3 upvotes, 1 direct replies (showing 1)
View submission: Ask Anything Wednesday - Physics, Astronomy, Earth and Planetary Science
I'm just generally confused about the details of relativity. I've invented a scenario to explain my confusion. I made a (bad) diagram to explain my confusion[1]. Basically, a car moving at 0.5c shoots a burst of light at a target, but between the target and the car is a trap door that will close in just over 1 second (timer is in the same inertial frame as the target). The trapdoor is 1.5 light seconds away from the car. Does the light beam hit the target or is it blocked by the door? From the inertial reference frame of the target, the light will take 1.5 seconds to reach the door and so will be blocked, and a clock on the car will be slow. I get that part. But from the car's inertial reference frame, the target and door are moving closer at 0.5c, and the light will hit the target in 1 second (before the door shuts). This would be resolvable by having the timer on the target count fast relative to the car's clock, but shouldn't the timer count slow relative to the car, since from the car's reference frame, the timer is moving and should experience time slower? Does the trap door actually block the light? Why does time slow down for the car but not the target? I understand that the twins paradox is caused by acceleration, but there isn't any acceleration here.
Comment by DaemonOfDamn at 14/09/2022 at 21:33 UTC
2 upvotes, 1 direct replies
First off nothing can ever travel faster than light - meaning the trap door must close before it is hit by light.
You cannot simply add speeds together in a relativistic setting (e.g. with speeds above 0.1c typically - although can be lower depending on your margins of error).
What instead happens is that to an outside observer the light seems to expand as if released from a stationary object. While from the moving object it appears to move normally (e.g. extending outwards at Lightspeed from the already moving object). Which in effect seems to be the contradiction troubling you.
The answer to this problem is time and length dilation, two components of special relativity.
Within the inertial system of the moving car the progress of time slows. Within the outside inertial system the object itself seems to dilate in the direction of movement (getting squished down).
As such for both an outside observer as well as the crew of the ship, the light beam both moves at the speed of light. It is their sense of distance and time which changes to reflect that fact. In both cases however the light will hit the trapdoor.
To visualize further if we assume the object to be moving at the speed of light the time dilation would be infinite - meaning no time passes no matter the distance travelled thus explaining why there is no distance between object and light (the light had no time to move away yet).
I understand that this can be a somewhat disturbing answer as we tend to think of time and distance as absolute, and our daily lives collaborate that illusion. However in reality special relativity applies even here - it's just that the differences and changes are so minimal to barely matter.
Since this was likely somewhat hard to grasp, I'd recommend looking up some videos on YouTube for a more in depth explanation.
