Wheeler's delayed choice doesn't change the past

  • #26
OCR
880
744
I just cannot parse this statement at all... did you leave out some words, or punctuation, or is it just me ? . :oldconfused:
Obviously, deductions or interpretations would be more mingled with the theory on the bench than it occurred the past.
 
  • #27
RUTA
Science Advisor
Insights Author
1,247
310
There is a recent interpretation of QM called Relational Blockworld. It is now quite well developed. It is an adynamical/acausal theory (they do not consider it retrocausal). You might be interested in it:

Relational Blockworld: Towards a Discrete Graph Theoretic Foundation of Quantum Mechanics
https://arxiv.org/abs/0903.2642
We propose a discrete path integral formalism over graphs fundamental to quantum mechanics (QM) based on our interpretation of QM called Relational Blockworld (RBW). In our approach, the transition amplitude is not viewed as a sum over all field configurations, but is a mathematical machine for measuring the symmetry of the discrete differential operator and source vector of the discrete action. Therefore, we restrict the path integral to the row space of the discrete differential operator, which also contains the discrete source vector, in order to avoid singularities. In this fashion we obtain the two-source transition amplitude over a "ladder" graph with N vertices. We interpret this solution in the context of the twin-slit experiment.

One of the authors is a PF member. They have a book that just came out which goes much deeper:
https://global.oup.com/academic/product/beyond-the-dynamical-universe-9780198807087?cc=us&lang=en&
Here is a more recent paper on RBW http://www.ijqf.org/wps/wp-content/uploads/2015/06/IJQF2015v1n3p2.pdf. There is a series of Insights on Blockworld (aka Block Universe) that I wrote which actually formed the starting point of our book. Here is the first in that series https://www.physicsforums.com/insig...time-dilation-length-contraction/#toggle-id-1. These Insights aren’t promoting RBW (rarely mentioned in fact), they’re just pointing out the power of adynamical explanation in the block universe where dynamical explanation in the mechanical universe leads to confusion.
 
  • Like
Likes entropy1
  • #28
9,487
2,572
I am astonished, that this has been written by Hawking.
Of course - so am I - but to be fair in the transactional interpretation it just may. So the correct response is we don't know - but most would say - of course not.

Thanks
Bill
 
Last edited:
  • #29
vanhees71
Science Advisor
Insights Author
Gold Member
2019 Award
15,993
7,295
That's not a fair statement. It is more fair to say that such experiments can be interpreted in other ways. For example: the below referenced experiment is dismissed by you (as we have discussed previously). However, I present to thread readers an example (from a top team) of entangling particles via swapping. The swapping occurs AFTER the entangled particles have already been detected. That is certainly an observation that hints at retrocausation.

https://arxiv.org/pdf/quant-ph/0201134.pdf
Middle of page 5 is the entangle-swap after detection: "... Alice’s measurement projects photons 0 and 3 into an entangled state after they have been measured."

Of course, there is no signalling possible with this scheme, as the projection of the specific entangled state is itself random.
Entanglement swapping or teleportation is no hint at retrocausation either, because to enable it again you need also well prepared entangled photons, which then by coincidence measurements lets you, also in a delayed-choice setup, entangle other pairs which never have been in causal contact to an event before. Again, there cannot be retrocausation in QED (and any local microcausal relativistic QFT as is underlying the Standard Model), and as far as I know, nobody ever claimed that entanglement swapping, Bell experiments, etc. contradict standard QED/relativistic QFT, and indeed one can describe all these experiments within the standard theory. So there is no need to assume retrocausation and other acausalities based on any empirical finding yet, and as long as this is the case, there is no reason to give up the scientific method, which is strongly based on causality. Acausal behavior would be the end of science as we know it!
 
  • Like
Likes zonde
  • #30
vanhees71
Science Advisor
Insights Author
Gold Member
2019 Award
15,993
7,295
There is a recent interpretation of QM called Relational Blockworld. It is now quite well developed. It is an adynamical/acausal theory (they do not consider it retrocausal). You might be interested in it:

Relational Blockworld: Towards a Discrete Graph Theoretic Foundation of Quantum Mechanics
https://arxiv.org/abs/0903.2642
We propose a discrete path integral formalism over graphs fundamental to quantum mechanics (QM) based on our interpretation of QM called Relational Blockworld (RBW). In our approach, the transition amplitude is not viewed as a sum over all field configurations, but is a mathematical machine for measuring the symmetry of the discrete differential operator and source vector of the discrete action. Therefore, we restrict the path integral to the row space of the discrete differential operator, which also contains the discrete source vector, in order to avoid singularities. In this fashion we obtain the two-source transition amplitude over a "ladder" graph with N vertices. We interpret this solution in the context of the twin-slit experiment.

