Then answer the simple question of why you believe that the Lorentz equations should be used other than I’m using them.
I’m not dismissing your position out of hand, but you are still only asserting that I’m making a mistake; you have yet to back that up. We’ve agreed for a while that if I’m using the equations incorrectly, then I have not resolved your paradox, and if I am using them correctly, there is nothing left to resolve. To decide the question, you need to support your position.
I’ve provided examples of my use of the equations by others, and I can provide more:
-this is a power-point from a physics class at Brown University. Slides 9-14 show almost exactly what we’ve been talking about, and use the equations as I use them.
-this is a page by a physics professor at Syracuse. If you scroll down to “The Fall of Absolute Time”, you’ll see this picture, strikingly similar to the example in question and almost exactly the same diagram as I drew 18 pages ago:
-This page from the Internet Encyclopedia of Philosophy, and supports my assertion that the Lorentz transformation is visualized using Minkowski diagrams like those I provided. It specifically mentions using the (x,t) coordinates of a point to calculate its (x’,t’) coordinates, and does not use ∆x.
Here are a couple diagrams from that site, showing the use of the Minkowski space as a proxy for the Lorentz equations, and implicitly calculating for x’ and t’ for paths than never intersect the point (0,0):
I’ve argued for my case, I’ve provided sources supporting it. All I’m asking of you is that you tell me what besides your assertion should lead me to believe that I am making a mistake.
It is pointless to explain to an illogical person that his logic is illogical. You have to physically show it. That is why they invented Science. But you only hear rumors of what “they” have seen and worship.
Not being a thinker, he has nothing with which to verify himself but his ethos and faith. He is a literalist who thinks he has properly interpreted his bible and expects someone to show him chapter and verse where it says otherwise. Everything he reads tells him the same thing. Amazing - “relativity of belief”.
To verify anything, as I said before, you have to have a DIFFERENT method entirely. You misreading different sources in the same way isn’t a different method.
-this is a page by a physics professor at Syracuse. If you scroll down to “The Fall of Absolute Time”, you’ll see this picture, strikingly similar to the example in question and almost exactly the same diagram as I drew 18 pages ago:
Well if that was what you were trying to show with your unlabeled dots and lines, why did you object to my diagrams of EXACTLY that same diagram that foretells the paradox that you say isn’t there;
This makes at least 5 diagrams that you cannot refute. Yet when you use Lorentz, you get different results.
In every one of your attempts to use Lorentz, the mistake that you make is that you do not consider the original reading of each timer when you try to calculate what they will read in the station frame. But when you agreed that they indeed will read the same to the station frame, then you profess that there is this mystical “train frame” where the train’s clocks magically look different to the train observer.
YOU have shown NO equations AT ALL concerning such a superstition.
t = station time as seen by the station.
t’ = train time as seen by the station. ?? = mystery train time as seen by the train?? - WHERE is the equation for that? Where is your “textbook” or website?
What do you mean “train frame as seen by the station”? The station doesn’t see the train’s frame. Ever. Even when the light from flashers reaches the station, the station is seeing that event in its own frame.
t=station frame
t’=train frame
Pure and simple.
The two diagrams you show contain different information. In the first, the flashes occur on t=0, time zero according to the station. In the second, the flashes occur on t’=0, time zero according to the train. You are simply omitting either t’=0 (as in the first diagram) or t=0 (as in the second diagram). No matter how you interpret the Lorentz equations, it’s clear that t≠t’, so why not draw in both lines? You draw in both the x and x’ lines, showing that you are overlaying the frames, and just leaving certain things out.
What do you think the station FRAME is seeing when it looks at the train’s FRAME clocks and sees them at 3:00 while its own clocks are at 3:30?
That is all the Lorentz equations are about. Both FRAMES always see everything about the other FRAME. The Lorentz (somewhat inaccurately) merely lets you calculate the other FRAME.
