Basically, how can we accept a theory as mainstream when examples of paradoxes make theories contradict themselves or simply just don't make sense?

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No theory applies to everything. Quantum mechanics does not apply to things the size of galaxies; does that mean it should be trashed? Same thing with relativity: it is a theory that operates on a large scale. Should relativity be expected to work where it was not made to work, e.g. for a black hole's singularity?

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Any particular paradoxes you want people to address?

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Ok, as an example, I once read in a physics book about a time paradox. I can't remember exactly how it goes, but I'm sure someone can fill in the blanks.

We have 2 people traveling in space ships at the speed of light towards each other, and each person is holding a clock out the window, and each of them see the time on the clock as they pass by each other. Now I can't remember if the clocks are supposed to be stopped or going faster/slower, but I know it's a paradox of relativity.

I didn't mean anything along the lines of 1 theory being used in a completely different area such as quantum mechanics being used to explain relativity.

I'm just wondering here, that's all.

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How is that a paradox?

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We don't generally accept a theory as mainstream until the internal problems are consistent. I was just reading about Quantum Electrodynamics and there were a bunch of problems with infinities, like when certain quantum mechanical principles of the electron worked out by Dirac were applied to entire atoms, it gave nonsensical answers like the atom has infinite energy. Once a theory came along that got rid of these problems, it was accepted, especially since it was in accordance with experimental observations.

Fill in the blanks. As I said I don't remember how it ends, and I don't have enough of a grasp on relativity to give the answer, but it was a paradox. It didn't add up somehow and they even said it was a paradox in the book, so I'm looking for someone else that can maybe answer.

I think it may have been along the lines of, both travelers would appear to be frozen in time, but in their own POV the clock is still ticking.

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dvb, at least in regards to Relativity, there are no real paradoxes. There are some things that appear to be paradoxes at first glance, but once you understand the entire theory, you can see that they are not.

Yes, under Special Relativity, two observers who are moving relative to each other will each see the other's clock as ticking more slowly than their own clock - in fact, each clock is ticking more slowly than the other clock. But that's not a paradox (although it is a pair o' clocks).

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#-o

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1 Paradox concerning Quantum mechanics involiving the decay of a particle.
a stationary spinless particle decays into two others with equal mass (the daughters have equal mass) that are traveling in opposite directions at the velocity of light. Now thats the conservation laws covered... except that of spin.
in the later frame the total spin must be zero.... BUT by quantum mechanics Spin is a property that does not exist untill you try to measure it. (this is comming from lecture notes and not thin air before you lot try and flame me)
SO... if you measure the spin of one of the particles and it is spin up, then at that point in time the other particle (which is two times the speed of light multiplyed by time away) instantly takes spin down to create a system of spin zero.
It is known as the Teleportation Paradox.

"Spooky action at a distance", some call it

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Bears repeating: there are no actual paradoxes, just apparent paradoxes. They are apparent paradoxes because if you approach (for example) an SR problem with Newtonian logic, you will see a paradox. The purpose of using the paradox as an example is to show how the theory resolves the apparent paradox..

Thank you everyone for helping me out. Especially SeanF and russ_watters. I think you guys hit the nail right on the head there with the apparent paradox thing. Since it was so long ago that I read this book, it may have been explaining how something appears to be a paradox at first, but goes into more detail explaining how really it isn't.

good one

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Just for completeness the Merriam-Webster entry for paradox:

a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true b : a self-contradictory statement that at first seems true c : an argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises

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Actually Quantum Mechanics cn be applied to galaxies, and other large objects, it's just that the effects are generally un-noticable. Consider Hisenberg's Uncertainty pinciple. When applied to a moon the distance of uncertainty is much less that the size of the moon and so we ignore it. It doesn't mean that it doesn't exist.

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I should say it's less than the size of the moon. Perhaps much smaller than atomic widths?

Yes, you are right. This is the standard version of quantum theory that is in most textbooks.

I'd just add that more recent developments suggest that the spins seemingly matching instantaneously when one particle is measured is actually just the result of using a mathematical shortcut called "wave function collapse" and this is not a physical effect, and that the spins match from the moment of the initial split.

[There are technical issues here that I'd rather not get into right now about particles not possessing x and z spins simultaneously.]

The standard textbook version works fine and gives the exact same results, though, despite its slight hiccups with special relativity if the spins matching instantaneously is interpreted as a physical effect.

Ah, but how do you know that the spins match without measuring them? And how do you know that it's not the act of measuring that makes them match?

(I love QM! It's so... Zen.)

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Because they always match when we measure them. :P

We don't know for sure but with this standard, measurement-orientated way of thinking about it we get effects travelling faster-than-light, effects visually travelling backwards in time, effects which precede their causes and even effects without causes. Which is nice.

But if we get rid of this "wave function collapse" then things settle down nicely. 8)

With the more recent developments of quantum theory, the theory is not so Zen anymore, it's more a case of following everything carefully otherwise Schrodinger's Cat sneaks up from behind and smacks us around the head until we see paradoxes everywhere.

Poor, Ives, Dingle, Beckmann, Lynch, Sachs, Essen, Zappfe, Phipps, Marinov, Aspden, and Hayden claimed that Relativity involves circular logic, violates the Second Law of Thermodynamics, is riddled with anomalies and paradoxes such as the Ehrenfest Paradox, the Paradox of Self-Reference, the Curvature of Space Paradox, the Ruler Paradox, the Clock Paradox, the Simultaneity Paradox etc. and as formulated cannot be correct.

I'm happy for them. Mind providing more than a list of names?

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