2,686 reputation
11338
bio website
location
age
visits member for 4 years, 5 months
seen 9 hours ago

Jun
14
awarded  Popular Question
May
28
reviewed Approve Why friction increases with increase in normal force?
May
19
comment Does General Relativity imply loops in space?
Fine, but the set of orbits that are perfectly circular are measure zero.
May
19
comment Does General Relativity imply loops in space?
Even an orbiting planet doesn't go around in a loop, as GR causes precession of the perihelion.
May
12
revised Planck length paradox
copyedit
Apr
17
comment Looking for a simple example of generating unequal probabilities in QM
@Rococo, pinging you once in case the chat doesn't notify you of a message on my end. I don't think it does...
Apr
17
reviewed Approve Why do we get the same result using different ensembles?
Apr
13
comment Looking for a simple example of generating unequal probabilities in QM
@Rococo, thanks, I'm not sure either but I created one for us here
Apr
12
comment Looking for a simple example of generating unequal probabilities in QM
@Rococo, I am awarding you the bounty because you've been helpful, although I'm still not satisfied. I don't see how Schrodinger evolution can split a wave packet in two equal parts where the amplitudes are not one half the original, because of linearity. I thought superposition was linear. If I imagine it in reverse, you have two wave packets, each of amplitude 1/sqrt(2), and when they combine by linear addition the amplitude is 2/sqrt(2) and unitarity is violated. What am I not understanding correctly?
Apr
12
accepted Looking for a simple example of generating unequal probabilities in QM
Apr
12
comment Looking for a simple example of generating unequal probabilities in QM
@adipy, yes I am equating the two, intentionally, in the sense that it seems like one implies the other. Maybe see my question here. That my thinking here is not obviously stupid is justified by Gleason's theorem. Normalization is related to Born in that it is saying that the squared amplitudes sum to probability = 100%. While I may ultimately be wrong, this is the heart of my question, and it cannot be so trivially dismissed without significantly more engagement and explanation.
Apr
9
comment Looking for a simple example of generating unequal probabilities in QM
@adipy, as for your second point, yes, I understand that. What I don't understand is the connection between the amplitude and the probability (Born rule) via branch counting. It's a bit subtler than I think you give credit for, and I think you don't understand my confusion, again see the edit to my original question.
Apr
9
comment Looking for a simple example of generating unequal probabilities in QM
@adipy, I think it would help you understand where I'm coming from if you read the edit below my original question, where I state a confusion that is even simpler than the one you are pointing to.
Apr
7
comment Looking for a simple example of generating unequal probabilities in QM
@Timaeus, I've edited my question to reflect the fact that I now understand at least the kernel of my confusion. Maybe that will help clarify what is going wrong in my thinking.
Apr
7
revised Looking for a simple example of generating unequal probabilities in QM
Based on comments added clarification
Apr
7
comment Looking for a simple example of generating unequal probabilities in QM
it pains me to say that you are still not understanding me. I will edit my original question based on the recent conversation with you and Rococo, which might help clarify.
Apr
7
comment Looking for a simple example of generating unequal probabilities in QM
@Timaeus, (continued). Note there is nothing "wrong" with that if it is what is done, but I just want to very clearly understand which it is. Can the $1/\sqrt{2}$ amplitude when you split a beam 50-50 be derived from Schrodinger evolution, or are you just renormalizing it in to enforce that you get 50-50 probabilities?
Apr
7
comment Looking for a simple example of generating unequal probabilities in QM
@Timaeus, (continued), unless you are making an implicit assumption about how those amplitudes relate to probability? In other words you are assuming the Born rule when positing that when you split the initial beam in two, each amplitude goes as $1/\sqrt{2}$. You are essentially enforcing unitarity by fiat by declaring (or renormalizing) the state of equal amplitudes so that the sum of probabilities remains 1. Unless there is some rule I'm not aware of by which Schrodinger evolution unitarily evolves the state to the $1/\sqrt{2}$ amplitudes without you having to make that declaration.
Apr
7
comment Looking for a simple example of generating unequal probabilities in QM
@Timaeus, I never said my 66% calculation is correct, you are completely and totally misunderstanding me if you think I am insisting that I am correct. But you don't seem to have grokked my misunderstanding, and as a result I am still confused. This is the rub: "When someone says they split a beam into two equal parts they mean they split the probability into two equal probabilities." This is the source of my confusion. How can you split 100% of something (the amplitude, not the probability) into two equal piles, and say that the size of each pile is not 50% of the original, unless (continued)
Apr
7
comment Looking for a simple example of generating unequal probabilities in QM
@Timaeus, I understand, but you are still I think not understanding the source of my confusion, which is the same as my comment to Rococo above. If you use, say, SG to split a first beam 50-50 and then a second beam 50-50, it seems self-evident that by simple "counting" the amplitudes should be 1/2, 1/4, 1/4, but like you point out this violates unitarity. Obviously there is something that gives. I suspect you both are tautologically assuming the Born rule in a way to keep unitarity, otherwise I don't see how you can possibly split a beam 50-50 and result in $\sqrt{2}:1$ ratio of amplitudes.