Ask Science
Ask a science question, get a science answer.
Community Rules
Rule 1: Be respectful and inclusive.
Treat others with respect, and maintain a positive atmosphere.
Rule 2: No harassment, hate speech, bigotry, or trolling.
Avoid any form of harassment, hate speech, bigotry, or offensive behavior.
Rule 3: Engage in constructive discussions.
Contribute to meaningful and constructive discussions that enhance scientific understanding.
Rule 4: No AI-generated answers.
Strictly prohibit the use of AI-generated answers. Providing answers generated by AI systems is not allowed and may result in a ban.
Rule 5: Follow guidelines and moderators' instructions.
Adhere to community guidelines and comply with instructions given by moderators.
Rule 6: Use appropriate language and tone.
Communicate using suitable language and maintain a professional and respectful tone.
Rule 7: Report violations.
Report any violations of the community rules to the moderators for appropriate action.
Rule 8: Foster a continuous learning environment.
Encourage a continuous learning environment where members can share knowledge and engage in scientific discussions.
Rule 9: Source required for answers.
Provide credible sources for answers. Failure to include a source may result in the removal of the answer to ensure information reliability.
By adhering to these rules, we create a welcoming and informative environment where science-related questions receive accurate and credible answers. Thank you for your cooperation in making the Ask Science community a valuable resource for scientific knowledge.
We retain the discretion to modify the rules as we deem necessary.
view the rest of the comments
There are an infinite number of velocities I can use to get up off the couch right now.
That does not mean that I will get up off the couch at infinite velocity.
Yes, there are an infinite number of velocities you can use, but if you look at their distribution, you'll find that it quickly goes to zero somewhere around 1-2 m/s, so the expectation value of the velocity is convergent.
If you have an object with a velocity taken from a distribution that doesn't approach zero sufficiently fast as the velocity goes to infinity, the expectation value diverges. A simple example would be a person that would be half as likely to get up at a velocity of 2 m/s as 1 m/s, and half as likely to get up at 4 m/s as 2 m/s, etc.
The more mathematical version of the same argument is to compute the kinetic energy of a particle whose wavefunction is a delta pulse (i.e. a particle whose position is exactly defined), and you'll find that the particle has infinite energy.
You choose a velocity from an infinite number of options, but the electron exists in a superposition of all those options.