|
|
Post by Eugene 2.0 on Aug 8, 2020 18:15:55 GMT
This logic has no distributive law.
If p is a particle that located at the center of the coordinates;
If q is a particle that located left to the center; and
If r is a particle that located right to the center, then:
~{(p&(qvr))≡(p&q)v(p&r)}
They say that p&q, and p&r can't be taken as true, because it would be nonsense if we took "left" or "right" as something self-enough.
Anyway, I don't really get it. Anybody knows how we should understand it?
|
|
|
|
Post by xxxxxxxxx on Aug 8, 2020 18:59:35 GMT
This logic has no distributive law. If p is a particle that located at the center of the coordinates; If q is a particle that located left to the center; and If r is a particle that located right to the center, then: ~{(p&(qvr))≡(p&q)v(p&r)} They say that p&q, and p&r can't be taken as true, because it would be nonsense if we took "left" or "right" as something self-enough. Anyway, I don't really get it. Anybody knows how we should understand it? P is the medial term between Q and R, as a medial term P is divided between Q and R thus has two identities. P is simultaneously true and false given P and R or P and Q divided P into two identities. As such P cannot be correct given it is a term which means nothing, it is intrinsically empty of value given its dualistic nature. Because P is empty or value P and Q and P and R cannot be taken as true. The premise as being grounded in P being empty necessitates both P&Q and P&R as empty of truth value as well given Q and R derive their identities from P. |
|
|
|
Post by Eugene 2.0 on Aug 9, 2020 21:13:12 GMT
This logic has no distributive law. If p is a particle that located at the center of the coordinates; If q is a particle that located left to the center; and If r is a particle that located right to the center, then: ~{(p&(qvr))≡(p&q)v(p&r)} They say that p&q, and p&r can't be taken as true, because it would be nonsense if we took "left" or "right" as something self-enough. Anyway, I don't really get it. Anybody knows how we should understand it? P is the medial term between Q and R, as a medial term P is divided between Q and R thus has two identities. P is simultaneously true and false given P and R or P and Q divided P into two identities. As such P cannot be correct given it is a term which means nothing, it is intrinsically empty of value given its dualistic nature. Because P is empty or value P and Q and P and R cannot be taken as true. The premise as being grounded in P being empty necessitates both P&Q and P&R as empty of truth value as well given Q and R derive their identities from P. Hi, 9x! Very glad to see you again! Sorry, that I didn't answered last time. All the best to you and your relatives! Thank you for answering, but I can't say I understood you either. This QM logic is what really pisses me off. Semantically p&(qvr) and (p&q)v(p&r) are both the same. Or, for instance, using Sheffer's stroke: 1) (P|((Q|Q)|(R|R)))|(P|((Q|Q)|(R|R))) = p&(qvr) 2) (((P|Q)|(P|Q))|((P|Q)|(P|Q)))|(((P|R)|(P|R))|((P|R)|(P|R))) = (p&q)v(p&r) So? P|Q can't be uttered four times? I take each: (p&(qvr)), and (p&q)v(p&r) as whole. For me there's no difference. According to what I guessed I had learned previously (to make this post) was that Q and R are interchangeable. If Q is a direction to, but R is an opposite direction to Q, then Q and R are both complement (I'm not sure about the term). In other words, Q or R are true, because we don't know which of which (Q or R) are true, but we do know where the range the micro-particles in is somewhere between those two. While P is without any sure good position we can to describe. P is the medial term between Q and R, as a medial term P is divided between Q and R thus has two identities. P is simultaneously true and false given P and R or P and Q divided P into two identities. - I can't say it is. Well, this interpretation is interesting, but it might be. P equals to P, right? QM doesn't deny it. Then, P in (P&R) and P in (P&Q) has the same identity. While (QvR), if we take those as the "rotating deities" (as I said they might be interchangeable), it works.
