Special Relativity and momentum

[SDG]

...

But let's actually do the calculations for this completely different scenario anyways. In the rest frame, we have no magnetic field, and an electric field vertical. To use your equations, we need the direction y to be vertical (positive up), sideways is x (positive right), and out of the page z. These equations were written with the assumption that positive v is to the right, but that's the velocity of the moving frame relative to the rest frame. You've actually got the frame moving to the left, so keep in mind that v is negative.
...
OK, but what if the electron is already moving? Then you've got a vertical component of velocity, when you cross that with the B field you should get a sideways component for the force. Doesn't that make the electron deflect to the side?

No, it doesn't. And this is where things get really weird. If the electron is moving vertically, then in the moving frame its momentum is at an angle. And one of the weird aspects of special relativistic mechanics is that because momentum isn't linear with velocity anymore, the direction of any VELOCITY change doesn't need to be parallel to the direction of MOMENTUM change. Basically, to keep the electron moving to the right at the same velocity as it picks up speed vertically, we actually need to add momentum to the right as well. And how do we get that extra momentum to the right to maintain rightward velocity? From your magnetic field.

Thanks for this post!

Right, after the electric field is turned on and the electrons accelerate upwards, there is an electron velocity in the Y, Y' direction.
Where is the force pointing out from this upward velocity and the magnetic field?

Have you heard about spin orbit interaction?
This is where the relativity failed. It did not predict/expect spin orbit interaction.
The experiments/observations prove the drift is there.

 

[Ziggurat]

Thanks for this post!

Right, after the electric field is turned on and the electrons accelerate upwards, there is an electron velocity in the Y, Y' direction.
Where is the force pointing out from this upward velocity and the magnetic field?

I told you: it points forward. We require that forward force in order to maintain velocity to the side. Otherwise, as my last problem demonstrates, you actually LOSE velocity to the side as you accelerate upwards with a purely vertical force. Force is not always parallel to acceleration in special relativity. You still haven't grasped the significance of this fact.

Have you heard about spin orbit interaction?
This is where the relativity failed. It did not predict/expect spin orbit interaction.

You can't stay on topic, can you? Free electrons do not have spin orbit interactions, because they do not have orbits.

Whenever you're proved wrong on one thing, you try to change the subject. You couldn't get LED's right, so you switched to an electron in a capacitor gap. You can't get the electron in a capacitor right, so now you're trying to drag in spin-orbit coupling. And, no surprise, you have it wrong here too. Spin orbit coupling comes from relativistic effects, that's exactly what relativity predicts when you apply it to quantum mechanical models of hydrogen.

 

[SDG]

...

No, it doesn't. And this is where things get really weird. If the electron is moving vertically, then in the moving frame its momentum is at an angle. And one of the weird aspects of special relativistic mechanics is that because momentum isn't linear with velocity anymore, the direction of any VELOCITY change doesn't need to be parallel to the direction of MOMENTUM change. Basically, to keep the electron moving to the right at the same velocity as it picks up speed vertically, we actually need to add momentum to the right as well. And how do we get that extra momentum to the right to maintain rightward velocity? From your magnetic field.
...

The magnetic field and upward velocity are slowing down the electron in -x direction.

 

[SDG]

...
You can't stay on topic, can you? Free electrons do not have spin orbit interactions, because they do not have orbits.

Whenever you're proved wrong on one thing, you try to change the subject. You couldn't get LED's right, so you switched to an electron in a capacitor gap. You can't get the electron in a capacitor right, so now you're trying to drag in spin-orbit coupling. And, no surprise, you have it wrong here too. Spin orbit coupling comes from relativistic effects, that's exactly what relativity predicts when you apply it to quantum mechanical models of hydrogen.

My bad

The upward v and B point in -x direction.
There is a relativistic model of electron as a rotating flywheel, this is on topic, to understand electrons.
The flywheel is an isolated system when the flywheel rotates and is not accelerated.
The flywheel has different centroids that are frame dependent.
When the flywheel is accelerated then different frames predict different outcomes.

The relativity failed to predict the Lamb shift.
The Lamb shift, spin orbit interaction, is linked to the electron model, it is on topic.

