- #1

- 462

- 0

- Thread starter Gold Barz
- Start date

- #1

- 462

- 0

- #2

- 137

- 0

- #3

- 196

- 0

Yes, faster than light communication would cause major problems with causality. To quote d'Inverno (1992, page 22):Gold Barz said:Because if it is then it could cause problems with causality.

Particles that move faster than the speed of light are calledsuperluminalparticles ortachyons. There was some excitement in the 1970s surrounding the possible existence of tachyons, but all attempts to detect them to date have failed. This suggests two likely possibilities: either tachyons do not exist or, if they do, they do not interact with ordinary matter. This would seem to be just as well, for otherwise they could be used to signal back into the past and so would appear to violate causality. For example, it would be possible theoretically to construct a device which sent out a tachyon at a given time and which would trigger a mechanism in the device to blow it upbeforethe tachyon was sent out!

- #4

Chronos

Science Advisor

Gold Member

- 11,408

- 741

- #5

Danger

Gold Member

- 9,607

- 246

Our 'laws' are definitely incomplete, or science would be at a standstill and we would know everything. That particular law, however, is pretty firmly entrenched. New laws, as they are discovered, don't negate the old ones; they expand upon them. OldGold Barz said:

- #6

- 39

- 1

Yet, it does not conflict with the core principle of Special Relativity.

- #7

- 3,763

- 9

Good question,Gold Barz said:

scroll down to the https://www.physicsforums.com/journal.php?s=&action=view&journalid=13790&perpage=10&page=7 [Broken] entry

Your answer is in there

regards

marlon

Last edited by a moderator:

- #8

JesseM

Science Advisor

- 8,496

- 13

No, you can't actually use quantum entanglement to send messages faster than light. With quantum teleportation, you need to send a classical signal (speed of light or slower) between the two locations in order for the quantum state to be correctly "teleported".Yaaks said:Faster than light communication is possilble through Quantum Entanglement, though no one knows how??. The idea of quantum teleportation uses this principle....

- #9

turbo

Gold Member

- 3,077

- 46

True, in the case of quantum entaglement, you are not sending a signal from receptor A to receptor B faster than the speed of light, you are transmittingJesseM said:No, you can't actually use quantum entanglement to send messages faster than light. With quantum teleportation, you need to send a classical signal (speed of light or slower) between the two locations in order for the quantum state to be correctly "teleported".

- #10

- 462

- 0

So it looks like it is not possible?

- #11

ohwilleke

Gold Member

- 1,566

- 451

Not true. You can know all the "laws of chess" and still not be a master.Danger said:Our 'laws' are definitely incomplete, or science would be at a standstill and we would know everything. That particular law, however, is pretty firmly entrenched. New laws, as they are discovered, don't negate the old ones; they expand upon them. Oldtheoriesfall by the wayside all of the time, but it isn't considered a 'law' unless it's inviolable.

Also, the line between "theory" and "law" is pretty meaningless. It is more a matter of social convention than any real difference between the two. For example, we seek of Newton's Law of Gravity, but Einstein's Theory of General Relativity. We have the theory of evolution, and Murphy's Law (OK that was a cheap shot).

- #12

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,916

- 19

No.True, in the case of quantum entaglement, you are not sending a signal from receptor A to receptor B faster than the speed of light, you are transmitting information about the state of the partner particle at the other receptor faster than the speed of light.

Anyways, observers A and B will indeed have a shared bit of information. However, that usage of shared is

- #13

- 39

- 1

u can have a 'Morse code' type of information transmitted like, spin=clockwise=1 & spin=counter-clockwise=0...

decode using binary language of 10101010...