One of the authors is a PF member. They have a book that just came out which goes much deeper:
https://global.oup.com/academic/product/beyond-the-dynamical-universe-9780198807087?cc=us&lang=en&
Is this still science? Is this something beyond standard QT or just another mathematical technique to evaluate path integrals? I'm a bit sceptical ;-)). Last but not least the preprint (on a theoretical subject) is written in Word...
 
  • Like
Likes bhobba
  • #31
9,487
2,572
On the other hand, a measurement is simply an amplification of a microscopic property so that it produces a macroscopic effect.
I think I get your drift in that decoherence transforms a superposition to a mixed state - but 'amplification' is not the word I would use - more like something along the lines of making 'clearer' by interacting with it. Also what it interacts with determines exactly what is now 'clearer'. Sorry for the semantic quibble - I usually think semantics is a rather silly thing to ague about, but sometimes it does help in clarifying things for others.

Thanks
Bill
 
  • #32
Lord Jestocost
To me, the Copenhagenish belief that "nothing is real unless it is observed......"
That means that either the theory is incomplete or classic reality is an illusion of the macroscopic world.
To my mind, Copenhagen says nothing but: Microscopic entities are not „real“ in the sense that we cannot speak about them directly; we cannot describe these entities at all, we can only represent them by means of a quantum mechanical formalism; as distinguished from macroscopic entities which allow at least an approximate classical description.
 
  • #33
9,487
2,572
To my mind, Copenhagen says nothing but: Microscopic entities are not „real“ in the sense that we cannot speak about them directly; we cannot describe these entities at all, we can only represent them by means of a quantum mechanical formalism; as distinguished from macroscopic entities which allow at least an approximate classical description.
Basically yes - but there are issues, just like with ordinary probability what exactly does probability mean eg frequentest vs Bayesian. Copenhagen is more Bayesian - Ensemble more frequentest. And then their is the issue of is it complete.

Your view is more like that of Dirac. Heisenberg and other Copenhagenists thought it was complete - Einstein thought not - Dirac was not sure of either - he was open:
http://philsci-archive.pitt.edu/1614/1/Open_or_Closed-preprint.pdf

That's part of the reason I think of all the early pioneers Dirac was the closest to correct.

Added Later:
Oh I forgot to mention future developments seem to prove him correct - QFT was not a big change from the principles of QM but was certainly closer to 'correct' accounting for things that standard QM could not account such as spontaneous emission.

Thanks
Bill
 
Last edited:
  • #34
stevendaryl
Staff Emeritus
Science Advisor
Insights Author
8,401
2,581
Basically yes - but there are issues, just like with ordinary probability what exactly does probability mean eg frequentest vs Bayesian. Copenhagen is more Bayesian - Ensemble more frequentest. And then their is the issue of is it complete.

Your view is more like that of Dirac. Heisenberg and other Copenhagenists thought it was complete - Einstein thought not - Dirac was not sure of either - he was open:
http://philsci-archive.pitt.edu/1614/1/Open_or_Closed-preprint.pdf

That's part of the reason I think of all the early pioneers Dirac was the closest to correct.

Thanks
Bill
I don't see how Bayesian versus Ensemble matters for the interpretation problems. It seems to me that the "rules of thumb" for using QM make a distinction between macroscopic and microscopic systems. Microscopic systems can be in superpositions, and so don't have definite values for observables, in general. Macroscopic systems, particularly measuring devices, are assumed to give definitive answers. In the terms you've used so often, the distinction is between improper and proper mixed states. QM doesn't describe how an improper mixed state becomes a proper mixed state. So if that actually happens, it seems that QM is incomplete, and the various interpretations of probability don't seem to make a difference (or I don't see how).

Of course, there is a possibility that the transition never happens, which to me implies Many Worlds, which has its own interpretation problems.
 
