216 thoughts on “Relatively Speaking

  1. phoodoo: But it can be done by wing nuts who say wait a second, I don’t think the Hafele-Keating experiment really worked, even though practically the entire internet claimed it did.

    Wing nuts always manage to look wing nutty.

    And it can be done by wing nuts who say, I don’t think there is really as much evidence for Darwinian evolution as all these textbooks, and famous selling authors, and every forum on the internet claims, I think I will remain skeptical and do some of my own thought and investigating.

    Wing nuts look especially wing nutty when they say that about evolution.

    They are, of course, correct. There isn’t enough evidence to conclusively prove X. But the wingnuts thereby show that they don’t understand that the science is mostly about Y. Here X is the history of life, and Y is the process of change.

    However, if science is right about Y, then X is highly likely even if the evidence falls a bit short of a knock down proof.

    Still, it’s okay for wingnuts to be skeptical about the history, if that is important to them. But couldn’t they be a bit more skeptical about the history of their own religion, which should also be important to them?

  2. DNA_Jock:

    Wingnuts stand out in the manner in which they dispute. Dishonesty, lack of precision, failure to address counter-arguments, deflection, equivocation and lame-ass rhetorical gambits are their stock-in-trade. So, with phoodoo, as with Sal, Mung, colewd, J-Mac, and Erik, it’s the failure to engage that is a dead giveaway.
    Mung stands out in this bunch as being the only one smart enough to realize that he should never attempt to engage.

    Which is also a dead giveaway.

  3. DNA_Jock: it is comparatively easy to spot the wingnuts. Wingnuts stand out in the manner in which they dispute.

    …it’s the failure to engage that is a dead giveaway.

    Mung stands out in this bunch as being the only one smart enough to realize that he should never attempt to engage.

    I bet Mung is also smart enough not to contradict himself right in the same paragraph.

  4. phoodoo: DNA_Jock:

    it is comparatively easy to spot the wingnuts. Wingnuts stand out in the manner in which they dispute.

    …it’s the failure to engage that is a dead giveaway.

    Mung stands out in this bunch as being the only one smart enough to realize that he should never attempt to engage.

    I bet Mung is also smart enough not to contradict himself right in the same paragraph.

    Very good, phoodoo, you are learning from Mung, and not even attempting to engage, ‘cos whenever you do, you fail.
    OTOH, I see I have to add ‘paragraph’ to the list of things that phoodoo doesn’t understand.

  5. DNA_Jock,

    You mean your contradiction was in the next paragraph, not the one where you said wing nuts don’t engage as you were calling Mung a wing nut?

    He is just a smart wing nut for not engaging.

    You use a space bar before you contradict!

  6. Nice to see phoodoo revert to his old ways, and attempt to engage.
    I didn’t contradict myself, phoodoo, I drew a contrast. See if you can follow the logic:
    Wingnuts do not engage.
    Mung is a wingnut, thus he does not engage.
    phoodoo is a wingnut, thus he does not engage.
    Mung does not even attempt to engage. This is smart.
    phoodoo attempts to engage, but fails. This is dumb.
    Neither of you actually engage.
    As a result, phoodoo’s wingnuttery is evident in almost every comment that he writes, whereas Mung is a troll with well-hidden wingnut tendencies, detectable only over the long-haul. Mung stands out as being a lot smarter than Sal, Erik, and colewd.

  7. phoodoo: I bet Mung is also smart enough not to contradict himself right in the same paragraph.

    Indeed I am, except when I am not.

  8. phoodoo: You seem to think the thought experiment relies on Sarah actually seeing and analysing what happens. Jesus, if that is what you think no wonder you can’t imagine it.

    They are different events. That’s what matters.

    No, this is exactly wrong. They are the same events, just analyzed an described differently. More specifically, they are described using different coordinate systems to assign location and time coordinates to the various points in spacetime — that’s basically what a reference frame is.