Actually, QM must be based on non-classical logic, and we have to see at semantic table smth like this: 1, 1/3, 1/6, 2/3, and so on. |
|
|
|
Post by karl on Aug 10, 2020 6:49:10 GMT
This logic has no distributive law. If p is a particle that located at the center of the coordinates; If q is a particle that located left to the center; and If r is a particle that located right to the center, then: ~{(p&(qvr))≡(p&q)v(p&r)} They say that p&q, and p&r can't be taken as true, because it would be nonsense if we took "left" or "right" as something self-enough. Anyway, I don't really get it. Anybody knows how we should understand it?
I don't think I understood what you wrote. One just needs to agree on a fixed coordinate system, and then define left and right by the X-axis.
Could you explain the meaning of the symbols you used? What does, for example, p&(qvr) mean in this context?
|
|
|
|
Post by Eugene 2.0 on Aug 10, 2020 7:58:55 GMT
This logic has no distributive law. If p is a particle that located at the center of the coordinates; If q is a particle that located left to the center; and If r is a particle that located right to the center, then: ~{(p&(qvr))≡(p&q)v(p&r)} They say that p&q, and p&r can't be taken as true, because it would be nonsense if we took "left" or "right" as something self-enough. Anyway, I don't really get it. Anybody knows how we should understand it? I don't think I understood what you wrote. One just needs to agree on a fixed coordinate system, and then define left and right by the X-axis.
Could you explain the meaning of the symbols you used? What does, for example, p&(qvr) mean in this context?
You're right. I definitely needed to correct it. I took my own example, but it might be poorly presented. Actually I've met two or more types of QL examples. Firsts had standard representations as: p = a particle goes right q = a particle at the left to the center of a (given?) coordinate system r = a particle at the right to the center of a (given?) coordinate system Seconds had something like this: p = a particle is at [-1; 1/6] q = a particle is at [-1; 1] r = a particle is at [1; 1/3] (I can't be sure; the last example is similar to Wikipedia's one). Knowing almost nothing about QM (I can't say I understand it properly; instead of analytical way, I use phenomenological path - trying to imagine the processes). I guess that either there, in the formula I wrote, is a violation of some rules of QM, or "left" or "right" do nothing/make no sense in QM. I will be very appreciate if you explain it what examples (alike such above) may represent that (qvr) is always true, however (p&r and (p&q) is always false. |
|
|
|
Post by karl on Aug 10, 2020 10:15:37 GMT
I don't think I understood what you wrote. One just needs to agree on a fixed coordinate system, and then define left and right by the X-axis.
Could you explain the meaning of the symbols you used? What does, for example, p&(qvr) mean in this context?
You're right. I definitely needed to correct it. I took my own example, but it might be poorly presented. Actually I've met two or more types of QL examples. Firsts had standard representations as: p = a particle goes right q = a particle at the left to the center of a (given?) coordinate system r = a particle at the right to the center of a (given?) coordinate system Seconds had something like this: p = a particle is at [-1; 1/6] q = a particle is at [-1; 1] r = a particle is at [1; 1/3] (I can't be sure; the last example is similar to Wikipedia's one). Knowing almost nothing about QM (I can't say I understand it properly; instead of analytical way, I use phenomenological path - trying to imagine the processes). I guess that either there, in the formula I wrote, is a violation of some rules of QM, or "left" or "right" do nothing/make no sense in QM. I will be very appreciate if you explain it what examples (alike such above) may represent that (qvr) is always true, however (p&r and (p&q) is always false.
Let's take particle q and particle r. To state their position is to state the probability for where they'll be if you measure them. So the position you gave is where they're most likely to be. But where they actually are isn't determined before they're measured. If you measure them both using high energy photons, you can pinpoint fairly accurately where they were at that time, but such a measurement will make it widely unclear what their momentum is, so you don't know where they'll be the moment after. If you use a low energy photon, you can determine the momentum fairly well, but the position will be widely inaccurate. And if you don't know their position accurately, you might not even know whether q is to the left of r or vice versa.
Could you provide me with a link to the Wikipedia article you referred to? I want to make sure I didn't misunderstand what you wrote.
|
|
|
|
Post by Eugene 2.0 on Aug 10, 2020 10:37:40 GMT
O k. thanks again for explaining it.
