According to general relativity, speed is relative, so for example if you are running at  20 km/h and a car passes you at 30 km/h, the runner is actually moving at 50 km/h relative to the car.  Now imagine that 2 spaceships are traveling both at 99% the speed of light, and they pass each other in a linear fashion. Could it be argued that from 1 spaceships perspective,  you are traveling at 198% the speed of light relative to the other spaceship, according to special relativity, yet violating the constant speed of light?.
3678
Let's say I fire a bus through space at (almost) the speed of light in vacuum. If I'm inside the bus (sitting on the back seat) and I run up the aisle of the bus toward the front, does that mean I'm traveling faster than the speed of light? (Relative to Earth that I just took off from.)
106585
I have mixed intuitions about this.  On one hand, nothing can travel faster than the speed of light and if there is enough space between you and an event then a signal will get stuck in the middle of nowhere traversing an ever-expanding void.  But, on the other hand, it seems reasonable enough that we could share information with other distant observers. That coupled with the fact that every observer has their own observable universe centered on them suggests to me that it would be possible to transmit an account of an event that another observer could never experience firsthand. While the information would have to travel farther than the radius of an observable universe, no individual particle would have to.    Would we be able to learn about something outside our observable universe if someone sent us pictures of, for example, the cosmic background radiation of their observable universe? Is this even a possibility?    Edit: To clarify, I'm talking about an observable universe limited by the  caused by the expansion of space and not the  caused by how far particles could have traveled given the age of the universe. As it stands right now, a mediator wouldn't be able to see anything novel since, as HDE226868 points out, our Particle horizon would have expanded to encompass the event by the time their forwarded signal would have reached us.    Edit2: Several answers have stated that any mediator would have been taken outside of our observable universe by the time it was able to transmit anything novel. But, is that going to always be the case? I was under the impression that gravity was sufficient to counteract the expansion of space to bind galaxies together. Is it unreasonable to suppose the existence of a mediator that has the appropriate velocity and acceleration to maintain a constant position relative to us for an arbitrary length of time despite the expansion of space?  Perhaps the movement of such an object has a relativistic effect on its observable universe?    Edit3: I think I figured out a good lead. While the Particle horizon is a ball around every observer and based on particles just not having had enough time to travel, the Future horizon is based on redshift which in turn is based on relative velocity among other things.  $$1 + z = \sqrt{\frac{1 + \frac{v}{c}}{1 - \frac{v}{c}}}$$  This suggests to me that two observers at a fixed position relative to each other (i.e. ) will have the same Future horizon due to the Doppler effect. However, there seems to be some room to reduce redshift back from infinity with some engineering.  For instance, a telescope in orbit around a planet would be able to see farther while pointing prograde than anyone on the planet since its relative velocity to distant events would be lower and signals would be blueshifted back up from infinity. This actually seems to suggest that a mediator could peer beyond our Future horizon for us.  However, there are some other factors that go into redshift other than the Doppler effect. Gravity wells and the expansion of space also have an effect. But, would these other effects frustrate this scenario?
15651
The speed of light is the same in all inertial frames.  Does it change from a non-inertial frame to another? Can it be zero?  If it is not constant in non-inertial frames, is it still bounded from above?
93624
How do you prove that the time for two objects traveling towards each other at relativistic velocities is still d/(v1+v2).  Answer seems to have something to do with velocity addition but I'm stumped...
68035
Assume we have a ball with diameter 1 meter and mass 1 kg rotating at 99,5% speed of light (Suppose I'm an observer placed above the ball, I see under me a disk wich external  speed is 99,5% the speed of light)  Then we accelerate such ball to 99.5% of speed of light, to make clear from wich position we look at the ball when it's moving so fast I did a picture (there's a black ring around the ball, as you se the rotational axis is vertical to our observer)    I'm interested in a full explanation of what we observe (measured rotation speed, color etc.) and why that happens, as far as I know we should not measure something moving faster than light but I'm not sure how relativity constraints would alter the "measured state" of the ball as long as we accelerate it.  What we see change while the ball accelerates?  EDIT:  A precisation, I assume the ball is spherical when I start rotating it before even moving, this is because commenters made me to note that shape may change.
30666
I am currently studying the motion of relativistic charged particles in electromagnetic fields. More exactly, we first derived the equation of motion in the 4-vector formalism.  I was a bit confused when my teacher talked about acceleration in special relativity. In which cases are we allowed to talk about it specifically in special relativity? (I mean that I have not studied general relativity yet) What stay constant ? Or are we making an approximation?  It may of course have a sense, though I have the feeling that in my courses, we only talked about constant speeds in special relativity.  I hope my question has a sense,  Isaac
41963
What does general relativity say about the relative velocities of objects that are far away from one another? In particular:--  Can distant galaxies be moving away from us at speeds faster than $c$? Can cosmological redshifts be analyzed as Doppler shifts? Can I apply a Lorentz transformation in general relativity?
69148
Consider the standard arrangement in special relativity. Let $S'$ move in the +ve $x$-axis with a velocity $v$ with respect to $S$. This implies that $S$ moves with a velocity $-v$ with respect to $S'$. Is this an assumption or a theorem of special relativity? If theorem - How can it be derived? @RogerJBlarlow below provided an answer with basically says $f(f(v))=v$ hence $f(v)= -v$. There are many other solutions to this so why do we only choose where $f(v)=-v$ This question has been puzzling me for a while now. Any help is much appreciated. Thanks
2304
Gravity causes anything with energy to accelerate toward the source. Black holes, for example, have such strong gravity that they pull in light and don't let any escape. But can acceleration still apply to light? The speed of light is constant, of course, but why are photons affected by gravity yet aren't accelerated by it?  Edit: My main question is why photons aren't affected in the same way as most other particles. I'm perfectly aware that it cannot surpass lightspeed, but I want to know what makes it unaffected by acceleration while other particles are affected.
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?
22829
The title says it all.  If I was on a bus at 60 km/h, and I started walking on the bus at a steady pace of 5 km/h, then I'd technically be moving at 65 km/h, right?  So my son posed me an interesting question today: since light travels as fast as anything can go, what if I shined light when moving in a car?  How should I answer his question?
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?
2041
I read with interest about Einstein's Theory of Relativity and his proposition about the speed of light being the universal speed limit.    So, if I were to travel in a spacecraft at (practically) the speed of light, would I freeze and stop moving?  Would the universe around me freeze and stop moving?  Who would the time stop for?
68184
I understand that the closer something travels to the speed of light, that time will stretch by a factor, and distance will compress by the same factor.  My question is, if something travels in a circle, close to the speed of light, what does the distance of the journey look like to them? They measure that the trip took them 10 minutes. And an outside observer says that the journey took 20 minutes, and the outside observer measured that they did, for example, 1000 laps of a circle circumference 1000 km.  So if the plane had a distance trip counter, what would it read? And if they were looking out of the window, would the circle still look like it had a circumference of 1000km?
61258
While the speed of light in vacuum is a universal constant ($c$), the speed at which light propagates in other materials/mediums may be less than $c$. This is obviously suggested by the fact that different materials (especially in the case of transparent ones) have a particular .  But surely, matter or even photons can be accelerated beyond this speed in a medium?  If so, what are the effects?
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
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?