Why does FTL violate causality?

[Lvl 2 Expert]

But kept in perspective, relativistic theory was just ONE step in the long history of physics, ultimately just one other big theory that expanded upon the ones before it.

And if you ask me: It won't be the last, either.

But that doesn't mean it's wrong in this aspect, or any more wrong than any alternative. Quite the opposite, it's the best model for the way the universe at this scale works that we currently have.

I'd highly recommend reading the thread linked earlier. It's complicated, I already forgot most of what I learned from it and how this all worked, but theresult of it is this: Any form of information transfer* faster than the speed of light can result in you receiving your own message before you sent it. I think back then I figured out a way to do it with a fast spinning space station with an instant messaging antenna on one end. (It still works even if the messaging is not instant, that just makes this a bit easier to think about.) And if you can send a message even a millisecond back in time it stands to reason you can just repeat the process to receive any information you will ever send right on the moment your machine was started up.


* Quantum entanglement has an effect that goes faster than the speed of light, but the only way to know the effect has taken place and get any kind of information out of it is to have a second slower than light information channel running alongside it. That's kind of creepy in its own right, it seems almost designed to fit the rules of the universe, rather than having a good physical reason for doing what it does.

[Roland St. Jude]

I was thinking the same thing, but figure it's barely acceptable because of the media impact of it. But I'm flexible on it.

Sheriff: That's a fair judgment.

I should have read through the thread before I moved it. Oh well, what's done is done.

[Anymage]

In other words: physics theory is best at describing things we know. Put it into equations. I would not trust physcis to predict EVERYTHING that is impossible. In fact, the historical development went in cycles: each cycle someone discovered something that went against the current equations, against the current theory. And then devised a new all-encompassing theory that explained everything better. But so far, none of them had proven to last forever. Some day, I expect someone will discover a phenomenom that breaks the concept of relativistic theory. And then people will come up with another theory that us better suited to describe reality as we - or they - know it.

The only constant in the history of humankind is that every single one who thought they knew everything has been proven wrong ultimately.

Einstein didn't just say that Newton was a fool and that everything Newtonian was wrong. He had to work within the observations that Newton worked quite well within familiar parameters, and only started breaking down as you got far outside of those.

We know that our current model of the universe has some very deep flaws. We even have a few geeks hypothesizing ways to go faster than light while within our current understanding of physics. How these pan out will inform future models of physics. But we can only answer questions to the best of our current understanding now. And "here's what our current understanding says" is a lot more productive than "well, you can never know for absolutely sure..."

[factotum]

Yeah, I agree. Newtonian mechanics are not "wrong" per se--they describe the universe pretty well so long as you're not going very fast. Einstein's work added to Newton, it didn't entirely supersede it. Anything that comes along which describes the universe better than Einstein similarly won't likely replace relativity but add more accuracy to the corner cases.

[keybounce]

I said: "The universe itself is a non-moving, non-rotating reference frame -- perhaps that is special?"

Then the laws of physics as we understand them don't apply, and your original question is moot. Sure, you can imagine a universe in which Newtonian Physics apply. But in that universe, the speed of light isn't special. Going FTL just requires a sufficient amount of thrust. The speed of light would be like the speed of sound.

One of us is not understanding the other here.

General relativity takes as an assumption that the laws of physics appear the same to all observers. (Before you get all techie on me, yes I know that's only approximately what it says). From that assumption, it derives some numerical predictions, and those predictions match actual observation.

All this means is that the fundamental assumption -- that the laws of physics appear the same to everyone -- is probably close to accurate.

It is possible to add the axiom, "there exists a privileged reference frame" to relativity without disturbing either of the existing 2 axioms. You will still get the same behaviors -- special relativity's apparent change in observed length and passage of time, general relativity's space-time, etc.

I said:

(It's one thing to say that all observers see the same laws of physics -- that's confirmed.
It is something else to say that you cannot detect a privileged frame -- that's an assumption, at best we can say that we don't know how to detect one.
It is something else entirely to say that a privileged frame cannot exist -- there's nothing to support that.)

No, actually it is the other way around: physicist say there can't be a privileged frame of reference because otherwise not all observers would see the same laws of physics. For example, it could be that observers moving towards the light would measure the speed of light as being slower than observers at rest. Therefore we could find that absolute rest state by adjusting our speed until it maximized the speed of all incoming light.