This from Wiki "Quantum logic":
Quantum logic has some properties that clearly distinguish it from classical logic, most notably, the failure of the distributive law of propositional logic:[7]
p and (q or r) = (p and q) or (p and r),
where the symbols p, q and r are propositional variables. To illustrate why the distributive law fails, consider a particle moving on a line and (using some system of units where the reduced Planck's constant is 1) let
p = "the particle has momentum in the interval [0, +1/6]"
q = "the particle is in the interval [−1, 1]"
r = "the particle is in the interval [1, 3]"
Note: The choice of p, q, and r in this example is intuitive but not formally valid (that is, p and (q or r) is also false here); see section "Quantum logic as the logic of observables" below for details and a valid example.
We might observe that:
p and (q or r) = true
in other words, that the particle's momentum is between 0 and +1/6, and its position is between −1 and +3. On the other hand, the propositions "p and q" and "p and r" are both false, since they assert tighter restrictions on simultaneous values of position and momentum than is allowed by the uncertainty principle (they each have uncertainty 1/3, which is less than the allowed minimum of 1/2). So,
(p and q) or (p and r) = false
Thus the distributive law fails.
|
|
|
|
Post by karl on Aug 10, 2020 10:44:45 GMT
O k. thanks again for explaining it. This from Wiki "Quantum logic": Quantum logic has some properties that clearly distinguish it from classical logic, most notably, the failure of the distributive law of propositional logic:[7] p and (q or r) = (p and q) or (p and r), where the symbols p, q and r are propositional variables. To illustrate why the distributive law fails, consider a particle moving on a line and (using some system of units where the reduced Planck's constant is 1) let p = "the particle has momentum in the interval [0, +1/6]" q = "the particle is in the interval [−1, 1]" r = "the particle is in the interval [1, 3]" Note: The choice of p, q, and r in this example is intuitive but not formally valid (that is, p and (q or r) is also false here); see section "Quantum logic as the logic of observables" below for details and a valid example. We might observe that: p and (q or r) = true in other words, that the particle's momentum is between 0 and +1/6, and its position is between −1 and +3. On the other hand, the propositions "p and q" and "p and r" are both false, since they assert tighter restrictions on simultaneous values of position and momentum than is allowed by the uncertainty principle (they each have uncertainty 1/3, which is less than the allowed minimum of 1/2). So, (p and q) or (p and r) = false Thus the distributive law fails.
Thanks. Then I had understood what you wrote correctly, except for that I didn't know the unit was one Planck length. With such small distances, you can't get a sufficiently accurate answer for position, no matter what photon you use, since no photon can be smaller than one Planck length. So the relation between the three particles in terms of left and right, can't be established.
|
|
|
|
Post by Eugene 2.0 on Aug 10, 2020 10:46:31 GMT
This wiki's explanation, for my opinion, suffers with some weird formalization. I can't ve sure, for certain, because i don't know much here, but doesn't this formalization look adequate:
qvr ~ [-1;3] (chaining two areas)
p&q ~ [0] (multiplying or crossing areas)
p&r ~ [1] (the same)
This is inadequate to the plain PL. We can't sum or multiple just like that. It is not an algebra, but logic.
|
|
|
|
Post by Eugene 2.0 on Aug 10, 2020 10:52:53 GMT
The meaning of a formula in PL is 'true' ir 'false', whatever it is: "T", "F"; "1", "0"; "Good", "Bad", etc. If in p&(qvr) we have x&(-1;3) (-1;3) is where a particle might be placed, so qvr is true,
while (p&r)v(p&q) ~ [0;1]? - it's not correct.
I don't object that the distribution doesn't work in QM, but definitely the explanation in Wiki still seem to be strange.
|
|
|
|
Post by karl on Aug 10, 2020 11:01:55 GMT
The meaning of a formula in PL is 'true' ir 'false', whatever it is: "T", "F"; "1", "0"; "Good", "Bad", etc. If in p&(qvr) we have x&(-1;3) (-1;3) is where a particle might be placed, so qvr is true, while (p&r)v(p&q) ~ [0;1]? - it's not correct. I don't object that the distribution doesn't work in QM, but definitely the explanation in Wiki still seem to be strange.