An individual, being located at a particular position, must wait for the light to travel to him and thus he doesn’t get to literally see either frame clock until the light gets to him. But that has nothing to do with Lorentz. Lorentz isn’t calculating light travel times. Lorentz is merely telling you the difference in the FRAMES, not different individuals within the frames. ALL Lorentz references are about only that difference in FRAME. The time for the light to travel is a separate issue, just as your, Einstein’s, and my diagrams have shown. The paradox arises due ONLY to the light travel time, NOT Lorentz time dilations.
Yes, it IS that simple. But you throw in some mystical “but the train frame doesn’t see what the station frame sees”. Bullshit. They both see each other entirely. It is only at a particular position that anything varies due to light travel time, which has NOTHING to do with Lorentz.
Bullshit. Do you not see the “T0” and “T0+tt” markers in BOTH diagrams?
In this diagram the station is our reference, thus t’ = train’s frame;
See the “T+tt” for the flash time?
And again, where the train is our reference, thus t’ = station’s frame;
It looks at a clock, not a frame. It’s seeing the train’s clock from within its own frame.
Whatever the constant (0, t0+tt, a, b, r, s, etc., etc.), it’s only a constant in one frame. In the other frame, it is a sloped line.
But since we know that t≠t’ (these lines cannot be parallel), we know that these diagrams cannot show the same information.
This, James, is bullshit. You are just refusing to justify your position, and in the absence of such an justification, your premises are without force. I can simply agree that if it were true that I am mistaken in my application of the Lorentz equations, you would have proved your case, but since it is not true, I have proved my case, and the paradox is resolved.
And what is the equation for that? But since you refuse to answer any other pertinent and revealing questions, I am not holding my breath for you to answer that one either.
That is probably why it is shown as a sloped line in each diagram, but that is just a guess. We have the paradox setup with either one of them.
I suspect that one was labeled, “Station Frame of Reference” and the other, “Train Frame of reference” to indicate something “different” about them. Of course, the Train’s frame is superfluous since each shows the entire setup and even your own source showed EXACTLY the same diagram (surprisingly even labeled identically).
As you said before, from YOUR perspective, there is no paradox. But then from YOUR perspective 2+2=3, so I’d say it is YOUR perspective that is “without force”. “I don’t see it, so it doesn’t exist. Problem solved.” There isn’t really much difference at all between a denier and a liar. Online is a paradise for both.
This paradox was presented for thinking people, not faithful worshipers for whom their Lords have resolved all things despite all evidence to the contrary (because they “see no evidence” - not seeing has been known to be a symptom of blindness as well as denial and lying).
Since even your own sources display the exact same setup that you deny can exist and the real paradox issue is something entirely different, why don’t you leave this up to the few thinking people who might want to discuss it and stop making Science into a faith based religion.
It’s actually two equations.
We can think of the time at which certain light is reflected from the face of the clock as an event. We know what time that event happens in one frame (depending on which run we’re talking about), and we can calculate the time at which it happens in the other frame using the Lorentz equations. We can then find out what time that light reaches the observer at the station (the station clock) by calculating how long it takes in the station frame for the light to travel from the train clock to the station clock.
Please elaborate on this. The only slopped lines in your diagram are those representing position.
I’m not saying they show different frames, I’m saying that, as drawn, they depict different events. In one (the second), the flashers are set to go off at the same time in the train frame. In the other, they are set to go off at different times in the train frame. As I’ve said, both these diagrams show both frames for two different situations.
I’m not believing in spite of evidence to the contrary, I’m believing in the absence of evidence to the contrary, and every evidence in the affirmative. Again, though, if you’d provide evidence, I’m happy to have a look.
In spite of your ironic ruminations on faith and a willingness to be wrong, you just aren’t making a case. Every time I ask for your evidence, you call me illogical, accuse me of being a “faithful worshiper” of some unnamed “Lords”, but that isn’t a substitute for the evidence I’m requesting.
When two people differ on whether or not some object exists, there are at least two possibilities: That the one person is blind, or that the other is hallucinating. How do we determine between the two?
FRAMES don’t have a location. Every frame is inside every other frame. How long it takes for the light to travel is irrelevant to the question.
