Velocity Goes Into Itself.

talanum1

talanum1

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We have $\gamma = 1/sqrt(1-v^2/c^2)$ and then: $\vector{v}=\gamma (\vector{e}_0c+\vector{u}(t))$. This has $\vector{v}$ ill defined: it occurs in it's own definition.
 
talanum1 said:
We have $\gamma = 1/sqrt(1-v^2/c^2)$ and then: $\vector{v}=\gamma (\vector{e}_0c+\vector{u}(t))$. This has $\vector{v}$ ill defined: it occurs in it's own definition.
Click to expand...

How are you doing?
 
talanum1 said:
We have $\gamma = 1/sqrt(1-v^2/c^2)$ and then: $\vector{v}=\gamma (\vector{e}_0c+\vector{u}(t))$. This has $\vector{v}$ ill defined: it occurs in it's own definition.
Click to expand...

ChatGPT:

It only looks like a circular definition because two different things are being called “velocity.” In relativity, there’s the ordinary 3-velocity u (how fast something moves through space) and the 4-velocity U (how it moves through spacetime — space and time together). The familiar Lorentz factor comes from the 3-speed:
(\gamma = 1/\sqrt{1 - |\mathbf{u}|^2/c^2}).
Once you have that, the 4-velocity is built from it as
(\mathbf{U} = \gamma(\mathbf{u})(c,\mathbf{e}_0 + \mathbf{u})).
If you accidentally use the same symbol for both, it looks like the velocity is hiding inside its own definition — but that’s just a labeling mix-up. Keep the two meanings separate, and the formula makes perfect sense.


(Think of it as the difference between how fast you move through space and how fast you move through time.)
 
@talanum1 , why is it that you usually choose not to first check with ChatGPT, you've done so before.... could have saved yourself the embarrassment
If it's off-track, try a couple of minutes fine tuning your questions / directives, thrown into a squashed single input if need be.

Anyway I'm done doing that.
 
@bwana @The_Librarian I would like to propose a suggestion , that all these threads could be in one single thread for the OP:
talanum1

Thread 'Different Properties when Looked at than if not.'

Objects have different magneto-optical properties when looked at versus when not. Objects not looked at are similar to objects in dreams. I had a dream in which water flowed over a wall, and there were little circular waves in it.
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talanum1

Thread 'Different Properties when Looked at than if not.'

Objects have different magneto-optical properties when looked at versus when not. Objects not looked at are similar to objects in dreams. I had a dream in which water flowed over a wall, and there were little circular waves in it.
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talanum1

Thread 'The Belief that an Emitted Particle was not Contained in the Emitting Particle is Wrong.'

Proof:

If it was not wrong, then at least a part of the Emitted Particle must have been created from energy. Since the corresponding anti-matter parts are not also produced the Emitted Particle has been illegally produced. Since the Emitted Particle is actually produced, the assumption must be false.

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talanum1

Thread 'Where does the Color go?'

When a pion decays to an electron and electron antineutrino, what happens to the color charge the pi-minus had?
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talanum1

Thread 'I can Prove Neutrons don't Decay by Quarks Transforming.'

Proof:

Take the reaction:

u+e^-→d+ν_e (1)

Since the process is called "electron capture" the electron can't have changed into the neutrino, which is therefore illegally produced. So the reaction can't happen like that. Now if we rewrite (1) as:

u+e^-+(ν_e)¯+ν_e→d+ν_e (2)

and we cancel the neutrino on both sides to get:

u+e^-+(ν_e)¯→d (3)

we see that the reaction couldn't have happened like this because the electron anti-neutrino illegally ceased to exist. Instead, we must find a way for the electron and electron anti-neutrino to combine into energy. The first step toward this is...
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talanum1

Thread 'Particles must Carry Quantum Numbers Inside them: here's why.'

Spacetime must read particle quantum numbers because it has to bind electrons with no strangeness to electron antineutrinos differently than electrons with strangeness = -1 and it must compute conservation of energy differently in the two cases.

It is well known that a s-anti-u can decay into an electron and electron antineutrino. In this case the resulting electrons will have strangeness = -1.
 
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