Will the light beam appear to move slower than the speed of light or not ? If not why ? Please tell I don't understand.
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It will still move at the speed of light by the second postulate of special relativity.
Tofi
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This can be challenging to comprehend because the phenomenon of special relativity is outside all of our life experience, but the measured speed of the speed of light will be the same, both for an observer not traveling near the speed of light and for an observer looking at a beam of light while themselves traveling near the speed of light. To understand how this is possible, consider first logically how you calculate the speed of something: you first measure the distance an object has moved (i.e. distance delta) and then you divide that by the amount of time you measured it to have taken to travel that distance (i.e. time delta). So for example, if an object moves 10 meters in 10 seconds you would calculate the speed as 1 meter/second.
Since special relativity says the measured speed of the speed of light is the same for all observers, things are going to have to work differently than you would expect from our experience. In our experience, if we are in a vehicle traveling 100 kilometers (km) per hour and we launch a drone that can fly 50 km/hour (ignoring wind resistance), then the total speed of the drone as we would measure it is additive, meaning that if the drone moves at 50 km/hour along the same direction we are traveling, we would measure its speed as 100 + 50 = 150 km/hour. This logic leads to the confusing interpretation of how you would calculate the speed of light while traveling in a spaceship moving near the speed of light and then turning on the headlights. Wouldn't we measure the speed as our speed + the speed of light from the headlight to get something faster than the speed of light?
The short answer is no. For the why not consider again how we measure speed, which is distance delta / time delta. If the speed of light will be measured the same for all observers, then not all observers can have the same distance and time. And this is what special relativity tells us. Time and distance change depending on how fast your are traveling, with both getting smaller as you approach the speed of light. So if you measure the distance before you speed up you might say the distance from where you are to some other spot is 100,000,000 km away. But as you speed up to near the speed of light a funny thing will happen. The distance will now appear to only be, for example, 1,000,000 km away. In addition, although you won't notice it, time will get slower for you as well. So you may think you've only been traveling for, say 10 seconds, when to someone watching you who isn't moving they might see you traveling for 10 minutes!
The bottom line is that no matter how fast you are going, the changed distances and times will make the calculations of the speed of light for all observers the same. There are formulas that allow you to calculate exactly what the changes to time and distance would be, so you'd be able to calculate what your distance and time was from a different observer's perspective, you just wouldn't see their perspective yourself. Technically there are tiny differences even for speeds like traveling in cars or planes, but the magnitude of these differences are so small you'll never notice them. It only really kicks in at much higher speeds than you will ever travel. Interestingly however, people realized some time ago that GPS satellites, which are traveling pretty fast in space, actually do have to consider the impact that both their speed and their greater distance from earth's mass has on their time and make little corrections every once in a while to stay in sync with us. The distance from a large mass also alters time, with being closer to large masses slowing time down, which turns out to have a bigger impact than the speed of a satellite has on its time, meaning our time on earth is actually measurably slower than time for a satellite, but that's a separate issue.
I hope this explanation helped. It's a very strange concept to wrap your brain around because it's as if two aspects of the universe that we see as unchanging, time and distance, suddenly shift arbitrarily to make something we don't typically ever think about, the speed of light, constant, but very clever tests designed and executed by people way smarter than me have proven the basic ideas of special relativity to be accurate, so that does seem to be the weird, wonderful universe we live in.
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If the observer moves with speed v (relative to the light source), he will measure the speed of the light to be c'=c-v. Einstein's "speed of light is the same for all observers" (c'=c) was "borrowed" from the Lorentz equations but even the authors of the equations did not believe in it:
https://en.wikipedia.org/wiki/Lorentz_ether_theory Albert Einstein: "...it is impossible to base a theory of the transformation laws of space and time on the principle of relativity alone. As we know, this is connected with the relativity of the concepts of "simultaneity" and "shape of moving bodies." To fill this gap, I introduced the principle of the constancy of the velocity of light, which I borrowed from H. A. Lorentz's theory of the stationary luminiferous ether..."
http://www.jstor.org/stable/3653092 "It is clear from the context that Poincaré meant here to apply the postulate [of constancy of the speed of light] only in an ether-bound frame, in which case he could indeed state that it had been "accepted by everybody." In 1900 and in later writings he defined the apparent time of a moving observer in such a way that the velocity of light measured by this observer would be the same as if he were at rest (with respect to the ether). This does not mean, however, that he meant the postulate to apply in any inertial frame. From his point of view, the true velocity of light in a moving frame was not a constant but was given by the Galilean law of addition of velocities."
Pentcho Valev
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Yes
This phenomenon is what causes a form of time dilation. The light would indeed appear to travel slower, because light has a static speed. Apparently this actually has an influence on time itself, making time travel slower for you than for others. This means that if you traveled at 99.999999% the speed of light, you would see the universe be destroyed.
This was the explored in a novel called Tau Zero, where people in a Bussard-ramjet-powered spacecraft experience a problem where they cannot decelerate, resulting in them experiencing the Big Crunch (the unanimously accepted fate of the universe at the time), and then slowing down to land on a planet after the universe reforms.