Grey Wolf

Please explain how the existence of a privileged frame of reference implies that the assumptions of general relativity cannot hold.

[Jasdoif]

I said: "The universe itself is a non-moving, non-rotating reference frame -- perhaps that is special?"
....
General relativity takes as an assumption that the laws of physics appear the same to all observers.

General relativity is based on (and named after) the general principle of relativity; that the laws of physics are the same in all frames of reference.

A special frame of reference such as you describe would necessarily vary on those laws of physics which make it special; therefore physical laws would not be the same in all frames of reference, therefore general relativity would not hold.

[Brother Oni]

For all three PoR we'll say a minute passes.

This right here. This is the false assumption you're making. Precisely because there is no constant universal reference frame, a minute on the ship is not equal to minute on the station is not equal to minute on Earth. True simultaneity does not exist. Once you introduce FTL, the math actually works out to negative time passing in some frames in relation to others. To give a rough idea, your "instant messaging" device would need tachyons or similar hypothetical particles to work.

As a biochemist, I too have trouble wrapping my head around the mechanics of how time passes differently at relativistic speeds, until I saw this Christmas lecture by Brian Cox: "Is time travel possible? The Science of Dr Who".

Since the speed of light is fixed, the passage of time is personal to an individual (ie to a reference frame) as Frozen_Feet said.

Time passing differently the faster you go isn't just a scientific curiosity, it's a fundamental problem that has ramifications for today's technology - GPS satellites have a timing adjustment specifically for relativistic effects: wiki link.

[shawnhcorey]

To understand why FTL flight violates causality and is time travel can be explain easily with light cones. I'm not going to explain what light cones are but here are some consequences of them.

If there are two events, A and B, such that B is in A's future light cone, then A is in B's past light cone. An observer, by changing their velocity, can change the distance and time between A and B but their order never changes. B is always in A's future light cone and A is always in B's past light cone. Note that A need not cause B. They may be independent of each other.

If there are two other events C and D such that they are not in each other's light cones, then an observer, by changing their speed, can change the order of the events. For half of a possible velocities, C will come before D and for half, D will come before C.

Now to look at FTL flight. You enter FTL flight (event C) and leave it some distance away (event D). These two events are outside of each other's light cone because of FTL flight. The FLT flight causes them to be outside of each other's light cones. In your initial frame of reference (before the flight) C happens before D.

Now that you have arrive at your destination (after D), you change your velocity so that C is in the far future. This violates causality. Your arrival happens before its cause, that is, your departure.

Now you use FLT flight to jump back to your starting location. But C, your departure is in the far future. You have travelled back in time.

So, FTL flight both violates causality and can be used for time travel.

[Mightymosy]

Einstein didn't just say that Newton was a fool and that everything Newtonian was wrong. He had to work within the observations that Newton worked quite well within familiar parameters, and only started breaking down as you got far outside of those.

We know that our current model of the universe has some very deep flaws. We even have a few geeks hypothesizing ways to go faster than light while within our current understanding of physics. How these pan out will inform future models of physics. But we can only answer questions to the best of our current understanding now. And "here's what our current understanding says" is a lot more productive than "well, you can never know for absolutely sure..."

Well, Newton described how matter moved in our universe, and Einstein showed that Newton's rules weren't quite right in all circumstances.

But your last sentence is actually exactly what I mean:

The sentence "FTL speed is impossible and incompatible with physics" is a much worse sentence than "TFL speed seems impossible to do with the methods we have now and with the current understanding of interstellar physics we have now, but you can never know for sure".

[NichG]

Well, Newton described how matter moved in our universe, and Einstein showed that Newton's rules weren't quite right in all circumstances.

But your last sentence is actually exactly what I mean:

The sentence "FTL speed is impossible and incompatible with physics" is a much worse sentence than "TFL speed seems impossible to do with the methods we have now and with the current understanding of interstellar physics we have now, but you can never know for sure".

I'm more bothered by the confident assertion that it is impossible to know, than the confident assertion that a particular specific thing has been shown to be nonsensical. The degree of surety matters, and your second sentence hides that by essentially equating a 10^-80 uncertainty to a 1% uncertainty.

