A question from another thread: Why would a choice of coordinates produce physical consequences?
Assumption: A selection of coordinates (inertial reference system) does not change an objective physical reality.
All inertial observers should agree on physics.
Question: Does the transformation of the Maxwell-Hertz Equations change the physical reality? Specifically proper acceleration analysis?
Proper acceleration is absolute, meaning an accelerometer measures only one value and all inertial observers agree what is that value.
So if F=q(E+v x B) and F=ma and the transformation of the Maxwell-Hertz Equations is done;
Can we say a=a', the proper acceleration what the accelerometer measures?
A question from another thread: Why would a choice of coordinates produce physical consequences?
Assumption: A selection of coordinates (inertial reference system) does not change an objective physical reality.
All inertial observers should agree on physics.
Question: Does the transformation of the Maxwell-Hertz Equations change the physical reality? Specifically proper acceleration analysis?
Proper acceleration is absolute, meaning an accelerometer measures only one value and all inertial observers agree what is that value.
So if F=q(E+v x B) and F=ma and the transformation of the Maxwell-Hertz Equations is done;
Can we say a=a', the proper acceleration what the accelerometer measures?
In special relativity, F does not equal ma. F = dp/dt. In Newtonian mechanics, p = mv and a = dv/dt, so these two versions are equivalent. But in special relativity, p does not equal mv so dp/dt does not equal ma. So it's important to use F = dp/dt and not F = ma.
So no, a does not equal a', but it's not a problem with electromagnetism and special relativity, it's a problem with using the wrong definition of force.
ETA: one of the counter-intuitive consequences of the fact that F does not equal ma in special relativity is that F and a are not always even parallel to each other. Also note that proper acceleration doesn't equal coordinate acceleration.
This is a calculation of time dilation using fields, force, acceleration and all adds up.
There are many details in it.
One of them is smaller force acting on the electron in moving frames K'.
This has huge consequences. That lead to some interesting hypothesis.
We can discuss more, once the calculations are checked.
If the (as yet unidentified) author of that calculation agreed with you about the underscored factors being zero, he or she would have taken advantage of that to simplify equation (9.121).
The author of that calculation does not agree with you. For the underlined factors to be zero, the acceleration would have to be collinear to the force, but the author quite explicitly says "the major difference between (9.121) and" the "(nonrelativistic)" "(9.122 is that in the relativistic case, the acceleration is no longer collinear to the force exerted onto the particle."
Ziggurat pointed that out a mere 10 minutes after you started this thread.
If this thread is to consist of copy/pasted excerpts, it would be a good idea to give a citation when copy/pasting so readers can check the context. In 1905, for example, Einstein rather famously wrote more than one paper.
The following excerpt is Exercise 11.5 from page 569 of
John David Jackson. Classical Electrodynamics. John Wiley & Sons, 1999.
In the rest frame K at the event C v=0 and \beta=1 therefore we are left with F=ma based on the relativistic 9.121.
In the moving frames K' v' and a' are 90 degrees to each other the dot product is 0 and we are left with F'=\beta ma' based on the relativistic 9.121.
That's why the time dilation checks out based on the field calculations. This is a proof the calculation is correct based on the relativistic 9.121 F.
The most important observation is the objective reality consequence - the acceleration force is smaller in the moving frames K', the real cause for the time dilation.
I apologize for making such a mess of my original post. My edited post probably makes fewer mistakes, but it looks as though my mistakes, bad as they were, are turning out to be irrelevant.
In the rest frame K at the event C v=0 and \beta=1 therefore we are left with F=ma based on the relativistic 9.121. In the moving frames K' v and a are 90 degrees to each other
the dot product is 0 and we are left with F=\beta ma based on the relativistic 9.121.
Why are v and a perpendicular to each other in K' ?
ETA: For that matter, what does "the event C" (which did not appear within this thread until your copy/pasta earlier this morning) have to do with the copy/pasta you posted yesterday, in which you said the underlined factor is zero?
I apologize for making such a mess of my original post. My edited post probably makes fewer mistakes, but it looks as though my mistakes, bad as they were, are turning out to be irrelevant.
