Special Relativity and momentum

[Ziggurat]

The diagram I showed is simplified but close enough.
There is a possible design; anode and cathode as I showed it.

You didn’t actually answer my question. And I don’t think you understand what those diagrams represent. You googled some words, found a link, and that’s as far as you could actually go. You don’t know enough to actually make sense of what you found.

 

[Dave Rogers]

Jesus Christ, you're trying to define a thought experiment involving a single photon in free space and you decided an eye diagram was relevant? This is like watching a chimpanzee trying to use Wikipedia. OK, if introducing irrelevant concepts is what floats your boat, is the semiconductor material you use for your LED direct or indirect gap, and what are the electron, light hole and heavy hole effective masses? None of it has the slightest relevance to your thought experiment, but neither does aberration or Bremsstrahlung.

Dave

 

[SDG]

To achieve a light emission electrons have to separate from the cathode.
Electrons flow in the magnetic field and they will drift to the left considering the setup from the above.
That's the physical cause for the rotation, this is what determines the recoil direction.

 

[SDG]

Jesus Christ, you're trying to define a thought experiment involving a single photon in free space and you decided an eye diagram was relevant? This is like watching a chimpanzee trying to use Wikipedia. OK, if introducing irrelevant concepts is what floats your boat, is the semiconductor material you use for your LED direct or indirect gap, and what are the electron, light hole and heavy hole effective masses? None of it has the slightest relevance to your thought experiment, but neither does aberration or Bremsstrahlung.

Dave

The thought experiment is simplified but it holds.
The key attribute is to see how electrons drift in the magnetic field.

 

[Ziggurat]

To achieve a light emission electrons have to separate from the cathode.
Electrons flow in the magnetic field and they will drift to the left considering the setup from the above.
That's the physical cause for the rotation, this is what determines the recoil direction.

No, it isn't. First off, the scaling is wrong. The magnetic field due to the diode current will scale with current, the deflection of individual electrons will scale with current, so the total deflection will scale with current squared, but the photon output will only scale with current.

Second and even more damningly, the magnetic field can be controlled independently. You can apply a static magnetic field to point whichever way you want, and it won't change the photon output. You could deflect the electrons in any direction you want, and nothing would change. So none of this can have anything to do with your idea.

You are, as usual, just completely and utterly wrong.

 

[SDG]

No, it isn't. First off, the scaling is wrong. The magnetic field due to the diode current will scale with current, the deflection of individual electrons will scale with current, so the total deflection will scale with current squared, but the photon output will only scale with current.

Second and even more damningly, the magnetic field can be controlled independently. You can apply a static magnetic field to point whichever way you want, and it won't change the photon output. You could deflect the electrons in any direction you want, and nothing would change. So none of this can have anything to do with your idea.

You are, as usual, just completely and utterly wrong.

Please, pause for a second.

This is in the rest frame. There is only -Y electric field nothing else.
Are electrons going to move in the straight direction in the rest frame?

 

[Ziggurat]

Please, pause for a second.

[qimg]https://i.imgur.com/pQbT8bJ.png[/qimg]

This is in the rest frame. There is only -Y electric field nothing else.
Are electrons going to move in the straight direction in the rest frame?

It doesn't matter the frame. Your picture is not an accurate drawing of what's happening inside the diode. There's actually very little electric field at the junction when driven with forward bias. The electric field isn't what drives the transition. In fact, the electric field at the junction is larger when there is NO bias and NO current than when there is current under forward bias..

Your understanding has no connection to what's actually going on in an LED. You are completely clueless.

 

[SDG]

It doesn't matter the frame. Your picture is not an accurate drawing of what's happening inside the diode. There's actually very little electric field at the junction when driven with forward bias. The electric field isn't what drives the transition. In fact, the electric field at the junction is larger when there is NO bias and NO current than when there is current under forward bias..

Your understanding has no connection to what's actually going on in an LED. You are completely clueless.