  • #35
9,487
2,572
I don't see how Bayesian versus Ensemble matters for the interpretation problems.
Well Copenhagen states the state is subjective, the ensemble states its a conceptual very large number of possible outcomes (actually infinite - but I don't know about you but I cant imagine that) associated with each observable. They are different - the same way Bayesian and frequentest are different. Is it of any practical importance - IMHO no. Having studied probability nobody that applies it worries about it, although sometimes they, without stating there is controversy about it, chose one in solving problems, but usually it doesn't matter at all. Same in QM - but here people like to make a distinction - in practice it makes just as much difference - basically none.

In the terms you've used so often, the distinction is between improper and proper mixed states. QM doesn't describe how an improper mixed state becomes a proper mixed state. So if that actually happens, it seems that QM is incomplete, and the various interpretations of probability don't seem to make a difference (or I don't see how).
You can look at it that way - Einstein probably would. If that's your wont - go for it - fine by me.

The other view is every theory, every single one has things that are simply accepted as true - that improper mixed states become proper ones is simply one that's accepted as true - you may find an explanation for that - and of course such would be an advance - but then you are faced with the question - why is that true? It has no logical status any different than the original explanation - aside from truth of course. The new explanation you may like, not like or even think it's worse. All this is just a personal reaction. I am in that camp - its just an assumption we make. It may have a deeper explanation - or not. Personally it doesn't worry me one way or the other.

These things are nothing but personal preference. I have mine - you have yours - Einstein has his. I don't really care. Any could be correct - doesn't bother me one way or the other. Got an experiment to decide - then progress has been made. Without experimental support the only benefit IMHO is they shed light on the formalism which is the important thing and why I like reading them. I don't care what one you or anyone else chooses - I just want to understand the formalism better.

Thnaks
Bill
 
  • #36
stevendaryl
Staff Emeritus
Science Advisor
Insights Author
8,401
2,581
Well Copenhagen states the state is subjective, the ensemble states its a conceptual very large number of possible outcomes (actually infinite - but I don't know about you but I cant imagine that) associated with each observable.
But it seems to me that there is a "preferred basis" problem with such an ensemble view. In a classical use of ensembles, you have some undetermined variable, such as the precise location of the system in phase space, and the ensemble consists of many similar systems in which this variable has a definite value (but different in different elements of the ensemble). So you could try to do something similar with quantum uncertainty: You have an uncertain variable, such as the spin of a particular particle along the z-axis. And then you have an ensemble of similar systems that differ in the value of that variable.

But here's where the basis problem comes in, it seems to me. Why in the ensemble do the individual systems have definite values for spin in the z-direction, as opposed to, say, spin in the y-direction? You could answer: Because spin in the z-direction is what we're measuring---there would be a different ensemble for each kind of measurement you might want to perform.

Okay, that's fine for some purposes, but presumably the measurement device and the observer doing the measurement are themselves quantum systems, although very complex ones. Presumably what it is that you're trying to measure is a fact about the configuration of atoms making up the measurement devices. And the fact that the outcome was "spin up in the z-direction" rather than "spin up in the x-direction" is again a fact about the configuration after the measurement. So it seems to me that in principle, it should not be necessary to specify what is being measured, because that is itself a property of the state.

The other view is every theory, every single one has things that are simply accepted as true - that improper mixed states become proper ones is simply one that's accepted as true
Well, I'm fine with it just being an additional assumption of the theory. However, there is no way for that transition to take place in a basis-independent manner. The usual assumption, in agreement with our intuitions and observations, is that the transition happens so that after the transition to proper mixed states, macroscopic variables--whether cats are alive or dead, whether you are in London or Beijing--have definite values. That seems to me to be a breaking of the basis-independence of the quantum formalism.

I know that there is a reason for "preferring" a position basis for macroscopic objects, because only in the position basis are interactions local. That's a clue, but it isn't an answer. The question is whether adding a transition from improper to proper mixed states involves some violation of quantum mechanics, or is it derivable from quantum mechanics, or is it merely consistent (thought not implied by) quantum mechanics? I don't think that just assuming that it happens actually answers the questions.
 