With my highlighting:
Why are v and a perpendicular to each other in K' ?
When you spoke of the underlined factors being zero, there was no such context. You didn't mention "plates" until this morning.
Furthermore, it seems to me you are also forgetting the acceleration due to the electric field in K' is almost as great as it was in K, so the net acceleration in frame K' is not perpendicular to the velocity in K' even under the assumptions made by that thought experiment. The acceleration and ensuing velocity in frame K are both perpendicular to the velocity of frame K' with respect to K, but that's not how frame K' sees it.
ETA: To put it another way, the velocity of the charged particle starts out as zero (in K, which is the rest frame of the plates) but becomes non-zero as the particle is accelerated by the electric field. In frame K, the charged particle's path looks like a straight line with velocity always perpendicular to the plate. In frame K', the charged particle's motion is curved, as the combined result of acceleration due to the electric field as viewed by K' and an acceleration perpendicular to its velocity due to the magnetic field as viewed by K'.
Editing yet again: Please let me correct that ETA paragraph. The "acceleration perpendicular to its velocity due to the magnetic field as viewed by K' " is in the direction of the plate, so I think the particle's path looks like a straight line even as viewed by K'. But that path, as viewed by K', isn't perpendicular to the motion of the plates (as viewed by K'), so I still don't understand why v and a are perpendicular to each other in K'.
In the rest frame K at the event C v=0 and \beta=1 therefore we are left with F=ma based on the relativistic 9.121.
In the moving frames K' v' and a' are 90 degrees to each other the dot product is 0 and we are left with F'=\beta ma' based on the relativistic 9.121.
That's why the time dilation checks out based on the field calculations. This is a proof the calculation is correct based on the relativistic 9.121 F.
The most important observation is the objective reality consequence - the acceleration force is smaller in the moving frames K', the real cause for the time dilation.
I'm kind of over the whole crackpot breakthrough game.
Get back to me when you can make money off this discovery. Give me one practical application of your insight. One product or service you can offer, based on this knowledge, that people will actually want to pay you for. Something that can't be done if people don't look at the world the way you do.
I'm kind of over the whole crackpot breakthrough game.
Get back to me when you can make money off this discovery. Give me one practical application of your insight. One product or service you can offer, based on this knowledge, that people will actually want to pay you for. Something that can't be done if people don't look at the world the way you do.
When you spoke of the underlined factors being zero, there was no such context. You didn't mention "plates" until this morning.
Furthermore, it seems to me you are also forgetting the acceleration due to the electric field in K' is almost as great as it was in K, so the net acceleration in frame K' is not perpendicular to the velocity in K' even under the assumptions made by that thought experiment. The acceleration and ensuing velocity in frame K are both perpendicular to the velocity of frame K' with respect to K, but that's not how frame K' sees it.
ETA: To put it another way, the velocity of the charged particle starts out as zero (in K, which is the rest frame of the plates) but becomes non-zero as the particle is accelerated by the electric field. In frame K, the charged particle's path looks like a straight line with velocity always perpendicular to the plate. In frame K', the charged particle's motion is curved, as the combined result of acceleration due to the electric field as viewed by K' and an acceleration perpendicular to its velocity due to the magnetic field as viewed by K'.
Editing yet again: Please let me correct that ETA paragraph. The "acceleration perpendicular to its velocity due to the magnetic field as viewed by K'" is in the direction of the plate, so I think the particle's path looks like a straight line even as viewed by K'. But that path, as viewed by K', isn't perpendicular to the motion of the plates (as viewed by K'), so I still don't understand why v and a are perpendicular to each other in K'.
Very thorough thinking, I appreciate that.
The evolution of trajectory is more complicated and eventually we will get there. There are more details to investigate.
The K' frames have electron velocity along x' only and acceleration a in -y' direction at the event C'.
At the moment one step calculation is presented. The fun starts when we split the time of flight into multiple pieces.
Would we get the correct time dilation result through fields if there was a mistake in the field transformation from one frame to another?
Again, the force F' in K' is smaller, that's very important observation.
No, I wouldn't think so, but I haven't bothered to check because I'm still puzzled as to what you're getting at. Indeed, I am still wondering why you think a is perpendicular to v in K' (other than at the initial event C).