You said:

We can make this an unrealistic flashlight (ie, it could output more power than any actual flashlight),

I am doing that all along. I know the effect is very tiny, nevertheless, the electron flow is there and the diagram above is very much simplification.

The question stands.
Are electrons going to move in the straight direction in the rest frame?

 

[Ziggurat]

You said:


I am doing that all along. I know the effect is very tiny, nevertheless, the electron flow is there and the diagram above is very much simplification.

The question stands.
Are electrons going to move in the straight direction in the rest frame?

They can take whatever path you want them to, it doesn't matter. The direction of motion is not relevant. The electrons can even be stationary when they emit a photon. LEDs do not work the way you think they work. You insisted that it was important that this was an LED (it isn't), but your entire conception of them is wrong.

 

[SDG]

They can take whatever path you want them to, it doesn't matter. The direction of motion is not relevant. The electrons can even be stationary when they emit a photon. LEDs do not work the way you think they work. You insisted that it was important that this was an LED (it isn't), but your entire conception of them is wrong.

Let us briefly talk electromagnetism to clarify the idea of the thought experiment and the setup.
If we had the anode and cathode in a shielded quartz vacuum chamber in a decent vacuum (non-collisional plasma), collisions mean free path is bigger than distance between anode and cathode, then electrons would move in a straight line more or less within uncertainty boundaries of the path.
Do you agree?

 

[SDG]

The Hall effect

Not only in vacuum...

 

[Ziggurat]

The Hall effect

[qimg]https://i.imgur.com/8BJxBC3.png[/qimg]

Not only in vacuum...

Why the hell do you keep going on about vacuums? There are no vacuums in an LED. An LED does not behave like a vacuum tube. No part of an LED operates anything like your vacuum tube drawing. Electrons are never accelerated across any gap.

And I know plenty about the Hall effect. I've used Hall probes to measure magnetic field strength.

But the Hall effect isn't relevant here. You can make a magnetic field point in any direction you want. Hell, you can make the electon travel in any direction you want. It won't make any difference.

You still have no clue about how an LED works. They are not sensitive to magnetic fields.

 

[tusenfem]

You still have no clue about how an LED works. They are not sensitive to magnetic fields.

Maybe we should go back to the OP and like already proposed, do a classical version of a gun firing a bullet. It is obvious that SDG will come up with more and more complex stuff (e.g. bring up the magnetic vector potential and the behaviour of electrons, the experiment's name is avoiding me at the moment ) only to keep away from the actual discussion that was started in the OP.

 

[SDG]

Why the hell do you keep going on about vacuums? There are no vacuums in an LED. An LED does not behave like a vacuum tube. No part of an LED operates anything like your vacuum tube drawing. Electrons are never accelerated across any gap.

And I know plenty about the Hall effect. I've used Hall probes to measure magnetic field strength.

But the Hall effect isn't relevant here. You can make a magnetic field point in any direction you want. Hell, you can make the electon travel in any direction you want. It won't make any difference.

You still have no clue about how an LED works. They are not sensitive to magnetic fields.

Here is the equation from Einstein's 1905 paper:

If the rest frame has all values 0 and only -Y electric field exists then there is additional N' magnetic field in the moving frame after transformation from the rest frame to the moving frame.
That is the reason why electrons will start to drift.
Electrons are suppose to move in a 'straight' path in the electric field in the rest frame.
But they are going to drift in the moving frame due to N' magnetic field.
This is a contradiction between inertial reference frames.

Pointing out the Hall effect shows this happens in (semi)conductors as well.
This is the physical reason for the flashlight rotation.

 

[The Man]

Here is the equation from Einstein's 1905 paper:

[qimg]https://i.imgur.com/36SuI5J.png[/qimg]


If the rest frame has all values 0 and only -Y electric field exists then there is additional N' magnetic field in the moving frame after transformation from the rest frame to the moving frame.
That is the reason why electrons will start to drift.
Electrons are suppose to move in a 'straight' path in the electric field in the rest frame.
But they are going to drift in the moving frame due to N' magnetic field.
This is a contradiction between inertial reference frames.