- #14

JesseM

Science Advisor

- 8,496

- 13

It really depends on your interpretation of QM. In a hidden-variables interpetation like Bohmian mechanics, it is true that the particles are affecting one another's state faster-than-light. In the http://mist.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html [Broken] you might say that the measurement of one particle had a backwards-in-time influence on the other's state when the two were created. And the many-worlds interpetation tries to explain everything about entanglement without any FTL or backwards-in-time influences, by way of each observer locally splitting into multiple copies during a measurement and the copies in different locations not being matched up until a signal has had time to pass between them. I came up with a simple example to show howturbo-1 said:True, in the case of quantum entaglement, you are not sending a signal from receptor A to receptor B faster than the speed of light, you are transmittinginformation about the state of the partner particle at the other receptorfaster than the speed of light.

say Bob and Alice are each recieving one of an entangled pair of photons, and their decisions about which spin axis to measure are totally deterministic, so the only "splitting" necessary is in the different possible results of their measurements. Label the three spin axes a, b, and c. If they always find opposite spins when they both measure their photons along the same axis, a local hidden-variables theory would say that if they choose different axes, the probability they get opposite spins must be at least 1/3 (assuming there's no correlation between their choice of which axes to measure and the states of the photons before they make the measurement). The actual probability of finding opposite spins when measuring different axes will depend on the angle between the three axes they choose to measure, but all that's important is that it's less than 1/3, so for the sake of the argument let's say it's 1/4.

So suppose Bob's decision will be to measure along axis a, and Alice's decision will be to measure along axis c. When they do this, suppose each splits into 8 parallel versions, 4 measuring spin + and 4 measuring spin -. Label the 8 Bobs like this:

Bob 1: a+

Bob 2: a+

Bob 3: a+

Bob 4: a+

Bob 5: a-

Bob 6: a-

Bob 7: a-

Bob 8: a-

Similarly, label the 8 Alices like this:

Alice 1: c+

Alice 2: c+

Alice 3: c+

Alice 4: c+

Alice 5: c-

Alice 6: c-

Alice 7: c-

Alice 8: c-

Note that the decision of how they split is based only on the assumption that each has a 50% chance of getting + and a 50% chance of getting - on whatever axis they choose, no knowledge about what the other one was doing was needed. And again, only when a signal travelling at the speed of light or slower passes from one to the other does the universe need to decide which Alice shares the same world with which Bob...when that happens, they can be matched up like this:

Alice 1 (c+) <--> Bob 1 (a+)

Alice 2 (c+) <--> Bob 2 (a+)

Alice 3 (c+) <--> Bob 3 (a+)

Alice 4 (c+) <--> Bob 5 (a-)

Alice 5 (c-) <--> Bob 4 (a+)

Alice 6 (c-) <--> Bob 6 (a-)

Alice 7 (c-) <--> Bob 7 (a-)

Alice 8 (c-) <--> Bob 8 (a-)

This insures that each one has a 3/4 chance of finding out the other got the same spin, and a 1/4 chance that the other got the opposite spin. If Bob and Alice were two A.I.'s running on classical computers in realtime, you could simulate Bob on one computer and Alice on another, make copies of each according to purely local rules whenever each measured a quantum particle, and then use this type of matching rule to decide which of the signals from the various copies of Alice will be passed on to which copy of Bob, and you wouldn't have to make that decision until the information from the computer simulating Alice was actually transmitted to the computer simulating Bob. So using purely local rules you could insure that, after many trials like this, a randomly-selected copy of A.I. Bob or A.I. Alice would record the same type of statistics that's seen in the Aspect experiment, including the violation of Bell's inequality.

Note that you wouldn't have to simulate any hidden variables in this case--you only have to decide what the spin was along the axes each one measured, you never have to decide what the spin along the other 2 unmeasured axes of each photon was.

He doesn't know the state of the other particle, he just knows thatturbo-1 said:If the emitter of the entangled particles is exactly in the center of the path between the receptors of the particles, receptor A "knows" the state of the particle at receptor B in half the time that it would take for a classical transmission between A and B.

Last edited by a moderator:

- #15

Danger

Gold Member

- 9,607

- 246

That's not quite the same situation. Knowing all of the laws of chess gives one theohwilleke said:Not true. You can know all the "laws of chess" and still not be a master.

My interpretation of the the difference is that a theory becomes a law when it has proven itself to be unbreakable.ohwilleke said:Also, the line between "theory" and "law" is pretty meaningless. It is more a matter of social convention than any real difference between the two.

Newton's Law of Gravity has been proven unbreakable within the framework to which it applies. You can stand around dropping bricks for the rest of your life and every single one of them is going to hit the ground in accordance with that law. Einsteinian and quantum gravity don't negate that law, they supplement it. Think of them as being like ammendments to your constitution.ohwilleke said:For example, we seek of Newton's Law of Gravity, but Einstein's Theory of General Relativity. We have the theory of evolution, and Murphy's Law (OK that was a cheap shot).