A question from another thread: Why would a choice of coordinates produce physical consequences?
Assumption: A selection of coordinates (inertial reference system) does not change an objective physical reality.
All inertial observers should agree on physics.
Question: Does the transformation of the Maxwell-Hertz Equations change the physical reality? Specifically proper acceleration analysis?
No. In that other thread, however, you seemed to think a choice of coordinates can change physical reality. In this thread, so far, you have not yet suggested any way in which physical reality could be affected by a coordinate transformation.
If your goal here is to show that physical reality is not affected by your choice of coordinates, then this is likely to remain a boring thread (unless of course the author and sole proponent of Helland physics decides to participate).
If your goal is to show the opposite, then it might be a good idea to get around to stating your thesis one of these days.
The rest frame a, v are always parallel, 0 degrees between them, the electron is supposed follow a straight line along y axis, F does not change any direction.
The moving frames are different. The a', v' angles are changing, the F' forces in K'1 and K'2 are changing direction.
Different frames predict different location where the electron is going to hit the red plate.
This is the problem!
Yes, that would be a problem, but I don't think you have established that the problem actually exists. The two frames predict different spatial coordinates for where the electron hits the plate, but that of itself doesn't mean anything because those coordinates are, to coin a phrase, coordinate-dependent.
To establish that a problem actually exists, you'd have to show that the K' coordinates for the location at which the electron hits the plate are different from what the K coordinates for that location would be after transforming from K to K' coordinates.
Yes, that would be a problem, but I don't think you have established that the problem actually exists. The two frames predict different spatial coordinates for where the electron hits the plate, but that of itself doesn't mean anything because those coordinates are, to coin a phrase, coordinate-dependent.
To establish that a problem actually exists, you'd have to show that the K' coordinates for the location at which the electron hits the plate are different from what the K coordinates for that location would be after transforming from K to K' coordinates.
The y axis of K rest frame is at -4.54383m on x' in K'1 and at 4.54383m on x' in K'2 at the D' event when electron hits the anode.
If the electron is deflected and there are -dx', dx' then it means the electron hits the red plate at -4.54383-dx' in K'1 and 4.54383+dx' in K'2.
What transformation is going to erase the -dx', dx'?
The y axis of K rest frame is at -4.54383m on x' in K'1 and at 4.54383m on x' in K'2 at the D' event when electron hits the anode.
If the electron is deflected and there are -dx', dx' then it means the electron hits the red plate at -4.54383-dx' in K'1 and 4.54383+dx' in K'2.
What transformation is going to erase the -dx', dx'?
The deflections have opposite signs when calculated in the two non-rest frames, which might serve as something of a clue that the deflection is frame-dependent.
As I said, what you need to do is to calculate whether each frame's frame-dependent coordinates of the event, when transformed into the coordinates of another frame, coincide with that other frame's coordinates for the event.
It often seems like half the problems that students work on when learning special relativity involve learning why something that looks at first like a contradiction isn't actually a contradiction. And at least half of those problems only look like a contradiction because it's easy to screw up the calculations and do them wrong, because doing them right can be quite hard sometimes.
If you think you found a contradiction, you didn't. You screwed up somewhere.
The deflections have opposite signs when calculated in the two non-rest frames, which might serve as something of a clue that the deflection is frame-dependent.
As I said, what you need to do is to calculate whether each frame's frame-dependent coordinates of the event, when transformed into the coordinates of another frame, coincide with that other frame's coordinates for the event.
Here is a challenge for you.
\beta = 1.005
Electron hit event is H'=[1.516\times 10^{-7},-4.54383-0.1005,-0.5,0] of K'1.
Where is the event in K reference frame when we know the K origin is at -4.54383 of K'1?
It often seems like half the problems that students work on when learning special relativity involve learning why something that looks at first like a contradiction isn't actually a contradiction. And at least half of those problems only look like a contradiction because it's easy to screw up the calculations and do them wrong, because doing them right can be quite hard sometimes.
If you think you found a contradiction, you didn't. You screwed up somewhere.
Please, point out where?
