Lorentz Jr

For the horizontal beam, a "sketch" of the train can be as simple as a horizontal bar that represents the car's 5m contracted length, and the light beam can be a dot that starts at the left end of the first bar. Then a series of sketches at .1sec intervals would each be 86.6cm to the right of the previous one, and the dots would be separated by 1m. Even simpler, the entire diagram of the car could be an x-vs-t chart of a parallelogram with sides 5m apart, to represent the moving ends of the car, and sloping to the right at 86.6cm for every .1 second. Then the light beam would be a diagonal line (also x-vs-t) that starts at the left corner of the parallelogram and slopes to the right at 1m per .1 second. Whatever works for you. 🙂

It does take different amounts of time for the straight and the slanted beams to reach the end of the car, and calculating the (apparent) desynchronization of moving clocks is somewhat complicated. The snapshot version is worthless if you ignore the train's motion. That makes no difference at all. A continuous beam can just as easily be thought of as a series of "pulses" with no empty spaces between them. No. The light beam has to catch up to the front of the train while the front is moving away from it. I'm sorry, Otto, but that's simply not true.

Right, that would be a literal photograph taken by a single camera. But interpreting the word "snapshot" literally isn't very useful in relativity. The intent in taking a snapshot is to record the state of some system at one instant in time, and I think most people understand that. So many diagrams in relativity problems are reconstructions that show the positions of the various parts of a system at the same time in the specified frame. And that's what Otto's diagram does. I don't know how other people think about this (although I thought it was the standard procedure), but I imagine that there's a whole string of cameras or detectors along the train track, pre-synchronized and pre-set in the ground frame to each simultaneously record what's in its immediate vicinity. Or they can all just keep recording constantly and mark each image with a timestamp once they've been synchronized. Anyway, a simpler and more useful "snapshot" in relativity (because it eliminates the transit times) is to reconstruct the moving object from all of those local detections. Likewise, a "snapshot" from the train's perspective would be reconstructed from cameras lined up along the train's length (and maybe even beyond it) and synchronized in the train's frame. Or you can reconstruct it in either frame from video taken at one location, sort of "reverse engineering" the video by calculating all the transit times and taking them into account after the images have arrived. But that's kinda complicated! 😨 And of course there are other uses of the word "snapshot" in other contexts, like analyzing a business or an economy or other social, biological, or ecological system. The common factor of all these uses is that they approximate a picture of some system at some point in time, even if the tools and information used are surveys, data from medical monitoring devices, or any other source, rather than literal photographs from a camera.

You're ignoring the motion of the car. In the ground frame, the front of the car is moving away from the light beam, so the beam has to catch up to it. Light beam: [math]x = c t[/math] Front of the car: [math]x = L/\gamma + v t[/math] When they meet: [math]c t = L/\gamma + v t[/math] [math](c-v) t = L/\gamma[/math] [math]\displaystyle{ t = \frac{ L}{\gamma(c-v)} }[/math] [math]\displaystyle{ x = \frac{ L}{\gamma(1-v/c)} = \frac{10m}{2(1 - .866)} }[/math] = 37.3m. t = 3.73 sec. These numbers are much larger than 5m and 0.5sec because the front of your train is running away from the light beam almost as fast as the beam is chasing it. The snapshot is instantaneous (i.e. the diagram is correct) from the ground's perspective. Snapshots don't move. The train passes the ground observer while the light beam approaches the front of the car from behind.

Sorry, that first one is wrong. It corresponds to measurements that are simultaneous in the train, so, in the ground frame, the distance between the two measurements is [math]\gamma L = 20[/math]m, i.e. twice the length of the car. The second result (.866) is the right one. Light travels at the speed of light in all frames. In the train, it travels 10m in one second. In the ground frame, it travels a longer distance in a longer period of time to catch up to the front of the car, because the front is moving away from the back at almost the speed of light, but the beam of light still travels at the speed of light. So the source of the conundrum is your incorrect suppositions. The only way to solve SR problems is to apply the Lorentz transformations to the specific times and locations of the events in each individual problem.

