"When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute-- and it's longer than any hour. That's relativity."

-- Albert Einstein

  • July 19, 2001: Twin Paradox (from George)

    Here's a description that I think is a good description of the problem,
    although it doesn't get me any closer to an answer:

    I don't get it. It seems to me that the guy in the caboose of one train
    would have to pass the engineer of the other train at the exact same time as
    the engineer in his train sees the caboose of the other. Consequently it
    would have to be obvious to the observers that the two trains are the same
    length. I'm obviously missing something here.

  • September 6, 2001: More on the Twins Paradox

    George and I are still having trouble with relativistic time effects (a.k.a. the Twin Paradox). When we think about one twin staying on Earth and the other twin leaving Earth traveling near the speed of light (let's say for a year) and returning, we can imagine that the higher velocity of the traveling twin (relative to the twin remaining on Earth) could lead to the traveling twin being younger. But since it is relative, who is really moving? If we only consider the two twins, then they are traveling AWAY from one another near the spped of light. If it is relative, how does the one twin "know" to age more slowly? George says the only differing factor is the acceleration of the traveling twin. I agree that it is the only difference, but George also points out that Dr. Tom later eliminates acceleration from the whole relativistic time effect issue!
          George found another site which discusses the Twins Paradox and also eliminates acceleration.  You can read it here. George said "I don't get it. It seems to me that the guy in the caboose of one train would have to pass the engineer of the other train at the exact same time as
    the engineer in his train sees the caboose of the other. Consequently it would have to be obvious to the observers that the two trains are the same length. I'm obviously missing something here.
    Maybe Feynman can help me!"

    Yikes! Gotta read more.

    Dr. Tomhas a dandy explanation (that I have not yet read) using four spacecraft and quadruplets. George has created his own version of the hypothetical experiment in which two 4-lightyear-long spaceships carry two quadruplets each, with them standing (perhaps sitting) at the ends of the spacecraft. I'm hopeful that george will draw a cool diagram, and I can scan it in and post it here!

  • September 13, 2001: Lorentzian Relativity and more

    Before diving into the relativity stuff, I need to share the following quotes from the two Physics authors I'm currently reading:
    "The universe should look essentially the same at all scales."

    -- Tom Van Flandern

    "Things on a small scale behave nothing like things on a large scale."

    -- Richard P. Feynman

    George and I talked about Dr. Tom's 8-page essay on GPS clocks (it actually appeared as a chapter in the book Open Questions in Relativistic Physics). the full text is at

    Here are some interesting points:

    • Relativistic Effects are Caused By Velocity, Not Accceleration
      Even at accelerations of 1019 g (where g is Earth gravity, i.e., 10 m/s2), clock rates are unaffected. This has been demonstrated in cyclotron experiments.

    • Lorentzian Relativity
      Unlike Einstein's Special Relativity, which allows for no special frame of reference, LR assumes an absolute (i.e., preferred) frame of reference, and universal time!  Dr. Tom says that the 11 independent experiments which support SR do not discredit LR, either.

    • Time Slippage
      So... under SR, Dr. Tom says you can't say things like "right now, it's 12:30 in the afternoon on September 9th, 2001 on Alpha Centauri" in any absolute way (unless you are ON Alpha Centauri). People whose distance from Alpha Centauri differs will each have their own differing view of the time & date there.
    OK. I'll be honest-- I LIKE Lorentzian Relativity! Even if it isn't true, it sure works for me. I also have to admit that I'm disappointed that two of Dr. Tom's three references in the article are to papers which he authored, neither of which were submitted for peer review. I finally have to admit that I'm still just as confused by the many variations of the Twins Paradox, but George thinks he has a handle on it. George and I have committed to reading more about SR before next week. 
  • September 15, 2001: Relative to WHAT? -- Mail from George

    It seems like every time I start to think I've got some understanding of relativity, you feel compelled to throw in a new wrinkle. I was pretty satisfied with my understanding of the twins paradox, and then you threw in acceleration, which I had taken pains to avoid, deliberately crafting models that didn't include it. So I was forced to develop a degree of comfort with
    acceleration thrown into the mix, and then you had to start questioning inertia. Now I think I've come to a bit of resolution with that - basically I'm happy to take inertia as a given: things don't change course unless they're acted upon. But your question was 'change course relative to
    what?', ever seeking that elusive preferred frame of reference. The answer I've come up with is relative to *anything*. Screw the two-particle universe, which I never could follow. In a many-particle universe, if one thing starts changing course relative to another thing, one of them is being acted upon. And if you attach an inertial guidance system to your thing, it can serve as 'the other thing', and tell you if it's being accelerated or not. And if it's being accelerated, then it's being acted upon by some force, e.g. gravity in the case of a satellite orbiting earth.

