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The uncertainty principle shouldn't be regarded as the fact that you cannot exactly and simultaneously know both the position and momentum of a particle. It sho

The uncertainty principle shouldn't be regarded as the fact that you cannot exactly and simultaneously know both the position and momentum of a particle. It should be regarded as the fact that such a concept doesn't even make sense, the same way that the concept of "instantaneous spectral content" of a signal doesn't even make sense.

aswanson 7y ago
Exactly. I remember asking a prof in undergrad what the spectrum of a single time sample would be. He didn't give me a straight answer, but I realized later that question was equivalent to asking what the average age of a single person was.
- aswanson 7y ago
  Seems like a few folks here know how to project a single sample onto a vector valued function. Brilliant people.
- kevinwang 7y ago
  Hm... I think I get what you're saying, but isn't computing the average age of a person over their lifetime pretty straightforward? integral of their age divided by their total lifespan, which would be their (total lifespan)/2.
  - aswanson 7y ago
    Yeah. It's misworded. It's more like, given a particular person, and a given instant in time, compute the average of an ensemble of people. It makes no sense.
lisper 7y ago
The problem is that the simultaneous position and momentum of a particle does make sense, it just happens not to be how our world works because the world is not actually made of particles, it's made of fields, and those fields obey wave equations. A better analogy IMO is that it's impossible to have a wave whose position and direction are simultaneously well defined. If you throw a stone into a pond you will get a circular wave front with a well-defined position (where the stone landed) and a completely undefined direction. Likewise, you can get a wave that has a well-defined direction (as you do along a seashore, where the waves move perpendicular to the coastline) but to make that happen the wave has to be very wide. It's impossible to make a wave (in open water) that is simultaneously well-localized and moving in a particular direction.
- deleted 7y ago
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aswanson 7y ago

Exactly. I remember asking a prof in undergrad what the spectrum of a single time sample would be. He didn't give me a straight answer, but I realized later that question was equivalent to asking what the average age of a single person was.

aswanson 7y ago
Seems like a few folks here know how to project a single sample onto a vector valued function. Brilliant people.
kevinwang 7y ago
Hm... I think I get what you're saying, but isn't computing the average age of a person over their lifetime pretty straightforward? integral of their age divided by their total lifespan, which would be their (total lifespan)/2.
- aswanson 7y ago
  Yeah. It's misworded. It's more like, given a particular person, and a given instant in time, compute the average of an ensemble of people. It makes no sense.

lisper 7y ago

The problem is that the simultaneous position and momentum of a particle does make sense, it just happens not to be how our world works because the world is not actually made of particles, it's made of fields, and those fields obey wave equations. A better analogy IMO is that it's impossible to have a wave whose position and direction are simultaneously well defined. If you throw a stone into a pond you will get a circular wave front with a well-defined position (where the stone landed) and a completely undefined direction. Likewise, you can get a wave that has a well-defined direction (as you do along a seashore, where the waves move perpendicular to the coastline) but to make that happen the wave has to be very wide. It's impossible to make a wave (in open water) that is simultaneously well-localized and moving in a particular direction.

deleted 7y ago
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