Actually, that last step was unnecessarily complicated. After dividing both sides of the previous equation by [math]\gamma^2[/math], it should have been [math](c^2 - v^2)\Delta = v(L - v\Delta)[/math], and then you just add [math]v^2\Delta[/math] to both sides.

c = 10 m/s, v/c = .866, [math]\gamma [/math] = 2, and L = 10m. To calculate the difference between the two clocks on the train, we'll read them simultaneously at a time t in the ground frame. The time on the clock in back is [math]\displaystyle{t_{B}' = \gamma (t - \frac{v x_B}{c^2})}[/math]. The time on the clock in front is [math]\displaystyle{t_{F}' = \gamma (t - \frac{v x_F}{c^2})}[/math]. So [math]c^2(t_{B}'-t_{F}') = \gamma v(x_F - x_B)[/math]. Now we need to calculate [math]x_F[/math] and [math]x_B[/math]. [math]x_B = \gamma(x_{B}' - v t_{B}') = \gamma v t_{B}'[/math]. [math]x_F = \gamma(x_{F}' - v t_{F}') = L + \gamma v t_{F}'[/math]. So [math]x_F - x_B = \gamma(L + v(t_{F}' - t_{B}'))[/math]. Now we get the desynchronization [math]\Delta = t_{B}'-t_{F}'[/math]: [math]c^2(t_{B}'-t_{F}') = \gamma v(\gamma(L + v(t_{F}' - t_{B}')))[/math] [math]c^2\Delta = \gamma^2 v(L - v\Delta)[/math] [math](1 - \beta^2)\Delta = \beta(L/c - \beta\Delta)[/math] [math]\Delta = \beta L/c = vL/c^2[/math]

Don't suppose anything except the given parameters of the problem. Work everything out with the Lorentz transformations. I haven't gotten to that point yet. I have to keep going back to Wikipedia to remind myself that the sign is negative when you're going from the ground to the primed frame and positive going the other way. 🙄 The leader lags. That's a good way to remember. 🙂 To calculate the difference between the two clocks on the train, we'll read them simultaneously at a time t in the ground frame. The time on the clock in back is [math]\displaystyle{t_{B}' = \gamma \left(t - \frac{v x_B}{c^2}\right)}[/math]. The time on the clock in front is [math]\displaystyle{t_{F}' = \gamma \left(t - \frac{v x_F}{c^2}\right)}[/math]. So [math]c^2(t_{B}'-t_{F}') = \gamma v(x_F - x_B)[/math]. Now we need to calculate [math]x_F[/math] and [math]x_B[/math], taking [math]x' = 0[/math] at the back of the car. [math]x_B = \gamma(x_{B}' + v t_{B}') = \gamma v t_{B}'[/math]. [math]x_F = \gamma(x_{F}' + v t_{F}') = \gamma(L + v t_{F}')[/math]. So [math]x_F - x_B = \gamma(L + v(t_{F}' - t_{B}'))[/math]. Now we combine the first and last equations to get the desynchronization [math]\Delta = t_{B}'-t_{F}'[/math]: [math]c^2(t_{B}'-t_{F}') = \gamma v(\gamma(L + v(t_{F}' - t_{B}')))[/math] [math]c^2\Delta = \gamma^2 v(L - v\Delta)[/math] [math](1 - \beta^2)\Delta = \beta(L/c - \beta\Delta)[/math], where [math]\beta \equiv v/c[/math] [math]\Delta = \beta L/c = vL/c^2[/math]

Oops! Sorry about that. With [math]c = 10[/math]m/s, and as seen from the ground frame, the clock in the back of the car is ahead of the one in front by [math]\displaystyle{\frac{vL}{c^2} = .866}[/math] seconds.

WARNING: still editing, please don't comment yet..... [math]c = 10m/s [/math] [math]\gamma = 2 [/math] The time on the clock in back, as seen from the ground frame, is [math]t_B = \gamma (t' + v * 0) = \gamma t' [/math] The time on the clock in front is [math]t_F = \gamma (t' + v L) = t_B + 2 ( .866c * 10m/c^2) = = t_B + 1.732 [/math] So the desynchronization is 1.732 seconds. Assuming the length and height of the car are both L, and having the diagonal beam go from y = 0 up to y = L instead of downward, [math]x_{i}' = 0[/math] [math]x_{f}' = L[/math] [math]x_{1}'(t') = c t'[/math] [math]s_{2}'(t') = c t'[/math] [math]y_{2}'(t') = x_{2}'(t') = s_{2}'(t')/\sqrt{2} = c t'/\sqrt{2}[/math] [math]T_{1}' = L/c[/math] [math]T_{2}' = \sqrt{2} t_{1}' = \sqrt{2} L/c[/math] In the ground frame: [math]x_{i} = vt = 0[/math] [math]x_{1f} = \gamma ( x_{1f}' - v T_{1}') = \gamma (L + v L/c)[/math] [math]x_{2f} = \gamma ( x_{2f}' - v T_{2}') = \gamma (L + v \sqrt{2} L/c)[/math]

Common knowledge, I guess. Does the claim seem questionable to you? How often do career politicians or businessmen or religious leaders convert to different ideologies? Not very often, I would say. It may be possible for an old dog to learn new tricks, but that doesn't mean it's easy.