  • October 4, 2001: Paul Still Wants an Absolute Frame of Reference

    ...and in particular: a system which is rotating at a uniform angular velocity.

    It is this last item which got me asking the question again: RELATIVE TO WHAT???? Here's my issue:

    If you're on a spaceship moving at a uniform velocity in a straight line and you can't look out the
    window, you have NO WAY of knowing whether you are moving or stationary. I get this, and I can understand that motion itself is entirely relative in terms of the physical laws of the Universe.

    But if you are in that same spaceship and it is set spinning about it's center, even though you can't see out a window, you can STILL KNOW YOU ARE MOVING! Not only that, but you can also tell that you are spinning around a particular axis, which implies to me an absolute frame of reference in the Universe.

    George gave me that look again (I would call it one of "consternation"), and proceeded to show me that I was "all wet".  He was saying that all you would see on the spinning spaceship are the affects of acceleration caused by the spinning, and that the perceptions are relative to that acceleration. Oh well. I still want an absolute frame of reference!  Of course, I want dogs to never grow old and Space: Above and Beyond to come back to TV, but that doesn't mean
    they'll ever happen!

  • Octover 11, 2001: Special vs. Newtonian Relativity

    I read ahead a little in the next chapter: The Special Theory of Relativity. I won't go into it much, but the lightbulb finally went on for me, at least a glimmer! Feynman talks about synchronizing clocks and perceiving clock progress from difference frames of reference, etc., and I was inspired by his description of a very simplistic clock used onboard a fast-moving spaceship.

    Before I address relativistic effects, I want to describe a scenario in the Newtonian universe. Let us consider "Paul's Pair-o-docs:"

    Initial conditions: Dr. Richard Feynman and Dr. Tom VanFlandern are riding on a train. The train is moving in a straight line at 18 kph (5 m/s). The train car in which they are riding is made of transparent materials. Drs. Tom and Dick are standing on opposite sides of the train, facing one another, 5 meters apart, playing catch with a ball. They are throwing the ball such that it takes one second for the ball to travel from one person to the other. The lateral path of the ball is perpendicular to the direction of the train.
    Dr. Emmet Brown, an eminent temporal scientist, is the observer outside the train. He will be standing near the tracks, measuring the movement of the ball from outside the train.

    Figure 1. "Train" Frame of Reference.

    In Figure 1, we see the "train" frame of reference-- the frame of reference for those riding the train. At time t1, Dr. Tom throws the ball. At time t2, Dr. Dick catches it. Drs. Tom and Dick make the following observations:

    • The ball travels 5 meters, in a direction perpendicular to the direction of the train.
    • the velocity of the ball is 5 meters/second. 
    Now let's consider the view from outside the train:

    Figure 2. "Stationary" Frame of Reference.

    In Figure 2, we see the "stationary" frame of reference, as perceived by Dr. Emmet. At time t1, Dr. Tom throws the ball from position P1. At time t2, Dr. Dick catches it at position P2 (the two positions are 5 meters apart along the tracks). Dr. Emmet makes the following observations:

    • The ball travels roughly 7.1 meters (5 times the square root of 2), along a vector resulting from the train's vector (v||) and the vector of the thrown ball (v^).
    • the velocity of the ball is 7.1 meters/second.
    Ok. So what can we say about this? The observations made by Dr. VanFlandern and Dr. Feynman are completely correct for their frame of reference. The observations made by Dr. Brown are completely correct for his frame of reference. Here's the point I want you to remember while we now look at Special Relativity: Since the ball traveled further (from Dr. Brown's point of view) in the same amount of time, it necessarily traveled faster.
    Now I want to address relativistic effects, as described by Dr. Feynman in Chapter Three. Here he envisions a very simple clock and shows why time passes more slowly on a spaceship which is moving relative to the observer. 
  • October 18, 2001: Intertia & The Twins Paradox (again!)

    Well, we've both caught up-- we're done with chapter 3. I was particularly interested in the concept that under Special Relativity that as velocity increases, mass increases. As the velocity approaches the speed of light, forces applied to a body do not add much to its velocity, but do continue to add to its momentum. This also increases the inertia. So I was thinking... Let's say I'm on a spaceship traveling at .99c. I'm holding a cannonball, which to me still seems to weigh about 8 pounds (but to a stationary observer, it appears to mass MUCH more... something near, say, infinity!). According to the theory of special relativity, its mass and intertia are extremely large, yet I have no trouble at all throwing it across the cabin! How can this be??!?!?