If we look at 9.121, we can see the dot product is a scalar and then a + v makes the force F frame dependent because v is frame dependent.
I just showed how the Lorentz 4-force is frame dependent, how it rotates due to increase of the cross velocity and v x B changes direction.
Here is a challenge for you.
\beta = 1.005
Electron hit event is H'=[1.516\times 10^{-7},-4.54383-0.1005,-0.5,0] of K'1.
Where is the event in K reference frame when we know the K origin is at -4.54383 of K'1?
The real challenge here is for you to explain why you're subtracting 0.1005 from the x' coordinate of event D (which you are calling H' for reasons unexplained).
Except for the 0.1005, you got those numbers from some copy/pasted images written by an as-yet-unidentified author.
According to that author, event C is the spacetime event in which an electron departs from the cathode. Event D is the spacetime event in which that same electron arrives at the anode, which is 1m away from the cathode.
According to the author, in the coordinate system K for which the anode and cathode are at rest, and the electron is also at rest as of event C, the spacetime coordinates (t, x, y, z) of event C are (0, 0, 0.5, 0). According to the author, the spacetime coordinates of event D in coordinate system K are (1.508 × 10−7, 0, −0.5, 0).
According to the author, coordinate system K'1 is an inertial frame moving at v = −0.1c in the x direction, with its four coordinate directions aligned with those of the rest frame K. (The author also discusses a coordinate system K'2 moving in the opposite direction at 0.1c, but that's silly because the calculations for K'2 will be essentially the same as for K'1. I will therefore drop the subscript and refer to K'1 as K'.)
The author stipulates that event C has coordinates (0, 0, 0.5, 0) in the K' coordinates as well.
The Lorentz transformation tells us how to transform the coordinates of events C and D from coordinate system K to coordinate system K':
That time coordinate agrees with the author's 1.516 × 10−7 to within roundoff error. The value I calculated for x' = −4.546791076232676 does not quite agree with the author's value of −4.54383, but the discrepancy is small.
You, however, are saying the value of x' at event D (which you have renamed to H' for reasons unexplained) is −4.54383−0.1005 = −4.64433, so you are disagreeing with both the author (you failed to identify) and with my (higher precision) calculation.
It therefore appears you have made some kind of mistake. The challenge for you is to find your error and to correct it.
ETA:
γ = 1.005, so your 0.1005 probably came from multiplying γ by 0.1. As for why you subtracted that value from the approximately correct value, I'd guess you just applied the Lorentz transformation incorrectly.
It's not worth my time and effort to find your error. But far smarter people than both of us have examined relativity for a century now from angles you haven't even conceived of, and there are no inconsistencies. You aren't going to find any now. As I said, if you think you have, then you screwed up. And I don't really care about the details of how.
The real challenge here is for you to explain why you're subtracting 0.1005 from the x' coordinate of event D (which you are calling H' for reasons unexplained).
Except for the 0.1005, you got those numbers from some copy/pasted images written by an as-yet-unidentified author.
According to that author, event C is the spacetime event in which an electron departs from the cathode. Event D is the spacetime event in which that same electron arrives at the anode, which is 1m away from the cathode.
According to the author, in the coordinate system K for which the anode and cathode are at rest, and the electron is also at rest as of event C, the spacetime coordinates (t, x, y, z) of event C are (0, 0, 0.5, 0). According to the author, the spacetime coordinates of event D in coordinate system K are (1.508 × 10−7, 0, −0.5, 0).
According to the author, coordinate system K'1 is an inertial frame moving at v = −0.1c in the x direction, with its four coordinate directions aligned with those of the rest frame K. (The author also discusses a coordinate system K'2 moving in the opposite direction at 0.1c, but that's silly because the calculations for K'2 will be essentially the same as for K'1. I will therefore drop the subscript and refer to K'1 as K'.)
The author stipulates that event C has coordinates (0, 0, 0.5, 0) in the K' coordinates as well.
The Lorentz transformation tells us how to transform the coordinates of events C and D from coordinate system K to coordinate system K':
That time coordinate agrees with the author's 1.516 × 10−7 to within roundoff error. The value I calculated for x' = −4.546791076232676 does not quite agree with the author's value of −4.54383, but the discrepancy is small.
