Was Einstein wrong and newton right?

[Mecill]

RurouniZakku

the equations show us why it happens, or how it's like it is.

That should be the experiments. The equations describe the results also...  

[RurouniZakku]

they both show us what happens, equations and theories show us what supposed to happen, and experiments show us what actually happens. Assuming everything is done right.  

[Mecill]

Ahh, you are right! Theory and experiment: you can't have one without the other. This is such a good thread.  

[Mecill]

Though theories can be wrong too. They are also our own constructs. So it's more like they are what we think is supposed to happen. Observations are very strong and theories, in a way, are observations of mathematical properties. But you also have to consider the limits to what we can observe - things we can overlook.  

[RurouniZakku]

yes, that is where experimentation comes in, it proves our theories, or disproves them, though checking your theories, and having someone else check them is much safer. Then their is also the observation of how it all worked. All of it works together to give us the answer.  

[Mecill]

Experimentation also relies on observation. What we observe depends on physical "laws" because we make our observations from inside the system. For example, what we see depends on how light travels. Quantum mechanics tries to incorporate this concept with the Heisenberg Uncertainty Principle.  

[Layra-chan]

Mecill

Experimentation also relies on observation. What we observe depends on physical "laws" because we make our observations from inside the system. For example, what we see depends on how light travels. Quantum mechanics tries to incorporate this concept with the Heisenberg Uncertainty Principle.

Actually, the Heisenberg Uncertainty Principle has nothing to do with light. It's a fairly straightforward theoretical result regarding the actual values that observable quantities can take, not what we actually happen to observe. We could observe things via shooting electrons at them and the Uncertainty principle would still hold.  

[Mecill]

Do photons have quantum behavior?

I thought the uncertainty principle theoretically means that if you constrain one variable there is uncertainty in another. How does this arise, theoretically? (... should probably research this myself. XD)  

[VorpalNeko]

From the point of view of Fourier analysis, the position-basis and momentum-basis wavefunctions are a Fourier transform pair, whose variances are bounded below by a constant. This is a mathematical fact about Fourier transforms and has no physical content by itself; all the physics is in identifying physical state as a wavefunction in the first place.

More abstractly, quantum observables are operators on a Hilbert space, on which again it is a mathematical theorem that for any state, the expectation values satisfy 4 ≥ |<[A,B]>|², where [A,B] = AB-BA is the commutator. You should be able to find the standard proof using the Cauchy-Schwarz inequality rather easily.

For example, it the position basis, the position operator is just q = x, while the momentum operator is p = -iℏ d/dx. Hence [q,p]f = -iℏ( x(d/dx)f - (d/dx)(xf) ) = -iℏ[ xf' - (f + xf') ] = iℏf, meaning [q,p] = iℏ. Substituting into the above, ≥ ||²/4 = ℏ²/4, i.e., the product of the variances of the position and momentum measurements is bounded below by ℏ²/4.

And yes, photons are about as quantum as it gets. Layra-chan's point was simply that there's absolutely nothing in the HUP that depends on photons. It's a purely geometric consequence of having non-commuting observables living in a Hilbert space.  

[Mecill]

Thanks, that was very helpful!