    Well, George says that to me it seems like I just throw it across the room in no time at all... according to my frame of reference. From the frame of reference of a stationary observer (for whom the mass/inertia of the cannonball seem to be nearly infinite), the force I apply has little or no effect-- the ball cannot even be seen to shift position within his lifetime! Oh yeah... from his viewpoint, time is now moving verrry slowwwwwwly for me. OK, I'll buy it.

    More on the Twins Paradox

    I cheated a little and read ahead into the next chapter (Relativistic Energy and Momentum). Feynman talks about the Twin Paradox, and answers the question of the "Philospher" (I have to say here that Feynman really trashes philosophers): If one twin is stationary and the other is in motion, how can either one tell which one is moving and which one isn't? Especially since Special Relativity says that when moving in a straight line at uniform velocity, one cannot detect (without looking out the window) that they are moving.

    Dr. Feynman says "That's easy!" In order for the twins to be reunited and compare their differing rates of aging, the moving one must slow down and turn around. When he does, everything will get slammed into the other side of the ship, and he'll know he was moving!

    George liked this answer just fine, but I can't live without an absolute frame of reference! So I set about thinking again. Here's my new scenario:

    My twin and I are each given a synchronized atomic clock, and a sedative that puts us to sleep (we're currently exactly the same age). We're each placed on a spaceship, and sent to an area of space where the light from distant stars is blocked by interstellar dust (i.e., we can't see anything but each other's ship outside our own). Before we awaken, one of our ships is accelerated to .9c. Once we awaken, we can observe that we are moving away from one another at a very high rate of speed. I was instructed that once I awoke, I should apply my thrusters in the direction away from my twin (I guess I'm turning around!). I'm to use the thrusters until our relative velocity is zero. Then we both apply equal thrust to bring our ships together. Once I enter his ship through the airlock, I'm astounded to find that it is my twin's atomic clock that has run slower-- even though I'm the one who applied thrust and slammed everything against the wall of my spaceship! How can this be?

    Well, it was my twin's ship that was accelerated to 0.9c, while I remained stationary. I then applied thrust, and caught up with him! So... I do not believe that Feynman's answer is sufficient. In my scenario, the only way we could differentiate between moving and stationary was by the values on the clocks... no experiment could detect the difference. So how did the one clock know to move at a slower pace? It could not do so without the existence of an absolute frame of reference, I don't think!

    OK George, help me out and set me straight.

  • October 25, 2001: George Responds re: Twins Paradox

    Twin A, scenario 1:

    1. Wakes up, sees twin B rapidly receding, figures B is moving very fast away and concludes B is aging more slowly than himself.

    2. Sees B slow down and stop, concludes they're both aging at same rate now, although he expects B is still younger from B's time slowdown at point 1.

    3. Accelerates toward B, and sees B accelerate toward self. Figures they're still both aging at the same rate, although a bit more slowly than they were at point 2. Expects B is still younger.

    4. Meets B, not surprised to find B is younger than himself.

       Twin A, scenario 2:
      1. Wakes up, sees twin B rapidly receding, figures B is stationary and A is moving rapidly away from him. Figures he is aging more slowly than B.

      2. Sees B accelerate toward A, so they're both now zipping along very fast in the same direction. Figures they're both aging at the same rate now, although he expects B is still older due to his own time slowdown at point 1.

      3. Slows his ship down, and sees B speed up. Expects that B is now aging more slowly than himself, since B is now moving faster.

      4. Meets B, does some math, and is not surprised to find B is now younger than himself, since the time changes in step 3 have more than countered the time change from step 1.

      1. July 15, 2003: GPS Clocks and the Twins Paradox

        I visited the site recently, and found a new article by Dr. Tom Van Flandern: What the Global Positioning System Tells Us about the Twin's Paradox. I read some if it, but I always find myself wondering how acurately he is representing the theories of Einstein and Lorentz. I also read the conclusion, and I'm not quite sure what his conclusions are! I better try again. Here's the abstract:

        Abstract. In the GPS, all atomic clocks in all reference frames (in orbit and on the ground) are set once and stay synchronized. We can use this same trick to place a GPS-type clock aboard the spacecraft of a traveling twin. That clock will stay synchronized with Earth clocks, allowing a clear resolution of the twin's paradox in special relativity - why the traveler expects to come back younger, and why the stay-at-home twin is not entitled to the same expectation.