You, however, are saying the value of x' at event D (which you have renamed to H' for reasons unexplained) is −4.54383−0.1005 = −4.64433, so you are disagreeing with both the author (you failed to identify) and with my (higher precision) calculation.
It therefore appears you have made some kind of mistake. The challenge for you is to find your error and to correct it.
ETA:
γ = 1.005, so your 0.1005 probably came from multiplying γ by 0.1. As for why you subtracted that value from the approximately correct value, I'd guess you just applied the Lorentz transformation incorrectly.
The number -0.1005 is just an example of -dx. It is not an exact calculation of -dx.
I meant to type 0.1/\beta = 0.1/1.005=0.0995, this is K Lorentz contracted 0.1m in the moving K'1 frame.
The hit event in K would be D=[1.508 x 10-7,-0.1,-0.5,0] after the transformation from K'1 to K.
There is the disagreement on the x position between the frames.
The bold part, did you use c=299792458 in the calculation?
It's not worth my time and effort to find your error. But far smarter people than both of us have examined relativity for a century now from angles you haven't even conceived of, and there are no inconsistencies. You aren't going to find any now. As I said, if you think you have, then you screwed up. And I don't really care about the details of how.
No, I used c=3e8. My calculation was rough and ready, involving a couple of operations that weren't ideal with regard to roundoff error. That's why I wasn't at all bothered by small discrepancies. I left all of the calculated digits in the results because I was lazy.
I have no idea of what you think you mean by dx, but that's for you to figure out. I've seen enough of this thread.
It's not worth my time and effort to find your error. But far smarter people than both of us have examined relativity for a century now from angles you haven't even conceived of, and there are no inconsistencies. You aren't going to find any now. As I said, if you think you have, then you screwed up. And I don't really care about the details of how.
SDG has either made a rookie error, or is destined for a Nobel Prize in physics and scientific fame achieved previously by a small handful of people in the history physics.
I found this video to be a helpful illustration of why time dilation, length contraction, and gravity exist as explained by general relativity. https://m.youtube.com/watch?v=ZccTTUX-dBc&
Yes, there's now a horizontal component to the force. But so what? Do you think this means that there's going to be a horizontal deflection, leading to an inconsistency? Nope. There isn't. As I said, force isn't always parallel to acceleration. The acceleration remains vertical.
Yes, there's now a horizontal component to the force. But so what? Do you think this means that there's going to be a horizontal deflection, leading to an inconsistency? Nope. There isn't. As I said, force isn't always parallel to acceleration. The acceleration remains vertical.
No, I did not say that at all. Pay closer attention. I'm saying acceleration isn't parallel to force. You're assuming that it is, but this assumption is wrong.
No, I did not say that at all. Pay closer attention. I'm saying acceleration isn't parallel to force. You're assuming that it is, but this assumption is wrong.
The Lorentz force affects the trajectory. "Change" is too vague a word to be useful here, because change has to be relative to something and you haven't specified what.
You've made one error already, assuming that the acceleration is always parallel to the force when it's not. I suspect you may have made an additional error as well. Did you know that the Coulomb force is not invariant between reference frames? It's larger in the frame where the charged plates are moving. If you only look at the addition of the Lorentz force and don't account for the change in the Coulomb force, you're going to get the wrong answer.
Again: if you think you found an inconsistency, you didn't. You screwed up somewhere. Sometimes finding where can be a challenge, but it's a guarantee.
It is easy to show that the magnetic vxB x component does not cancel out with the x component of v(v.E)/c2.
If x components do not cancel out there is some dx change.
The electron is a spin particle. Spin particles have torques related to spin and orbit.
The orbital torque is frame dependent, the spin torque is independent/absolute.
The interaction between the spin and orbital torques breaks the symmetry between x components.
The known observations prove the spin-orbit interaction.
The hydrogen Lamb shift, hydrogen 21cm line, ...
You changed the scenario you are examining. Torque played no role in your first scenario. You claimed an inconsistency but could not show it. Now you are claiming another separate inconsistency and still can't demonstrate it. I'm sure you are messing this one up too.
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