Q: Will there always be things that will not or cannot be known?

Mathematician: Unfortunately, limits to knowledge seem to be built into the nature of the universe, and even into logic itself.

Relativity: Einstein’s theory of special relativity implies that no information can travel faster than the speed of light. That means that information from sufficiently recent, sufficiently far away events will not have had the time to propagate to us yet, making detailed knowledge of such events impossible. In physics speak, we say that these events are outside of our “past light cone“, “space-like separated” from us, or just “elsewhere”. As long as new events of this type keep happening, there will always be things about which we do not and cannot know.

Quantum Mechanics: The Heisenberg uncertainty principle states that the uncertainty \Delta x we have in a particle’s position and the uncertainty \Delta p we have in the particle’s momentum cannot both be very small at the same time. In particular, the product of these uncertainties is greater than a constant (\Delta x \Delta p > \frac{\hbar}{2}). This implies a fundamental limit to the knowledge that is possible because we can know x accurately or p accurately, but not both.

What’s more, the vast majority of physicists agree that quantum mechanics demonstrates the universe is random at a fundamental level. This means that some events, like the time at which an atom will decay, can be predicted only probabilistically. We can say how likely an atom is to decay in a given time interval, but we will never be able to say precisely when the decay will occur, placing another limitation on what knowledge is possible. (Physicist’s note: After the decay you still can’t say when exactly it happened because according to quantum mechanics the exact time doesn’t actually exist!)

Mathematics: Gödel’s  first incompleteness theorem states (essentially) that any mathematical system  that is able to express elementary arithmetic (and doesn’t contain any contradictions) must contain true arithmetical statements that cannot be proven within that system. Essentially this implies that there will always be true mathematical statements that we cannot prove.

Add to all of these theoretical considerations the enormous (and possibly infinite) number of things that could be known about our physical universe, and the (most definitely) infinite number of true mathematical statements that could be known, and it is clear that there will always be knowledge that is beyond our reach.

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6 Responses to Q: Will there always be things that will not or cannot be known?

  1. Ames says:

    Somehow the flying brains in Futurama overcame this difficulty. HOW?

  2. The Physicist Physicist says:

    They can learn anything, for they are gigantic brains.

  3. create14all says:

    How about “I don’t know and you don’t either.” as an answer?

  4. christopher says:

    given a couple hundred billion years we (or something else) could possibly make a universe sized computer that runs on some particle that passes though (most) universes without disturbing them but returns to the universe computer with information on it based on where it has been. if the uni-computer worked in a massively parallel way, and was sufficiently larger then the studied universe i think it seems possible. this assumes a multiverse, and the ability to generate universes with specific laws (and particles that can interact with other universes separated by -not-space-time-, or lack of anything whatsoever, whatever that is). perhaps my mind works ‘too sifi’, but seems theoretically not impossible to me.

  5. Kyle says:

    Quantum entanglement allows for information to travel faster than light.. Instantly to be certain.

  6. The Physicist The Physicist says:

    That’s an extremely common misconception, but it turns out that entanglement can’t be used to transmit information. There’s a post here (entanglement omnibus!) that tries to talk about the whys and whats of entanglement.

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