 

[Ziggurat]

My bad

The upward v and B point in -x direction.

B doesn't point in the -x direction in your capacitor problem. It points in the -z direction. I went through the calculations in post 117.

There is a relativistic model of electron as a rotating flywheel, this is on topic, to understand electrons.

I guarantee that you don't understand electrons.

The relativity failed to predict the Lamb shift.

Why would it? That's a quantum electrodynamics effect, not a special relativity effect. Relativity doesn't predict interest rates either.

The Lamb shift, spin orbit interaction, is linked to the electron model, it is on topic.

No, it's not on topic, it's another attempt at a goal post shift. But this time, you don't even have a claim to go along with it.

You are running out of excuses. None of your claims add up. You're just laying on more and more layers of ignorance. Which is a shame, because there's some interesting stuff to learn here, if only you were willing to.

 

[SDG]

B doesn't point in the -x direction in your capacitor problem. It points in the -z direction. I went through the calculations in post 117.

Your point about v being negative is wrong.
You did not change observers. You are stuck in the rest frame.
The velocity v of the the field Y in the rest frame is 0.
When we switch observers then the velocity is v (not -v).
The right side of the N' equation is from the moving frame point of view.
The question is what is Y velocity in the moving frame?

Edit: N' points in the in Z' direction, outside of the screen.

 

[Ziggurat]

Do the problems in post 120. They are easy and you might actually learn something.

 

[SDG]

Do the problems in post 120. They are easy and you might actually learn something.

The scenario is more complex.
When the initial electric field is turned on the first magnetic field points out.
Then the electrons start to drift to the left.
When this happens electron 4-torques will evolve.
The situation is dynamic.
Here is how this might look from the moving frame.

The image is just a wire example from the internet.
There is no wire involved in our case but the electrons will move under angle (not a straight line though), the wire is for illustration (not perfect though).
The 4-torque evolution will initiate electron motion in helix trajectories.
The helix trajectories are not predicted by the rest frame.
The rest frame predicts straight electron current and a circular magnetic field as a response.

 

[Ziggurat]

The scenario is more complex.

No ****, Sherlock. The whole point was to make it as simple as possible. Nevertheless, understanding that simple problem is a prerequisite for understanding more complex ones.

And you don’t understand that simple problem.

 

[Ziggurat]

In post 115, The Man pointed out that the "gap" in an LED is not a physical gap between an anode and a cathode, and in fact doesn't even exist in space. I suspect he's right. I suspect you have confused diagrams of capacitors with diagrams of semiconductor bands. That would explain much of your confusion. Because none of what you're trying to talk about has any real connection to what's going on in an actual LED. And remember, you were the one who insisted on using an LED for this problem, not me.

 

[SDG]

No ****, Sherlock. The whole point was to make it as simple as possible. Nevertheless, understanding that simple problem is a prerequisite for understanding more complex ones.

And you don’t understand that simple problem.

The relativity does not explain properly momentum, change of momentum of electrons.
The Relativistic Hall Effect paper
shows how the relativistic flywheel model works for electrons.

Ziggurat, any objections to the paper?
Do you agree the centroids of isolated rotating systems are frame dependent?

 

[Ziggurat]

The relativity does not explain properly momentum, change of momentum of electrons.
The Relativistic Hall Effect paper
shows how the relativistic flywheel model works for electrons.

[qimg]https://i.imgur.com/G8YLStS.png[/qimg]


Ziggurat, any objections to the paper?
Do you agree the centroids of isolated rotating systems are frame dependent?

From the abstract:

"The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales: from elementary spinning particles, through classical light, to rotating black-holes."

I haven't dug through the paper in detail. On the surface, I have no objections. But I am left wondering what your point is. The paper doesn't claim that there is any flaw in special relativity, or any contradiction between SR and quantum mechanics. Quite the reverse, they explicitly state that there's agreement. I don't know why you think this is going to get you anywhere.

ETA: and you still don't understand LED's or special relativistic mechanics.

 

[SDG]

From the abstract:

"The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales: from elementary spinning particles, through classical light, to rotating black-holes."