The Theory of GR is still being tested. Also, the proven fact of Evolution is more or less a law. The theories relate to what mechanisms and time-scales are most likely true.

- #16

DaveC426913

Gold Member

- 18,968

- 2,455

No.ohwilleke said:Also, the line between "theory" and "law" is pretty meaningless. It is more a matter of social convention than any real difference between the two. For example, we seek of Newton's Law of Gravity, but Einstein's Theory of General Relativity. We have the theory of evolution, and Murphy's Law (OK that was a cheap shot).

A law describes something we see; it describes

eg. There is no 'alternate' Law of Gravity. The Law of Gravity simply describes what every scientist on every planet in the universe will jot down on her notepad. They will all describe what speed objects fall and what speed the Moon revolves. Generalizing, they will

OTOH, a theory attempts to describe

Every one of those scientists on those planets could have a different theory about how/why objects fall or how/why their moon revolves (gravity particles, warped space-time, invisible tendrils), all of which can be negotiated and refuted.

In fact, I'll boil that down:

Last edited:

- #17

JesseM

Science Advisor

- 8,496

- 13

That distinction doesn't make any sense to me. Are you saying Newtonian gravity is a "law" because it just describes what happens, while General relativity is a "theory" because it describes why? Seems to me that GR just describes what happens too--it doesn't sayDaveC426913 said:No.

A law describes something we see; it describeswhathappens. It is simply a quantified observation.

eg. There is no 'alternate' Law of Gravity. The Law of Gravity simply describes what every scientist on every planet in the universe will jot down on her notepad. They will all describe what speed objects fall and what speed the Moon revolves. Generalizing, they willallarrive at G=(m2*m1)/r^2. It's not negotiable.

OTOH, a theory attempts to describehow or why.

Every one of those scientists on those planets could have a different theory about how/why objects fall or how/why their moon revolves (gravity particles, warped space-time, invisible tendrils), all of which can be negotiated and refuted.

Note item 17 on physicist John Baez's crackpot index:

Likewise, Feynman talks about the issue of whether we need a "mechanism" to explain why a particular abstract mathematical theory works in chapter 2 of his book "The Character of Physical Law", which is entitled "The Relation of Mathematics to Physics":10 points for arguing that while a current well-established theory predicts phenomena correctly, it doesn't explain "why" they occur, or fails to provide a "mechanism".

On the other hand, take Newton's law for gravitation, which has the aspects I discussed last time. I gave you the equation:

F=Gmm'/r^2

just to impress you with the speed with which mathematical symbols can convey information. I said that the force was proportional to the product of the masses of two objects, and inversely as the square of the distance between them, and also that bodies react to forces by changing their speeds, or changing their motions, in the direction of the force by amounts proportional to the force and inversely proportional to their masses. Those are words all right, and I did not necessarily have to write the equation. Nevertheless it is kind of mathematical, and we wonder how this can be a fundamental law. What does the planet do? Does it look at the sun, see how far away it is, and decide to calculate on its internal adding machine the inverse of the square of the distance, which tells it how much to move? This is certainly no explanation of the machinery of gravitation! You might want to look further, and various people have tried to look further. Newton was originally asked about his theory--'But it doesn't mean anything--it doesn't tell us anything'. He said,'It tells youButhowit moves. That should be enough. I have told you how it moves, not why.'people are often unsatisfied without a mechanism, and I would like to describe one theory which has been invented, among others, of the type you migh want. This theory suggests that this effect is the result of large numbers of actions, which would explain why it is mathematical.

