Special Relativity and momentum

[Ziggurat]

For SDG to believe otherwise is akin to thinking the island of Greenland changes shape when he flips a page of his atlas.

Don't give him ideas.

 

[SDG]

You have confused "constant" for "invariant". These are not the same thing, at all. See if you can figure out the distinction, it is both incredibly basic and incredibly important. And if you can't understand that distinction, you have no hope of understanding anything else.
...

Being constant in both frames means invariant between the frames.
If something is NOT invariant between the frames it means the change in one frame is not equal to the change in the other frame.
There is no change at all in both frames meaning the angular momentum is invariant between the frames.

 

[Ziggurat]

Being constant in both frames means invariant between the frames.

No, that is precisely NOT what it means.

"Constant" means it doesn't change with changing time. "Invariant" means it doesn't change with changing reference frame. Changing time and changing reference frame is very different.

Velocity can be constant, but it can never be invariant.

Proper time is invariant. But it is never constant.

 

[SDG]

You have confused "constant" for "invariant". These are not the same thing, at all. See if you can figure out the distinction, it is both incredibly basic and incredibly important. And if you can't understand that distinction, you have no hope of understanding anything else.

Furthermore, the wire is not an isolated system. The wire PLUS your capacitor PLUS whatever you use to charge your capacitor may together form an isolated system, but not the wire alone. And you asked about the wire.

Well, agreed, there is 'an external field' acting on the wire.
Having said that, what happens to the wire in the middle when the E field is turned on?
Is there an energy exchange between the wire and the field that would cause the wire to move in relation to the anode and the cathode?
Is there an energy exchange in the anode cathode setup that would cause a motion of the setup?
If we assume the field is not strong enough to release any electrons from the wire, just to move electrons towards the end of the wire and the cathode.

 

[SDG]

No, that is precisely NOT what it means.

"Constant" means it doesn't change with changing time. "Invariant" means it doesn't change with changing reference frame. Changing time and changing reference frame is very different.

Velocity can be constant, but it can never be invariant.

Proper time is invariant. But it is never constant.

Invariant as unchanged under some transformation.
If something is constant in one inertial frame then transformed then it has to be constant in the other inertial frame as well.
If an AM is not invariant it means it is constant in one frame and it keeps being transformed to different AM in the other frame.

 

[SDG]

No, that is precisely NOT what it means.

"Constant" means it doesn't change with changing time. "Invariant" means it doesn't change with changing reference frame. Changing time and changing reference frame is very different.

Velocity can be constant, but it can never be invariant.

Proper time is invariant. But it is never constant.

Angular velocity is constant in both frames under the transformation. It is invariant.
Even though the rim and the spokes deform and they 'appear' to have different velocity at different points in space.

Edit: If we take the 9 o'clock spoke in the rest frame, it will transform to a space position in the moving frame.
Each spoke that comes to 9 o'clock in the rest frame will transform to the same space position (in reference to the axle) in the moving frame.

 

[Crossbow]

Invariant as unchanged under some transformation.
If something is constant in one inertial frame then transformed then it has to be constant in the other inertial frame as well.
If an AM is not invariant it means it is constant in one frame and it keeps being transformed to different AM in the other frame.

This exceptional posting reminds me of something that a famous knight once explained to King Arthur many centuries ago:

"And that, my liege, is how we know the world to be banana shaped!"

 

[SDG]

...

Proper time is invariant. But it is never constant.

Proper time along the world line of an observer on the rim ticks at a constant rate.

Edit:

 

[Hellbound]

This exceptional posting reminds me of something that a famous knight once explained to King Arthur many centuries ago:

Meow! *thump*




Sent from my volcanic island lair using carrier pigeon.

 

[Ziggurat]

Invariant as unchanged under some transformation.
If something is constant in one inertial frame then transformed then it has to be constant in the other inertial frame as well.

This sounds superficially like it could be true, but it isn't.

And forget special relativity, it isn't even true in Newtonian mechanics. Angular momentum in particular can be constant in one frame and not constant in another frame. Hell, we don't even need to move to reference frames which are moving with respect to each other, we can have two inertial frames which are STATIONARY with respect to each other but only displaced, and angular momentum can be constant in one frame and changing in another.

You keep failing at the most basic levels of physics. You don't actually understand any of this stuff.

 

[Ziggurat]

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

Angular velocity is constant in both frames under the transformation.

It is most decidedly not. Even the picture should have clued you in. Note the spacing between spokes: in the frame where the wheel moves, the angular velocity at the top of the wheel is much greater than the angular velocity at the bottom of the wheel. Each point on the rim experiences a changing angular velocity as it travels around the wheel. This is why there is no paradox that a relativistically fast rolling wheel will travel more than pi*d in one revolution (in the road frame of reference), even though the length around the outside edge of the wheel is actually less than pi*d. The wheel contacts the road where the angular velocity is higher.