OH NOW I see the problem. You need glasses.
The brown line is the sloped line that you are talking about in the Train’s reference view. In the station’s, the 3 sloped lines are the sloped lines that you are talking about. The train’s clock is the one with the little t’ located on it;
But don’t let the slope fool you. It really is sloped.
That is your superstition that you have actually proved to be wrong yourself. Well, to a thinking person anyway.
Yeah and if the Church would produce evidence that there was a God, people would believe that too. Some evidence requires thinking to “see”.
It is a little hard to prove to a blind man that the apple is red, especially when the blind man can’t think either and wants to believe otherwise.
Well, thinking people use Logic for that. You use ethos.
What? You said “what equations”, and I explained which equations and why. Direct question, direct answer.
As I said, those lines represent positions. They are lines for which x’ is constant. For instance, the center line, the t’ axis, is x’=0. I’m asking for the line t’=0. We know that t=0 and t’=0 aren’t parallel, so they should be depicted as sloped relative to each other, and intersecting at zero.
I realize this is revelation to you, but equations are those things with little “=” signs, variables and numbers.
I’m curious how a constant can be represented as a sloped line obviously changing in both t and x positions. But in any case, you are merely arguing with yourself (again). Your Syracuse diagram is the exact same diagram as mine.
To a thinking person, showing him his blindness is a kindness. To a faithful worshiper it as curse. This being a Science forum and Science being a supposedly thinking person’s realm, rather than your politicking and obfuscation, I thought I’d do you the favor and give you the hint.
But seeing how you play online in this and other forums, I’ll leave your antics behind as so many others have.
If you were really curious, then you wouldn’t have to ask this question because it is explained in every textbook that covers special relativity. The line determining t’=0 does not pick out a line of constant t or constant x.
There is one big difference between the Syracuse diagram and yours: the author of the Syracuse diagram doesn’t make the assumption that the corresponding diagram for the other frame is the mirror reflection of the one he or she presents. The error (<—edited by Liteninbolt) is all yours and that’s what makes you see a paradox. If you would stick to your station frame of reference stipulations and use the Lorentz equations properly, then the train clock does not stop in any reference frame. No paradox.
And this is exactly why you fight against using the Lorentz equations properly. When used properly, there is no paradox. When used your way, there is a paradox. To a sane person, this would indicate a problem with your way of doing things.
I won’t belabor the points that PhysBang made in his response to the substantive parts of your post. But I do have something to add about this:
Since we disagree, and since only in resolving our disagreement can we determine who is thinking properly on this issue, in assuming yourself to be the “thinking person” and me to be “blind”, you take for granted the very issue in question. We’d both be better off if you would spend more of your time clarifying and supporting your case, and less cluttering your posts with condescension. This is not politicking; it is the expression of a sincere desire to continue an objective discussion of the point at issue, as opposed to seeing it dissolve into a pissing contest.
I’m transferring a discussion from here to this old thread. The case in discussion is exactly the same as in the OP of this thread.
The definitional setup is that the flashers, no matter where they are moving, go off at the time the clock on the train is at equal distance from the flashers as the clock on the station, as seen from both reference frames.
Reasoned from the train, 2 photons simultaneously arrive at the clock on the train. Reasoned from the station, 2 photons simultaneously arrive at the clock on station.
Reasoned from the train, the photons aimed at the station would arrive at a point on the station alongside the clock on the train.
Reasoned from the station, the photons aimed at the train arrive at a point alongside the clock on the station.
All this IF the flashers go off at a moment when, as seen from both train and station reference frame, the clocks on both train and station are at equal distance from the flashers
But does one establish a moment when station clock and train clock are perceived from both frames to be at equal distance from the flashers?
To get to the bottom of the problem, we need to look at the precise way in which RM would establish this moment, i.e. how it would materialize the definitional setup.
As far as I understand, relativity holds that the moment when the flashers are seen to be at equal distance from both clocks is different in each frame. So one would have to have a third reference frame, in terms of direction and momentum right between the two others, from which a moment of simultaneous equal distance in both reference frames is established.