Suppose that in the world everywhere there are a lot of particles, flying through us at very high speed. They come equally in all directions--just shooting by--and once in a while they hit us in a bombardment. We, and the sun, are practically transparent for them, practically but not completely, and some of them hit. ... If the sun were not there, particles would be bombarding the earth from all sides, giving little impuleses by the rattle, bang, bang of the few that hit. This will not shake the earth in any particular direction, because there are as many coming from one side as from the other, from top as from bottom. However, when the sun is there the particles which are coming from that direction are partially absorbed by the sun, because some of them hit the sun and do not go through. Therefore the number coming from the sun's direction towards the earth is less than the number coming from the other sides, because they meet an obstacle, the sun. It is easy to see that the farther the sun is away, of all the possible directions in which particles can come, a smaller proportion of the particles are being taken out. The sun will appear smaller--in fact inversely as the square of the distance. Therefore there will be an impulse on the earth towards the sun that varies inversely as the square of the distance. And this will be the result of a large number of very simple operations, just hits, one after the other, from all directions. Therefore the strangeness of the mathematical relation will be very much reduced, because the fundamental operation is much simpler than calculating the inverse of the square of the distance. This design, with the particles bouncing, does the calculation.

The only trouble with this scheme is that it does not work, for other reasons. Every theory that you make up has to be analysed againstallpossible consequences, to see if it predicts anything else. And this does predict something else. If the earth is moving, more particles will hit it from in front than from behind. (If you are running in the rain, more rain hits you in the front of the face than in the back of the head, because you are running into the rain.) So, if the earth is moving it is running into the particles coming towards it and away from the ones that are chasing it from behind. So more particles will hit it from the front than from the back, and there will be a force opposing any motion. This force would slow the earth up in its orbit, and it certainly would not have lasted the three of four billion years (at least) that it has been going around the sun. So that is the end of that theory. 'Well,' you say, 'it was a good one, and I got rid of the mathematics for a while. Maybe I could invent a better one.' Maybe you can, because nobody knows the ultimate. But up to today, from the time of Newton, no one has invented another theoretical description of the mathematical machinery behind this law which does not either say the same thing over again, or make the mathematics harder, or predict some wrong phenomena. So there is no model of the theory of gravity today, other than the mathematical form.

If this were the only law of this character it would be interesting and rather annoying.But what turns out to be true is that the more we investigate, the more laws we find, and the deeper we penetrate nature, the more this disease persists. Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics.

...[A] question is whether, when trying to guess new laws, we should use seat-of-the-pants feelings and philosophical principles--'I don't like the minimum principle', or 'I do like the minimum principle', 'I don't like action at a distance', or 'I do like action at a distance'. To what extent do models help? It is interesting that very often models do help, and most physics teachers try to teach how to use models and to get a good physical feel for how things are going to work out. But it always turns out that the greatest discoveries abstract away from the model and the model never does any good. Maxwell's discovery of electrodynamics was made with a lot of imaginary wheels and idlers in space. But when you get rid of all the idlers and things in space the thing is O.K. Dirac discovered the correct laws for relativity quantum mechanics simply by guessing the equation. The method of guessing the equation seems to be a pretty effective way of guessing new laws.This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way.

It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypothesis that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities. But this speculation is of the same nature as those other people make--'I like it', 'I don't like it',--and it is not good to be too prejudiced about these things.

Last edited:

- #18

- 196

- 0

Then why do general relativity's predictions deviate from Newtonian gravity's predictions? For an example, look to the perihelion shift in Mercury's orbit, which cannot be explained by Newton's Law of gravity. Obviously, Newton'sDaveC426913 said:eg. There is no 'alternate' Law of Gravity. The Law of Gravity simply describes what every scientist on every planet in the universe will jot down on her notepad. They will all describe what speed objects fall and what speed the Moon revolves. Generalizing, they willallarrive at G=(m2*m1)/r^2. It's not negotiable.

Last edited:

- #19

- 78

- 0

In our now actual life experiences, it very seems that it is impossible. I ever read a book the writer is a Cambridge University professor, he thinks that speed can faster than light speed, he put much hypothesis, but I feel the book's hypothesis is impossible and fantastic. I now have no enough reasons to believe Einstein's hypothesis is wrong, so I trust his idea.Gold Barz said:

- #20

- 3,763

- 9

This kind of discussion bothers me sometimes. I mean, at what point do we decide our laws are incomplete ? What is incomplete ? For example, general relativity allows for time reversal to be applied in the mathematical framework. When applied to the (correct ) physics of black holes (eg : Schwarzschild metric or Kerr metric for rorating black holes AND the Einstein equation) we get the white holes (the vomoting stars), yet we have not yet found such white holes. When combined with black holes we get the famous worm holes. The problems involved with these are legendary, yet GR is proven to be very correct. You see my point ?Danger said:Our 'laws' are definitely incomplete, or science would be at a standstill and we would know everything. That particular law, however, is pretty firmly entrenched. New laws, as they are discovered, don't negate the old ones; they expand upon them. Oldtheoriesfall by the wayside all of the time, but it isn't considered a 'law' unless it's inviolable.