    Let me remind you of an analogy I made earlier:

    Ok, take a simple example: Bob, Claire, and Doug are describing the location of two rocks, on big and one small. Bob says that the big rock is four feet past the small one, and three feet to the right. Claire agrees that the big rock is for feet further ahead, but says that the small one is three feet to the left. Doug, on the other hand, says that the big rock is five feet straight ahead from the small one. Do they disagree? No, they’re just looking at the rocks from three different angles, and therefore are using different definitions of “ahead”, “left”, and “right” to describe their locations. They are using different coordinate systems to describe the rocks, and if you take into consideration the difference in their coordinate systems their descriptions are all perfectly consistent.

    The same thing are true of Adam and Sarah, except instead of “disagreeing” about the ahead-behind-in-space and left-right directions, they’re “disagreeing” about the ahead-behind-in-time and left-right directions. (That, and with spacetime we’re dealing with Minkowski rather than Euclidean geometry, which means some things are backward/different from how you’d expect.)

    It’s important to realize that some things that are invariant, which is to say that they are the same in all coorinate systems. For instance, in the Bob-Claire-Doug example, they all agree about the distance between the two rocks (spaceDistance^2 = xDistance^2 + yDistance^2 + zDistance^2, so the distance between the rocks is 5 feet).

    In relativity, there’s a similar quantity called the interval, s^2 = c^2*timeDistance^2 – xDistance^2 – yDistance^2 = zDistance^2 = c^2*timeDistance^2 – spaceDistance^2. This is sort of the spacetime equivalent of distance. But s^2 is a bit weird, because it’s not really the square of anything, it’s a thing itself. It can also be positive (temporal distance bigger than spatial distance, known as a timelike interval), negative (spatial distance bigger, known as a spacelike interval), or zero (distances “equal” except for a conversion factor of c, known as a lightlike interval). Also, for timelike intervals, which event happens first is invariant.

    In the case of a dome coming down over the train and maybe-maybe-not cutting off Adam’s head, consider two points in spacetime (“events” is the technical term): First, the point where the right side of the dome passes an Adams-head-height marking on a post planted beside the track at right next to where the dome is coming down. And second, the point in spacetime where Adam’s head passes that same mark.

    In Sarah’s reference frame, these are the same point in space, so spaceDistance^2 = 0 and s^2 = c^2*timeDistance^2, so the interval will either be positive (timelike) or zero (lightlike). If it’s lightlike, that means they’re actually the same point in spacetime and the dome juuuuust gives Adam a close shave as it comes down. On the other hand, if the interval is timelike there are two possibilities: if Sarah sees the dome passing the mark before Adam does, she sees his head getting sheared off; if she sees Adam passing passing the mark first, she sees him surviving.

    Now let’s consider it from Adam’s reference frame. s^2 is invariant, so he sees the same zero (lightlike) or positive (timelike) value that Sarah sees. If it’s zero, he agrees with Sarah that he got a close shave. If it’s timelike for Sarah he agrees about that and he also agrees about which event happens first, so if Sarah sees the dome getting there first he does too, and gets to watch the dome smack him in the face; if Sarah saw him getting there first, he sees the same and passes safely under the dome.

    If you do the coorinate transform properly, you’ll realize that they see consistent events, and just describe them differently. If you see those invariants changing when you do the coorinate transform, it means that you botched the transform.

    Now, on to the question of what happens if Adam does hit the dome, but Adam and Sarah disagree about the angle it’s at:

    phoodoo: I need to demonstrate that striking an object at a different angle is a different event?

    Go back to those rocks. Bob, Claire, and Doug saw them at different angles too; does that mean they’re really different? Of course not, they’re just being described differently.

    But what if a truck ran into those rocks; the collision’s going to depend on the relative placement of the rocks, right? ‘Cause, you know, hitting a couple of rocks at a different angle is a different event, right?