But this would create a situation where from both the stations and the trains perspective, the flashes go off at slightly different times at a point where the train appears slightly misaligned.
==========================================
Below is a post from the BTL thread. Because I’m new to this, I’m hoping someone can tell me whether or not I’ve correctly represented Relativity’s position with respect to this problem.
FC, this OP led to what turned into an 800 post debate concerning the proper use of the Lorentz equation. It was extended into another thread. The reason the Lorentz got involved was that I had used timers to ensure that the flashers went off together. But there is a common misunderstanding as to how to use the Lorentz that leads one to believe that you can’t make two flashers go off together from the perspective of both frames. So I changed that part of the setup avoiding the use of the flash timers.
So if we are going to discuss this in detail here, let me start a new thread for us to analyze the Stopped Clock Paradox.
In the mean time,
I don’t really understand what you are saying there.
I don’t believe that SR has anything to disallow both frames from accepting that the train is centered on the station clock at the moment of flash. The relativity of simultaneity will state that the observer clocks will report/perceive that the flashes were not simultaneous due to the photon flight time. The question posed as the paradox is
Are you sure about that though? Because this is what I’ve seen everywhere I look - that there is no objective time frame wherein a moment of simultaneity that applies to both frames can be established.
I get the impression that relativity of simultaneity is not about that. From wiki:
“According to the special theory of relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York. The question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first.”
Note the bolded part. What is described to cause the non-simultaneity is not the distance and the longer distance light has to travel, but the different states of motion relative to the event.
Wiki is often presumptuous and erroneous. Read Einstein’s words;
He is REDEFINING the word “simultaneous” to mean “perceived by an observer to be simultaneous”.
He admits that the moving observer will move out from what he already defined as the center between the actual simultaneous strikes. So he defines the scenario in the same way that I define mine, with a couple of important differences.
1) I do not redefine what a word means. 2) I make it physically impossible for the “lightening strikes” to occur separately in time from anyone’s perspective (the trigger arms, although there are other methods). 3) I arrange for a record to serve as testimony of what actually took place (the stopped clocks).
Thus unlike Einstein’s version wherein no one has any way to know for sure what really took place due to the light travel time involved and having no remaining evidence of simultaneity, thus forced to make subjective guesses, my scenario arranges that there can be no doubt as to whether the flashes (lightening strikes) actually did occur together.
In effect, he was redefining what it means to say, “simultaneous”, and other words throughout the paper so that each was to mean ONLY “relative my subjective perspective”, thus seemingly removing the need for knowing any actuality, any absolute frame. But as reality would have it, words do not dictate the truth. Truth dictates the situation and if you want to hide the situation with your words, then you simply don’t know the truth (The Matrix). But the real situation cannot be hidden from ALL perspectives.
“You can fool some of the people some of the time and all of the people some of the time. But you can’t fool all of the people all of the time.”
The Stopped Clock Paradox reveals the truth that the redefined words attempt to hide.
And I bet that you thought Science was above such mind games of manipulation.
And in case you haven’t caught on, this all relates to; Clarify, VERIFY, Remember/Instill/Record/Document…
Sadly, no he is not. He requires that an ideal observer be in a specific place, half-way between the two spacetime events in question. In the example he is using, these events correspond to things that can be observed. It is not the judgment of the observer that matters, but the relationship of the events.
Hardly. For one thing, he does not use the word “actual”. What he does is clearly indicate that when we use one specific way of determining lengths (the rails), then we get a specific definition of simultaneity. Using a different means of determining lengths (the train), we get another definition of simultaneity. Ignoring this means ignoring the text and the actual physics.
Unfortunately, your scenario does not seem to be physically possible, since it is inconsistent.
It certainly reveals that you don’t know how to take the relativity of simultaneity into account so you constantly perform straw man arguments against relativity theory.
Well, you are the one presenting a theory here. You like to claim that it is Einstein’s but you are clearly wrong. You also like to play the victim and distract from the fact that you often ignore cogent points and questions. Like you just did.