I haven't dug through the paper in detail. On the surface, I have no objections. But I am left wondering what your point is. The paper doesn't claim that there is any flaw in special relativity, or any contradiction between SR and quantum mechanics. Quite the reverse, they explicitly state that there's agreement. I don't know why you think this is going to get you anywhere.

ETA: and you still don't understand LED's or special relativistic mechanics.

The relativity and hydrogen atom:

In physics, the Lamb shift, named after Willis Lamb, is a difference in energy between two energy levels 2S1/2 and 2P1/2 (in term symbol notation) of the hydrogen atom which was not predicted by the Dirac equation, according to which these states should have the same energy.

The Lamb Shift

In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928.

Dirac equation

I hope this sheds some light on the subject of quantum and relativistic approach.

 

[SDG]

...
I don't know why you think this is going to get you anywhere.

...

What happens if the flywheel is accelerated/decelerated through the wheel axle in -x direction?
What is predicted by S frame?
Notice the S' deceleration is not through the centroids, center of mass, what is going to happen?

 

[Ziggurat]

[qimg]https://i.imgur.com/eqmP8dC.png[/qimg]

What happens if the flywheel is accelerated/decelerated through the wheel axle in -x direction?
What is predicted by S frame?
Notice the S' deceleration is not through the centroids, center of mass, what is going to happen?

You seem to think you have stumbled upon a contradiction here, but you have not. Force is not invariant. The force you apply in the S fame doesn't have to be in the same direction as the force you apply in the S' frame. And the force direction does not have to be parallel to the acceleration direction either. This is a messy problem, and none of the assumptions you are likely relying upon to come up with what you think the answer is are actually true.

You would know at least some of this if you had done the problem I asked in post 120. But that would require actually doing calculations. They are easy calculations, but you would still have to do them.

 

[Ziggurat]

The relativity and hydrogen atom:

I'm not sure why you're hung up on the Dirac equation not predicting the Lamb shift. You seem to think that the Dirac equation is supposed to capture the entirety of quantum mechanincs + relativity. This is false. In particular, the Dirac equation does not include the quantization of the electromagnetic field. On its own, the Dirac equation is not, and never was, the complete theory of quantum mechanics. The fact that it is not complete is not a strike against quantum mechanics or relativity. The only problem here seems to be your insistence that it should be.

 

[SDG]

I'm not sure why you're hung up on the Dirac equation not predicting the Lamb shift. You seem to think that the Dirac equation is supposed to capture the entirety of quantum mechanincs + relativity. This is false. In particular, the Dirac equation does not include the quantization of the electromagnetic field. On its own, the Dirac equation is not, and never was, the complete theory of quantum mechanics. The fact that it is not complete is not a strike against quantum mechanics or relativity. The only problem here seems to be your insistence that it should be.

The Hydrogen atom orbitals

Let us assume there is a stationary Hydrogen atom in ground state (1,0,0) in the intergalactic space.
After a long time the Hydrogen atom is going to be attracted by a galaxy gravity and the atom starts to fall towards the galaxy.
The Hydrogen atom achieves let's say 0.5c speed towards the galaxy.
What is the shape of the Hydrogen atom at this moment in the rest frame of the atom and the galaxy center inertial frame?

 

[SDG]

You seem to think you have stumbled upon a contradiction here, but you have not. Force is not invariant. The force you apply in the S fame doesn't have to be in the same direction as the force you apply in the S' frame. And the force direction does not have to be parallel to the acceleration direction either. This is a messy problem, and none of the assumptions you are likely relying upon to come up with what you think the answer is are actually true.

You would know at least some of this if you had done the problem I asked in post 120. But that would require actually doing calculations. They are easy calculations, but you would still have to do them.

I agree, this is a messy problem.
How about we try...

Let us split the flywheel into top and bottom parts with their respective centroids.
The force does not propagate instantaneously.
It starts on the axle and moves towards centroids.
The force propagates evenly towards the top and the bottom centroids in the rest frame.
The force does not propagate evenly in the moving frame.
It has to travel longer to the bottom centroid and even slower because the flywheel bottom moves faster than the top.