The key to understanding it is to realise that it's not just a matter of us not knowing the position of a particle, but that the position isn't determined before we measure it. It's not like a hidden information. Rather, it's a matter of that the information isn't there to begin with.
One faces a similar issue in regards to free will. Let's, for the sake of the argument, agree on that humans do have at least some level of free will. Then take the statement: "You will stay indoors tomorrow." Since whether you will or not is a matter of what choice you make, that statement is neither true, nor untrue at the point of it being said. When tomorrow has passed, the statement will become true or untrue. Same thing with determining a particle's position. Before you measure it, it's not determined what the measurement will show.
|
|
|
|
Post by Eugene 2.0 on Aug 10, 2020 21:32:26 GMT
The meaning of a formula in PL is 'true' ir 'false', whatever it is: "T", "F"; "1", "0"; "Good", "Bad", etc. If in p&(qvr) we have x&(-1;3) (-1;3) is where a particle might be placed, so qvr is true, while (p&r)v(p&q) ~ [0;1]? - it's not correct. I don't object that the distribution doesn't work in QM, but definitely the explanation in Wiki still seem to be strange.
The key to understanding it is to realise that it's not just a matter of us not knowing the position of a particle, but that the position isn't determined before we measure it. It's not like a hidden information. Rather, it's a matter of that the information isn't there to begin with.
One faces a similar issue in regards to free will. Let's, for the sake of the argument, agree on that humans do have at least some level of free will. Then take the statement: "You will stay indoors tomorrow." Since whether you will or not is a matter of what choice you make, that statement is neither true, nor untrue at the point of it being said. When tomorrow has passed, the statement will become true or untrue. Same thing with determining a particle's position. Before you measure it, it's not determined what the measurement will show.
Karl, you did so amazingly detailed explanations, I never had read previously in my life! Honestly. If we met one day I'd like to offer you a cold beer =) Or, if you don't like it I'd offer you a cocktail. (I don't drink beer, except for days when I occasionally meet some friend in cafe or a bar, I like to drink lemonades, oranges, fruit-mixes.) To the example of "leaving an apartment": but keep asking such questions we can narrow the range (a location) of where I will be. Aren't we able to locate an apartment? We can find its borders, we can determine it, can't we? The same is with ranges. If I know that a particle is withing [-1;3], then it's obviously that the particle isn't place at -2, right? We know where the limits, and we can make it be narrower by asking questions about the limits of it: "Will a particle be at -1 at the moment X"? It might be there, right? - Or, if we don't know about the position according to not be able to locate it before any determination we can say - "Ok, at -1 there's no the particle, but when we thought it was at -1, the particle was at 0". We can't say there's no particles. We can say that the position of a particle must be measured not precisely, we need to use some ranges. So, therefore, it is impossible to say that the particle at -1, but it's possible to say that the particle within [-1;0], right? And each of our measurement will require such a correction. If how I understood it (I apologize that every time I re-imagine your words in my way; I do it because it makes my understanding to be easier. This stuff is pretty hard to me, so that's why I tried to move it in such a method) it could work, then we have relation-like method of measurement. And all the precise numbers like 1, 2, 3... we can rewrite to its limits Lim(x->1), Lim(x->2), and so on, right? |
|
|
|
Post by xxxxxxxxx on Aug 11, 2020 0:42:16 GMT
P is the medial term between Q and R, as a medial term P is divided between Q and R thus has two identities. P is simultaneously true and false given P and R or P and Q divided P into two identities. As such P cannot be correct given it is a term which means nothing, it is intrinsically empty of value given its dualistic nature. Because P is empty or value P and Q and P and R cannot be taken as true. The premise as being grounded in P being empty necessitates both P&Q and P&R as empty of truth value as well given Q and R derive their identities from P. Hi, 9x! Very glad to see you again! Sorry, that I didn't answered last time. All the best to you and your relatives! Thank you for answering, but I can't say I understood you either. This QM logic is what really pisses me off. Semantically