the ship.  In terms of concrete numbers, say the ship is 4 kilometers in radius (as an O'Neill Cylinder would). At this size, the rate of rotation to generate 1g in centrifugal force (the artificial gravity) is under 0.5 rpm. If a vehicle travels on the inside of the cylinder against the spin fast enough, eventually the vehicle would cease moving when looked at from a static reference frame. I would think at this point, the vehicle could simply push off from the edge of the cylinder and float towards the center of the station. Is this correct?  Furthermore, would this method of "getting into air", as it were, be easier than it would be to counteract real gravity on Earth (with things like planes that generate lift with their wings)?
62934
So I've been doing a lot of reading about the twin paradox and have encountered several different explanations that strive to resolve it. First off let me start by saying general relativity is not an adequate explanation and in fact has nothing to do with resolving the paradox. (That much has been made clear to me from what I have read, as it has been pointed out that believing general resolves the paradox is a common misconception) To drive that point home let me propose a slight variation on the twin paradox that removes acceleration all together.   Some ancient race of aliens long ago set up an experiment for us without our knowledge to help us understand space time. The experiment contains two space craft with clocks on board separated by a very large distance. The first clock, clock A, was accelerated to .866 speed of light millions of years ago (Thus time runs at half speed) and is set on a trajectory to fly past earth. As it flies past earth it resets its clock to 0 and continues on its way. (The aliens also left behind a clock on Earth, clock C, that starts ticking the moment Clock A passes earth and resets itself to 0) The other clock, clock B, was also accelerated to .866 the speed of light long ago and is on the same trajectory as clock A but in the opposite direction so that it heads towards Earth. The two ships and their respective clocks pass each other at a distance of four light years away from earth at which point clock A transfers its time reading to Clock B. Clock B flies past earth and relays its time measurement so as to be compared to Clock C. The time reads half the time elapsed by Clock C, but how could this be possible if time dilation is always symmetrical?
64866
I am implementing steering algorithms with group management for spaceships (fighters). I select a leader and assign the target positions for the other spaceships based on the target position of the leader and an offset. This works well. But when my spaceships arrive they all have a different direction. I want them to keep to look in the same direction (target - start).   I also want to combine this behavior with a minimum turning radius that is based on the speed. The only idea I have is to calculate a path for each spaceship with an point before the target position, so the ships have some time left to turn into the right position. But I dont know if this is a good idea. I guess there will be a lot of rare cases where this can cause a problem.  So the question is, if anybody knows how to solve this problem and has some (simple code) or pseudocode for me or at least some good explanation.
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.
50612
So, I'm traveling to another star 100 light years away in my spaceship. This ship has a solar sail pushed by a laser beamed from my home star system, so can achieve a velocity close to c. It's also got a robust parachute to slow down with.  I understand that if I measure light coming from my origin star, it will always still seem to be streaming past me at light speed (but will red shift as my speed increases). Light coming from my destination star also travels past me at light speed, and will become increasingly blue shifted as I gain speed.  I also understand that an observer checking on my speed at my origin or destination will always find it to be less than c.  However, will I perceive that in terms of the time it apparently takes me to reach my destination, my speed was greater than c? In other words, will it seem to take less than 100 years to reach the destination? 10 years on my watch, say. Or 1 year. Or a week?  Ie, as far as I'm concerned, while light keeps zipping past me at light speed, do I continue to accelerate unabated to an arbitrary apparent speed?  If not, how do I notice my continued acceleration being prevented?
79363
I'm in trouble with time dilation: Suppose that there's two people on the Earth (A,B), they are twins and each other has a clock. (So they are at the same reference frame). B travels in a spaceship and is orbiting around the Earth, as B's speed has increased there's some time dilation. So it's supposed that if A "looks" to B, B's clock will run slower than A's, and viceversa. And if one day B decides come back to the Earth, he will be younger than his twin and the hour of his clock would be different (earlier than A's clock) because of time dilation.  My first question is, why each person see the other's clock as the slow one? (In fact, I found some information that may solved it but I'm not sure if it's the right answer, and if it is, I don't understand it. -> It's because everyone thinks about himself as the reference frame. In other words, that for B, he is the stationary and who moves is A, so he sees A's clock run slower as B is "stopped" and the same for A. B is who is moving and A the stationary.)  The other question I have is that if it's true that each one sees the other as the slow one there's something that i missed out. We all agree that B (after going to the space and came back to the Earth) he is younger than his brother. So, why B don't see A moving and aging very fast if A see his brother and his things going very slow? Let's imagine they were looking to each other all the time, if both of them see the other going slowly once they meet and "discover" B is the young one... how is that possible?  [I think that in one episode of Cosmos of Carl Sagan (though may be I'm mistaken) he said that a neutrino "borned" in the Big Bang could have seen the creation of the Universe until today in few seconds due to its high speed, here starts my doubts: or i misunderstood something or there's contradictory information]  (I don't know anything about physics, only what is taught at high school as I'm a teenager so it'd be better to answer with no kind of calculation as I'd not understand it.)
