In school, I was taught that the speed of light is constant, in the sense that if you shoot a laser off of a train going 200 km/h, it still just goes at a speed of c=299,792,458 m/s, not at c + 200 km/h.

What confuses me about this, is that we’re constantly on a metaphorical train:
The Earth is spinning and going around the sun. The solar system is going around the Milky Way. And the Milky Way is flying through the universe, too.

Let’s call the sum of those speeds v_train.

So, presumably if you shoot a laser into the direction that we’re traveling, it would arrive at the destination as if it was going at 299,792,458 m/s - v_train.
The light is traveling at a fixed speed of c, but its target moves away at a speed of v_train.

This seems like it would have absolutely wild implications.

Do I misunderstand something? Or is v_train so small compared to c that we generally ignore it?

  • Spzi@lemm.eeEnglish
    10·
    1 year ago

    the speed of light is constant, in the sense that if you shoot a laser off of a train going 200 km/h, it still just goes at a speed of c=299,792,458 m/s, not at c + 200 km/h.

    Yes. It is counterintuitive, but correct.

    What confuses me about this, is that we’re constantly on a metaphorical train: The Earth is spinning and going around the sun. The solar system is going around the Milky Way. And the Milky Way is flying through the universe, too.

    Do I misunderstand something? Or is v_train so small compared to c that we generally ignore it?

    The magnitude of v_train does not affect the speed of light coming in from, or going out in different directions. c simply is constant to all observers, regardless if and how they are moving.

    Light emitted or absorbed by a train will always have the speed of c, not c + v_train. Even if that train moves nearly at the speed of light itself.

    However, v_train affects wavelength, or color. Light coming in from the front will be more blue, and light coming in from the back will be more red (see ‘red shift’ in the context of distant galaxies). Geometry will warp. But light will always move at the speed of light.

    This seems like it would have absolutely wild implications.

    Sounds as if the fun begins here. Of what implications are you thinking?

    • Knusper@feddit.deOPEnglish
      2·
      1 year ago

      Sounds as if the fun begins here. Of what implications are you thinking?

      Well, to massively simplify all of this, let’s assume the Earth is moving in the direction of the North Pole at c/2.

      That means, if you’re at the equator and send a signal to a satellite over the North Pole, it’s going to take twice as long as a signal sent across the same distance from the equator outwards.

      That feels like it would be quite relevant for GPS.

      • Spzi@lemm.eeEnglish
        3·
        1 year ago

        Ah, yes! Here, we have at least three entities:

        1. source of light (at equator)
        2. target satellite (North Pole)
        3. observer(s)

        The crucial question is, do they move relative to each other? If they all move together at c/2, their relative speed to each other is (compared to c: very close to) zero.

        So in the context of an application like GPS, you do not want your satellite to smash into Earth at c/2, but have it in a stable orbit. Which means, it’s relative speed is very low. This is why I think the following is a misconception:

        if you’re at the equator and send a signal to a satellite over the North Pole, it’s going to take twice as long as a signal sent across the same distance from the equator outwards.

        Since both source and target move roughly at the same speed, the signal would take roughly the same amount of time even if the speed of light could be different.

        Imagine being in a train and throwing a ball in the direction of movement, and in the opposite direction. As long as you target something in/on the train, it makes no difference. Similarly, the equator light source targeting an orbiting satellite does not care how fast the combined system is moving.

        On top of that, the speed of light can not be different for different observers. It is the same for everyone, in each direction, in every motion. This is where relativity deviates from classical mechanics. In classical mechanics, we can make sense of things by imagining interacting billiard balls. Their individual speeds add up when they collide. In relativity, the speed of light is fixed. Nothing adds to it or subtracts from it.

        Coming back to GPS: Even at these low relative speeds, there are still relativistic effects big enough to introduce significant errors in GPS positioning. We have to account for these errors: https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Relativity

        • Knusper@feddit.deOPEnglish
          1·
          1 year ago

          Imagine being in a train and throwing a ball in the direction of movement, and in the opposite direction. As long as you target something in/on the train, it makes no difference. Similarly, the equator light source targeting an orbiting satellite does not care how fast the combined system is moving.