Just because mathematically, something makes sense, it does not mean that physically it is also ok. You can find similar situations with QM.

Even, you can turn this around. Look at renormalization theory in QFT, in order to fit physical reality, we perform some mathematical tricks that are merely interpretative, though mathematically not correct. However, when holding on to such a system, we are ablt to describe the quark behaviour and we are able to describe quasi all atomic phenomena with incredible accuracy.

I say we just need to be pragmatic about this and hold on to the hole falsification process. If we don't do that, all structure is lost

Just my two cents

regards

marlon

Last edited:

- #21

Danger

Gold Member

- 9,607

- 246

I do, and it bothers me as well. That's why I stick to my own definitions in order to keep things a bit clearer in my head. Until someone nails it down precisely, I figure they're as good as anyone else's. (There... I stroked my own ego this time so you don't have to.)marlon said:This kind of discussion bothers me sometimes. I mean, at what point do we decide our laws are incomplete ? What is incomplete ? You see my point ?

With my extremely limited knowledge of physics, and particularly QM, I've always sort of considered 'renormalization' to be cheating. It works, but is it the right approach? From what little I've read of it (keeping in mind that I don't even try to understand the math), it seems as if they just invented an identical but opposite entangled universe in order to force parity in situations where it appears to be violated. (Sort of like having 2 glasses each partially filled with water. If glass 'A' has 20% more than glass 'B', they stick a mirror behind them and say "now glass 'A' and glass 'B2' combined have the same amount as glass 'B' and glass 'A2' combined. Now it's all nice and even.") It grits my gears just a bit without being too intolerable, like having a pimple on your ass.marlon said:Look at renormalization theory in QFT, in order to fit physical reality, we perform some mathematical tricks that are merely interpretative, though mathematically not correct. However, when holding on to such a system, we are ablt to describe the quark behaviour and we are able to describe quasi all atomic phenomena with incredible accuracy.

If you mean what I think by that, then it's how I look at it... beat the hell out the theory until you run out of sticks. If it's still alive, it's a law.marlon said:I say we just need to be pragmatic about this and hold on to the hole falsification process.

- #22

ohwilleke

Gold Member

- 1,566

- 451

I'll just join the chorus saying that the distinction you make doesn't work in the very example I provided. Other examples: Fermat's Theorem does not explain why numbers are related as they are. Conservation laws, in contrast, come very close to being "how/why" laws. Some laws do not even give you a specifical numerical formula (The Second Law of Thermodynamics, e.g.).DaveC426913 said:No.

A law describes something we see; it describeswhathappens. It is simply a quantified observation.

eg. There is no 'alternate' Law of Gravity. The Law of Gravity simply describes what every scientist on every planet in the universe will jot down on her notepad. They will all describe what speed objects fall and what speed the Moon revolves. Generalizing, they willallarrive at G=(m2*m1)/r^2. It's not negotiable.

OTOH, a theory attempts to describehow or why.

Every one of those scientists on those planets could have a different theory about how/why objects fall or how/why their moon revolves (gravity particles, warped space-time, invisible tendrils), all of which can be negotiated and refuted.

In fact, I'll boil that down:

A law describes something; a theory tries to explain it.

Probably the best first approximatation of whether something will be called a law or a theory has to do with when it was proposed. Many formulas which would have been called "Laws" if they had been discovered in the 19th century or earlier, are called theories when they are discovered in the 20th century. Hence, you have effective field theories, the theory of special relativity and the theory of general relativity, but Ohm's Law, Maxwell's Laws, and Newton's various laws.

- #23

- 3,763

- 9

Well, i say, the fact 'that it works' justifies 'it' being the right approach. know there is lots of discussion on this but i chose for the very pragmatic path. For example, i really see no point in all this QM measurement related problems...I know Vanesch will disagree with me on this. But once again i really do not see the problem here.Danger said:With my extremely limited knowledge of physics, and particularly QM, I've always sort of considered 'renormalization' to be cheating. It works, but is it the right approach?