Based on the evidence, we should probably assign more confidence to the statement 'faster than light transmission of information would lead to non-directed causal structures' than the statement 'I will be alive tomorrow'. For example, in the case of a particle physics experiment collecting ~10^10 total events (about 15 years worth of runtime), this would correspond to any observation better than ~6 sigma.

[Mightymosy]

It is hard to assign actual numbers to probabilities of things you consider "impossible".

Either we think they are impossible with our current understanding, or we don't.

Expressing that as numbers doesn't make much sense to me.

"FTL seems impossible with the methods we have, and the understanding of interstellar physics we have" is good enough, if you ask me.

It says that we can not do it right now, but we can not know if it is impossible in the future, but to be possible it would require new methods and a partially new understanding of space physics.

I wouldn't put any numbers into it.

[NichG]

It is hard to assign actual numbers to probabilities of things you consider "impossible".

Either we think they are impossible with our current understanding, or we don't.

Expressing that as numbers doesn't make much sense to me.

"FTL seems impossible with the methods we have, and the understanding of interstellar physics we have" is good enough, if you ask me.

It says that we can not do it right now, but we can not know if it is impossible in the future, but to be possible it would require new methods and a partially new understanding of space physics.

I wouldn't put any numbers into it.

A scientific theory doesn't just rest on whether people feel that it makes sense or is compelling. Generally, it has to provide some predictive or explanatory power which is then backed up by experimental tests. Those tests have some distribution of results, and errors or fluctuations can occur - by characterizing those, we can construct an error model, and thereby ask the question 'if we were to repeat all of these experiments, what is the probability that we would come to a different conclusion?'

That number, for physics experiments, tends to be extremely small. Something like 10^-80 is actually not out of the question for measurements that are easy to repeat or produce large amounts of data.

It's not about thinking things are possible or impossible, it's about establishing the constraints which any theory must satisfy in order to be consistent with what we have observed. So relativity had to fit inside the space carved out by Newtownian mechanics experiments, and whatever might replace relativity has to fit inside the space carved out by relativity experiments. While it's possible for the experiments to have been mistaken, it's not the case that we have no way of assigning numbers to the probability that they were mistaken.

[shawnhcorey]

FTL is impossible because every observer measures the speed of light in a vacuum to be the same. FTL would not just break our understanding of the universe; it would break the universe. Most people do not realize how important the fundamental constants are and how closely coupled to each other they are. FTL would mean nothing is possible any more.

[Anymage]

Well, Newton described how matter moved in our universe, and Einstein showed that Newton's rules weren't quite right in all circumstances.

But your last sentence is actually exactly what I mean:

The sentence "FTL speed is impossible and incompatible with physics" is a much worse sentence than "TFL speed seems impossible to do with the methods we have now and with the current understanding of interstellar physics we have now, but you can never know for sure".

I have an idea that next time you're sick, you let me open fire at you with a machine gun under the expectation that only the unhealthy cells will be hit. Sure, every time the "people getting shot" experiment has been conducted the result has been severe injury or death, but this time it might work out perfectly and in fact grant superpowers.

Whattya say? After all, medical science is changing all the time, so we can never know exactly for sure.

[Grey_Wolf_c]

Well, Newton described how matter moved in our universe, and Einstein showed that Newton's rules weren't quite right in all circumstances.

Newton knew that his laws and equations weren't right in all circumstances. Mercury was a dead giveaway.

Science progresses by reducing the number of scenarios it cannot explain & predict. At this point, the speed of causality of the Universe is pretty well established and tested. Pretending that because science doesn't know everything, we can assume that what it does know can be doubted is NOT how science works.

Grey Wolf

[Jay R]

I said: "The universe itself is a non-moving, non-rotating reference frame -- perhaps that is special?"

No, it isn't.

I can define a reference frame in which the solar system is not moving or rotating.
I can define a reference frame in which the Milky Way is not moving or rotating.
I can define a reference frame in which the Local Group containing the Milky Way is not moving or rotating.
I can define one in which the Laniakea Supercluster (which includes the Local Group) is not moving or rotating.
I can define one in which the Centaurus Great Wall (which includes the Laniakea Supercluster) is not moving or rotating.
I can even define one in which the center of all currently known extra-galactic structures is not moving or rotating.

But I cannot define "The universe itself" and have any idea what that frame of reference is.

There is no single reference frame that is "The universe itself".

Please explain how the existence of a privileged frame of reference implies that the assumptions of general relativity cannot hold.

