If an object in space accelerated at $9.8$ms$^{-2}$ constantly, and no other forces were experienced, how long would it take for the object to reach the $99.9\%$  of the speed of light $c$.
15219
A question has recently come up that goes beyond my knowledge of special relativity.  Suppose a pilot has his foot on the gas pedal of a rocket ship and keeps it applied to achieve a constant acceleration, and he has a magical engine that can maintain the thrust needed to accomplish such acceleration even as the vehicle acquires mass.  He measures his acceleration at periodic intervals and sums it up as he goes.  Observers perceive the rocket to increase in speed and gradually approach the speed of light (but never reach it). Two possibilities are being debated for what the pilot observes, and my preference is for the first:   Time dilation gives him the impression that the summation of his readings are approaching light speed at a constant rate, but there is an asymptote involved here even in the inertial frame such that he never actually perceives himself to reach, let alone exceed, $c$, because time slows down to a crawl (as seen from the reference frame) before this can happen. Although to observers he is only approaching $c$, it is possible for the summation of the measurements on his accelerometer to indicate that he has surpassed $c$ and is now traveling faster than light.  From the reference frame he is approaching $c$ and his instruments in the inertial frame tell him that he has surpassed it.   I assume (1) is true beyond a doubt?  If so, is there a straightforward explanation for this?
82948
How fast is Impulse, Warp and Warp X speed?  As I have understood it, Warp (1) speed = 1x Speed of Light (SoL), i.e. ~300.000 km/s. However, in ST:VOY, they are hurled 70.000 LY  from Earth, which will take 70 years to travel at Warp 9, i.e. Warp 9 = 1000x SoL. That makes no sense to me.  If Warp doubles for each full number (binary numbers), then Warp 10 would be 1024x SoL ~ 68 years journey. That works fine, in approximation, given they need to make various stops on the way and/or take small detours to fly through star systems on the way. But no... Not only is Warp 10 impossible (why is that, anyway?), but anything over Warp 9,0 is reserved for burst only. Thus sustained travel is limited to Warp 9, which would (by my calculations) be 512x SoL ~ 135-140 years journey. But this doesn't match any known numbers..  Bonus question: How fast is Impulse drive? You can travel in a shuttle from Earth to Jupiter in a few hours. We only ever hear about quarter, half and full Impulse speed. But at the same scale, you can travel to Jupiter in a few hours, but you can also navigate a safe landing on a planet/moon, through the atmosphere.. Again, I see no consistancy in this..
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.
36549
Is the Lorentz transform applicable to speeds that are lower than light only?Because I'm trying to calculate length contraction of objects moving at speed $c$ (not near it) and it turns always 0. Is my calculation correct?Please help I'm just a beginner  Suppose a 5 m object is traveling at $c$,so $$        x'=x/γ$$  \begin{align} x&amp;=x'\sqrt{(1- (v^2)⁄(c^2)}\\ x&amp;=5\sqrt{1-1}\\ x&amp;=5\sqrt0\\ x&amp;=0 \end{align} Not infinite right? If so then the rule will have no length?
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...
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?
118492
If we are in a free fall which implies we are accelerating at 9.8 m/sec every sec. And let's say that we are falling into a pit that has enormous depth. So isn't this be possible that we may accelerate and surpass the magnitude of speed of light?
14407
I read that an object at rest has such a stupendous amount of energy, $E=mc^2$ because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension of space-time at 1 second per second as time goes forward.  What troubles me here, is the fact that it is traveling through space-time at the speed of light. Why is it at the speed of light?
61731
No matter how fast you go, you will aways perceive the speed of light as constant. Taking that as a fact, the special relativity theory was formulated. Now, for what I understand about general relativity, just by standing here on the surface of the planet under the effect of gravity, my frame of reference is a little different from someone in geostationary orbit, and time goes by a little slower for me.  So, considering me and someone in geostationary orbit, does both of us would perceive light at the same speed? If so, does that means that the light is slower down here than up there?
12609
It has already been  how fast a probe would have to travel to reach Alpha Centauri within 60 years.  NASA has done  into a probe that would take 100 years to make the trip.  But I am interested in this question from a slightly different perspective.  I would like to know how long the trip from our solar system to Proxima Centauri would take for both a ship and for an observer on Earth while accounting for the effects of general relativity on a .  The following assumptions may be made:   The ship starts and ends at 0 km/s relative to the Earth observer. The ship experiences a constant force of acceleration of 20 g until the half-way point and then a constant force of deceleration of 20 g until the destination. The path traveled is such that accleration is in only one spatial direction. The distance traveled is 4.25 light years.   Calculate (accounting for general relativistic effects):   Time of trip for Earth-based observer. Time of trip for ship-based observer. Maximum speed.   You don't need to consider mass, or life-support systems, or method of propulsion; I am really only interested in the effects of relativity on the perceived time of the trip.
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
42735
Is there any theoretical proof for the constant speed of light in all frames of references? I know it is experimentally proven but just curious.
101388
As we know the speed of light in vacuum is constant for everyone (at least for all inertial frames), i.e., if we run away or toward a beam of light (in vacuum) the speed would be $c$. It doesn't change. But imagine a beam of light traveling in a denser medium (where the speed of light decreases), say, water. Let the speed of light in water be $s$. Suppose a fish is swimming away from that beam of light at velocity $V$. For the fish will the speed of light will be $s-V$ or $s$? Thank you for spending your precious time.
66259
After all, it does change direction when reflection occurs. So shouldn't it also accelerate? And since the acceleration cannot increase the speed of light, mustn't it slow down?
32345
We know that gravity speeds up a body; for instance, a meteor which enters the earth gets constantly accelerated up by earth's gravity. And from relativity we know that light bends near a massive body, because Newton's law of gravitation is just an approximation and actually gravity depends on energy and momentum. So my question is: If a ray of light is aimed exactly at the center of a body, then will it get accelerated like a meteor? And if does get accelerated, then won't it surpass the universal speed limit of 3,00,000 km/s (approx.)?
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.)
72397
I don't fully understand what would happen if we could travel at the speed of light. But I saw somewhere here that it would mean events happen out of order. But why is this a problem. It is said that cause has to happen before the effect, but why does this have to be linear?   And why is it that the speed of light is the maximum? I take it that light (photons?) are massless, so why can't they travel faster?