  • #37
RUTA
Science Advisor
Insights Author
1,247
310
Is this still science? Is this something beyond standard QT or just another mathematical technique to evaluate path integrals? I'm a bit sceptical ;-)). Last but not least the preprint (on a theoretical subject) is written in Word...
RBW specifically and adynamical explanation in the block universe in general focus on empirical science rather than metaphysics. We want to move physics beyond theories like string theory and inflation where you have to abandon empirical verification, as we argue at length in chapter 1. But, in the context of this thread, just read https://www.physicsforums.com/insig...elayed-choice-no-counterfactual-definiteness/ to see how adynamical explanation in the block universe resolves the mystery of delayed choice that results from dynamical explanation in the mechanical universe. Yes, RBW has implications for quantum gravity (theory beyond QT as we detail in chapter 6), but there is no mention of RBW in the Insight — you don’t need RBW to appreciate the explanatory power of the “God’s-eye view” over the “ant’s-eye view” (Wilczek, F. : Physics in 100 Years. Physics Today 69(4), 32-39 (2016)). You can read Parts 3 and 4 on GR as well to appreciate that. As for the last sentence, I fail to see the relevance. Five respected foundationalists (to include Rovelli) gave the thumbs up on the book or Oxford UP would never have given us a contract. Several others since have sent us their input and/or given us blurbs (you can read those on Amazon). Does it matter what word processor we used to write it?
 
  • Like
Likes DrChinese
  • #38
DrChinese
Science Advisor
Gold Member
7,361
1,151
... Acausal behavior would be the end of science as we know it!
I'm sure there were lots of people who thought the same when the probabilities of QM appeared on the scene. And yet, here we are, nearly 100 years later and the science just keeps getting better and better.
 
  • #39
RUTA
Science Advisor
Insights Author
1,247
310
Acausal behavior would be the end of science as we know it!
Moving “Beyond the Dynamical Universe” is a paradigm change, yes. I’ve been doing foundations of physics for 23 years and it’s my impression that most in the community believe experiments like delayed choice will lead to a new scientific worldview. Here is a nice quote from Richard DeWitt that sums up the atmosphere in foundations of physics (Worldviews: An Introduction to the History and Philosophy of Science, DeWitt, R., 2004, p. 304, Blackwell Publishing):

In the past, fundamental new discoveries have led to changes -- including theoretical, technological, and conceptual changes -- that could not even be imagined when the discoveries were first made. The discovery that we live in a universe that, deep down, allows for Bell-like influences strikes me as just such a fundamental, important new discovery. ... If I am right about this, then we are living in a period that is in many ways like that of the early 1600’s. At that time, new discoveries, such as those involving Galileo and the telescope, eventually led to an entirely new way of thinking about the sort of universe we live in. Today, at the very least, the discovery of Bell-like influences forces us to give up the Newtonian view that the universe is entirely a mechanistic universe. And I suspect this is only the tip of the iceberg, and that this discovery, like those in the 1600’s, will lead to a quite different view of the sort of universe in which we live.
 
  • Like
Likes DrChinese
  • #40
I just cannot parse this statement at all...:
"Obviously, deductions or interpretations would be more mingled with the theory on the bench than it occurred [in] the past."
did you leave out some words, or punctuation, or is it just me ? . :oldconfused:
I missed [in] before "the past". But I see it is not enough to make sense of this thought of mine. I'll try to express it better.
First, usual theories address what is worth observing under circumstances that are partially generated by the experimenter's will and strategy, in the form of an experimental setting. The "quasi-deterministic" or "classic" character of the experimental apparatus and constraints can be obtained only operating in the macroscopic domain. Let's think to a particle accelerator. About this part of the experimental circumstances and constraints which is under our control, we suppose that are independent of the theory we want to probe. There is another part of the experimental circumstances that are "decided" and acted by and under the control of the "nature of things". The separateness of the two parts in determining the experimental circumstances warranted the realism of science. We were sure that what we were "observing" was not an artefact of our apparatus or preconception, but rather an expression of a sort of "freedom" of nature whether to correspond, or not, to our theory-based guesses.
If we go to devise experiments at the nanoscale or quantum scale, we must renounce at determinism, to the control of setting, of constraints, to the deterministic tuning of experimental variables. We are not anymore observing how our commanded actors influence and interact with common people on the stage. We would be engaged in simply collecting signals from the microscopic world: a certain particle decays, gamma rays are emitted at certain frequencies etc. We don't care about initial conditions because these are always statistically defined at most. An experiment wouldn't be anymore a "natural outcome" as determined by an artificial input entered into the black box. We will just observe outputs coming from the black box and try to make sense of them. If a classical experiment is the study of "if I do something then something happens", in an experiment at the quantum scale we haven't anymore the control of the "if I" part. The "if" part and the "then" part are both theory dependent footprints, to be interpreted within the theory before we can check the correlations as matching/not matching the theory itself.
We don't need to renounce at realism and believe that the way we rationally choose to interpret the signals and footprints could ever affect what the hell occurs in the black box. We don't need to renounce at studying phenomena. But we must adopt new concepts which are farther from our point of view and closer to the "nature of things" in studying phenomena. Sum over histories is possibly one of these.
 