Turn it around. The assumptions of general relativity say that if you define a frame of reference, for instance "The universe itself", then I can define another one that moves relative to that one, and which is just as definitive as that one.

Your frame of reference isn't privileged. It just isn't. It's as arbitrary as any other. If an object is moving at 0.5c in your reference frame, then whatever appears motionless to you is traveling at 0.5c to that reference frame.

The same equations needed to refer to another reference frame from yours will work to refer to yours from that one.

[Lvl 2 Expert]

This is an idea people have had before. They figured that if there is a privilidged reference frame it probably isn't locked to the surface of the earth. So they (I think) went about measuring the speed of light in several directions in several parts of our yearly cycle. Relativity is the result of these experiments failing to detect any changes. If there is no universal right frame of reference, but we still have a universal top speed, then time must be interacting with our reference frame somehow.

[gomipile]

Here's a relatively(heh) good video on this topic:

[Kato]

This is an idea people have had before. They figured that if there is a privilidged reference frame it probably isn't locked to the surface of the earth. So they (I think) went about measuring the speed of light in several directions in several parts of our yearly cycle. Relativity is the result of these experiments failing to detect any changes. If there is no universal right frame of reference, but we still have a universal top speed, then time must be interacting with our reference frame somehow.

Minor note(s) :
You're probably referring to the famous (among physicists) Michelson - Morley - experiment which indeed proved that lightspeed is independent of the movement of Earth, although it was meant to prove the existence of the Aether (which would be kind of that special reference frame)
Also, this is a great instance of an experiment proving scientists wrong and them not going 'oops, better do something else' but 'dang, time to change our opinions on this'.

[Lvl 2 Expert]

Minor note(s) :
You're probably referring to the famous (among physicists) Michelson - Morley - experiment

I didn't know the name, I couldn't find it by googling for aether and I left the comment rather quickly on my phone. Thanks for the added information!

[Rakaydos]

Question for the high level physics people.

So, all the lightcone diagrams I've seen are flat. But any number of FTL methods in fiction "Pinch", "Warp" or "wormhole" from one point in spacetime to another.

Assuming such an FTL, able to travel outside it's lightcone, but assume power requirements go asymptotic as it approaches a causality violation with anything that was in it's pre-jump lightcone.

So you detect a ship jumping in, telling you there's a disaster where they jumped from, two years from now. You can jump back there, with relief supplies at any time up to the moment the messanger ship left, two years AFTER it arrived, (though the power requirement goes up the closer you cut it) but no sooner, even though in a hypothetical universal frame, it hasnt happened yet. If another ship arrives or leaves, it resets the earliest arrival time, and if you wait long enough for the light of the disaster to arrive, you cannot violate what you could theoretically see happen.

Does this thoought expiriment hold up?

[DavidSh]

...

Does this thoought expiriment hold up?

A causality violation in this sort of model looks like a loop of hops, where each hop terminates in the past light cone of the next hop. In a two-hop loop, the first hop might go from time 0 at location 0 to time 10 at location 1000, and the second hop might go from time 20 at location 1000 to time -10 at location 0. (Coordinates as given by one observer.)

It looks like you are proposing making one of the hops in such a loop to be physically forbidden. This sounds superficially plausible, but there are some issues.
1) Which hop should be forbidden? You can construct cases that appear, from a carefully chosen frame of reference, to be perfectly symmetrical. E.g., maybe from one reference frame the first hop goes from location -100 at time 0 to location 100 at time -1, and the second hop from location 100 at time 0 to location -100 at time -1.
2) You can also use such a process to send 1 bit of information into the past, if you are willing to set things up in advance. Tell your distant partner to send you a message only if it doesn't get any message from your future. For example, you are going to do an experiment that might kill you. Arrange your distant partner to send a message telling you to stop, unless they get a message from your later self saying that you survived unscathed.

[Rakaydos]

A causality violation in this sort of model looks like a loop of hops, where each hop terminates in the past light cone of the next hop. In a two-hop loop, the first hop might go from time 0 at location 0 to time 10 at location 1000, and the second hop might go from time 20 at location 1000 to time -10 at location 0. (Coordinates as given by one observer.)

