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The Light Clock Toaster "Paradox"

  • 10-07-2019 12:33pm
    #1
    roosh
    Registered Users Posts: 2,552 ✭✭✭


    This one I can't find the answer to in relativistic velocity addition, or through the Lorentz Transformation. I asked a more basic version of it in another thread but didn't get a reply. I've since amended it and so I'm putting it in its own thread.

    Two parts to this one:
    It's the basic light clock thought experiment with a photon bouncing between mirrors, but we're considering two different scenarios:
    1) Light clock is oriented from floor to ceiling
    2) Light clock is oriented from one end of the carriage to the other.

    Let's label the mirrors. In #1 the floor mirror is "tick" the ceiing mirror is "tock"; in #2 the mirror closest the front of the train is "tick" the mirror at the rear is "tock"

    In the first scenario, Alice sees the photon in Boob's clock travel the longer diagonal distance between "tick" and "tock". She concludes that time for Bob has slowed down.

    In the second sceario, it is a situation similar to the clock syncing procedure. Alice sees the photon travel a shorter distance between "tick" and "tock" (bcos "tock" is moving towards the photon). Alice should conclude that time speeds up.

    As the photon reflects from "tock" and travels towards "tick", Alice sees the mirror labelled "tick" moving away from the photon. She sees the photon travel a longer distance from "tock" to "tick". Alice should conclude that time slows down even more than in scenario #1.

    Thermodynamics
    Same two scenarios except that the clock represents the timer on a toaster. When the photon reaches "tock" the toast is cooked and pops out. We can substitute the toast for any thermodynamical process being measured by Bob, the toaster is just easier to visualise.

    In scenario one Alice sees the toast take X amount of time to cook. In the second scenario, she observes a shorter cooking time. If the toaster is oriented in the opposite direction in scenario #2 Alice sees a longer cooking time than X.

    For Bob, the toast always takes the same time to toast, regardless of the orientation of the toaster. Alice sees the rate of the thermodynamical process affected by the orientation of the toaster.


    Is that a reasonable deduction, or what are the arguments against it?


Comments

  • #2
    roosh
    Registered Users Posts: 2,552 ✭✭✭roosh


    Another way to formulate the thought experiment would be to have a single light clock [oriented from end-to-end] with two photons traveling in opposite directions. In this scenario, the "stationary" observer would see time speed up and slow down in the same clock.

    Is there a way to resolve this without recourse to a Roundtrip Light Principle?


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