  • #41
zonde
Gold Member
2,941
213
Moving “Beyond the Dynamical Universe” is a paradigm change, yes. I’ve been doing foundations of physics for 23 years and it’s my impression that most in the community believe experiments like delayed choice will lead to a new scientific worldview. Here is a nice quote from Richard DeWitt that sums up the atmosphere in foundations of physics (Worldviews: An Introduction to the History and Philosophy of Science, DeWitt, R., 2004, p. 304, Blackwell Publishing):

In the past, fundamental new discoveries have led to changes -- including theoretical, technological, and conceptual changes -- that could not even be imagined when the discoveries were first made. The discovery that we live in a universe that, deep down, allows for Bell-like influences strikes me as just such a fundamental, important new discovery. ... If I am right about this, then we are living in a period that is in many ways like that of the early 1600’s. At that time, new discoveries, such as those involving Galileo and the telescope, eventually led to an entirely new way of thinking about the sort of universe we live in. Today, at the very least, the discovery of Bell-like influences forces us to give up the Newtonian view that the universe is entirely a mechanistic universe. And I suspect this is only the tip of the iceberg, and that this discovery, like those in the 1600’s, will lead to a quite different view of the sort of universe in which we live.
I don't see that the quote you gave suggests that we should move away from scientific approach and adopt some acausal philosophical view of reality.
 
  • #42
RUTA
Science Advisor
Insights Author
1,247
310
I don't see that the quote you gave suggests that we should move away from scientific approach and adopt some acausal philosophical view of reality.
Who said anything about moving away from scientific approaches? Acausal explanation is still scientific.
 
  • Like
Likes bhobba and DrChinese
  • #43
OCR
880
744
  • #44
DrChinese
Science Advisor
Gold Member
7,361
1,151
I don't see that the quote you gave suggests that we should move away from scientific approach and adopt some acausal philosophical view of reality.
If it works, it works. There's no sense in calling an approach that is aesthetically unpleasing to you "unscientific". I will point out that all interpretations posit probabilities - akin to throwing dice - as the BEST that can be offered as an explanation for quantum outcomes. That includes Bohmian Theories.

So I don't see what the objection is to an acausal theory if it provides explanatory power. If I observe the spin of a particle to be up, and can't explain that outcome deterministically, how is that NOT acausal anyway?
 
  • Like
Likes bhobba
  • #45
9,487
2,572
it should not be necessary to specify what is being measured, because that is itself a property of the state.
Ahhh. But that's not what the Born rule says is it - so 'seems to me' is obviously wrong. Intuition and QM are sometimes not good friends.

You keep mentioning basis independence - that in fact is the key assumption of Gleason and the root of that very Born Rule.

THanks
Bill
 
  • Like
Likes vanhees71
  • #46
zonde
Gold Member
2,941
213
Who said anything about moving away from scientific approaches? Acausal explanation is still scientific.
All our reasoning about reality is built on causal relationships. Say we believe that our records at present tell us something about experiments and their results in the past. And actually any information about the past is result of causal process. So acausal relationship is such that does not leave any trace of it in the future. So we can't gather knowledge about such relationship.
 