    Well, it turnes out that if you describe the collision from Bob, Claire, and Doug’s points of view, they see a whole bunch of differences: the relation between the rocks is different, and the truck comes in from different angles, and the truck’s trailer is at different angles behind the truck, and the wreckage comes off in various different directions, etc. But if you apply the same rotation transformation to absolutely everything involved — the rocks, the truck, its trailer, the wreckage, and everything else — it all comes out consistent.

    If you forget to apply the rotation tranformation to something, you get an inconsistency. And that’s basically what you’re doing with relativity and the Lorentz transformation. We start with a train and a tunnel, and doors at the end of the tunnel, and you forget to apply the transformation to the timing of the doors closing. Then you claim that the doors are the connected directly, and think this somehow makes them magically immune to the transformation, but it doesn’t. Then you add a descending dome and forget to apply the transformation to it. When DNA_Jock points this out, you apply parts of the transformation but not others and he has to drag you through all of the consequences of the transformation step by painful step. If you’d just applied the transform correctly to everything at the beginning, there would never have been any problem.

    The same thing applies to Adam bonking his head on the dome; a collision like this is actually really complicated, but if you apply the Lorentz transformation correctly and consistently to absolutely everything involved, you’ll get consistent results. Given the amount of trouble you’ve had applying the transform to something as simple as a dome moving at constant velocity, I have no hope that you can analyze this correctly.

    You haven’t even tried, you’ve just insisted that it’s intuitively obvious that there’s an inconsistency. This is due to a problem with your intuition, not with relativity.

  9. Thank you, Gordon, for the lucid and detailed exposition.

    Phoodoo, do you see how Gordon used math to explain the situation with clarity and precision? For your benefit alone (I’m sure even Sal and colewd could figure this one out), I offer the solution to the two-trains-colliding apparent paradox, which avoids the counter-intuitive effects of the Lorentz transformation, and is strictly High School physics. It’s much easier to understand.

    The set-up
    Here’s a much simpler paradox for you to figure out : suppose Adam’s train is traveling at a conventional speed, say 30metres/sec, and weighs a million kg, when it collides with an identical train coming in the opposite direction, leaving a smoldering heap of wreckage sitting on the tracks. Luckily, Adam was throw clear. What do Adam and Sarah calculate as the kinetic energy dissipated?
    Sarah says: Two trains, each 1/2mv^2, that’s ½ M x 30 x 30 + ½ M x 30 x 30 = 900 MJ”
    Adam says “No! my train was stationary when it was hit by a train doing 60m/s. 1/2mv^2 =
    ½ M x 60 x 60 = 1,800 MJ”
    See! Adam and Sarah can’t even agree on the energy dissipated in a conventional crash! Einstein was wrong!

    The solution:
    In Adam’s frame of reference, he sees the steaming pile of wreckage as traveling backwards at 30m/s. It has residual kinetic energy of ½ 2M x 30 x 30 = 900 MJ. Thus Sarah and Adam agree that the energy dissipated is 1,800 – 900 = 900 MJ.
    The teaching point here is that, as Gordon noted, you have to be careful to transform everything into the observer’s frame: less astute High Schoolers assume, intuitively, that a steaming pile of wreckage has no kinetic energy. But in Adam’s frame, it does…
    Also a dead giveaway, after the “two trains colliding at an angle” crash, Sarah sees the wreckage as traveling sideways across the ice-covered lake – that’s why the energy dissipated is reduced; if you had thought about it, that might have clued you in to the other motion Adam views the wreckage as having.
    Or not.

  10. DNA_Jock: For your benefit alone (I’m sure even Sal and colewd could figure this one out), I offer the solution to the two-brains-colliding apparent paradox…

    Yeah, you an leave me out of that one for sure.

  11. Erik,

    Thanks for posting the link. That actually is a really nice video. The ‘light-clock’ example of the light bulb moving up and down is very similar to the example that my Undergrad Physics textbook used to explain Special Relativity. I haven’t seen it explained that way in many years.

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