What is a Paradox? Understanding its Role in Physics and Astronomy

[BH Wiz]

I guess the title gives it all. I understand the concept on a basic level. What i don't understand is that how does it "fit" in physics and astronomy. Any and all opinions are appreciated. Thank you :) .

 

[jedishrfu]

One type of paradox is when theory says one result but experiment gives you another so that you left with a paradox. The Michelson Morley experiment fit this kind of paradox. We assumed there was a medium that light traveled in but could find no evidence of a preferred direction.

Another kind is in the time travel paradox where if time travel is true then you could go back and kill your grandfather insuring that you aren't born assuming you've killed him before your dad or mother were conceived so that now you don't exist to do the deed.

 

[sophiecentaur]

The definition of the word can be found all over the place. Was there a particular paradox that's been bugging you?

 

[George Jones]

Unfortunately, the dictionary definitions of "paradox" are somewhat paradoxical. From Merriam-Webster:

"2 a : a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true
2 b : a self-contradictory statement that at first seems true"

 

[Nugatory]

I guess the title gives it all. I understand the concept on a basic level. What i don't understand is that how does it "fit" in physics and astronomy. Any and all opinions are appreciated. Thank you :) .

In physics, the word "paradox" is generally used for two different sorts of problems:
1) A situation is described (often deliberately, to create a teachable moment) badly to create an apparent contradiction. The pole-barn paradox in its various forms is an example: The problem description contains the dangerously meaningless phrase "at the same time", and the teacher is working to make a point about the relativity of simultaneity.
2) A situation is described correctly in terms of some scientific theory, but the description leads to a some counter-intuitive or implausible result. Here the intention is to stimulate discussion about the theory: What does it "really" mean? What are its limitations and weaknesses? Is it complete? Schrödinger's cat is an example of this sort of paradox.

 

[BH Wiz]

Thank you all for your responses.

 

[DiracPool]

Colloquially, it just means that something you would expect to happen doesn't happen and vice-versa. No need to get too fancy about it. Like the twin paradox, you don't expect your twin to take a 10 year trip and come back only 2 years older.

 

[xAxis]

I think the twin paradox is not actually paradox, because it is logically consistent. I think paradox arises when there is a logical contradiction as a consequence. For instance the statement that the square root of 2 is rational number is paradox.

 

[jbriggs444]

I would say that the "set of all sets that do not contain themselves" (i.e. Russell's Paradox) is a paradox in the sense of an actual contradiction. It demonstrates that naive set theory is inconsistent.

In modern mathematics, a statement that the square root of 2 is rational is simply false. It does not demonstrate that arithmetic is inconsistent but merely that the rationals are not closed under root extraction.

 

[sophiecentaur]

I think the twin paradox is not actually paradox, because it is logically consistent. I think paradox arises when there is a logical contradiction as a consequence. For instance the statement that the square root of 2 is rational number is paradox.

That goes for most of the paradoxes that have come into Science over history. You take a model that predicts two mutually exclusive outcomes (the 'paradox'). That disproves the theory behind the model that's being tested and you have to start again. It's arguably an inappropriate of the term but I'm happy enough with it.

The term 'anomalous result' can also be used inappropriately. An error is sometimes described as an anomaly but imo an anomally will be a repeatable measurement that doesn't fit the original model - and needs the model (or the measurement system) to be modified. GCSE Science coursework used the word 'anomaly' rather than 'error for quite some length of time. I think this was some misplaced politically correct way not to upset students with the idea that they could be just plain wrong when they measured something. I'm surprised it wasn't referred to as 'teacher induced error'. That would have gone down OK.

 

[BH Wiz]

I think paradox is when the truth contradicts itself, the illusion would be that there is no truth. Is that correct?

 

[sophiecentaur]

I think paradox is when the truth contradicts itself, the illusion would be that there is no truth. Is that correct?

Ummm. 'Truth' may just be something we believe exists - or at least it could be that there is really no real systematic set of rules or truths that govern our Universe. We could find what we think is a paradox which is nothing more than a manifestation that there is no 'truth'.
As Scientists, of course, we have 'faith' that we can get ever closer to the truth and some of us even believe that the truth may actually be attainable - not me though.

 

[BH Wiz]

I'm not talking about the truth on universal standards, more like a basic level but i understand thank you.

 

[sophiecentaur]

I was waxing a bit philosophical there wasn't I?

 

[BH Wiz]

A bit yeah :P

 

[sreerajt]

"A paradox is an argument that starts with apparently acceptable assumptions and leads by apparently valid deductions to an apparent contradiction." by Quantum Paradoxes: Quantum Theory for the Perplexed by Yakir Aharonov, Daniel Rohrlich.

 

[algebrat]

Colloquially, it just means that something you would expect to happen doesn't happen and vice-versa. No need to get too fancy about it. Like the twin paradox, you don't expect your twin to take a 10 year trip and come back only 2 years older.

I think the twin paradox is not actually paradox, because it is logically consistent. I think paradox arises when there is a logical contradiction as a consequence. For instance the statement that the square root of 2 is rational number is paradox.

But isn't there a paradox in there? If they both accelerate away from each other, shouldn't they both be two years younger than each other. That looks like an apparent paradox to me.

 

[OCR]

I never tell the truth...

Or, more correctly, the statement... "this sentence is false." ← (link, btw)

http://plato.stanford.edu/entries/liar-paradox/

http://en.wikipedia.org/wiki/Paradox

http://en.wikipedia.org/wiki/List_of_paradoxes


I've always thought paradoxes are rather interesting... some, more than others.

http://en.wikipedia.org/wiki/Arrow_of_time

http://en.wikipedia.org/wiki/Time_travel

Even though Time's Arrow was one of the best, I could never quite figure out how Data could have two heads... relatively speaking, that is.



OCR

 

[Vorde]

But isn't there a paradox in there? If they both accelerate away from each other, shouldn't they both be two years younger than each other. That looks like an apparent paradox to me.

It is an apparent paradox, it is not a paradox. When you look closely at the situation it turns out the paradox disappears.

Paradoxes pop up all the time in hypothetical situations and philosophical musings (like the links posted above me). They do not show up in physics and math. In physics a paradox tells you that either you're not thinking of everything or your theory is wrong/incomplete, and in fact in math paradoxes are commonly used to prove the nonexistence of things. That's called a proof by contradiction and they are very common.

 

[sophiecentaur]

I think it would be safe to say that all Scientific 'paradoxes' can be resolved by widening the way they're looked at. Something else (like an expanding Universe) needs to be added to the scenario and the paradox collapses. - relief all round when that happens.