          But that example with the ball works, because everything is going at 200 km/h, while the ball is going e.g. at 205 km/h.

          My understanding is that light is supposed to work differently. That it does not go at 200 km/h + c when fired from a train. Its speed is capped at c.
          That means, relative to the train going at 200 km/h, its relative speed should only be c - 200 km/h.

          • Spzi@lemm.eeEnglish
            2·
            1 year ago

            that example with the ball works, because everything is going at 200 km/h, while the ball is going e.g. at 205 km/h.

            Or 195 km/h. The point is, the ball is moving relative to the train (at 5 km/h). As long as this movement is perfectly constant (no acceleration / deceleration), the overall speed is entirely irrelevant. You can throw a ball the same way at -200 km/h, 0 km/h or a million km/h. Note there is no difference between the system being in motion and being in rest. And you can throw it in any direction, including in movement direction and the opposite. As long as the overall speed remains constant.

            Similarly, for the system of equator light source and orbiting satellite, it does not matter how fast this system moves, and in which direction. Or even if it moves at all. So even in classical physics, light classical cannon balls would reach the North Pole and South Pole in the same time.

            This feature (N/S reachable in the same time) does not change in relativistic physics. It adds another, equally self-sufficient reason: Light has the same speed in all directions, regardless of relative speeds.

            light is supposed to work differently. That it does not go at 200 km/h + c when fired from a train. Its speed is capped at c. That means, relative to the train going at 200 km/h, its relative speed should only be c - 200 km/h.

            c is not capped at c, but fixed at c. Light always moves at c, for every observer. Regardless of relative speeds between observer and light source, light will always travel at exactly c.

            • Knusper@feddit.deOPEnglish
              2·
              1 year ago

              Man, I hate how it sounds like you’re contradicting yourself. As if you’ve somehow gotten extremely confused by my questions or hit your head or something.

              Someone else posted this video: https://www.pbs.org/video/pbs-space-time-speed-light-not-about-light/
              At least for me personally, that explanation made it click better that we’re not talking about traditional speed, but rather about a general propagation speed limit for causality.

              I certainly don’t understand the implications yet, but I feel like I just have to think about it and re-read everyone’s responses a few times over.

              Thanks a ton for your help!

    • Wutchilli@feddit.deEnglish
      2·
      1 year ago

      So is the speed of light constant because light is a particle and a wave? And when the particle moves at a constant speed the change in speed/energie is achived by a modulation of the wave?

      • Spzi@lemm.eeEnglish
        2·
        1 year ago

        the change in energy is achived by a modulation of the wave?

        Yes. Since speed is constant, all you can change is wavelength/frequency. If you try to add speed, you instead add energy, which increases frequency or shortens wavelength.

        E = hc / λ

        where

        • E is photon energy
        • λ is the photon’s wavelength
        • c is the speed of light in vacuum
        • h is the Planck constant

        So is the speed of light constant because light is a particle and a wave?

        Here, the ground is becoming shaky for me. You’re asking a good question; why. Maybe all we can find out is how. From what I understand, we have piles of solid evidence that the speed of light is constant. These observations confirmed a theoretical prediction made by special relativity, which can be summarized by …

        treating space and time as a unified structure known as spacetime (with c relating the units of space and time), and requiring that physical theories satisfy a special symmetry called Lorentz invariance, whose mathematical formulation contains the parameter c. Lorentz invariance is an almost universal assumption for modern physical theories, such as quantum electrodynamics, quantum chromodynamics, the Standard Model of particle physics, and general relativity. As such, the parameter c is ubiquitous in modern physics, appearing in many contexts that are unrelated to light. For example, general relativity predicts that c is also the speed of gravity and of gravitational waves, and observations of gravitational waves have been consistent with this prediction.

        So it seems that

        • c happens to be the speed of many things, including light
        • c does not depend on any characteristic of light waves or photons
        • c follows from spacetime mathematics

        But again, this is shaky ground for me. I’ll be happy to read corrections.