Not in the least, a magnetic field results from a time varying electrical field. In the rest frame the electric field doesn't vary over time and only varies over space. In the moving frame it varies over both time and space. The "drift" as you put it in the moving frame is what keeps the electrons moving apparently straight in the electrical field of the rest frame. Just as space and time vary from one to the other in relativity so too do electrical and magnetic fields. That's the basses of the interchangeability "between inertial reference frames" and not a "contradiction between inertial reference frames". Part of the spatial component of the rest frame becomes the time component of the moving frame. ETA: As such part of the static electrical field of the rest frame becomes a magnetic field in the moving frame.

ETA2: Again, as noted before by Ziggurat this vacuum gap type application is not how LEDs work.

Pointing out the Hall effect shows this happens in (semi)conductors as well.
This is the physical reason for the flashlight rotation.

No, as noted by Ziggurat before the "gap" in an LED or any solid state component is a band gap not some kind of vacuum gap. Basically the difference in energy states from being in a bound state with an atom of the lattice structure (in the valance band) and more free to move about the lattice structure (in the conduction band). Such electrons (conduction band) are generally modeled as an electron gas infusing the positively charged lattice structure.

 

[Dave Rogers]

If the rest frame has all values 0 and only -Y electric field exists then there is additional N' magnetic field in the moving frame after transformation from the rest frame to the moving frame.
That is the reason why electrons will start to drift.
Electrons are suppose to move in a 'straight' path in the electric field in the rest frame.
But they are going to drift in the moving frame due to N' magnetic field.

You have that precisely arse about face. The N' magnetic field is what makes the electrons move in a straight, but diagonal, line in the moving frame when the electric field is still entirely in the Y direction.

This is a contradiction between inertial reference frames.

Wrong. It's the reason why there isn't a contradiction between inertial reference frames.

Dave

 

[Ziggurat]

If the rest frame has all values 0 and only -Y electric field exists then there is additional N' magnetic field in the moving frame after transformation from the rest frame to the moving frame.
That is the reason why electrons will start to drift.

If.

But again, this isn't how an LED works. The outgoing photon produces whatever impulse it produces REGARDLESS of which way the electron is drifting. The electron's direction of motion isn't relevant. The magnetic field isn't relevant. How do I know? Because you can change them all without changing the photon's impulse.

Electrons are suppose to move in a 'straight' path in the electric field in the rest frame.
But they are going to drift in the moving frame due to N' magnetic field.
This is a contradiction between inertial reference frames.

OK, now you're talking about something completely different. This has NOTHING to do with LED flashlights. This is a completely different claim.

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.

So using arbitrary units (they won't end up mattering), we have

X = 0
Y = -1
Z = 0

L = 0
M = 0
N = 0

OK, so let's do the transformations.

X' = X = 0
Y' = gamma*[Y - (v/c)N] = -Beta
Z' = gamma*[Z - (v/c)M] = 0

L' = L = 0
M' = gamma*[M + (v/c)Z] = 0
N' = gamma*[N - (v/c)Y] = gamma*(v/c)

So we've got a magnetic field pointing into the page (remember, v is negative)

Now things are going to get a bit weird, and this is another case where you know enough to set up a problem with some subtleties, but not enough to actually understand them or how they resolve.

We start with an electron at rest in the rest frame. It experiences an upward force from the electric field. In the moving frame, the electric field is the same, so this force is also the same. But now it's moving to the right in a magnetic field, using vxB to get the direction, there's a force from the magnetic field pointing vertically. It will not deflect at all, it's still just being pushed vertically.