It looks like you are proposing making one of the hops in such a loop to be physically forbidden. This sounds superficially plausible, but there are some issues.
1) Which hop should be forbidden? You can construct cases that appear, from a carefully chosen frame of reference, to be perfectly symmetrical. E.g., maybe from one reference frame the first hop goes from location -100 at time 0 to location 100 at time -1, and the second hop from location 100 at time 0 to location -100 at time -1.
2) You can also use such a process to send 1 bit of information into the past, if you are willing to set things up in advance. Tell your distant partner to send you a message only if it doesn't get any message from your future. For example, you are going to do an experiment that might kill you. Arrange your distant partner to send a message telling you to stop, unless they get a message from your later self saying that you survived unscathed.

1) So, to expand- The FTL would cost more energy to use the closer it gets to the light cone. So the first jump in the universe, the most energy efficent jump is a T=0 translation- equally distant from the future and past time cones. But any reply (being by definition some miniscule amount of time, locally, after recieving the message) would have a minimum energy to target a time halfway between when the message was sent, and when the light from the message would be seen- effectively, traveling at 2c. You can spend more energy to get the reply closer to the time the message was sent from, but to send it back to the same instant it left costs infinite energy. It also dosent matter how long you wait to send the reply (as long as you dont wait so long the light from the original message catches up with you), it only matters to your power requirements where the light cone is in relation to your destination.

This also applies to any FTL arrival "seen" by the message before it was sent. If station 1 sent a message to station 2s past, station 2 could send it to staion 3's past, but station 3 could only send it back to station 1's future.

2) I may be channeling Whaetly from Portal here, (This statement is false? Hmm, True! That was easy) but it would seem to me the natural course is that the partner never recieves a message telling them to not send a message, because the message they will send blocks you from telling them not to send it. Whether you succed at your expiriment or not, if you cant transmit, you will have recieved the stand down command, and the stand down command keeps you from transmitting.

[Anymage]

You might as well institute a paradox system directly into your setting, a'la Continuum. Fictionally speaking it's reasonable that I couldn't affect anything I have "future" information on, but involving multiple actors either locks causality down such that you might as well have real-world causality (since any lightcone skipping might mess with a sequence of information known to someone else), or that the universe be treated as a nigh-sentient force keeping everything lined up.

Honestly, if I were making a setting, I'd go with it being common knowledge that the universe will arrange coincidences to ensure that time is self-consistent, growing more extreme to match the potential damage to the timestream. You could trick out time by swapping your girlfriend's body in the plummeting car with a nonsentient cloned replacement, but leaving an empty car means that increasingly odd events conspire to have someone who looks very much like her sent back. (Usually at ever increasing frustration to the time traveler, because that's how stories work.)

If we we're talking real life, the multiple actor issue quickly makes it nigh impossible that someone, somewhere wouldn't see a causal break if you made a FTL hop, and indeed the energy costs for a given hop would reveal a lot about who in the universe has information about what other parts. You complicate a ton of things, and have no real-life reason to assume it might work this way.

[NichG]

Question for the high level physics people.

So, all the lightcone diagrams I've seen are flat. But any number of FTL methods in fiction "Pinch", "Warp" or "wormhole" from one point in spacetime to another.

Assuming such an FTL, able to travel outside it's lightcone, but assume power requirements go asymptotic as it approaches a causality violation with anything that was in it's pre-jump lightcone.

So you detect a ship jumping in, telling you there's a disaster where they jumped from, two years from now. You can jump back there, with relief supplies at any time up to the moment the messanger ship left, two years AFTER it arrived, (though the power requirement goes up the closer you cut it) but no sooner, even though in a hypothetical universal frame, it hasnt happened yet. If another ship arrives or leaves, it resets the earliest arrival time, and if you wait long enough for the light of the disaster to arrive, you cannot violate what you could theoretically see happen.

Does this thoought expiriment hold up?

There are papers which solve for clean systems (billiard-like setups) in the presence of time-travel boundary conditions, and basically it's generally possible to find solutions even in cases where you set things up so that only causality-violating solutions are capable of being self-consistent, even though finding those solutions is (in principle) computationally NP. So causality violations aren't an immediate non-starter mathematically.

The bigger issue for me is, if you take basic linear models from physics such as the wave equation and solve them in the presence of time travel boundary conditions, you find that it forces the solution space into the set of exponentially growing and shrinking periodic functions. So it seems like in the presence of time travel, you would actually need a non-local conservation law in order to retain things such as energy conservation (and if you don't have this, then the universe either exponentially-quickly fills with energy or goes dark).

