This is a little thought experiment that has been bugging me, and I’d like to know if I’m even close:
Imagine a string tied between the Sun and Earth. You are holding this string.
You wiggle the string, generating a wave that travels from the Earth to the Sun, along the string. You watch this wave move along the string with a telescope.
When we look at the sun from Earth, we see it as it was 8 minutes ago, because it takes 8 minutes for the light to travel to Earth.
When the wave reaches the sun, you will see it 8 minutes after it has actually reached it. But you have watched it travel away from you in real time, uninterrupted. You have essentially watched the wave move backwards in time.
So my question is, how is causality and a present moment maintained in this scenario? Is it simply that, from the waves POV, time would move 8 minutes slower relative to the observer on Earth? The string isn’t actually moving backwards in time, but instead experiencing it at a slower rate, thus resolving the seeming paradox of watching the wave go back in time and preserving causality?
Let me know if this is stupid thank you <3
In: Physics
>So my question is, how is causality and a present moment maintained in this scenario?
How do you think causality breaks here?
Let t be the time it takes the wave to travel to the sun. At time 0, you see the wave start next to you. At time t+8 minutes you see the wave reach the sun.
At time 0.5t+4 minutes, you saw the wave get halfway to the sun.
Nothing is happening out of the expected causal order.
> When the wave reaches the sun, you will see it 8 minutes after it has actually reached it. But you have watched it travel away from you in real time, uninterrupted. You have essentially watched the wave move backwards in time.
When you first wiggle the string you look at the sun as it was 8 minutes ago. From your perspective the wave in the string is going to take at least 8 minutes to reach the sun, as it cannot travel faster than light.
However you won’t be able to see it reach the sun 8 minutes after you saw it leave. After all that would imply it traversed the distance instantly! Instead you would see it arrive 16 minutes after it left; 8 minutes to travel there and another 8 minutes for the light to reach you on the way back. As the wave moves away from you it is going to seem to slow down because your news is smoothly becoming more and more behind.
Causality is not breached by this state of affairs.
You don’t see the string in real time, the light it reflects still has to travel to you in order to see it. As the wave in the string gets further and further away, it’ll be further removed from your real time. When the wave reaches the halfway point, you won’t see it for about four minutes after that.
Essentially, the total time you see the wave traveling will be about eight minutes longer than the wave actually took to travel that distance. But its offset from your time while change continuously so you won’t notice a discrepancy.
> When the wave reaches the sun, you will see it 8 minutes after it has actually reached it. But you have watched it travel away from you in real time, uninterrupted. You have essentially watched the wave move backwards in time.
You see the wave moving along the string slower than it is actually moving.
Imagine that you were able to wiggle the string and the wave moved at the speed of light. How long before _you saw_ the wiggle reach the sun? 16 minutes (because it take 8 minutes to get there and then another 8 minutes for the light from that event to get back to you).
> You have essentially watched the wave move backwards in time.
So when you move the string you actually see the wave in the string moving away from you at _half_ the speed of light. It’s not moving backward in time, but the information you’re getting from it is getting more and more out of date as it moves away from you.
No matter how fast the wave in the string actually moves, you’re going to see it moving slower, by an amount that exactly accounts for that extra 8 minutes. The distance to the sun is 1 astronomical unit (AU), so if the wave moves at the speed of light it’s moving at 1 AU / 8 minutes, but you see it moving at 1 AU / 16 minutes.
A more reasonable speed for the wave to move would be about 500 m/s (speed of sound in a guitar string), which would take about 9.5 years to get to the sun. But instead you’d see it moving at a speed that lets it get to the sun in 9.5 years + 8 minutes. So the difference in speed that you see is such a tiny fraction of the overall speed that you’d need to measure it very closely to see the difference.
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