Now at this point, you might be asking why the force vertically should be changing. And now it's really getting messy. In relativity, F = dp/dt. But p is NOT equal to mv. p = mu/(1-u²/c²) (I'm using u as the speed of the electron, separate from the speed of the moving frame). Both p and u are vectors. So taking the time derivative of this is messy. There's no reason to expect F to remain reference-frame dependent.

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.

This is actually a really interesting aspect of relativistic mechanics that you've stumbled upon. But you don't actually understand any of it, and you aren't equipped to even make any sense of it.

Furthermore, all of this can be set up with just an electron and a capacitor plate. You don't need an LED, you don't need any photons, you don't need any battery. It's a completely different problem which there's no point in needlessly complicating.

Pointing out the Hall effect shows this happens in (semi)conductors as well.
This is the physical reason for the flashlight rotation.

No, it isn't.

Yet one more irony to all of this, and another indicator that you really don't know what you're talking about in any of this, is that an LED works by using a p-n junction. And in a p-n junction, the Hall effect will show negative charge carriers on one side of the junction and positive charge carriers on the other. So the Hall voltages will be reversed, which means the electrons will be deflected in different directions on each side of the junction.

None of this works the way you think it does.

 

[Ziggurat]

You have that precisely arse about face. The N' magnetic field is what makes the electrons move in a straight, but diagonal, line in the moving frame when the electric field is still entirely in the Y direction.

It's actually more complicated than that. Much more complicated (see my above post). But he's still wrong, he still has no idea what he's doing, and he doesn't have the capacity to actually solve any of this.

 

[Ziggurat]

OK, SDG, here's a really simple (well, as simple as I can make it) relativistic mechanics problem.

Step 1:
We have mass m starting at rest. Then we push on it really hard in the +x direction, so that it has a momentum of m*c.

Question 1) What is its velocity? (hint: it's not c)

Step 2:
So it's travelling in the +x direction, but now we push on it in the +y direction, giving it the same impulse in that direction. Its momentum is now m*c i + m*c j, where i and j are unit vectors in the +x and +y directions.

Question 2) What is its velocity now? What is the velocity component in the x direction?

Question 3) Did it accelerate parallel to the applied force in step 2?

These calculations are actually quite easy (especially by the standards of relativistic mechanics), but the results are not intuitive. But they can provide some insight into why you are wrong about what's going on in your parallel plate capacitor problem. In order to attain that insight, though, you need to actually open your mind to the possibility that other people might know more than you do, and you might actually learn something from them if you pay attention.

 

[Ziggurat]

I know SDG won't actually do the calculations, so for those who are curious, here they are.

Question 1:

In relativistic mechanics, p does not equal mv. Instead, p = mv/sqrt[1-(v²/c²)]. So we have
p = mc = mv/sqrt[1-(v²/c²)]
p² = m²c² = m²v²/[1-(v²/c²)]
[1-(v²/c²)]c² = v²c² - v² = v²c² = 2v²v² = (1/2)*c²v = [1/sqrt(2)]*c

Question 2:

p = mc (i + j)
p² = m²c² (i² + j²)
= 2m²c²2m²c² = m²v²/[1-(v²/c²)]
2*[1-(v²/c²)]c² = v²2*c² - v² = v²2*c² = 3v²v² = (2/3)*c²
Now we note that the i and j components of v must be equal (since p and v are parallel), so v
v = v_xi + v_yj
where v_x = v_y
v² = v_x² + v_y² = 2v_x²2v_x² = (2/3)*c²v_x² = (1/3)*c²v_x = [1/sqrt(3)]*c
v = [1/sqrt(3)]*c i + [1/sqrt(3)]*c j

Question 3:

Our acceleration was NOT parallel to our applied force. We applied a force only along y, but we accelerated both along y and along x. Our mass decreased its velocity in the x direction, even though it increased its total velocity. Even though we did not push along the x direction, the mass experienced acceleration along the x direction.

Which brings us to the punch line. In special relativity, when you apply a force in a direction other than the direction our object is moving, the acceleration WILL NOT be parallel to the applied force.