Even though the rim and the spokes deform and they 'appear' to have different velocity at different points in space.

They do not appear to have different velocities. They do have different velocities. This isn't an optical illusion. And your ETA's aren't relevant.

 

[SDG]

This sounds superficially like it could be true, but it isn't.

And forget special relativity, it isn't even true in Newtonian mechanics. Angular momentum in particular can be constant in one frame and not constant in another frame. Hell, we don't even need to move to reference frames which are moving with respect to each other, we can have two inertial frames which are STATIONARY with respect to each other but only displaced, and angular momentum can be constant in one frame and changing in another.

You keep failing at the most basic levels of physics. You don't actually understand any of this stuff.

It appears to me you are working with a preferred observers, that's not correct.
The inertial frame is defined by a grid of inertial observers and they have to agree on the angular velocity by definition.
Otherwise one is preferred over the other.
If we go by your definition then your observers predict different centripetal/centrifugal forces for an accelerated observer on a curved trajectory.
This observer cannot measure two different accelerations.

 

[Ziggurat]

Proper time along the world line of an observer on the rim ticks at a constant rate.

A constant rate with respect to what? Proper time does NOT have a constant rate with respect to coordinate time. Proper time has a constant rate with respect to a clock traveling along the world line of interest. And that clock measures... (wait for it)... proper time. So proper time has a constant rate with respect to proper time.

Congratulations, you have discovered a tautology. Want a prize?

But I didn't say the rate of proper time wasn't constant (which, depending on what you're measuring it with respect to, is either trivially true or simply false). I said proper time wasn't constant. Because, get this, time keeps going. Time never stops.

 

[Ziggurat]

It appears to me you are working with a preferred observers, that's not correct.

I'm not. You are, as usual, deeply confused.

The inertial frame is defined by a grid of inertial observers and they have to agree on the angular velocity by definition.

They can all agree on the angular velocity of any one point. But that point will change its angular velocity as it travels around the wheel. And all the inertial observers in that frame will all agree that it does, and they will all agree on how it does.

If we go by your definition

My definition of what?

then your observers predict different centripetal/centrifugal forces for an accelerated observer on a curved trajectory.
This observer cannot measure two different accelerations.

Different observers in different frames can measure different forces and different accelerations. Those are not invariant.

Different observers in the same frame will agree with each other. But each of them will see that the forces and accelerations of any given point will change as it travels around the wheel.

 

[SDG]

I'm not. You are, as usual, deeply confused.



They can all agree on the angular velocity of any one point. But that point will change its angular velocity as it travels around the wheel. And all the inertial observers in that frame will all agree that it does, and they will all agree on how it does.



My definition of what?



Different observers in different frames can measure different forces and different accelerations. Those are not invariant.

Different observers in the same frame will agree with each other. But each of them will see that the forces and accelerations of any given point will change as it travels around the wheel.

You stated this:

And forget special relativity, it isn't even true in Newtonian mechanics. Angular momentum in particular can be constant in one frame and not constant in another frame. Hell, we don't even need to move to reference frames which are moving with respect to each other, we can have two inertial frames which are STATIONARY with respect to each other but only displaced, and angular momentum can be constant in one frame and changing in another.

And this:
Different observers in different frames can measure different forces and different accelerations. Those are not invariant.
This is wrong in Newtonian mechanics.

 

[SDG]

Everything in the universe is moving at gamma = 2 in some reference frame, so anything that can happen at all can happen at gamma = 2.

But galaxies don't collide at relative velocities of gamma = 2. They aren't moving that fast.

Electrons and protons move fast in the intergalactic medium.
GZK limit

The Greisen–Zatsepin–Kuzmin limit (GZK limit) is a theoretical upper limit on the energy of cosmic ray protons traveling from other galaxies through the intergalactic medium to our galaxy. The limit is 5×1019 eV (50 EeV), or about 8 joules (the energy of a proton travelling at ≈ 99.99999999999999999998% the speed of light).

What would be a reason that they do not recombine?

 

[Ziggurat]

You stated this:


And this:
Different observers in different frames can measure different forces and different accelerations. Those are not invariant.
This is wrong in Newtonian mechanics.

That part wasn’t about Newtonian mechanics. The fact that a constant angular momentum in one frame doesn’t have to be constant in another was. Do try to keep up.

 

[Ziggurat]

Electrons and protons move fast in the intergalactic medium.
GZK limit


What would be a reason that they do not recombine?

How is it you think particles reach those speeds in the first place?

They could only recombine if their relative velocities were almost identical. Otherwise, they have too much kinetic energy even in their center of gravity frame to bind together. And what are the odds that two particles with such incredible speeds would be both traveling at the same velocity and in the same place? Basically zero.