[Lvl 2 Expert]

And then there's the quantum entanglement solution, which makes something travel faster than light by making it actually not a thing at all.

Confused? Well, so am I and I'm sort of hoping anyone here can explain it better than I can.

Two particles can when they are in each other's vicinity be entangled. That is, the spin of these particles (which is nothing like what you're currently imagining, but keep imagining it like that anyway because it's a decent model for thinking about it) is now the same, either left or right. That spin can still change, but at the exact moment the spin on one end changes the spin on the other end will change as well. This has been done experimentally with the particles having been transported kilometers apart, researchers are unable to find any delay in the effect. It's instantaneous or at the very least much faster than light. (Or there is something really weird going on that makes us think we're seeing this effect, but assuming physics is to a certain degree right it's instantaneous or much faster than light.)

Here's the catch: You can't tell by measuring the spin of a particle whether it's been entangled. You can only tell two particles have been entangled by comparing measurements from both sides. So you need information send through other channels to know anything happened at all. The effect transfers a single bit of data (was couples or was not coupled), but only does so when combined with a regular light speed or slower channel of information. To further complicate it measuring or altering the spin of either particle breaks the entanglement. (No, I don't know how they even confirmed this effect exists if you per definition can only ever measure the spin on one of these particles. My guess is it has to do with measuring as close after each other as possible and applying statistics about how quickly the spin on the other end would be expected to change after the entanglement broke.)

The creepy thing to me (but I'm not very good at this physics stuff, my world exists between roughly 0.1nm and 40,000km) is that this is the only thing in nature I know off that seems almost designed. Sure, the universal constants are just right, but I can come up with explanations for that, even if it's just "there's a multiverse and most of the universes don't look like ours at all". Life? The explanation without a designer seems easily more fitting than the one with. But quantum entanglement is like something a particularly clever sci-fi writer made up to break his own rules without breaking them. (And then in the third act he uses it to plain break his own rules anyway and the story stops being fun.) Why have a universe that has a speed limit that can be ignored by one thing and one thing only, but it's okay because that one thing can't be used to send messages to the past because it can't be used to send messages? Is there some actual way for the universe to tell which phenomena carry information, and is it the information itself that is stuck behind light speed rather than any other property of matter? It's weird. Completely without consequences for being able to travel or communicate either faster than light or back in time, but weird.

[NichG]

And then there's the quantum entanglement solution, which makes something travel faster than light by making it actually not a thing at all.

Confused? Well, so am I and I'm sort of hoping anyone here can explain it better than I can.

Two particles can when they are in each other's vicinity be entangled. That is, the spin of these particles (which is nothing like what you're currently imagining, but keep imagining it like that anyway because it's a decent model for thinking about it) is now the same, either left or right. That spin can still change, but at the exact moment the spin on one end changes the spin on the other end will change as well. This has been done experimentally with the particles having been transported kilometers apart, researchers are unable to find any delay in the effect. It's instantaneous or at the very least much faster than light. (Or there is something really weird going on that makes us think we're seeing this effect, but assuming physics is to a certain degree right it's instantaneous or much faster than light.)

That's not quite how entanglement works. The key point is, you aren't ever actually changing the spin, you're deciding what basis in which the spin should have a defined value.

Lets say we have a block of marble that we could cut in various ways. Now, if we cut the marble in a known way such that it is split in two, box the two pieces without looking at them, and send them off in different directions, then we could say that 'the moment someone opens the box, they instantly know the shape of the marble piece in the other box' - but no information was transmitted faster than light here, it's purely virtual (and classical).

The quantum version of that says, you can cut the marble in such a way that you can only ask one question about the shape of the cut on your piece when you open the box - and, having done so, no other information can be obtained (and furthermore, rather than this being a destructive measurement, no other information ever existed about the cut in the first place). Now, you have an interesting situation, because you might ask a different question than the person with the other half of the marble block asks, but there is a global constraint that the information you both obtain about the block together through your questions is bounded in a particular way.

