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What are some important examples of paradoxes in physics which are still currently unresolved?

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You can't have real paradoxes in physics, so you either have ones where you misunderstood a theory, or where it's valid (twins paradox) or we don't have a theory yet (hairy black holes) –  Martin Beckett Mar 26 '11 at 15:03
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Looking at dbrane's wiki list, many of these paradoxes are historical, which helped develop a better theory or a clearer understanding of consequences of a given theory. These are now part of "physics history". Only some are currently active as a source of investigation by researchers. Did you only mean the latter? –  Roy Simpson Mar 26 '11 at 15:42
    
I'm not quite sure whether this should be closed or not, but it is definitely at least appropriate for wikification so I did that. –  David Z Mar 26 '11 at 16:22
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I interpreted the question to be "Are there any unsolved problems today like the ultraviolet catastrophe problem that Planck solved? If so, list them." In other words, unsolved problems where the laws of physics as currently understood seem to lead to ridiculous answers. Though maybe that isn't what he meant. –  Donald Mar 26 '11 at 20:34
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closed as not constructive by David Z Jan 15 '13 at 1:54

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6 Answers

Superluminal tunneling.

Quanta may travel faster than light via tunneling. This seems to violate special relativity, could this be counted as a paradox?

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The Vacuum Catastrophe. Quantum theory implies a vacuum or zero-point energy, and the Casimir effect tends to confirm this, but then general relativity tells us this should have a gravitational effect, which we don't observe. This is an unresolved paradox.

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I mention this because it wasn't on the Wikipedia list, but it certainly qualifies under the above interpretation of unresolved paradox as something where current laws of physics lead to ridiculous answers, like the ultraviolet catastrophe did historically. –  Retarded Potential Jan 14 '13 at 23:15
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I think that this question has been little bit misunderstood. Paradox word came from ancient greek words para (beyond) and doxa (doctrine), so strictly speaking means "beyond the doctrine". Thus in not possible define as paradox something that simply is counterintuitive. Then a paradox is by definition "temporary". Said that, the true physical currents most famous paradoxes are:

-EPR pardox. Quantum mechanics breaks the limit of speed of light.

-Black hole information paradox. Black holes breaks the second law of thermodyamics.

-Planck length paradox. Plank length is the most little length measurable and is invariant in any reference in rest in the contrary of what GR say. 
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I will put in my two cents of the euro. Paradoxes arise when two axiomatic systems are mixed up. Paradoxes are resolved with the meta (often content versus context)concept in general cases.

Famous example: All Cretans are liars, said the Cretan. It is resolved by the meta language level concept, where one level is the Cretan speaking, and the other is the statements coming out of his/her mouth.

One cannot mix, for example, classical thermodynamics and quantum statistical mechanics concepts without a thorough investigation of underpinnings, because both are axiomatic systems valid in certain regions of phase space and one has to be very careful of overlaps in order not to double count, the energy, as an example. ( which happens in climate studies).

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In quantum gravity, we have the black hole information paradox. If information is thrown into a black hole past the event horizon and is destroyed at the singularity inside, and the black hole subsequently decays away via Hawking radiation, where does the information go to? If information can't travel faster than light, it can't escape from inside the black hole to outside it. But if information is truly lost, this would lead to violations of unitarity in quantum mechanics, with terrible consequences.

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What do you mean by "terrible consequences"? Do you mean it would imply current theories are incorrect? That the Earth would be destroyed? That someone would lose tenure? –  yakiv Jun 12 '12 at 17:55
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Let me assure you that all paradoxes are false paradoxes if you understand the physics. There are many misunderstandings for naive mortals like us for a period which are called "paradoxes" until resolved. Some familiar examples are

  1. Twin paradox
  2. EPR paradox
  3. Schrödinger's cat paradox
  4. Faradays rotating disc paradox (quite an old one)
  5. Black hole information paradox (a recent one) (solution of this is still controversial)
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+1 I think it is fine. A paradox means physicists have to try harder :). Let ,me tell you a funny story: next to our house there was a community orphanage where the children would go to public school and to private schools if their guardians payed for it. All the children called the directrice : mama , which is usual in such situations in Greece. My daughter coming back from first grade asked me: how can she have so many children? I hmmed and hawed, and she said : I know, Iknow, she tried harder. –  anna v Mar 26 '11 at 15:42
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Schrödinger's cat paradox: Schrödinger is already dead, the cat is still alive. –  Vladimir Kalitvianski Mar 26 '11 at 22:56
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