p&(qvr) and (p&q)v(p&r) are both the same. Or, for instance, using Sheffer's stroke: 1) (P|((Q|Q)|(R|R)))|(P|((Q|Q)|(R|R))) = p&(qvr) 2) (((P|Q)|(P|Q))|((P|Q)|(P|Q)))|(((P|R)|(P|R))|((P|R)|(P|R))) = (p&q)v(p&r) So? P|Q can't be uttered four times? I take each: (p&(qvr)), and (p&q)v(p&r) as whole. For me there's no difference. According to what I guessed I had learned previously (to make this post) was that Q and R are interchangeable. If Q is a direction to, but R is an opposite direction to Q, then Q and R are both complement (I'm not sure about the term). In other words, Q or R are true, because we don't know which of which (Q or R) are true, but we do know where the range the micro-particles in is somewhere between those two. While P is without any sure good position we can to describe. Q and R are interchangeable through P.P is the medial term between Q and R, as a medial term P is divided between Q and R thus has two identities. P is simultaneously true and false given P and R or P and Q divided P into two identities. - I can't say it is. Well, this interpretation is interesting, but it might be. P equals to P, right? QM doesn't deny it. Then, P in (P&R) and P in (P&Q) has the same identity. While (QvR), if we take those as the "rotating deities" (as I said they might be interchangeable), it works.
They rotate through P.
Actually, QM must be based on non-classical logic, and we have to see at semantic table smth like this: 1, 1/3, 1/6, 2/3, and so |
|
|
|
Post by karl on Aug 11, 2020 6:23:21 GMT
The key to understanding it is to realise that it's not just a matter of us not knowing the position of a particle, but that the position isn't determined before we measure it. It's not like a hidden information. Rather, it's a matter of that the information isn't there to begin with.
One faces a similar issue in regards to free will. Let's, for the sake of the argument, agree on that humans do have at least some level of free will. Then take the statement: "You will stay indoors tomorrow." Since whether you will or not is a matter of what choice you make, that statement is neither true, nor untrue at the point of it being said. When tomorrow has passed, the statement will become true or untrue. Same thing with determining a particle's position. Before you measure it, it's not determined what the measurement will show.
Karl, you did so amazingly detailed explanations, I never had read previously in my life! Honestly. If we met one day I'd like to offer you a cold beer =) Or, if you don't like it I'd offer you a cocktail. (I don't drink beer, except for days when I occasionally meet some friend in cafe or a bar, I like to drink lemonades, oranges, fruit-mixes.) To the example of "leaving an apartment": but keep asking such questions we can narrow the range (a location) of where I will be. Aren't we able to locate an apartment? We can find its borders, we can determine it, can't we? The same is with ranges. If I know that a particle is withing [-1;3], then it's obviously that the particle isn't place at -2, right? We know where the limits, and we can make it be narrower by asking questions about the limits of it: "Will a particle be at -1 at the moment X"? It might be there, right? - Or, if we don't know about the position according to not be able to locate it before any determination we can say - "Ok, at -1 there's no the particle, but when we thought it was at -1, the particle was at 0". We can't say there's no particles. We can say that the position of a particle must be measured not precisely, we need to use some ranges. So, therefore, it is impossible to say that the particle at -1, but it's possible to say that the particle within [-1;0], right? And each of our measurement will require such a correction. If how I understood it (I apologize that every time I re-imagine your words in my way; I do it because it makes my understanding to be easier. This stuff is pretty hard to me, so that's why I tried to move it in such a method) it could work, then we have relation-like method of measurement. And all the precise numbers like 1, 2, 3... we can rewrite to its limits Lim(x->1), Lim(x->2), and so on, right?
Thank you. It would have to be coffee. I don't drink alcohol.
Yes, if I understood you correctly, I agree with that presentation.
In the given example, the momentum had an uncertainty of 1/6. Uncertainty of momentum multiplied with the uncertainty of position equals 1/2. That means the uncertainty of position is 3. So if I have a particle that is determined to be somewhere in the range of +/- 1,5 around origin, I know that it's to the left (as defined by the X-axis) to another particle which is known to be somewhere around [0,4], with an uncertainty of +/- 1,5.
|
|