The resolution of this paradox is, neither of your measurements is actually deterministic, so you can't actually know whether you were the one who got the 'real' information while the other guy got noise, or vice versa. Furthermore, even if you compare notes, you can't say that one person in the end had the deterministic measurement and the other had the random one, because that would in some sense establish a privileged order, which doesn't actually exist. So you can at best say that, if you both asked the same question, you will have both gotten the same answer (because it has to be consistent with the original shape of the block that it came from), whereas if you asked different questions then in the end, you both got equally random answers that didn't have anything to do with the initial cut.

That statistical effect, where the distribution of outcomes depends on whether the question asked at both ends was the same, is the 'spooky action at a distance' of entanglement, but because you cannot know whether you asked the same question or a different one without receiving a (slower than light) signal from the other person, or without deterministically deciding to ask the same question ahead of time, you can't use the effect to transmit information.

In the case of spins, the 'marble block' is the fact that both spins must add up to zero, but they could add up to zero in different ways: (1/2, 0, 0) + (-1/2, 0, 0) ; (0, 1/2, 0) + (0, -1/2, 0) ; (0, 0, 1/2) + (0,0,-1/2), for example. The question you get to ask is, in essence, picking an axis (after which, you will always get an answer of +1/2 or -1/2 on that axis, never 0). If you and the other person pick different axes, then (effectively) what happened in the end was that each of you had a 0 that resolved randomly to either +1/2 or -1/2. If you and the other person pick the same axis, then one of you gets +1/2 (and, given that the other person picked that axis as well, you know that the other person has -1/2) and vice versa.

[Radar]

The thing with entanglement is not the only sort of exception - any quantum measurement is in fact global in a way (at least in the most basic forms of quantum mechanics - there are some local definitions, but I failed to grasp them fully during my student years). How it can be so, You may ask?

Consider the reknown electron self-interference experiment, where it goes through two slits at the same time. So the electron is bahaving like a wave spreading over a considerable area until it is observed, right? It suffices to say that until we detect the electron its wavefunction is reaching the whole detector, but then in a split moment, the electron concentrates itself at the exact spot, where it is detected.

We can do it even more clearly: we can shine light on one of the slits, where electron should pass. The light can scatter from the electron and as such we can detect it. Simple? Pretty much, but consder this: if we see the electron on one slit we also gain information that it most certainly is not going through the other (we do not even need to look there) and as a consequence we see no interference pattern. So a measuremet in one place changes the possible behaviour of an object spanning over an arbitrarily large area.

It is exactly the same kind of problem as with entanglement of many particles, since we have initial information that there is exactly one electron and there are two roads it can take, so the states of the slits (electron or no electron) are entangled.

This also neaty shows that we can entangle objects that aren't close to each other - there aer some neat experiments, where people entagle particles that could never directly interact, which is really cool, if you think about it. But that is another story.

[Rockphed]

Consider the reknown electron self-interference experiment, where it goes through two slits at the same time. So the electron is bahaving like a wave spreading over a considerable area until it is observed, right? It suffices to say that until we detect the electron its wavefunction is reaching the whole detector, but then in a split moment, the electron concentrates itself at the exact spot, where it is detected.

We can do it even more clearly: we can shine light on one of the slits, where electron should pass. The light can scatter from the electron and as such we can detect it. Simple? Pretty much, but consder this: if we see the electron on one slit we also gain information that it most certainly is not going through the other (we do not even need to look there) and as a consequence we see no interference pattern. So a measuremet in one place changes the possible behaviour of an object spanning over an arbitrarily large area.

It is exactly the same kind of problem as with entanglement of many particles, since we have initial information that there is exactly one electron and there are two roads it can take, so the states of the slits (electron or no electron) are entangled.

This also neaty shows that we can entangle objects that aren't close to each other - there aer some neat experiments, where people entagle particles that could never directly interact, which is really cool, if you think about it. But that is another story.

This is where the "you cannot know both an object's position and momentum" comes from. Technically, the product of the errors of your measurement of position and momentum (which can be extrapolated from the self-interference pattern) is always greater than some number (I think it is h or h-bar, but cannot remember their names). So if you have 0 error on one of your terms, you must have infinite error on the other.

[Delusion]

This is where the "you cannot know both an object's position and momentum" comes from. Technically, the product of the errors of your measurement of position and momentum (which can be extrapolated from the self-interference pattern) is always greater than some number (I think it is h or h-bar, but cannot remember their names). So if you have 0 error on one of your terms, you must have infinite error on the other.

Planck constant and reduced Planck constant. And IIRC its always greater than h-bar/2.