Do you agree there is no angular velocity change predicted in the rest frame?
Could there be an angular velocity change in the moving frame?
... leading to a 4-torque evolution?

 

[Ziggurat]

Cut to the chase. You seem to think that there's a contradiction. Tell us what you think it is.

You did that with your first post. You were wrong, but at least you stated plainly what it is you were trying to say. Which allowed me to find your mistake pretty quickly.

You aren't using that initial setup anymore, but you also haven't acknowledged your mistakes with that initial setup. There are several possibilities. One is that you realize your mistakes, but you still think there are other problems with relativity. That would be the best case scenario.

But... I don't think that's what's happening. What I think is happening is that you still don't understand your mistake, and you're changing scenarios because you think that *I* didn't understand your initial scenario so you need a new one in order to show the same problem you imagine exists. And if I'm right, this is going to go nowhere. You're just going to over-complicate the problem in a vain attempt to find a contradiction which doesn't exist, because whenever you make it too complicated, your own misunderstandings crop up, but it becomes harder and harder to expose them plainly and harder and harder to solve the problem correctly, leading you to the mistaken impression that you're exposing problems with special relativity rather than your own misunderstandings.

And frankly, I've run out of patience. I'm not interested anymore. Not even for the sake of lurkers. I tried to teach you something about relativity, but you refuse to learn. You will only incorporate whatever I say to the degree it doesn't conflict with your own misconceptions.

You are not smarter than every physics Ph.D. of the last century. You are not even smarter than a single physics Ph.D. You have not discovered anything new, you have not found a fatal flaw in the theory of relativity. You just don't understand the subject well enough to figure it out yourself. It isn't any more complex than that.

 

[SDG]

Cut to the chase. You seem to think that there's a contradiction. Tell us what you think it is.

You did that with your first post. You were wrong, but at least you stated plainly what it is you were trying to say. Which allowed me to find your mistake pretty quickly.

You aren't using that initial setup anymore, but you also haven't acknowledged your mistakes with that initial setup. There are several possibilities. One is that you realize your mistakes, but you still think there are other problems with relativity. That would be the best case scenario.

But... I don't think that's what's happening. What I think is happening is that you still don't understand your mistake, and you're changing scenarios because you think that *I* didn't understand your initial scenario so you need a new one in order to show the same problem you imagine exists. And if I'm right, this is going to go nowhere. You're just going to over-complicate the problem in a vain attempt to find a contradiction which doesn't exist, because whenever you make it too complicated, your own misunderstandings crop up, but it becomes harder and harder to expose them plainly and harder and harder to solve the problem correctly, leading you to the mistaken impression that you're exposing problems with special relativity rather than your own misunderstandings.

And frankly, I've run out of patience. I'm not interested anymore. Not even for the sake of lurkers. I tried to teach you something about relativity, but you refuse to learn. You will only incorporate whatever I say to the degree it doesn't conflict with your own misconceptions.

You are not smarter than every physics Ph.D. of the last century. You are not even smarter than a single physics Ph.D. You have not discovered anything new, you have not found a fatal flaw in the theory of relativity. You just don't understand the subject well enough to figure it out yourself. It isn't any more complex than that.

My initial setup is OK, I'd like to return to it later.

Force is not invariant. The force you apply in the S fame doesn't have to be in the same direction as the force you apply in the S' frame.

I know forces point in different directions it is clear in my post #139 with the flywheel, body shape is frame dependent.
The important thing is to analyze 4-forces.
Still, the biggest problem is the 4-force change is frame dependent.
Very good example is the falling Hydrogen atom, my question from post #142.

Let us assume there is a stationary Hydrogen atom in ground state (1,0,0) in the intergalactic space.
After a long time the Hydrogen atom is going to be attracted by a galaxy gravity and the atom starts to fall towards the galaxy.
The Hydrogen atom achieves let's say 0.5c speed towards the galaxy.
What is the shape of the Hydrogen atom at this moment in the rest frame of the atom and the galaxy center inertial frame?

Hint: Does binding energy change in the galaxy center inertial frame? Does the binding energy change in the Hydrogen atom rest frame?