- #36
PAllen
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Isn’t that what this is?DaveC426913 said:Er. Is that something usually required for a Basic High School level thread?
Isn’t that what this is?DaveC426913 said:Er. Is that something usually required for a Basic High School level thread?
It is. You're asking me to do a Lorentz Transform. I picked Basic HS to limit mathematical explanations.PAllen said:Isn’t that what his is?
I thought Lorentz transforms were ok to expect for a B level thread. If not, I don’t see how to proceed except for you to accept the relativity of simultaneity requires what I said in post #31 to be true.DaveC426913 said:It is. You're asking me to do a Lorentz Transform. I picked Basic HS to limit mathematical explanations.
I intuit it, just never got past HS math.PAllen said:I thought Lorentz transforms were ok to expect for a B level thread. If not, I don’t see how to proceed except for you to accept the relativity of simultaneity requires what I said in post #31 to be true.
DaveC426913 said:Summary: If we fire two electrons at the same time, one metre apart, should they length contract till they're less than a metre apart?
I've managed to stump myself in attempting to answer a member on another forum.
He is attempting to demonstrate length contraction using two electrons a known distance apart and moving at a known velocity.My thought experiment is based on his proposal; that's why I've chosen the components I have.
We have two parallel electron guns. Ga and Gb. Gb is one metre behind Ga and sightly offset to one side. Both are dialed down so they fire only one electron at a time.
We have two detectors, Da and Db, each 10 metres away from its gun.
To sum: , we have two identical setups, Sa, and Sb, with Sb just happening to be displaced by one metre along the direction of travel.We fire both guns simultaneously. The electrons are fired with enough energy to achieve relativistic velocities, say, 0.87c.
Electrona and Electrona leave their gun at 0.87c, and travel to their detector 10m away.
The detectors should light up at exactly the same time. Right?
A Lorentz transform is high school math.DaveC426913 said:I intuit it, just never got past HS math.
I've always been talking about the lab frame. But I clarified here and there.pervect said:By "at the same time", I assume you mean "at the same time in the lab frame".
You didn't specify.
You use "at the same time" a lot in your analysis, without talking about an associated frame.
I'm interested in the lab frame. That's where the experiment is observed. The timing of the emissions, the timing of the detections and the length contraction are all observable in the lab frame.pervect said:It might be helpful to draw a pair of space-time diagrams, one space-time diagram of what happens in the lab frame, another space-time diagram that happens in the frame moving with the electrons.
DaveC426913 said:I've always been talking about the lab frame. But I clarified here and there.I'm interested in the lab frame. That's where the experiment is observed. The timing of the emissions, the timing of the detections and the length contraction are all observable in the lab frame.
I've used a wire. (I know it doesn't change anything in principle.) The wire is simply a one metre long "stick" which, when we observe it moving at .87c in the lab frame, will be observed to be only .5m long. We don't need to examine it from the wire's FoR (or some point on it) to know that, in the lab, we will observe it contracted.pervect said:Usually, the use of a string implies some interest in something other than the lab frame. If you never invoke any other frame, the distance between the two electrons does not change. But it's difficult to see why you'd introduce a string if you didn't care about something more than the lab frame. You might care about either the notion of the "proper length" of the string, the notion of the string as a "rigid body", and/or the closely related notion of the length of the string in its own frame. But if you don't for some reason care about any of those, it doesn't matter. But what is the purpose of the string, then, if you don't care about any of that?
If it is not attached to either electron, and it’s front end remains in touch with the front electron, do you understand that it’s rear will extend only half way to the rear electron? And this is because, in the lab frame, it’s rear accelerated more than its front.DaveC426913 said:I've used a wire. (I know it doesn't change anything in principle.) The wire is simply a one metre long "stick" which, when we observe it moving at .87c in the lab frame, will be observed to be only .5m long. We don't need to examine it from the wire's FoR (or some point on it) to know that, in the lab, we will observe it contracted.
I'm trying to figure out why the distance to the trailing electron does not likewise decrease.PAllen said:If it is not attached to either electron, and it’s front end remains in touch with the front electron, do you understand tat it’s rear will extend only half way to the rear electron?
Relativity of simultaneity is not signal delay, but what is left after you already accounted for signal delay.DaveC426913 said:My take:
If the leading electron - right after exiting the gun - were to look back at the trailing electron, it would not immediately see the trailing electron being fired. It takes time for that event to propagate (at c) to where the leading electron experiences it. ...
PAllen said:Please study the posts.
DaveC426913 said:I did.
I thought I already knew.Vanadium 50 said:... you shouldn't expect to immediately understand.
DaveC426913 said:If we fire two electrons at the same time, one metre apart, should they length contract till they're less than a metre apart?
PAllen said:If you force the electron acceleration profiles fo be simultaneous in the lab frame, the the string will have been stretched
They aren't. Who/what is being acted on by a force is different.metastable said:If the 2 scenarios are equivalent
They aren’t equivalent.metastable said:I'm confused on this point. How is the electrons being "fired" in the lab frame any different than an observer being fired away from the electrons? If the 2 scenarios are equivalent, why would the string between the electrons have any tension (ignoring the electric repulsion)?