I am not sure i know what you mean. Are you referring to something like this ?From what little I've read of it (keeping in mind that I don't even try to understand the math), it seems as if they just invented an identical but opposite entangled universe in order to force parity in situations where it appears to be violated.

Anyhow, let's just look at QFT renormalization in it's simplest form. If you have a groundstate energy that is infinitely positive, you incorporate anti-matter in your theory of which the ground state energy is infinitely negative. The 'sum' yields a finite ground state energy ? You see ? Now, this works because the mathematical formalism that follows this treatement (ie quantum field theory) has proven to be consistent with experimental back up.

I am just wondering, if a model works, why start thinking about socalled 'incompletenesses', yet you have an accuracy that you could only dream of ? Maybe, mathematically, this is not very correct (i mean, the example of renormalization , i gave here) but then again we know very well what we are doing. We are just getting rid of singularities (ie the infinities) because they block our sight, yet they have no influence on the physics or the physical reality.

Why ? Well, just realize that we do not need to know the ground state energy of a thousand harmonic oscillators that build up a quantum field (ie the springs of the mattress) because if we say a particle (this particle represents the physical reality) has energy value A, than what we really mean is this particle has energy value : A minus groundstate energy. We only look at energy differences, you see. Since this ground state energy is the same for every particle, the energy values of these particles are really independent of the ground state value for the above reasons. You see my point ?

That is indeed what i meantIf you mean what I think by that, then it's how I look at it... beat the hell out the theory until you run out of sticks. If it's still alive, it's a law.

regards

marlon

- #24

DaveC426913

Gold Member

- 18,968

- 2,455

That is what I am saying, yes.JesseM said:That distinction doesn't make any sense to me. Are you saying Newtonian gravity is a "law" because it just describes what happens, while General relativity is a "theory" because it describes why?

Netwon's law of gravitation doesn't make ANY predictions, it merely describes what we actually observe.JesseM said:Seems to me that GR just describes what happens too--it doesn't saywhymatter/energy curves spacetime, or why objects moving in curved spacetime follow geodesic paths, it just says that's what happens, and the predictions you get from this match observations. All of physics is just about mathematical models that make certain predictions, it doesn't deal with meta-explanations of why this model makes accurate predictions but that model doesn't.

We do not observe the curvature of space, it is a model that was made up by man to explain - and predict.

- #25

JesseM

Science Advisor

- 8,496

- 13

Sure it makes predictions! It can be used to predict the future trajectory of any object in a gravitational field. Of course this predicted trajectory matches what we actually observe in cases where Newtonian physics is fairly accurate, but then general relativity's predicted trajectories also match what we actually observe in a more general set of cases, like the precession of the perihelion of mercury. Would you say that using Newtonian physics to anticipate the trajectory of a spacecraft or a planet is not a prediction, but that using GR to anticipate the bending of light near a star or the precession of the perihelion of Mercury's orbitDaveC426913 said:Netwon's law of gravitation doesn't make ANY predictions, it merely describes what we actually observe.

The "curvature of space" can just be seen as some abstract mathematical machinery used to calculate the trajectory of objects in the presence of conglomerations of matter/energy, one needn't "believe in" curved spacetime as a real entity unto itself. Similarly, in Newtonian physics we do not directly observe force fields that fill space (or force vectors at any given point in space), and these can also just be seen as bits of abstract mathematical machinery rather than being treated as "real" in some ultimate sense. I see no difference between these cases.DaveC426913 said:We do not observe the curvature of space, it is a model that was made up by man to explain - and predict.

Also, do you disagree with the quotes from Baez and Feynman I posted above, or do you think I am misinterpreting them?

- Last Post

- Replies
- 8

- Views
- 2K

- Replies
- 4

- Views
- 2K

- Last Post

- Replies
- 5

- Views
- 1K

- Replies
- 6

- Views
- 2K

- Replies
- 7

- Views
- 2K

- Last Post

- Replies
- 7

- Views
- 714

- Replies
- 10

- Views
- 5K

- Last Post

- Replies
- 8

- Views
- 2K

- Last Post

- Replies
- 33

- Views
- 3K

- Last Post

- Replies
- 2

- Views
- 2K