I've never seen or heard anyone complain about that before in all my life, and I've seen and heard many other people use the expression. In most cases, the word "more" isn't meant to be taken literally when used with "entirely", and "less" isn't meant to be taken literally when used with expressions like "not at all". Please correct me any time I make a mistake, joigus. No kidd gloves required. Just make sure you correct what I actually said and not some exaggeration or fantasy that you made up in your imagination. I'm trying to understand how we have such different ideas of terms like "state of mind" and "impressionable". Mostly I'm referring to things like political and religious beliefs, prejudice, and other convictions that people tend to form later in life. Sometimes social theorists make too many assumptions about people. As I said, no one is born a capitalist or a communist, and I don't think anyone is born a bigot. I guess the tendency toward social activity is important, so maybe that and other factors predispose individuals to certain kinds of belief. I'm sorry if I didn't express myself clearly enough. Irked? Offended? Put off? Would one of those terms be better? You obviously had some kind of negative reaction to my message, joigus. I remember you said something about it some time ago, and now you've mentioned it again. When you're communicating in a foreign language with people from other cultures, maybe you should be more careful about how you interpret their comments. So you weren't upset, and I read too much into what people say, but you read the possibility of a threat into my attempt to help you with English wording on a science forum. You also read "insult" into "strawman argument", which I've never seen or heard anywhere else in my entire life, called "more or less entirely" a "notorious oxymoron", which I've never seen or heard anywhere else in my entire life, and interpreted "upset" in a more extreme way than I intended it. To be perfectly honest, joigus, I had a suspicion that you might object to the word "upset", because I think I already understand how you operate: Basically, you have a consistent habit of exaggerating what other people say, or interpreting what they said in the most extreme way possible, and you always use that interpretation as an excuse to criticize and disagree with them. Here in the US, we call that playing "Gotcha!". Disagreement as a form of competition rather than communication. You call me thin-skinned, but your "not upset" reaction to my message shows that you're even more thin-skinned than I am. You say I read too much into what people say, but you consistently start arguments by reading too much into what other people say. You act more like a paranoid lawyer than a science enthusiast, joigus. I really hate chatting with you, because you keep finding or making up fake or trivial things to argue about unproductively. In the simultaneity thread, I was describing a hypothetical scheme for accelerating a train to relativistic speeds by calculating the required acceleration of each car ahead of time, converting the resulting time series to proper times, using the time series to preprogram the engine in each car, and using synchronized timers to start the engines simultaneously (in the ground frame): Contrast this with the contents of your reply: Not a shred of support or explanation. What is this supposed to mean, studiot? Are you literally so senile that you think train cars can accelerate willy-nilly without breaking apart or crashing into each other, or that it's impossible to preprogram machines? And I'll just say now that I don't think you are, but I found this comment of yours very intimidating when I had just started posting on this forum. So what's the explanation, studiot? Do you think you're some kind of dictator who can tell everyone else what the forum's official doctrine is? This website is allegedly a science forum, not a tea party. I will be delighted to discuss science with anyone who cares to, but I'm not a high-society socialite.

I don't like fencing. Verbal fencing is for court trials, not science discussions. It's an exaggeration, just like saying I called it an "insult" is an exaggeration and emphasizing "entirely" and "nothing" but not "more or less" or "almost" is an exaggeration. I didn't say babies have no memories at all, I didn't say you insulted me, and I didn't say "entirely" or "nothing" without qualifiers. It's obviously a strawman. And that's the strawman, joigus. What you said was absurd, what I had said was not. So I really don't care what you call it. You call it fencing, I call it pamplinas. Because the implication you make is greater than what the person actually said. That's a strawman argument, and you're still doing it. You come up with this "I'm not insulting you" story as a way to pretend I was being unreasonable, but that's not what's happening. What's happening is that you're making up exaggerated stories about what I said and then criticizing me for seeing through them. That's not being thin-skinned, it's being perceptive. The only things I see being sharpened here are trolling and BSing skills. No thanks. Someone here once told me I should get into experimental physics instead of theoretical. I prefer theory, and the same thing applies to my interest in psychology. I'm more interested in depth psychology than behavioral. But many people on this forum seem to think in terms of concrete behaviors. So I make a comment about the lack of genetic programming for higher-level cognitive phenomena like beliefs and attitudes (which I associate with geordief's "psychic space"), and people try to correct me for not mentioning the genetic programming of behaviors and aptitudes. I'm sure I'm wrong just as often as you are, but there are also a lot of communication problems (and one or two trouble-makers) that unnecessarily lead to arguments. That's an interesting comment, joigus. Did my message bother you? I had no idea. It never even occurred to me. I corrected your wording because I wanted to help you with your English, and I did it privately because I didn't want to embarrass you. So you call me thin-skinned, and yet you got upset because I wasn't polite enough or diplomatic enough for your tastes in a short message. I hope you don't take this the wrong way, joigus, but I think you're even more thin-skinned than I am. I apologize for apparently offending you.

