Information about the speed of an elementary particle

[Cerveny]

Where is saved the information about the speed of an elementary particle? And how is its representation (what is its direction related to)?

[thalarch]

Where is saved the information about the speed of an elementary particle? And how is its representation (what is its direction related to)?

Disambiguation of topic required. Do you refer to its speed in the context of physical information as embodied by the particle itself, or are you more mundanely asking about an information resource somewhere dealing with the speed of particles? Situation muddled additionally toward the former by mention of representation, which is part of PI concept-babble:

representation (of information) --> encoding of some pattern of information within another pattern

[converge]

I agree with thealarch. I'm not sure I understand what you're asking. Could you explain?

I'll take a guess at what you mean though:

The information of the speed of a particle doesn't exist until a measurement is made and its waveform collapses. Before that, it exists as a wavefunction with a range of speeds. The information of the speed can be erased (see the "quantum eraser" experiment), and it gets re-created any time a measurement is taken that causes collapse.

As for its representation, it's the Schroedinger equation for the wave function when its in its unknown state, and it's represented as a discrete vector in a known state. The direction is relative to you, or whatever frame of reference you decide to measure from. There's no absolute direction or speed, only relative. The space and time that it's moving through will change depending on your frame of reference.

[Cerveny]

Suppose free electron (in STR “empty” space). It has some direction and some velocity (they can differ by related STR “frame”). Suppose another free electron (with the same spin). Now focus at these two “object”. How they differ? Again, where is saved information about they speeds and energy?

[converge]

As I understand it (and my understanding of quantum physics is a little fuzzy... no pun intended), both electrons are in a state of superposition, described only by their wavefunctions. Their absolute position and direction and velocity literally don't exist. They only pop into existence when a measurement is taken on one of them and it causes waveform collapse. It's like Schroedinger's cat; the information about whether the cat is alive or dead literally doesn't exist until the box is opened, before then, it's in a superposition of both states. (I'm not implying the cat experiment actually works like that, but it's a well known example.)

[Cerveny]

There is no quantum number that describes energy or speed direction of free particle :( Even there is no quantum description of common free particle (perhaps its creation or annihilation). Let us keep classical picture of electron...

[i blame blame]

Suppose free electron (in STR “empty” space). It has some direction and some velocity (they can differ by related STR “frame”). Suppose another free electron (with the same spin). Now focus at these two “object”. How they differ? Again, where is saved information about they speeds and energy?

They must differ in location as they would otherwise violate the Pauli exclusion principle.

[Cerveny]

Place is not substantial in this context - I suppose different places