105833
I recently watched  by Veritasium where he talks about the One Way Speed of Light and talks about the limiting case where in one direction the speed of light is $c/2$ while it's instantaneous in the other. He also says this is perfectly fine according to our Physics theories. He also points at Einstein's assumption in his famous 1905 paper where he assumes that the speed of light is same in all directions. This made me ask this question is taking the speed of light same in all directions an axiom of some sort? As I've often read no information can be sent at more than the speed of light but here one-way taking the speed to infinite makes no difference. So are all of our physics theories based on the assumption and what would happen if light turns out to be moving at different speeds in different direction? Will that enable transfer of information faster than the speed of light and is there any way for us knowing that the transfer happens faster than the speed of light? The video takes a Earth Mars case where he says it isn't possible for us to every realize this discrepancy but is there a more general proof which says it isn't possible
113155
This is related to  and  The idea is to shine a beam of light from a clock towards a heavy mass, like a black hole, in some manner such that the curvature of spacetime around the mass is sufficient to &quot;bend&quot; the light directly back to the clock. That is, to send the light along a self-intersecting geodesic using a sufficiently curved spacetime. Note that in this case the source and the detector are the same object, so no clock synchronization is required. Hypothetically, this should measure the one-way speed of light. None of the given refutations from the similar posts on this site are convincing. Here are some of the main refutations, as I understand them, and my counter to them: (1) In being curved by spacetime, the light is actually changing direction, hence this is not the one-way speed. To my understanding of General Relativity, the light travels along a geodesic; that is, a curve such that, ignoring technicalities of Differential Geometry, its tangent direction is constant. There is no reflection or acceleration. So in this sense, how can the light with a constant tangent direction be said to change direction? One might say that the path deviates from a straight line in Euclidean space, but given that spacetime is not Euclidean, has no , and has no global notion of direction, this is the only definition of straight or &quot;one direction&quot; that makes sense. Thus, either the light does not change direction and is &quot;one-way,&quot; or we need to be clearer about what exactly we mean by &quot;one-way&quot; in the context of General Relativity. (2) Such an experiment would be impossible or impractical. I think some posters were saying this because the original questions implied that the clock would have to be at the event horizon of a black hole, which is of course impossible or impractical; however, I don't think such an extreme closeness to the black hole is required. Given that the  of a black hole, where light orbits in a circle, is outside of the event horizon, shining the light at some distance outside of the photon sphere should be sufficient to curve the light back to the clock, regardless of the distance of the clock from the black hole (see my rough illustration). At the extreme, we could place the clock directly on the photon sphere, which should be theoretically possible. Regardless, the question is not about practicality, but whether the one-way speed is theoretically measurable.  Update: Essentially what this argument boils down to, I think, is that the average speed of light along a single self-intersecting geodesic may differ from the average speed of light along a non-geodesic self-intersecting path, which is always c. Put that way, however, it does seem a little ridiculous. It is hard to see how the anisotropy of the speed could be defined in such a way as to be consistent with this pathological case. Presumably, we could approximate a single self-intersecting geodesic with a non-geodesic path arbitrarily closely, so, logically, the average speeds over each path should be approximately the same, i.e., c. Furthermore, how would the &quot;preferred direction&quot; of the speed of light behave around a black hole, for instance? Regardless, I still think this experiment does actually solve the problem for the given notion of &quot;direction&quot;. Though the problem is usually posed in the flat spacetime of Special Relativity, with a global notion of direction, so the apparent unanswerability of this question should be seen as a limitation of Special Relativity only, which is then solved by General Relativity.
36801
Can someone help me giving a qualitative answer to this problem in General Relativity:  Imagine you are on earth with two perfectly synchronized clock's. If you hold on in your hand but you throw the other one in the air and catch it after a certain time interval, would they still give the same time?  I think that the one in the air would run faster but I cannot explain why.  Thank you!