  • Like
Likes vanhees71
  • #47
vanhees71
Science Advisor
Insights Author
Gold Member
2019 Award
15,993
7,295
Moving “Beyond the Dynamical Universe” is a paradigm change, yes. I’ve been doing foundations of physics for 23 years and it’s my impression that most in the community believe experiments like delayed choice will lead to a new scientific worldview. Here is a nice quote from Richard DeWitt that sums up the atmosphere in foundations of physics (Worldviews: An Introduction to the History and Philosophy of Science, DeWitt, R., 2004, p. 304, Blackwell Publishing):

In the past, fundamental new discoveries have led to changes -- including theoretical, technological, and conceptual changes -- that could not even be imagined when the discoveries were first made. The discovery that we live in a universe that, deep down, allows for Bell-like influences strikes me as just such a fundamental, important new discovery. ... If I am right about this, then we are living in a period that is in many ways like that of the early 1600’s. At that time, new discoveries, such as those involving Galileo and the telescope, eventually led to an entirely new way of thinking about the sort of universe we live in. Today, at the very least, the discovery of Bell-like influences forces us to give up the Newtonian view that the universe is entirely a mechanistic universe. And I suspect this is only the tip of the iceberg, and that this discovery, like those in the 1600’s, will lead to a quite different view of the sort of universe in which we live.
Well, I don't believe much in "philosophy of science". If there is a paradigm change this must come from reproducible objective observations not from scholastic thinking about "angles on the head of a pin".
 
  • Like
Likes bhobba
  • #48
vanhees71
Science Advisor
Insights Author
Gold Member
2019 Award
15,993
7,295
So I don't see what the objection is to an acausal theory if it provides explanatory power. If I observe the spin of a particle to be up, and can't explain that outcome deterministically, how is that NOT acausal anyway?
As often, this confusion comes from not clearly distinguishing between "deterministic" and "causal"

Deterministic means that all observables have precise values at any time, no matter whether we have prepared the observed system to have these values or not. That's the worldview of classical physics (both in point-particle mechanics and classical field theory).

Causal means that if the state of a system is known over the entire history of the past, the state is determined at any later time. On a fundamental level, even a much stronger assumption holds in all physics (including QT): If the state of the system is known at time ##t_0## than it's also known at any later time ##t>t_0##.

The difference between classical and quantum physics is that the preparation in a pure state, i.e., the complete preparation such that the values of a complete set of compatible observables are determined, in the quantum case does not imply that all observables have determined values. In QT, indeed it's impossible to prepare a system in a state, where this is the case, and all the complete state preparation implies are the corresponding probabilities for the outcome of measurements of any observable of the system.

In short: All of physics is causal. If there is no causality, physics (and all natural sciences) as we know it, is simply gone since the scientific method hinges on the assumption that there are causal natural laws and the objective observations are reproducible, i.e., when preparing a system in any pure states leads to the very same outcome of measurements of all observables. If this was not the case, particularly QT wouldn't make any sense as a physical theory since you can test the probabilistic (and only probabilistic!) predictions it makes about the outcome of measurement only if these probabilities are fixed. If the causality assumption is invalid, this wouldn't be the case but everything would be indetermined completely, i.e., we'd not be able to reproduce any previous empirical finding in the world.
 
Last edited by a moderator:
  • Like
Likes zonde
  • #49
9,487
2,572
Acausal behavior would be the end of science as we know it!
What's your view of the Wheeler-Feynman absorber theory?

I am not a fan of that or the transactional interpretation, but that scientifically means diddly squat. As usual I agree with you but I don't think the situation is quite as clear cut as you said - or maybe its is - but you can best explain what you mean because I think its a bit context dependent ie we cant send information backward in time - that would be exactly as you say.

Thanks
Bill
 
Last edited:
  • #50
324
43
Hi all
To my mind, Copenhagen says nothing but: Microscopic entities are not „real“ in the sense that we cannot speak about them directly; we cannot describe these entities at all, we can only represent them by means of a quantum mechanical formalism; as distinguished from macroscopic entities which allow at least an approximate classical description.
indeed, a "microsystem" is not perceptible, by us humain being, as a pebble can be. To study "microstates" that are not perceptible to us, we need recording devices that are capable of capturing brands (for example buble chamber), following interactions with "microstates", that are perceptible to us. We have to abandon our naïve realism assumptions, which is the idea that the senses provide us with direct awareness of objects as they really are (wave, corpuscle, trajectory, ..). In all intellectually honesty, we should not forget the mediation of our brains when building our scientific knowledge.

Best regards
 

Related Threads on Wheeler's delayed choice doesn't change the past

  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
7
Views
2K
  • Last Post
2
Replies
35
Views
6K
Replies
6
Views
2K
Replies
6
Views
4K
Replies
0
Views
957
  • Last Post
Replies
2
Views
2K
Replies
38
Views
8K
Replies
25
Views
2K
Replies
5
Views
266
Top