I have to agree. The Russian leadership is desperate for any kind of success that they can sell to the public politically, and I think they're sort of trying to bluff Ukraine with the new troops, trying to make them think they (Russia) have more troops than Ukraine can fend off. I don't think Russia will get much in the way of decisive gains though. They might get one or two more towns, something small, but their troops won't last long, and then Ukraine will have an easier time going on the attack again.

Well, they got Soledar, for whatever that's worth (which isn't much). Ukraine has been pretty well supplied for the last few months though. Hopefully enough ammo to stay alive until the tanks get there.

What is "None, obviously..." supposed to mean? First you complain that I'm thin-skinned, and then you turn around and post what appears to be a straw-man argument. Is there something about "None, obviously..." that you think is relevant to this thread?

How many memories do you think newborn babies have? I said I wasn't referring to aptitudes. Predicting a person's future actions requires knowing what specific memories the person has, not just how good they are at memorizing things. Yes, it decreases with age. That's what I said. It also varies between individuals, but I didn't say anything about that.

That wasn't specifically about you. I can't even find the post of yours that you and TheVat were discussing.

At a cognitive level, I would say it's pretty close. Most genetic traits control more concrete aspects of behavior. Maybe a bit combative. In my younger days, physics was almost a religion for me, so I have trouble sitting by and doing nothing when I see comments on a physics forum (or in mainstream research!) that seem absurd to me. This is a psychology thread, of course, but my sensitivity on this forum was activated a couple/few months ago. And @iNow (a) distinguished himself in the Time Wasters thread by making more abusive comments than anyone else (in both quantity and harshness), and (b) has made a couple of similar comments since then. One critical comment may be constructive, but a pattern of abuse and weakly supported criticisms doesn't seem so constructive to me. Financial markets are an interesting example. People bought stocks on ten-to-one margin in the late 1920s, and then in the early 1930s they wouldn't buy them at all with 14 percent dividend yields. Similar situations in the 1960s vs 1980, 2000 vs 2002-3, and 2007 vs 2009. And I mentioned the Victorian culture. Many psychological ideas that originated then fell apart in the liberal 1970s because people didn't have all those tensions and repressions anymore.

Same here. +1 to both of you. And such comments always will be. Fairness rules are strictly enforced until they work against the parties in charge.

Pretty similar though, I would say. "trusting" just means "open to suggestion or influence". I mentioned this in @geordief's thread because he was asking about experimentally supported theories. In addition to behavioral economics, I should lave listed developmental psychology, because it's significantly dictated by genetics. The problem with other theories (especially specific sociological areas, such as economics and political science) is exactly that human minds can develop into almost anything, and almost all social theories are based on assumptions about human nature that I think don't always apply. They may apply to large groups of individuals in the same culture (for example, Freud's ideas in the Victorian age), but then the culture changes and the theories don't work anymore. That was my whole point: Theories only seem to work for a while because they're tested on individuals who grew up with the same cultural influences. This is another comment I was going to make: I'm mostly referring to more abstract characteristics like culture and personality, which are important factors that influence how people behave (which, again, is what geordief was asking about). I'm going to assume that we all know crying is biologically built into human babies (as is laughing, which doesn't apply to other species), and I'm not sure what the point of the baby/mother thing is, except that it's (obviously) one of the primary influences in the baby's environment.

Neither will a rock, because it has no genes at all. And no theory about engines will apply to an engine with a broken crankshaft, a blown head gasket, or a blob of concrete stuck in the intake manifold. I was referring to normal, healthy (human) babies, which I don't think is an especially radical assumption for a general theory. Which assumption? I said people change over time, and I said older people enforce cultural norms, so that means they're part of the environment that affects young people. And I said babies are impressionable, meaning they can learn any language and grow into any belief system. I said they have little or no initial state, not that they have little or no initial aptitude, or that they all have the same aptitudes.

Wow! That's a great excuse. I'll have to brush up on my lawyering skills so I can make posts like that. Thanks for the tip, Dr. Moderator, and you have yourself a spectacular day!! 😆

The subject needs to be discussed without negative spin doctoring by people with hostile agendas. Where's the scary red warning for this post, Dr. Moderator?