Recent content by PeterDonis

  1. PeterDonis

    B New Paradox Discovered, I Think

    I called this a "personal preference", but perhaps I should expand on this. If you interpret "squashing together" of the light due to the relativistic Doppler effect as "the ship appears to travel faster than light", you are assuming that the light itself takes no time to travel to you--in...
  2. PeterDonis

    B New Paradox Discovered, I Think

    Yes. More precisely: I am saying that if you interpret what you describe above as "the ship appears to move faster than light", then you must also say that the light itself appears to move "faster than light"--indeed, infinitely fast. So it's your choice: either you can adopt the "appears to...
  3. PeterDonis

    B New Paradox Discovered, I Think

    How do we know how far away the Andromeda galaxy is? Do we know that just by looking at the light coming from that galaxy? The answer is no, we don't. We have to calculate how far away it is by combining the information in the light we see from it with other information from other sources. In...
  4. PeterDonis

    B New Paradox Discovered, I Think

    Yes, I know the terminology is used; I'm just saying that one has to be very careful in interpreting what it means. Scientists often use language to communicate with each other that, for them, is not a problem because they all understand the actual physics and don't get misled--but which can...
  5. PeterDonis

    I A Bold New Take on Quantum Theory

    Through interactions that spread entanglement over more and more degrees of freedom.
  6. PeterDonis

    B New Paradox Discovered, I Think

    What does "appearance of traveling faster than light" mean? The light signals that you see don't tell you how far away the ship was when they were emitted. So you can't calculate a speed just from the light signals alone. You have to bring in other information. What other information would you...
  7. PeterDonis

    B New Paradox Discovered, I Think

    Oops, yes, I see where I went wrong. The Doppler factor has to be applied to the shipboard elapsed time, not the Earth elapsed time. Fortunately it's easy to fix that: for ##v = 0.99999999999## we have ##\gamma = 1 / \sqrt{1 - v^2} = 223607##. So the shipboard elapsed time is ##2000000 / \gamma...
  8. PeterDonis

    B New Paradox Discovered, I Think

    No, we're not. We are both calculating the same invariant: the time interval registered by the observer's clock on Earth between seeing the light signal showing the ship departing Andromeda, and the ship arriving at Earth. I say that interval is 4.47 years. You say it's about a week. We can't...
  9. PeterDonis

    B New Paradox Discovered, I Think

    Not necessarily. I'm telling you how it can be the case that you see light signals arriving from the ship in a much shorter time interval than they were emitted (where "time interval" here is in your frame, not the ship's frame). But, as I pointed out in post #48, interpreting that observation...
  10. PeterDonis

    B New Paradox Discovered, I Think

    Actually it was post #3 by @Ibix.
  11. PeterDonis

    B New Paradox Discovered, I Think

    "Travel faster than light" is something of a misnomer. In post #45, I showed you the calculations that say that you see the ship leaving Andromeda 4.47 years before it arrives at Earth, and that the ship never outruns any of its light signals. That in itself should be enough to show that there...
  12. PeterDonis

    B New Paradox Discovered, I Think

    Actually, it's about 4.47 years. Remember you have to take the square root in the relativistic Doppler formula. See my post #45.
  13. PeterDonis

    B New Paradox Discovered, I Think

    No. This is not correct. What is correct, as @Ibix pointed out in post #3, is that you will see the light from the entire journey of the ship, from launch to arrival, arrive at your location in a much, much shorter time interval than 2 million years. The light signals all still arrive in...
  14. PeterDonis

    A Friedmann-Lemaitre-Robertson-Walker model

    Yes. And please note that anyone posting in an "A" level thread on this topic should not even need to ask this question. "A" level means you should have a graduate level knowledge of the subject matter, and one of the reasons for that level designation is to avoid having advanced threads...
  15. PeterDonis

    I A Bold New Take on Quantum Theory

    This claim (I assume it's originally the article's claim, not yours) is not correct in two ways. First, decoherence is unitary, so it can't "destroy" anything. All it can do by itself is spread entanglement among more degrees of freedom. That spreading is what decreases the correlations between...
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