- #1
Magatron
- 24
- 2
- TL;DR Summary
- A way of viewing light velocity measure which does not require time and/or length manipulation but has limitations
Let there be a track 450,000 km long and a rocket 300,000 km long with a laser attached to the bottom of it's back end with a clock beside it, and a second synchronized clock attached to bottom of its front end. Both clocks were also synchronized with a track clock while the rocket was parked there before the experiment. All observers agreed that the track was 1.5 light seconds long and the rocket 1 light second long by those three clocks.
The rocket travels left to right at a velocity of 150,000 km/s along a path which is directly vertically above and parallel to the track and when it reaches the point where its back end is at the left end of the track it fires the laser while recording the time on the back clock. When the rocket has traveled 150,000 km to the right, its front end will be at the right end of the track, its back end at the 150,000 km mark, and the light beam will have reached the front clock, stopping it at that time and also triggering a device at the right end of the track to show what the time on that clock was and that the front end of the rocket had been at the right end of the track at the same time.
From the track frame, it would seem as if the light beam had traveled 450,000 km, the full length of the track, in 1 second, while from the rocket frame it would seem that the same beam had only traveled 300,000 km, the length of the rocket, in 1 second. It would appear to an observer in the track frame that the light beam had traveled at 450,000 km/s, 50% faster than normal light speed.
Plugging the numbers into a Lorentz transformation calculator indicates that to prevent that from being the perceived outcome the length of the rocket, with v= 0.5 c, should be contracted to 0.8660254037844386 of 300,000 km= 259807.62113533158 km, and that its time should be dilated to 1.1547005383792515 normal. We know that the time of 1 second had been recorded on the rocket clock and it copied that figure on the right end of the track, so we know its time wasn't dilated. We also know that the rocket's front end had been traveling for 1 second at 150,000 km/s so we know it didn't travel farther than 150,000 km of track, so its length hadn't been contracted.
The Lorentz transformation isn't fooling us, we know what actually happened and that neither time nor length had really been altered in any way, therefore, we know that it is in fact possible to perceive light as traveling faster than 300,000 km/s but we also know that it's an illusion, it never really traveled that fast, we just had to measure the speed of light in the same frame that it was generated in and not from another frame in relative motion to it, because the result would not be the true velocity, it would be a trick of perspective.
From the perspective of the rocket, we saw the track move 150,000 km under us in 1 second, exactly as we should. Light velocity seemed normal, because we didn't measure it relative to the track, we measured it from inside the rocket, based on things also inside the rocket, and found that it traveled 300,000 km in 1 second, exactly as it should. We did the correct thing, we measured the velocity of light in the same frame which it had been generated in because we could not have measured it from the track frame, or based on things in the track frame, and obtained the correct reading. You could calculate the correct reading from the track perspective but you would need to use only things located inside the rocket for the calculation, which would be complicated and you would need information about the things in the rocket so why even attempt it? Why would you ever need to know the speed of light in another frame?
The rocket travels left to right at a velocity of 150,000 km/s along a path which is directly vertically above and parallel to the track and when it reaches the point where its back end is at the left end of the track it fires the laser while recording the time on the back clock. When the rocket has traveled 150,000 km to the right, its front end will be at the right end of the track, its back end at the 150,000 km mark, and the light beam will have reached the front clock, stopping it at that time and also triggering a device at the right end of the track to show what the time on that clock was and that the front end of the rocket had been at the right end of the track at the same time.
From the track frame, it would seem as if the light beam had traveled 450,000 km, the full length of the track, in 1 second, while from the rocket frame it would seem that the same beam had only traveled 300,000 km, the length of the rocket, in 1 second. It would appear to an observer in the track frame that the light beam had traveled at 450,000 km/s, 50% faster than normal light speed.
Plugging the numbers into a Lorentz transformation calculator indicates that to prevent that from being the perceived outcome the length of the rocket, with v= 0.5 c, should be contracted to 0.8660254037844386 of 300,000 km= 259807.62113533158 km, and that its time should be dilated to 1.1547005383792515 normal. We know that the time of 1 second had been recorded on the rocket clock and it copied that figure on the right end of the track, so we know its time wasn't dilated. We also know that the rocket's front end had been traveling for 1 second at 150,000 km/s so we know it didn't travel farther than 150,000 km of track, so its length hadn't been contracted.
The Lorentz transformation isn't fooling us, we know what actually happened and that neither time nor length had really been altered in any way, therefore, we know that it is in fact possible to perceive light as traveling faster than 300,000 km/s but we also know that it's an illusion, it never really traveled that fast, we just had to measure the speed of light in the same frame that it was generated in and not from another frame in relative motion to it, because the result would not be the true velocity, it would be a trick of perspective.
From the perspective of the rocket, we saw the track move 150,000 km under us in 1 second, exactly as we should. Light velocity seemed normal, because we didn't measure it relative to the track, we measured it from inside the rocket, based on things also inside the rocket, and found that it traveled 300,000 km in 1 second, exactly as it should. We did the correct thing, we measured the velocity of light in the same frame which it had been generated in because we could not have measured it from the track frame, or based on things in the track frame, and obtained the correct reading. You could calculate the correct reading from the track perspective but you would need to use only things located inside the rocket for the calculation, which would be complicated and you would need information about the things in the rocket so why even attempt it? Why would you ever need to know the speed of light in another frame?
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